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Temperature-dependent collector properties from stagnation measurements
Solar £nergy Vol.25, pp. 465-466 PergamonPress Ltd., 1980. Printedin Great Britain
TECHNICAL NOTE Temperature-dependent
collector properties from stagnation measurementst
J. M. GORDON, D. GOVAER a n d Y. ZARMI Institute for Desert Research, Ben Gurion University of the Negev, Sede Boqer, Israel
(Received 7 December 1979; revision accepted 2 May 1980)
In an analysis of the thermal characteristics of flat-plate solar collectors, one point of interest is the temperaturedependent behavior of t h e collector heat loss coefficient U,.. Although U~ is frequently taken to be a temperatureindependent collector property, it is, rigorously, a function of plate temperature. The theory and calculations for the temperature dependence of UL have been presented [1"1,yet experimental work on this issue has been sparse. The purpose of this note is to show h o w simple stagnationcondition measurements for solar collectors can provide a direct measurement of the temperature dependence of UL.
Hence, to a good approximation, we should be able to express the temperature dependence of UL in the form
UL = A'o + AI(Tp - Ta) + 0((Tr - T~)2),
(4)
where A~ includes back and edge heat losses. Our proposition, then, is to determine UL/(ra) from measurements of T, and T, at various constant values of 1 (from eqn 2), and to plot UL/(r~) against T~ - T,, so as directly to determine the temperature dependence of UL.
EXPERIMENT
THEORY
The stagnation point for a collector is a condition of no flow, at which no useful energy Q. is being collected. For constant insolation it, the collector achieves its maximum temperature at stagnation. The appropriate energy balance equation at stagnafioh can be written as Q. = 0 = l(rct) - UL(T~ - T~),
(1)
which can be rearranged as
ULI(r~) = iI(r, - T.).
(2)
At stagnation, plate temperature, inlet temperature and outlet temperature are all equal. Hence the stagnation temperature T,, strictly speaking the plate temperature T~ at stagnation, can alternatively be measured as the inlet or outlet temperature. Equation (2) indicates that if stagnation measurements (namely, T,, T, and I) can be made at various constant values of insolation, then a direct measurement of UL/(ra) at the various corresponding values of T ~ - T, results. Since ra is essentially temperature-independent for the temperature range of interest, it Will be thc temperature dependence of UL which will be observed in such stagnation measurements. To a good approximation, the temperature dependence of UL arises from the contribution of radiative heat losses. As UL is typically dominated by losses through the top collector surface (the glazing), and as radiative losses are predominantly through the top collector surface, a theoretical treatment of the temperature dependence of the top losses should be sufficient to describe the temperature dependence of UL. The theory of the temperature dependence of the top losses [1] indicates that the top heat loss coefficient Utop can be expressed as an expansion in rr - Y,,
Utop = Ao + At(T r - T,) + 0((T, - T~)2).
