- Email: [email protected]
Testing the thermal performance of uncovered solar collectors
S,,&, I>'lO:t't VOI 49. N o 4. pp 263-272. 1992 Prmtcd m Ihc 1; S A
0038-(~-12X/92 $5.(10 ~ .(J0 Cop~,nghl (c 1992 Pergamon Press I.Id
TESTING THE THERMAL PERFORMANCE OF UNCOVERED SOLAR COLLECTORS H. SOI/FAU* Department of Physics of the Ludwig-Maximilians-University,8{K)0MiJnchen 40, Germany Abstracl--A proposal tbr an international standard. "Io Determine the Thermal Performanceof Uncovered Collectors," is presented. Test particulars as the measurement of the Iongwavcradiation and the characterization of the wind field determining the convective losses of the absorber surface are discussed, both for indoor and outdoor conditions. The model includes testing under unsteady conditions. A comparison with alternate test approaches is performed. Experimental results arc presented.
I. I N T R O D U C I ' I O N
4. The collector performance is characterized by four (or five) parameter values. They are determined by Testing the thermal performance of glazed fiat-plate calorimetric measurements in a linear fit procedure. solar collectors at low temperature is well established. 5. Indoor and outdoor testing are considered. The For example, the ASHRAE test standard 93 [ 1] is used fundamentals of the experimental set-up and proworldwide. Such test methods developed for glazed cedure are adapted to the ASHRAE standard 9311] collectors cannot be applied to uncovered solar collecto simplify the implementation in existing laborators, however, because they do not specify the influence tories. of the longwave sky irradiation and the external wind 6. Unsteady weather conditions are admitted by field on the collector efficiency. The thermal performodelling the average energy yield over a reasonably mance of uncovered collectors is highly sensitive to long time period of about 1 h. both those effects, as the following examples illustrate: The collector model and the test procedure are pre• An uncovered collector may loose 150 W / m "~ through thermal radiation on a clear and sunny day sented in section 2. Section 3. I examines the Iongwave radiation measurement, and section 3.2 the characand 0 W / m 2 in a cloudy period. terization of the convective losses, for both indoor and • The energy yield of an unglazed collector exposed to an average wind speed of 1 m/s or 4 m/s, above outdoor testing. Testing under transient conditions is the collector surface, may differ by 50%, on a sunny discussed in section 3.3. The detailed guidelines for the day. The influence of wind speed is increased as the test conditions, the instrumentation, the numerical contribution of solar radiation to the energy yield is determination of the system parameters, and the repreduced. (This point is especially relevant if the un- resentation of the test results are expounded elsecovered collector is operated below ambient tem- where[4], and will not be repeated here. They were perature, e.g., if it is used as the low temperature worked out in cooperation with the team of Task 111 heat source of a heat pump system.) The dependence from the Solar Heating and Cooling Programme ofthe of the collector efficiency on wind speed is sum- International Energy Agency (lEA). Section 4 contains a comparison with the American [ 5 ] and the Austrian marized in Fig. I. Hence, for determining the thermal performance standard[6] and the test ideas of Svendsen[7], of uncovered solar collectors a new standard has to be France[ 8] and the European Community [9]. The test developed. The actual interest is large. Already, heating procedure has been examined indoors and outdoors, of swim ming pool water by large-area low-cost uncov- at the National Solar Test Facility of Canada [ 10 ] and ered collectors made of rubber or plastic materials is the University of Munich. The experimental results economically competitive. The costs of the solar energy are displayed. Conclusions are drawn in section 5 resulting in an outlook for future projects. range between 0.06 and 0.07 DM/kWh[2.3]. This paper presents and discusses a test method having the following features: 2. T I l E S T A N D A R D P R O P O S A L I. The energy yield of the collector is evaluated by a model resembling the Hottel-Whillier-Bliss equa2.1 The model tion. In the test procedure the energy yield of the un2. The longwave sky irradiation is part of the radiation covered collector is evaluated by a model which corbalance. 3. The optical efficiency and the heat loss factor are responds to the Hottel-Whillier-Bliss (HWB) equation of a flat-plate solar collector [I 1,12 ]: modelled as linear functions of the average wind speed above the collector array. ' ISES member. 263
264
H, SOl.TAt I
rl -
ity (~) of 0.9. its value is 5.0 W/m2K, when averaged over the permissible operation range) The dependence on ambient or collector temperature is neglected. The resulting error can be estimated by a standard deviation of 0.4 W / m2K. 3. The overall heat loss coefficient ( Ut ) contains the longwave radiation coefficient (h~,), wind induced forced convection (hf~) and conduction losses through insulation (hod):
n 1,5 m/,s
0.8 - ~
o ZSm/g ~ + 3 . 5 r n / s
o,4
Ul = hi, + hrs. + h c d .
