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Performance analysis of a solar glass tube collector
R¢'newabh, Enerfty Vol. 3, No. 8. pp. 877 883, 1993 Printed in Great Britain.
0960 1481 9 3 $6.00+.00 t 1993 Pergamon Press Lid
P E R F O R M A N C E A N A L Y S I S OF A SOLAR GLASS TUBE COLLECTOR RENYUAN ZHANG,* HUANLIAN ZHU,* HANBING WEN* a n d MEICUN L~+ * Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou, China : ) Cadre's College of Science and Technology, Guangzhou Univcrsil3, P.O. Box 753, Chandi Post Office, Guangzhou 510120, China ( R e c e i v e d 19 J u n e 1992 ; ac~ ~7~ted 23 Mar~'h 1993)
Abstract The thermal perforintince and thermal processes of a glass tube collector have been analysed in this paper. Its thermal performance can be improved by changing the thermal processes to take advantage of the glass tube's ability to transmit sunlight : that makes it possible lbr the working tluid to directly absorb part of solar radiation. Its thermal performance is even better in most parts of the working region than thai of a steel tube collector, even when the structure, meteorological conditions and thermodynamic properties of the working fluid arc exactly the same. An equation of steady-state instantaneous efficiency of a glass tube collector has been derived in the paper. Calculations of various operating conditions have been made with a computer, and the calculated results are quite agreeable with the experimental results. Thus the equation and the calculation method can bc used in the design of glass tube collectors and for comparison calculations. The calculations also show some other important features of a glass tube collector.
INTRODUCTION Glass is corrosion-resistant and unlikely to scale. It also has a high t r a n s m i t t a n c e to sunlight. The cost of a collector made of glass tubes is 9 2 5 % less than that of a collector madc of steel tubes. But the thermal p e r f o r m a n c e of a glass tube collector is redtlced, owing to the bad thermal conductivity of glass. However, the thermal performance of a glass tube collector can be improved, so long as the thermal processes of a glass tube collector are changed.
THE TEST RESULTS OF A GLASS TUBE
model G B R - I (1.9 in: each) conventional parallel tube-to-tube constrtiction and model G B R - l l (2.3 m-" each) single serpentine tube construction have been made. Their quasi-steady-state i n s t a n t a n e o u s efliciencies are measured and shown in Figs 2 and 3. In order to popularize the practical use of glass tube collectors, we constructed two solar water heating systems in G u a n g z h o u City. The first system, with a total area of 15.2 and 5() m ~, is a natural circulation system consisting of some model G B R - I glass tube collectors. The second system, with a total area of 42 m z is a "'once-through tinder controlled temperature'" system consisting of some model GBR-11 glass tube collectors.
COl,LECTOR A N D ITS T H E R M A L PERFORMANCE EQUATION OF TItERMAL P R O C E S S E S A N D STEADY-STATE I N S T A N T A N E O U S EFFICIENCY
The structure of the glass tube collector was similar to that of the fiat-plate steel tube collector, except lbr the upper half of the tubes being t r a n s p a r e n t and the lower half being coated with dim black paint. A small a m o u n t of graphite was used as a filler at the bond (see Fig. I ). To make a comparison, we designed two cxperilnental collectors a glass tube collector and a steel tube collector with the same structure, and carried out the m e a s u r e m e n t of quasi-steady-state instanlancous efficiency (see Fig. 1 and Tables 1 and 2). Based on experiments, two kinds of practical solar glass tube flat-plate collectors with dim black paint
It can be seen clearly in Figs 2 and 3, and Tables I and 2 that the thermal performance of a glass tube collector is better than that of a steel tube collector in most parts of the working region. The specialities of Ileal a b s o r p t i o n and transfer in a glass tube collector are that the working fluid not only a b s o r b s energy from the a b s o r b e r plate but also directly a b s o r b s the solar radiation energy, taking a d v a n t a g e of both the transmission of the sunlight through a t r a n s p a r e n t glass tube and the water's property of intensively a b s o r b i n g infiared radiation [1]. 877
R. ZHANG et al.
878
Upper-half tube is not coated
Glass tube , N
collector
J
Absorber
"Lower-half tube is coated
/
Joint is filled with graphite
I
O Absorption of plate and water Fig. 1. Schematic of the glass tube collector.