(3)
1"Research supported by the Center for Absorption in Science, The Ministry for Immigrant Absorption, State of Israel. 465
The collector used was a locally-manufactured flat-plate (liquid) sohr collector, with a copper plate, a single serpentine copper riser, no selective coating, and a commercially available glazing of one sheet of double-walled Lexan (4 mm spacing). Solar insolation was measured with an SS-100 Solar Sensor by Rostrack. The exit ports of the collector were stopped and two thermocouples were placed inside the collector in contact with the exit pipes to measure the stagnation temperature. Ambient and stagnatio n temperatures were measured with copper-constantan thermocouples and monitored by an HP 3465B digital multimeter. All measurements were performed on clear sunny~summer days during the hour symmetri c about solar nooil so ~ a t plate temperature and ambient temperature were constant to within 1½ per cent and insolation was constant to within ½ per cent for the periods of measurement. The average wind velocity was 3 m/see. The collector and solar!meter were set at a tilt angle so as to be normal to solar radiation at solar noon. Different values of insolation were achieved by shading the collector and solarimeter uniformly with a white rubber net mesh of square hole sizes varying from 4 × 4 mm to 8 x 8 mm, suspended about 30¢m above the collector. This allowed for free natural ventilation of the space between collector and net. The net used to reduce insolation absorbs some solar radiation,.and in principle the effective surroundings temperature may be different from the ambient dry bulb temperature. Given, however, the natural ventilation on both sides of the net, a typical net absorbance of 0.25, and an average wind velocity of 3 m/see, we can estimate the average net temperature to be less than 9°C above ambient. TMs difference between net and ambient temperatures will have a negligibly, small effect on the collector's heat loss coefficient UL I'll. The collector was allowed to reach the steady-state stagnation condition during the hour about solar noon, and measurements of T~, T~ and I were averaged over the period of stagnation. The results of the experimental measurements are summarized in Table 1. A graph of UJ(za) vs T~ - T, is displayed in Fig. 1. From the data presented in Table 1 and Fi& 1, it appears UL is well approximated by a linear function of Ts - Ta in this case, so that, with reference to eqn (4), we have
Technical Note
466
Table 1. Results of stagnation measurements I (W/m2)
Ts(°C) Ta(°C) U L I ( ~
1070
123.7
33.3
11.8
August 2
1040
123.4
37.6
12.1
June 19
1023
119.3
32.5
11.8
June 15
465
79.3
35.9
10.7
June 18
462
72.2
29.4
10.8
August 14
461
81.1
38.3
10.8
June 20
154
54.7
38.3
9.4
June 21
oo
/
P
/ .~
io
/
/
/
f
/e
8
i
i
20
i
I
40
i
i
I
60
I
80
i
I
I00
NOMENCLATURE
AT,°C
Fig. 1. UL/(z~t) vs T~- T~. The linear regression fit is UL/(Z~t) ----9.23 + 0.0314(T~ -- T~).
u L / ( ~ ) = Bo + Bl(Tp - ~ )
Date (1979)
considered here, UL is well approximated as linear in Tp - T~. It is also interesting to compare the degree of the temperature dependence of UL from our experimental results with the theoretical calculations for a collector of comparable thermal performance (from Ref.[1], the example of a glass single-glazed collector, non-selectively coated, at ambient temperature 30-40°C and wind speed 0-5 m/sec). Both the theoretical calculation and our experimental findings indicate about a 20-30 per cent change in UL with temperature in the temperature range considered. (Although the theoretical calculations are for Utop, the temperature dependence of Uc is, as noted above, dominated by the temperature dependence of Utop. Hence the comparison should be a valid one.) In light of the above observations, stagnation-point measurements for flat-plate solar collectors can provide an experimental method with a minimal degree of sophistication and equipment for the measurement of the temperature dependence of the collector heat loss coefficient UL (in the form Uc/(wt)).
/
/
(W/m2K)
(5)
with a linear regression fit yielding Bo = 9.23 W/m2K B 1 = 0.0314 W/m2K 2. (The scatter in the data presented in Fig. 1 probably arises primarily from the variability in wind velocity of 0-6 m/sec, the range of which can introduce variations of +15 per cent about the value of UL determined at an average wind velocity of 3 m/secl.) These findings are in agreement with the corresponding treatment in Ref. I-l] in that, for the temperature range
Q, I z~ U~. Utop Ao A~ AI Bo Bt T~ T~ Tp
useful energy, W/m e solar insolation, W/m 2 transmittance-absorbance product collector heat loss coefficient, W/m2K collector top heat loss coefficient, W/mZK coefficient in expansion for Utop, W/m2K coefficient in expansion for UL, W/m2K coefficient in expansion for Utop and UL, W/m2K 2 coefficient in expansion for U~./(~ct), W/m2K coefficient in expansion for UL/(zct), W/m'K 2 stagnation temperature, °C ambient temperature, °C plate temperature, °C
REFERENCE
1. J. A. Duffle and W. A. Beckman, Solar Energy Thermal Processes, Chap. 7. Wiley, New York (19741
TECHNICAL NOTE Temperature-dependent
collector properties from stagnation measurementst
J. M. GORDON, D. GOVAER a n d Y. ZARMI Institute for Desert Research, Ben Gurion University of the Negev, Sede Boqer, Israel
(Received 7 December 1979; revision accepted 2 May 1980)
In an analysis of the thermal characteristics of flat-plate solar collectors, one point of interest is the temperaturedependent behavior of t h e collector heat loss coefficient U,.. Although U~ is frequently taken to be a temperatureindependent collector property, it is, rigorously, a function of plate temperature. The theory and calculations for the temperature dependence of UL have been presented [1"1,yet experimental work on this issue has been sparse. The purpose of this note is to show h o w simple stagnationcondition measurements for solar collectors can provide a direct measurement of the temperature dependence of UL.