a;r JL 0
I 0
I o.ot
0,02
|--0.03
Fig. 1. The efficiency of an uncovered solar collector
speed (u~) on its surface. The presenteddata refer to a collector made of polypropylenetubes with a diameter of 6 mm[ 36]. operated by a flow rate of 250 I/hm:[10].
All variables are averaged over the collector area (A) and a time period (At) which is chosen in dependence of the weather dynamics: l h is a reasonable value, where
(2 = ( m c ) ( T , -
T,)
The state of the art in modelling combined forced and natural convection is contradictory [ 11]. Hence, the test procedure is restricted to wind velocities above 0.3 m/s, where the influence of the natural convection becomes negligible. 4. Forced convection is the dominant contribution to the heat loss. The heat transfer coefficient (hfc) ranges between 3 W/m2K and 60 W/m2K depending on the wind field conditions. The consequent variation of the heat removal factor (FR), which is a function of(UL), is considerable. Figure 2 gives an illustration. In eqn ( 1) the optical efficiency ( k R a ) and the heat loss factor (FRUL) are both modelled as linear functions of the average wind speed (uw) above the collector array (l~a)
= cj - c2u,,
(FRUt.) = c3 + c4u~,.
= energy yield of the collector system per square meter aperture area a shortwave solar irradiance in collector plane L = relative longwave sky irradiance (see eqn [2], below) shortwave absorptivity of the absorber Iongwave emissivity (absorptivity) of the absorber Ta ambient temperature ~ = exit temperature of the fluid Ti= inlet temperature of the fluid U|. overall heat loss coefficient F.= heat removal factor rnc= heat capacity rate of fluid. Equation (1) differs from the conventional HWB model [ 13 ] in the following ways: I. The insolation is not diminished by the transmittance of the cover. 2, The balance between the absorbed Iongwave sky irradiance (tL*) and the radiation of the collector plate (feTe) is included in the relative longwave sky irradiance (L) and the heat loss of the plate, as follows:
(3)
(4a) (4b)
The model, as presented in eqns ( 1 through 4), achieves an overall precision of 10% of the average energy yield: The characterization of the wind field by the average wind speed is a first order approximation. The nonlinear error due to the wind dependence of the heat removal factor is limited to 3%. The dynamic error is controlled by a correct choice of the averaging time period (At), as outlined in section 3.3. Equation ( 1) is designed as a test and simulation model. It refers to the inlet instead of the mean temperature of the fluid. The accuracy of the prediction is enhanced if the same effective parameters are used in test and simulation. The experimental determination of the mean fluid temperature may raise difficulties. The linear approximation by the measured values of the exit and the inlet fluid temperature, which is generally used for covered solar collectors, is less accurate if transferred to uncovered collectors with a heat loss coefficient of about 20 W/m2K, as illustrated in Fig. 7b. 2.2 T h e test p r o c e d u r e The values ofthe parameter coefficients {G, J = 1,4 } and the system parameter ( ~ ) characterize the collec-
~L* - , a T ~ = t ( L * - oT*~) - ( t t r T ~ - ,aT**) t L - hl~( Tp - T~).
(2)
The heat transfer coefficient (h~,) is part of the overall heat loss coefficient (UE). Assuming an emissiv-
The operation temperature T of the heat transfer fluid is restricted to 278K<(T+7~)/2<308K
and
IT-T,I
<20K.
Thermal performance of uncovered solar collectors
265
r ut j w
(FR~,)
m2 K
" =
.85 y x~
~1¢
16
.75
1l,.
x
txx
lg
x x
12.