Table 1. Comparison between the thermal performance of a glass tube collector and that of a steel tube collector Efficiency equation
Time constant (min)
Heat capacity (kJ m- 2 K ~)
Incident angle modifier
r / = 0.67-8.06(Ti- Tall)
6.4
60.3
k = 1-0.27[(I/cos 0) - 1]
~/= 0.68 9.46(Ti- Tall)
5.5
58.3
k = l~).21[(l/cos 0) - 1]
Tube type construction 20 x 1.5 Glass 0.6 m D / W = 0.2 20 x 1.5 Steel 0.6 m D / W = O.2
T h e energy b a l a n c e o n a flat-plate collector in a n i n s t a n t a n e o u s s t e a d y state c a n be w r i t t e n as
c o a t i n g o f t h e lower h a l f t u b e wall (s'). T h e e q u a t i o n is w r i t t e n as
q = qu+qL.
q = s+s'+s",
(1)
T h e t o t a l collected energy o f a glass t u b e collector consists o f three parts, i.e. the energy a b s o r b e d by the a b s o r b e r plate (s) a n d t h a t a b s o r b e d directly by the w o r k i n g fluid (s"), as well as t h a t a b s o r b e d by the Table 2. Comparison between the daily efficiency of a glass tube collector and that of a steel tube collector Date 10 July 1980 12 Dec. 1981 16 Dec. 1981
T i - Ta/l × 103
Glass tube collector
Steel tube collector
12 ~ 13 23 ~ 24 43 ~ 47
0.57 0.49 0.41
0.59 0.46 0.35
(2)
where s = l ( r la,,),
s' = l(z'at),
s" = l(z"aw),
•1 is the t r a n s m i t t a n c e o f o n e glass cover, z' is the t r a n s m i t t a n c e o f the glass c o v e r a n d glass t u b e filled with water, z" is the t r a n s m i t t a n c e o f the glass c o v e r a n d glass t u b e wall, aw is the a b s o r p t i o n o f water, a n d (ta) is the a v e r a g e t r a n s m i t t a n c e - a b s o r p t i o n p r o d u c t . A s a b s o r b e r plates a n d the lower halves o f the glass tubes are c o a t e d w i t h t h e s a m e paint, it is c o n s i d e r e d t h a t t h e a b s o r p t i o n o f t h e m b o t h is (Ip~ ap ~ a~.
879
Performance analysis of a solar glass tube collector ,q
0.~ xA
~
~~
Glass tube (calculated)
O.d t°e, ,u
0.2
I 0.0l
I 0.02 M ell
I 0.03
I 0.04
solar energy and that the heat transfer resistance of bond filler can be neglected. Thus the temperature of the tube outside wall is equal to the plate temperature (Tb) at the bond. According to ref. [2], the energy transferred to water from the plate and the tube lower wall is written as q~, = q (from plate)+ q (from tube wall)
=
I 0.05
W-D W- F[S- UL(Tb- ra) D
Tf-Ta - I
+ w [ S I - U ( T b - Ta)].
(5)
Fig. 2. The instantaneous efficiencycurves of the collectors. After rearranging, we obtain From the above equation, the useful energy gain absorbed per unit time per unit area by the working fluid under stable working conditions can be expressed as
qu = q-ql = S+S" +S"--qL.
W D D q~=('~V F+ w ) [ Q - U I ( T b -
(5')
where
Q ~ ( W - D)FS+ ..... DS" , (W-D)F+D
(3)
In fact, the useful energy gain is made of three parts, i.e. the useful energy gain transferred to the working fluid from the absorber plate and from the lower half coating, as well as from the direct absorption of the working fluid itself [2]. Thus the useful energy gain can also be given by
Ta)]'
The equation of heat transfer from plate to tube can be expressed as
rb- rf
q~ =
wi~>ThTS_-w/>(,
(6)
where C is the thermal conductance of the glass,
2gD c~= ~ ,
qu = q (energy from plate) + q (energy from lower tube wall coating) + q (energy absorbed directly by water).
(4)
It is assumed that the glass tube does not absorb
~t and 29 are, respectively, the thickness of the glass tube and the thermal conductivity of glass. Substituting eqn (6) into eqn (5) and dropping out Tb, we obtain
q~ = F'[Q- gt (7~1- Ta)],
(7)
where 0.6
I/UL ...............
F' =
/2
1 "11 0 . 4 -
"
~
1
1
"
W[UL[D+(W-D)F] C gDiIti]
~
Then the useful energy gain of the working fluid is
0.2--
3 t O.Ol
I 0.02
"~~.
I 0.03
I 0.04
I 0.05
M2.eC~V T f - T a I
Fig. 3. The instantaneous efficiencycurves of the collectors. (1) Model GBR-I (glass tube) t/= 0.72- 5.83(Tf-Ta/l). (2) Model GBR-1 (glass tube) tl = 0.67 5.02(TJ~- Ta/ll. (3) Model GTR-I (steel tubes, it is the same model and area as GBR-I, but there is no graphite at the bond) t/= 0.691 0 . 0 ( T [ ~ Ta/l).
D
qu = wS"+F'[Q-U,(T~--7~d)].