Hence, to a good approximation, we should be able to express the temperature dependence of UL in the form
UL = A'o + AI(Tp - Ta) + 0((Tr - T~)2),
(4)
where A~ includes back and edge heat losses. Our proposition, then, is to determine UL/(ra) from measurements of T, and T, at various constant values of 1 (from eqn 2), and to plot UL/(r~) against T~ - T,, so as directly to determine the temperature dependence of UL.
EXPERIMENT
THEORY
The stagnation point for a collector is a condition of no flow, at which no useful energy Q. is being collected. For constant insolation it, the collector achieves its maximum temperature at stagnation. The appropriate energy balance equation at stagnafioh can be written as Q. = 0 = l(rct) - UL(T~ - T~),
(1)
which can be rearranged as
ULI(r~) = iI(r, - T.).
(2)
At stagnation, plate temperature, inlet temperature and outlet temperature are all equal. Hence the stagnation temperature T,, strictly speaking the plate temperature T~ at stagnation, can alternatively be measured as the inlet or outlet temperature. Equation (2) indicates that if stagnation measurements (namely, T,, T, and I) can be made at various constant values of insolation, then a direct measurement of UL/(ra) at the various corresponding values of T ~ - T, results. Since ra is essentially temperature-independent for the temperature range of interest, it Will be thc temperature dependence of UL which will be observed in such stagnation measurements. To a good approximation, the temperature dependence of UL arises from the contribution of radiative heat losses. As UL is typically dominated by losses through the top collector surface (the glazing), and as radiative losses are predominantly through the top collector surface, a theoretical treatment of the temperature dependence of the top losses should be sufficient to describe the temperature dependence of UL. The theory of the temperature dependence of the top losses [1] indicates that the top heat loss coefficient Utop can be expressed as an expansion in rr - Y,,
Utop = Ao + At(T r - T,) + 0((T, - T~)2).