It w
J
.65
i
,
Uw Im/s) '~
1
2
3
z,
uw (m/s) 70
0
i
1
2
3
Fig. 2. The dependence of the collector parameters (FRa) (left) and (FRL"L) (right) on the wind speed (u,) is linear with a good approach to accuracy. The data have been recorded outdoors for a metal energy roof with a fiat surface and broad fins, operated by a flow rate of 50 l/hm:.
tor thermal performance. They are determined in the test. The energy yield ( 0 ) of the system is recorded as a function of the meteorological input variables (G, L*, Ta, u,) and the inlet temperature of the fluid (T,). The relative longwave sky irradiance (L) is calculated from (L*) and (T,). The heat capacity rate (rhc) is set in agreement with the manufacturers' recommendations. All quantities are averaged over the time period (At ~ 1 h) and the collector area (A). Using eqns ( 1) and (4), the parameter values { cj } are then estimated from the test data in a joint linear fit procedure. An ordinary least-squares method may be used to minimize the average deviation (a 2) between modelled and measured energy values: 1
(r2 =-
N-4
N
~ (O~,p.i - Qmod.,)2 ~ minimum. (5) t=l
Of course, the quality of the parameter values is related to the variance of the input data, which is specified in the test instructions. Generally, in outdoor testing, a continuous measurement over two to three days yields a good data basis. A minimum number of 10 data points is required for indoor tests. The test proposal suggests the independent determination of the parameter ( ~ ) by photospectrometry. In most cases the ratio will amount to about 0.95. Estimation on the basis of the calorimetric data is possible using nonlinear fit procedures provided the Iongwave sky irradiance varied sufficiently during the test. The test method is intended to apply to small flatplate uncovered collector arrays. It has been validated up to a maximum size of 12 m 2. The mounting of the system is arbitrary. However, it is preferable to build up the collector array directly on a well-insulated roof construction with a white surface with a low heat conductivity. Testing backside-ventilated collectors is very much dependent on the actual topology and the wind direction.
3. TEST
PARTICULARS
3. I Measuring the longwave radiation The longwave sky irradiance (L*) of the hemispherical field of view of the collector is measured in the collector plane using a pyrgeometer or a combination of a pyrradiometer and a pyranometer. Currently, only the Eppley PIR pyrgeometer [ 14 ] is available. It measures the longwave radiation with a wavelength (k) larger than 3 tzm by a method comparable to that ofa pyranometer. The temperature difference between the body of the instrument and the surface of a black receiver which is sheltered from shortwave irradiance by a coated silicon dome is the relevant signal. To obtain reliable data of the Iongwave irradiance by the Eppley pyrgeometer the following modifications are necessary: I. The dome of the pyrgeometer should be ventilated by an airstream with a volume of at least 25 m3/ h[15]. 2. The compensation for the longwave radiation emitted by the body of the instrument (aTe,d,) is performed electrically by a battery circuit. It should be replaced by digital calculation. The body temperature (Tt~y) is determined by a thermistor attached to the housing close to the cold junction of the thermopile [ 16 ]. The calibration procedure in the Eppley laboratory presupposes identity of the dome and the body temperature of the instrument. Yet, by absorption of shortwave irradiance the dome temperature is enhanced. The error in measurement is less than before 1979 when Eppley changed the dome material from KRS5 to silicon. Differences between dome and body temperature up to 2 K for G = 800 W / m 2 were measured, corresponding to an error in the longwave irradiance of about 20 W / m 2. For a more precise measurement the following actions are necessary: A small thermistor is attached to the lower edge o f the dome. The recorded value represents a first approximation of the dome temperature. The thermopile
H. SOLTAU
266
output (t5V) is then corrected by the difference between body and dome temperature, that is, L* = c,,SV+ aT~,d~ + c'o(Tt,,e~ - 7)om~),
(6)
where (co) is the calibration coefficient provided by Eppley laboratories and (co) is a correction factor. The Canadian Atmospheric Environment Service suggests[ 17 ] a correction proportional to the shortwave irradiance (G). To avoid dynamic errors averaging over time periods (At > 10 min) is necessary. Unfortunately, up to now no official calibration facility considers the influence of shortwave irradiance on the pyrgeometer performance and determines the correction factor. From a series of sun and shade experiments Berdahl and Fromberg[18] concluded a value of I I W/mZK for (c'o), in agreement with a calculated estimate of 12 W/m2K. Wardle and MeArthur [ 17 ] found a response of 0.026 W / m" per I W / m 2 shortwave solar irradiation. Provided the longwave sky irradiation is determined as given in eqn (6), an accuracy of about 5 W / m 2 in the hourly value of (L*) was observed. The principle of measurement of a pyrradiometer is equivalent to that of a pyrgeometer. In this case the dome covering the receiver consists of a material which is transparent to long- and shortwave irradiation (.3 tam < ;~ < 60 #m). The pyrradiometer allows determination of the longwave sky irradiance by comparison with a pyranometer output. Indoor testing with a solar simulator ( ~ 6 0 0 K) requires a pyrradiometer, as the sensitive wavelength range of the pyrgeometer is insufficient. The analysis of the pyrradiometer was less satisfactory. The relative error of the Iongwave radiation measurement is large, corresponding to the dominant contribution of shortwave radiation. The dynamic error of the pyrradiometer is substantial [ 19 ]. 