(8)
The differential equation for the temperature variation of the fluid along the long dimension of the tube is written as
l ril~pdTf dr-
w { D s " + F , [ Q _ UL(T-Ta)] }
880
R. ZHANGetal.
Let
qo FR [ Q ' - UL(Ti-- T.)] q = Io = Io
OS" WF' + Q = Q''
= F [(W-D)FS+DS' "L ( w - ~ F + D
then we can write
dTf riwP-dy = n W F ' [ Q ' - U L ( T - T a ) ] .
T f - T a - Q'/UL = exp [ T i - Ta - Q'/UL
U L
-UL(Ti-Ta)]/Io.
(9)
Solving the differential equation, we o b t a i n
WF" Yn/mcp] + C.
Assuming b o u n d a r y conditions as follows: when Y = O, T = 77; when Y = 1, Tf = To. After substituting, we can write
T o - T a - Q'/UL = exp [ - ULF'/GCp], Ti- Ta-Q'/UL G = rit/ W " L " n.
DS" + WF' (12)
It can be seen in eqn (2) t h a t the t r a n s m i t t a n c e a n d a b s o r p t i o n of water a n d the transmittance of a glass tube filled with water must be known. These data can be o b t a i n e d by calculation or by measurement. We can find out the equivalent water d e p t h [h = 0z/2)R] to substitute the d e p t h of water. Transmittance a n d a b s o r p t i o n of water can be o b t a i n e d by taking account of the reflection a n d a b s o r p t i o n of water, respectively. But in practice, we a d o p t the measured t r a n s m i t t a n c e curve (see Figs 4~6). A s s u m i n g that the t r a n s m i t t a n c e for one glass cover a n d water is z, a b s o r p t i o n of water is expressed as
Since
qu = G C p ( T o - Ti),
(10)
define
0.6i,.One glass cover I" 0.4 Two f
q~ = FR[Q'-- UL(Ti-- Ta)], FR =
GCp UL [l - e x p ( -
~
~
(1 1)
ULF'/GCp)]
I
0.2-
is yielded. Therefore, the i n s t a n t a n e o u s efficiency steady working conditions is written as
0.8
l
~
10
l 30
I
"%
50
70
90
i
under
Oneglass cover gla~
I
Fig. 5. Curve of the relation between the incident angle and transmittance for one glass cover and two glass covers, with water depth 50 mm.
0.6 O n e glass c o v e r
Twoglas~
0.6 -Two
'r 0.4 ¢ 0.2 0.4 '
0.2 I
10
50
I
I
30
I
70
"%
90
i Fig. 4. Relation between angle of incidence and transmittance for one glass cover and two glass covers, water depth 20 mm.
o
I
I
1o
30
I
I
50
70
90
i Fig. 6. Curve of the relation between the incident angle and transmittance for one glass cover and two glass covers, with water depth 70 mm.
Performance analysis of a solar glass tube collector T
aw = 1 - - - - ,
(13)
Tg
where ~g is the transmittance of glass when water is used as the medium (shown in Fig. 7) obtained from eqn (13) and is approximate to the data listed in ref.
[31. THE CALCULATION OF STEADY-STATE INSTANTANEOUS EFFICIENCY The calculation of steady-state instantaneous efficiency can be made in accordance with eqn (12), Figs 4 7 and with the transmittance curve of flat plate glass (Fig. 8), as well as with other formulae recommended in ref. [2].
1.0
•r
0.5
0
30
60
881
Calculation was made with a computer with the following two aims. (1) Given collector construction, property parameters and meteorological conditions, to calculate the steady-state instantaneous efficiency for various flow rates and various inlet temperatures. We input thc original date of the 0.6 m 2 experimental glass tube collector, mcteorological conditions, inlet temperature and flow rate at different experimental conditions so as to calculate its steady-state instantaneous efficiency in different operation conditions. The results are shown in Fig. 2. Obviously, the agreement between calculated and experimental results is satisfactory. (2) Given flow rate, inlet temperature, property parameters, meteorological conditions and some structure parameter, to make comparisons between the effects of various tube diameters and distances between the tubes on steady-state instantaneous efficiency, i.e. to lind out ~ I = . f ( D , D / W ) and 't = f(i, D / W ) . The curves from the calculation, which are subject to the original relative data of the experimental glass tube collector (area changed from 0.6 to I m 2), G = 50 kg/m2-h, Ti = 2 8 C , 6 = 23 08', and the meteorological conditions in Guangzhou City on 23 September 1978, are shown in Figs 9 and 10. ANALYSIS OF THE THERMAL PERFORMANCE OF A GLASS TUBE COLLECTOR
90
i
Fig. 7. Transmittance for glass with thickness 3 ram, water used as medium.