(3)
1"Research supported by the Center for Absorption in Science, The Ministry for Immigrant Absorption, State of Israel. 465
The collector used was a locally-manufactured flat-plate (liquid) sohr collector, with a copper plate, a single serpentine copper riser, no selective coating, and a commercially available glazing of one sheet of double-walled Lexan (4 mm spacing). Solar insolation was measured with an SS-100 Solar Sensor by Rostrack. The exit ports of the collector were stopped and two thermocouples were placed inside the collector in contact with the exit pipes to measure the stagnation temperature. Ambient and stagnatio n temperatures were measured with copper-constantan thermocouples and monitored by an HP 3465B digital multimeter. All measurements were performed on clear sunny~summer days during the hour symmetri c about solar nooil so ~ a t plate temperature and ambient temperature were constant to within 1½ per cent and insolation was constant to within ½ per cent for the periods of measurement. The average wind velocity was 3 m/see. The collector and solar!meter were set at a tilt angle so as to be normal to solar radiation at solar noon. Different values of insolation were achieved by shading the collector and solarimeter uniformly with a white rubber net mesh of square hole sizes varying from 4 × 4 mm to 8 x 8 mm, suspended about 30¢m above the collector. This allowed for free natural ventilation of the space between collector and net. The net used to reduce insolation absorbs some solar radiation,.and in principle the effective surroundings temperature may be different from the ambient dry bulb temperature. Given, however, the natural ventilation on both sides of the net, a typical net absorbance of 0.25, and an average wind velocity of 3 m/see, we can estimate the average net temperature to be less than 9°C above ambient. TMs difference between net and ambient temperatures will have a negligibly, small effect on the collector's heat loss coefficient UL I'll. The collector was allowed to reach the steady-state stagnation condition during the hour about solar noon, and measurements of T~, T~ and I were averaged over the period of stagnation. The results of the experimental measurements are summarized in Table 1. A graph of UJ(za) vs T~ - T, is displayed in Fig. 1. From the data presented in Table 1 and Fi& 1, it appears UL is well approximated by a linear function of Ts - Ta in this case, so that, with reference to eqn (4), we have
Technical Note
466
Table 1. Results of stagnation measurements I (W/m2)
Ts(°C) Ta(°C) U L I ( ~
1070
123.7
33.3
11.8
August 2
1040
123.4
37.6
12.1
June 19
1023
119.3
32.5
11.8
June 15
465
79.3
35.9
10.7
June 18
462
72.2
29.4
10.8
August 14
461
81.1
38.3
10.8
June 20
154
54.7
38.3
9.4
June 21
oo
/
P
/ .~
io
/
/
/
f
/e
8
i
i
20
i
I
40
i
i
I
60
I
80
i
I
I00
NOMENCLATURE
AT,°C
Fig. 1. UL/(z~t) vs T~- T~. The linear regression fit is UL/(Z~t) ----9.23 + 0.0314(T~ -- T~).
u L / ( ~ ) = Bo + Bl(Tp - ~ )
Date (1979)
considered here, UL is well approximated as linear in Tp - T~. It is also interesting to compare the degree of the temperature dependence of UL from our experimental results with the theoretical calculations for a collector of comparable thermal performance (from Ref.[1], the example of a glass single-glazed collector, non-selectively coated, at ambient temperature 30-40°C and wind speed 0-5 m/sec). Both the theoretical calculation and our experimental findings indicate about a 20-30 per cent change in UL with temperature in the temperature range considered. (Although the theoretical calculations are for Utop, the temperature dependence of Uc is, as noted above, dominated by the temperature dependence of Utop. Hence the comparison should be a valid one.) In light of the above observations, stagnation-point measurements for flat-plate solar collectors can provide an experimental method with a minimal degree of sophistication and equipment for the measurement of the temperature dependence of the collector heat loss coefficient UL (in the form Uc/(wt)).
/
/
(W/m2K)
(5)
with a linear regression fit yielding Bo = 9.23 W/m2K B 1 = 0.0314 W/m2K 2. (The scatter in the data presented in Fig. 1 probably arises primarily from the variability in wind velocity of 0-6 m/sec, the range of which can introduce variations of +15 per cent about the value of UL determined at an average wind velocity of 3 m/secl.) These findings are in agreement with the corresponding treatment in Ref. I-l] in that, for the temperature range
Q, I z~ U~. Utop Ao A~ AI Bo Bt T~ T~ Tp
useful energy, W/m e solar insolation, W/m 2 transmittance-absorbance product collector heat loss coefficient, W/m2K collector top heat loss coefficient, W/mZK coefficient in expansion for Utop, W/m2K coefficient in expansion for UL, W/m2K coefficient in expansion for Utop and UL, W/m2K 2 coefficient in expansion for U~./(~ct), W/m2K coefficient in expansion for UL/(zct), W/m'K 2 stagnation temperature, °C ambient temperature, °C plate temperature, °C
REFERENCE
1. J. A. Duffle and W. A. Beckman, Solar Energy Thermal Processes, Chap. 7. Wiley, New York (19741