3.2 Spec(l.ving the convective losses Corresponding to the physical effects which control the magnitude of the convective losses, the average velocity ( I ), the dynamics (2), and the topology (3) of the wind field on the collector surface, the experimental demands on the flow field are specified. Aiming at collector parameters which are representative for real operating conditions, the discussion is oriented by the properties of the natural wind field. The guidelines represent a first approach based upon present knowledge. The test method abstains from artificial wind generation in the open air. That effort is large[20]. The characterization of the flow field is not simplified, for example, the specification of the turbulence intensity cannot be avoided: Outdoors, the influence of the natural wind field persists. Indoors, the size of the collectors and the environmental chamber differ from classical wind tunnel dimensions. The flow field is turbulent and inhomogenous. 1. In the test procedure the collector parameters (FROt) and (FRU~) are correlated with the magnitude of
the average wind speed (u,~) on the collector surface. A linear model is a good approach, as the data entries in Fig. 2 illustrate. Depending on the surface structure, the heat loss coefficient varies between 30% and 50%, and the optical efficiency changes by about 5% per 1 m/s increase in wind speed. The wind speed is measured at several representative points in the collector plane a distance of 0.1 m above the absorber surface, that is, in the free-stream region outside the local boundary layer. As pictorially demonstrated by Keller [ 21 ], determining the wind speed in front of or significantly above the collector array involves a host of uncertainties, depending on the various nearby surroundings and the wind direction. 2(a). Testing is performed under turbulent flow conditions, indoors and outdoors. Under real operating conditions the collector is exposed to a flow field that is highly variable and turbulent: At the ground level of an urban environment the wind field is characterized by turbulence intensities between 35% and 55% and rapid and significant changes in the local flow direction [22 ]. The effect of the free-stream turbulence is large: the forced convection heat transfer coefficient of a fiat plate is enhanced by about 100°,* compared to wind tunnel studies where the oncoming flow is relatively undisturbed. Figure 3 compares experimental values to the classical solution for undisturbed parallel flow conditions[ 23]. The data have been recorded outdoors, at the collector test facility of the University of Munich ( LMU ), shown in Fig. 4. The open air measurements of Test et a1.[24] show the same magnitude. Also eqn (3) in Fig. 3, which is advised by Duffle and Beckman[13 ], represents a reasonable correlation model with regard to turbulent flow conditions. The formula has given rise to several critical publications (see, e.g., Sparrow and Tien [ 25 ]). It is validated by our data. As a consequence of Fig. 3 the test procedure requires testing under turbulent flow conditions so that outdoor and indoor testing is equivalent and a systematic deviation in the predicted energy yield is avoided. 2(b). The magnitude of the free-stream turbulence is quantified and reported with the test results. The scatter of the data and the correlation models in Fig. 3 indicate the variation of the heat transfer rate with the turbulence properties. Yet, so far no uniform standard model between the forced convection heat transfer coefficient of a fiat plate and turbulent free-stream conditions exists. For the present the turbulence intensity (Tu) is suggested as a reference quantity. It is defined as the relative variance (a~,) of the wind speed magnitude:
Tu = a~.__r.-. Uw
(7)
Thermal performance of uncovered solar collectors
20f
~ (41 ~hfc(W/m2K)
#
~
•
x
..x
,,
~
Z ~d~ ?~.,,/,¢
/
,o....... •
5 L .....
0.5
~
~[3)
x×
oo2o'L2'o, enwronmenf
~
~
/undlsfurbed pacollel .fl°w (I]
/ ......
/ 1,o
,
2,0
uw~/s_j ]
, 3,0
Fig. 3. The con~ective heat transli:r coe|ficient of a flat plate is significantl.~influenced by frcc-strcam turbulence: ( I ) Undisturbed flow. K,~rmfin equation (/,.h,, - 3.5 m)" h~ = 5.0 u~ o8 W/m:K. ( 2 ) l c s t et aL[24] (outdoors); hie
(m/s)
(8.6 ÷ 2.7
u~ ') W/m:K. U.qSS
(3) Dulfie and Beckman[13];
(5.7' 3,8 ( m/s ) ) W/m:K (4) Outdoor mcasurements //~
]lt~.