It can be seen in eqn (4) that the useful energy gain of the working fluid consists of the effective heat transfer from the plate and the tube lower wall to
0.7
0.9
I
0.8 0.7
32 \
2
~
0.6 1" 0 . 5 "71 0.6 0.4
2.1)=30
0.3
3. D = 4 0
0.2
4. DinS0 5. D=60
0.l
6. D ~ 7 0 I 10
30
50
70
90
i
Fig. 8. Curve of the relation between transmittance and incident angle for one window glass cover and two window glass covers with thickness 3 ram.
0.5
I
0.1
I
0.3
I
0.5 D/W
I 0.7
I
Fig. 9. Variation of the efficiency with tube-diameter and the distances between tubes.
R. ZHANGet al.
882 0.7
1
13:30
0.6
0.1
0.3
0.5
0.7
D/W
Fig. 10. Variation of the efficiency with time and the distances between tubes, for D = 20 mm.
water, and of that absorbed directly by water. The amount of energy gain depends on these three components and their rational distributions. We can see in Fig. 2 and Table 1 that the slope of the efficiency curve of a steel tube collector is greater than that of a glass tube collector, when
T i - Ta
and an increase in both q (energy absorbed directly by water) and q (energy gained by the lower part of the tube wall), such an increase is not able to compensate for the decrease in q (energy gained by the plate), owing to the decrease in the area of the plate. Thus the total useful energy gain decreases and its efficiency decreases. Curves 1-6 in Fig. 9 show that there is not much relation between the maximum value of efficiency and the size of tube diameter in the equation q = f ( D , D/W). They also show that the variation of D / W has little effect on efficiency when D / W is at its approximate optimum value. These make it unnecessary to use tubes with a large diameter, and there is no need to double tube numbers only for the sake of an increase by several per cent in efficiency. Figure 10 shows that the (D/W)opt. value does not vary from 12:30 till 15:30; only after 15:30 (when the incident angle is rather large), (D/W)opt. value decreases.
CONCLUSIONS × 103 ~> 10,
r/(glass tube) > r/(steel tube).
It can be explained as follows : as for a glass tube collector, the part of energy absorbed directly by water does not vary with variation of the mean temperature of the working fluid. Besides, the average tube temperature and plate temperature of a glass tube collector is lower than that of a steel tube collector, and its total heat loss decreases comparatively. Thus its total useful energy gain decreases less than that of a steel tube collector. It can also be seen in Figs 9 and 10 that an optimum value exists in D/[4I, whatever the size of the tube diameter of a glass tube collector. A collector's efficiency is highest when the optimum exists. The calculation shows that optimum values are different owing to different diameters, e.g. when D = 20-70 mm, the optimum value of D / W is 0.443.6. Such an important character of a glass tube collector can be explained as follows: when D~ W = (D/W)opt., the energy absorbed by water in the tube increases with the increase in D/W, i.e. the increase in tube numbers. At this time, there is an increase in the total useful energy gain. Since the increased gain is bigger than the decrease in energy transferred to the working fluid, which is caused by the decrease in the area of the absorber plate and by poor conductivity of glass. When D / W = (D/W)opt., the total amount of the three-part energy (shown in eqn 4) reaches its maximum. When D / W > (D/W)opt., although there is an increase in the number of tubes
(1) By changing the thermal processes of the glass tube collector, the slope of the efficiency curve for a glass tube collector will be smaller than that of a steel tube collector. (2) There is a satisfactory agreement between the test results and the theoretical analysis of the thermal processes of a glass tube collector. Calculations for steady-state instantaneous efficiency show that an optimum value exists in D~ W. The steady-state instantaneous efficiency is highest when the optimum value occurs. (3) According to the measured quasi-steady-state instantaneous efficiency (Fig. 3), and the agreement between test data and calculated results, it can be concluded that heat transfer is improved by using graphite as the bond filler.
NOMENCLATURE q= qu = qL = 0= 1= D=
Di = W= l= n= uL =
collected energy per unit time per unit area useful energy gain per unit time per unit area heat loss per unit time per unit area slope of plane from the horizontal total radiant intensity on a surface with a slope to the horizon tube o.d. tube i.d. distance between tubes length of tube number of tube overall heat loss coefficient of collector
Performance analysis of a solar glass tube collector heat transfer coefficient from tube wall to water incident angle flow rate per unit area of working fluid mass-flow rate of working fluid Cp= specific heat of water mean water temperature of collector th, Tb = plate temperature at bond ti, T i = inlet water temperature of collector to, To = outlet water temperature of collector ta, T a = ambient temperature 6 - geographical lalitude hi= i= G= ?n =
883
r/= instantaneous efficiency of collector under steady operating conditions. REFERENCES
I. J. P. Holman, Heat Transfer, Fourth Edn. McGraw-Hill, Maidenhead (1976). 2. J. A. Duffle and W. A. Beckman, Solar Engineering qf' Thermal Processes. John Wiley, New York (1980). 3. K. E. Kondrasief, Solar Radiation Eneryy. National Hydrometeorologic Press, Leningrad (1954).