3. The influence ofthe average wind field topology on the heat transfer coefficient (hfc) is much less for a finite plate than the effect of the free-stream turbulence. That is the conclusion of a detailed experimental investigation of Sparrow et al.[ 30]" for comparison, the numerical results have been transferred to the average wind speed on the collector surface by S o l t a u [ l l ] . The local variance of the flow velocity is restricted to a standard deviation of _+1 m/s.
/
;/"
/ /~/
•
~,~x
267
"
(IMU I. data entries denoted by (×). best tit: hr¢
9.3
u~ .8 W/m-'K.
(m/s)
A m i n i m u m value o f ( T u > 20%) is required during testing. Recently, promising results have been achieved at Munich [ 26 ]. The heat transfer coefficient of a flat plate has been measured outdoors as a function of statistical wind field parameters. The correlation with a parameternamed directional turbulence has been most successful. It quantifies the turbulence by the angular velocity of the local flow direction. It is easily measured by a wind vane. It reduces the scattering of the data to the uncertainty in measurement. 2(c). While the free-stream turbulence is an inherent characteristic of the natural environment, indoor testing requires auxiliary structures for its generation. Grids usually provide low levels of turbulence (Tu < 10%). Vertical three-edged profiled bars used by Hopfenziz[27] lead to a value of about 10%. McCormick et a/.[28] propose horizontal slats reaching a turbulence level of 30% to 40%. Maciejewski and Moffat placed a flat heat flux plate in the margin of a free jet and found turbulence intensities between 20% and 60%[29]. The environmental chamber of the Canadian National Solar Test Facility provides turbulence intensities between 20% and 30%, the generation of which is described in section 4.2.
3.3. Unsteady weather conditions Outdoor testing confronts us with arbitrarily varying weather conditions. For a precise evaluation of the energy yield a test model is required which considers the time variation of the input variables and the collector dynamics, that is, the heat capacities of the absorber plate (co) and the heat transfer fluid (Cr). Such a test model is less straightforward than the model given in eqn ( 1 )[31-33]. This test method avoids the problem by restricting the analysis to the average energy yield over a reasonable time period. The argument is: Provided the heat capacity rate (thc) is nearly constant, the collector can be treated as a linear system with a high accuracy. The nonlinear error in the energy yield due to a correlated change in the wind speed and the solar irradiation or the ambient temperature is small. It can be estimated to be about 3%[11]. The dynamic error (AQ) of a linear system due to the neglect of the heat capacities is a function of the difference between the initial and final state of the system only. It is independent of the time course of the input variables. Hence, the relative dynamic error ( A Q / O A t ) of the energy yield decreases with the length of the measurement period (At). For small uncovered collector arrays with a m a x i m u m size of about 10 m 2 made by conventional materials as metal or plastic, averaging the data over I h or 30 up to 100 times the fluid dwell time limits the error to 3% [ 11,12 ]. The simple equation AQ = (% + cr) × ( T i ( A t ) +2 T e ( A t ) - Ti(0) +2 T~(0))
(8)
provides a reasonable approximation, where (Ti(t)) and (Te(t)) are the inlet and the outlet temperature at time (t), respectively. 4. INSPECrlON OF THE TEST PROCEDURE The standard proposal has been investigated at the Canadian National Solar Test Facility ( N S T F ) and at the collector test facility of the University of Munich ( L M U ) . In Canada four different compact plastic absorbers have been tested indoors, under definite conditions in an environmental chamber. In Munich the calorimetric parameters of a metal energy roof have been determined by outdoor measurements over two days. The optical parameters ( a ) and (~) were deter-
268
H. SOI.TAU
Fig. 4. A 10 m 2 energy roof is tested at the outdoor collector test facility of the LMU.
mined independently by means of a Beckman spectrometer. The measurement result is in agreement with the data given by the manufacturer ( ( ~ )
f (FR/-:t) = /(9.5 --+ 0.9) +
llv. I W
=
(2.8 _+ 0.4) ( m / s ) J 0.95 _+ 0.01 ~.
with covariance matrix cov(c'j, c'~)
!