0960 1481 9 3 $6.00+.00 t 1993 Pergamon Press Lid
P E R F O R M A N C E A N A L Y S I S OF A SOLAR GLASS TUBE COLLECTOR RENYUAN ZHANG,* HUANLIAN ZHU,* HANBING WEN* a n d MEICUN L~+ * Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou, China : ) Cadre's College of Science and Technology, Guangzhou Univcrsil3, P.O. Box 753, Chandi Post Office, Guangzhou 510120, China ( R e c e i v e d 19 J u n e 1992 ; ac~ ~7~ted 23 Mar~'h 1993)
Abstract The thermal perforintince and thermal processes of a glass tube collector have been analysed in this paper. Its thermal performance can be improved by changing the thermal processes to take advantage of the glass tube's ability to transmit sunlight : that makes it possible lbr the working tluid to directly absorb part of solar radiation. Its thermal performance is even better in most parts of the working region than thai of a steel tube collector, even when the structure, meteorological conditions and thermodynamic properties of the working fluid arc exactly the same. An equation of steady-state instantaneous efficiency of a glass tube collector has been derived in the paper. Calculations of various operating conditions have been made with a computer, and the calculated results are quite agreeable with the experimental results. Thus the equation and the calculation method can bc used in the design of glass tube collectors and for comparison calculations. The calculations also show some other important features of a glass tube collector.
INTRODUCTION Glass is corrosion-resistant and unlikely to scale. It also has a high t r a n s m i t t a n c e to sunlight. The cost of a collector made of glass tubes is 9 2 5 % less than that of a collector madc of steel tubes. But the thermal p e r f o r m a n c e of a glass tube collector is redtlced, owing to the bad thermal conductivity of glass. However, the thermal performance of a glass tube collector can be improved, so long as the thermal processes of a glass tube collector are changed.
THE TEST RESULTS OF A GLASS TUBE
model G B R - I (1.9 in: each) conventional parallel tube-to-tube constrtiction and model G B R - l l (2.3 m-" each) single serpentine tube construction have been made. Their quasi-steady-state i n s t a n t a n e o u s efliciencies are measured and shown in Figs 2 and 3. In order to popularize the practical use of glass tube collectors, we constructed two solar water heating systems in G u a n g z h o u City. The first system, with a total area of 15.2 and 5() m ~, is a natural circulation system consisting of some model G B R - I glass tube collectors. The second system, with a total area of 42 m z is a "'once-through tinder controlled temperature'" system consisting of some model GBR-11 glass tube collectors.
COl,LECTOR A N D ITS T H E R M A L PERFORMANCE EQUATION OF TItERMAL P R O C E S S E S A N D STEADY-STATE I N S T A N T A N E O U S EFFICIENCY
The structure of the glass tube collector was similar to that of the fiat-plate steel tube collector, except lbr the upper half of the tubes being t r a n s p a r e n t and the lower half being coated with dim black paint. A small a m o u n t of graphite was used as a filler at the bond (see Fig. I ). To make a comparison, we designed two cxperilnental collectors a glass tube collector and a steel tube collector with the same structure, and carried out the m e a s u r e m e n t of quasi-steady-state instanlancous efficiency (see Fig. 1 and Tables 1 and 2). Based on experiments, two kinds of practical solar glass tube flat-plate collectors with dim black paint
It can be seen clearly in Figs 2 and 3, and Tables I and 2 that the thermal performance of a glass tube collector is better than that of a steel tube collector in most parts of the working region. The specialities of Ileal a b s o r p t i o n and transfer in a glass tube collector are that the working fluid not only a b s o r b s energy from the a b s o r b e r plate but also directly a b s o r b s the solar radiation energy, taking a d v a n t a g e of both the transmission of the sunlight through a t r a n s p a r e n t glass tube and the water's property of intensively a b s o r b i n g infiared radiation [1]. 877
R. ZHANG et al.
878
Upper-half tube is not coated
Glass tube , N
collector
J
Absorber
"Lower-half tube is coated
/
Joint is filled with graphite
I
O Absorption of plate and water Fig. 1. Schematic of the glass tube collector.
Table 1. Comparison between the thermal performance of a glass tube collector and that of a steel tube collector Efficiency equation
Time constant (min)
Heat capacity (kJ m- 2 K ~)
Incident angle modifier
r / = 0.67-8.06(Ti- Tall)
6.4
60.3
k = 1-0.27[(I/cos 0) - 1]
~/= 0.68 9.46(Ti- Tall)
5.5
58.3
k = l~).21[(l/cos 0) - 1]
Tube type construction 20 x 1.5 Glass 0.6 m D / W = 0.2 20 x 1.5 Steel 0.6 m D / W = O.2
T h e energy b a l a n c e o n a flat-plate collector in a n i n s t a n t a n e o u s s t e a d y state c a n be w r i t t e n as
c o a t i n g o f t h e lower h a l f t u b e wall (s'). T h e e q u a t i o n is w r i t t e n as
q = qu+qL.
q = s+s'+s",
(1)
T h e t o t a l collected energy o f a glass t u b e collector consists o f three parts, i.e. the energy a b s o r b e d by the a b s o r b e r plate (s) a n d t h a t a b s o r b e d directly by the w o r k i n g fluid (s"), as well as t h a t a b s o r b e d by the Table 2. Comparison between the daily efficiency of a glass tube collector and that of a steel tube collector Date 10 July 1980 12 Dec. 1981 16 Dec. 1981
T i - Ta/l × 103
Glass tube collector
Steel tube collector
12 ~ 13 23 ~ 24 43 ~ 47
0.57 0.49 0.41
0.59 0.46 0.35
(2)
where s = l ( r la,,),
s' = l(z'at),
s" = l(z"aw),
•1 is the t r a n s m i t t a n c e o f o n e glass cover, z' is the t r a n s m i t t a n c e o f the glass c o v e r a n d glass t u b e filled with water, z" is the t r a n s m i t t a n c e o f the glass c o v e r a n d glass t u b e wall, aw is the a b s o r p t i o n o f water, a n d (ta) is the a v e r a g e t r a n s m i t t a n c e - a b s o r p t i o n p r o d u c t . A s a b s o r b e r plates a n d the lower halves o f the glass tubes are c o a t e d w i t h t h e s a m e paint, it is c o n s i d e r e d t h a t t h e a b s o r p t i o n o f t h e m b o t h is (Ip~ ap ~ a~.
879
Performance analysis of a solar glass tube collector ,q
0.~ xA
~
~~
Glass tube (calculated)
O.d t°e, ,u
0.2
I 0.0l
I 0.02 M ell
I 0.03
I 0.04
solar energy and that the heat transfer resistance of bond filler can be neglected. Thus the temperature of the tube outside wall is equal to the plate temperature (Tb) at the bond. According to ref. [2], the energy transferred to water from the plate and the tube lower wall is written as q~, = q (from plate)+ q (from tube wall)
=
I 0.05
W-D W- F[S- UL(Tb- ra) D
Tf-Ta - I
+ w [ S I - U ( T b - Ta)].
(5)
Fig. 2. The instantaneous efficiencycurves of the collectors. After rearranging, we obtain From the above equation, the useful energy gain absorbed per unit time per unit area by the working fluid under stable working conditions can be expressed as
qu = q-ql = S+S" +S"--qL.
W D D q~=('~V F+ w ) [ Q - U I ( T b -
(5')
where
Q ~ ( W - D)FS+ ..... DS" , (W-D)F+D
(3)
In fact, the useful energy gain is made of three parts, i.e. the useful energy gain transferred to the working fluid from the absorber plate and from the lower half coating, as well as from the direct absorption of the working fluid itself [2]. Thus the useful energy gain can also be given by
Ta)]'
The equation of heat transfer from plate to tube can be expressed as
rb- rf
q~ =
wi~>ThTS_-w/>(,
(6)
where C is the thermal conductance of the glass,
2gD c~= ~ ,
qu = q (energy from plate) + q (energy from lower tube wall coating) + q (energy absorbed directly by water).
(4)
It is assumed that the glass tube does not absorb
~t and 29 are, respectively, the thickness of the glass tube and the thermal conductivity of glass. Substituting eqn (6) into eqn (5) and dropping out Tb, we obtain
q~ = F'[Q- gt (7~1- Ta)],
(7)
where 0.6
I/UL ...............
F' =
/2
1 "11 0 . 4 -
"
~
1
1
"
W[UL[D+(W-D)F] C gDiIti]
~
Then the useful energy gain of the working fluid is
0.2--
3 t O.Ol
I 0.02
"~~.
I 0.03
I 0.04
I 0.05
M2.eC~V T f - T a I
Fig. 3. The instantaneous efficiencycurves of the collectors. (1) Model GBR-I (glass tube) t/= 0.72- 5.83(Tf-Ta/l). (2) Model GBR-1 (glass tube) tl = 0.67 5.02(TJ~- Ta/ll. (3) Model GTR-I (steel tubes, it is the same model and area as GBR-I, but there is no graphite at the bond) t/= 0.691 0 . 0 ( T [ ~ Ta/l).
D
qu = wS"+F'[Q-U,(T~--7~d)].
(8)
The differential equation for the temperature variation of the fluid along the long dimension of the tube is written as
l ril~pdTf dr-
w { D s " + F , [ Q _ UL(T-Ta)] }
880
R. ZHANGetal.
Let
qo FR [ Q ' - UL(Ti-- T.)] q = Io = Io
OS" WF' + Q = Q''
= F [(W-D)FS+DS' "L ( w - ~ F + D
then we can write
dTf riwP-dy = n W F ' [ Q ' - U L ( T - T a ) ] .
T f - T a - Q'/UL = exp [ T i - Ta - Q'/UL
U L
-UL(Ti-Ta)]/Io.
(9)
Solving the differential equation, we o b t a i n
WF" Yn/mcp] + C.
Assuming b o u n d a r y conditions as follows: when Y = O, T = 77; when Y = 1, Tf = To. After substituting, we can write
T o - T a - Q'/UL = exp [ - ULF'/GCp], Ti- Ta-Q'/UL G = rit/ W " L " n.
DS" + WF' (12)
It can be seen in eqn (2) t h a t the t r a n s m i t t a n c e a n d a b s o r p t i o n of water a n d the transmittance of a glass tube filled with water must be known. These data can be o b t a i n e d by calculation or by measurement. We can find out the equivalent water d e p t h [h = 0z/2)R] to substitute the d e p t h of water. Transmittance a n d a b s o r p t i o n of water can be o b t a i n e d by taking account of the reflection a n d a b s o r p t i o n of water, respectively. But in practice, we a d o p t the measured t r a n s m i t t a n c e curve (see Figs 4~6). A s s u m i n g that the t r a n s m i t t a n c e for one glass cover a n d water is z, a b s o r p t i o n of water is expressed as
Since
qu = G C p ( T o - Ti),
(10)
define
0.6i,.One glass cover I" 0.4 Two f
q~ = FR[Q'-- UL(Ti-- Ta)], FR =
GCp UL [l - e x p ( -
~
~
(1 1)
ULF'/GCp)]
I
0.2-
is yielded. Therefore, the i n s t a n t a n e o u s efficiency steady working conditions is written as
0.8
l
~
10
l 30
I
"%
50
70
90
i
under
Oneglass cover gla~
I
Fig. 5. Curve of the relation between the incident angle and transmittance for one glass cover and two glass covers, with water depth 50 mm.
0.6 O n e glass c o v e r
Twoglas~
0.6 -Two
'r 0.4 ¢ 0.2 0.4 '
0.2 I
10
50
I
I
30
I
70
"%
90
i Fig. 4. Relation between angle of incidence and transmittance for one glass cover and two glass covers, water depth 20 mm.
o
I
I
1o
30
I
I
50
70
90
i Fig. 6. Curve of the relation between the incident angle and transmittance for one glass cover and two glass covers, with water depth 70 mm.
Performance analysis of a solar glass tube collector T
aw = 1 - - - - ,
(13)
Tg
where ~g is the transmittance of glass when water is used as the medium (shown in Fig. 7) obtained from eqn (13) and is approximate to the data listed in ref.
[31. THE CALCULATION OF STEADY-STATE INSTANTANEOUS EFFICIENCY The calculation of steady-state instantaneous efficiency can be made in accordance with eqn (12), Figs 4 7 and with the transmittance curve of flat plate glass (Fig. 8), as well as with other formulae recommended in ref. [2].
1.0
•r
0.5
0
30
60
881
Calculation was made with a computer with the following two aims. (1) Given collector construction, property parameters and meteorological conditions, to calculate the steady-state instantaneous efficiency for various flow rates and various inlet temperatures. We input thc original date of the 0.6 m 2 experimental glass tube collector, mcteorological conditions, inlet temperature and flow rate at different experimental conditions so as to calculate its steady-state instantaneous efficiency in different operation conditions. The results are shown in Fig. 2. Obviously, the agreement between calculated and experimental results is satisfactory. (2) Given flow rate, inlet temperature, property parameters, meteorological conditions and some structure parameter, to make comparisons between the effects of various tube diameters and distances between the tubes on steady-state instantaneous efficiency, i.e. to lind out ~ I = . f ( D , D / W ) and 't = f(i, D / W ) . The curves from the calculation, which are subject to the original relative data of the experimental glass tube collector (area changed from 0.6 to I m 2), G = 50 kg/m2-h, Ti = 2 8 C , 6 = 23 08', and the meteorological conditions in Guangzhou City on 23 September 1978, are shown in Figs 9 and 10. ANALYSIS OF THE THERMAL PERFORMANCE OF A GLASS TUBE COLLECTOR
90
i
Fig. 7. Transmittance for glass with thickness 3 ram, water used as medium.
It can be seen in eqn (4) that the useful energy gain of the working fluid consists of the effective heat transfer from the plate and the tube lower wall to
0.7
0.9
I
0.8 0.7
32 \
2
~
0.6 1" 0 . 5 "71 0.6 0.4
2.1)=30
0.3
3. D = 4 0
0.2
4. DinS0 5. D=60
0.l
6. D ~ 7 0 I 10
30
50
70
90
i
Fig. 8. Curve of the relation between transmittance and incident angle for one window glass cover and two window glass covers with thickness 3 ram.
0.5
I
0.1
I
0.3
I
0.5 D/W
I 0.7
I
Fig. 9. Variation of the efficiency with tube-diameter and the distances between tubes.
R. ZHANGet al.
882 0.7
1
13:30
0.6
0.1
0.3
0.5
0.7
D/W
Fig. 10. Variation of the efficiency with time and the distances between tubes, for D = 20 mm.
water, and of that absorbed directly by water. The amount of energy gain depends on these three components and their rational distributions. We can see in Fig. 2 and Table 1 that the slope of the efficiency curve of a steel tube collector is greater than that of a glass tube collector, when
T i - Ta
and an increase in both q (energy absorbed directly by water) and q (energy gained by the lower part of the tube wall), such an increase is not able to compensate for the decrease in q (energy gained by the plate), owing to the decrease in the area of the plate. Thus the total useful energy gain decreases and its efficiency decreases. Curves 1-6 in Fig. 9 show that there is not much relation between the maximum value of efficiency and the size of tube diameter in the equation q = f ( D , D/W). They also show that the variation of D / W has little effect on efficiency when D / W is at its approximate optimum value. These make it unnecessary to use tubes with a large diameter, and there is no need to double tube numbers only for the sake of an increase by several per cent in efficiency. Figure 10 shows that the (D/W)opt. value does not vary from 12:30 till 15:30; only after 15:30 (when the incident angle is rather large), (D/W)opt. value decreases.
CONCLUSIONS × 103 ~> 10,
r/(glass tube) > r/(steel tube).
It can be explained as follows : as for a glass tube collector, the part of energy absorbed directly by water does not vary with variation of the mean temperature of the working fluid. Besides, the average tube temperature and plate temperature of a glass tube collector is lower than that of a steel tube collector, and its total heat loss decreases comparatively. Thus its total useful energy gain decreases less than that of a steel tube collector. It can also be seen in Figs 9 and 10 that an optimum value exists in D/[4I, whatever the size of the tube diameter of a glass tube collector. A collector's efficiency is highest when the optimum exists. The calculation shows that optimum values are different owing to different diameters, e.g. when D = 20-70 mm, the optimum value of D / W is 0.443.6. Such an important character of a glass tube collector can be explained as follows: when D~ W = (D/W)opt., the energy absorbed by water in the tube increases with the increase in D/W, i.e. the increase in tube numbers. At this time, there is an increase in the total useful energy gain. Since the increased gain is bigger than the decrease in energy transferred to the working fluid, which is caused by the decrease in the area of the absorber plate and by poor conductivity of glass. When D / W = (D/W)opt., the total amount of the three-part energy (shown in eqn 4) reaches its maximum. When D / W > (D/W)opt., although there is an increase in the number of tubes
(1) By changing the thermal processes of the glass tube collector, the slope of the efficiency curve for a glass tube collector will be smaller than that of a steel tube collector. (2) There is a satisfactory agreement between the test results and the theoretical analysis of the thermal processes of a glass tube collector. Calculations for steady-state instantaneous efficiency show that an optimum value exists in D~ W. The steady-state instantaneous efficiency is highest when the optimum value occurs. (3) According to the measured quasi-steady-state instantaneous efficiency (Fig. 3), and the agreement between test data and calculated results, it can be concluded that heat transfer is improved by using graphite as the bond filler.
NOMENCLATURE q= qu = qL = 0= 1= D=
Di = W= l= n= uL =
collected energy per unit time per unit area useful energy gain per unit time per unit area heat loss per unit time per unit area slope of plane from the horizontal total radiant intensity on a surface with a slope to the horizon tube o.d. tube i.d. distance between tubes length of tube number of tube overall heat loss coefficient of collector
Performance analysis of a solar glass tube collector heat transfer coefficient from tube wall to water incident angle flow rate per unit area of working fluid mass-flow rate of working fluid Cp= specific heat of water mean water temperature of collector th, Tb = plate temperature at bond ti, T i = inlet water temperature of collector to, To = outlet water temperature of collector ta, T a = ambient temperature 6 - geographical lalitude hi= i= G= ?n =
883
r/= instantaneous efficiency of collector under steady operating conditions. REFERENCES
I. J. P. Holman, Heat Transfer, Fourth Edn. McGraw-Hill, Maidenhead (1976). 2. J. A. Duffle and W. A. Beckman, Solar Engineering qf' Thermal Processes. John Wiley, New York (1980). 3. K. E. Kondrasief, Solar Radiation Eneryy. National Hydrometeorologic Press, Leningrad (1954).