The results are promising, in the outdoor test the model error amounts to 9 W / m 2, or 5% ofthe average energy yield. In the indoor experiment an accuracy of 0.01 is achieved in the collector efficiency. 4.1. Outdoor test
At the outdoor collector test facility of the L M U a small array (A = 3.5 × 3.5 m 2) of four uncovered solar collectors has been tested. The metal absorber [ 34 ] has backside insulated parallel tubes with a fiat cross section and broad fins covering about two-thirds of its surface. The fin efficiency factor is high. The collector array is operated by a 30% Antifrogen-N-water mixture and a flow rate of 50 I / h m 2. The collectors are mounted on an artificial roof construction tilted 45 ° to south. The longwave irradiance is measured by a modified Eppley pyrgeometer in the collector plane. Five cup anemometers for wind speed measurement are mounted a distance of 0. l m above the collector surface, as illustrated in Fig. 4. Wind vanes are used for the determination of the directional turbulence. The estimation of the system parameters on the basis of a two-day measurement period in June with moderate cloudiness yields ( F R a ) = {(.83 + 0.2) - (.03 - .01 ) u(--~s) }
(9h)
(9a)
1.00
.
.
.
.
.
.
.
.
.
+0.96
1.00
......
+0.69
-0.66
1.00
• .-
+0.70
-0.75
-0.96
1.00.
All data are averaged over the collector array and a 20 rain period. The wind speed varied between 1.0 m / s and 3. I m/s. A turbulence intensity of 45% was measured as was a directional turbulence of 10°/s. The test results are pictured in Fig. 5. They agree with estimated values of a large number of data ( N = 150) within their standard deviation. The average model error accounts to 9 W / m 2 or 5% of the mean energy yield. 4.2 Indoor test At the environmental chamber of the NSTF, Harrison et a/.[10] investigated four different compact plastic collectors. Included is the FAFCO-collectot [ 36 ]. It consists of parallel polypropylene tubes with a diameter of 6 m m which are welded against each other. It is operated by a flow rate of 250 l / h m 2. An array of about 3 m 2 is mounted on a built-up section of roof tilted 60 ° to the floor. Uniform radiation is produced by a Vortek argon arc lamp. Chamber and air temperature are controlled by means of an air conditioning system. As the argon lamp is mounted outside
Thermal performance of uncovered solar collectors
269
/ ~.. ,~O~)%(F.,'
0,8~
(1) N = 20
18 _
(2) N = 150
"~.~,
///.7~_.36
~
.//Z/-
//.//~/////I"(HN 20 =
0,75
-~"~'~'~~'~ \\
o,650
I
1
1
2
UW (nVs)
-
(lJ "~(2)
-
I
1
3
4
/:~//"
(2) N=150
/~,/'//
10 0
/,
J
1
2
(a)
IuWtm/s) I 3 4 (b)
Fig. 5. (a) Optical efficiency (Faa). and (b) heat loss coefficient (FRUt.) of a metal absorber type as a function of wind speed (u,,), as determined outdoors in a two-day measurement period in June (N = 20). The results agree within the standard deviation (a) with estimated values of a large number of data (N = 150). the chamber, a vanishing relative Iongwave irradiance (L ~ 0) is achieved. The wind generator system creates a flow field upstream parallel to the collector surface with a stagnation line at its lower end. Hot sensor anemometers measure the wind speed each 0.3 m, a distance of0.15 m above the test area. The average wind velocity varies from 1.5 m / s to 3.5 m/s. The local variance is 0.5 m / s between the lower and the upper end of the plate. The ventilators are located 3 m downstream of the collector array. Turbulence intensities between 20% and 30% are generated by horizontal bars in front of the main ventilators and by the development of the free jet in the surrounding air. A moderate level of directional turbulence of about 6 ° / s is concluded from a preliminary paper vane test. The test shows significant wind dependence of the collector parameters; the results for the FAFCO-collector are (FRcO =
(FRUL) =
The
fly, 1
(10.2 + 4 . 7
influence on
Q/(. +
(10a)
0 . 8 8 -- .03 ( m / s ) J
u(---~s)}~-3-~. W
The linear dependence of the collector parameters on wind speed has been proved up to 3.5 m/s. It is challenged in the conclusions of Green and Cruz Costa[37] who conducted an indoor test at a 2 m 2 compact absorber area made of an EPDM rubber material. The collector is backside insulated. Figure 6 shows the test results. The value of the heat loss coefficient registrated at zero wind speed (Ut. > 15 W / m 2 K ) is large. A vanishing flow velocity is difficult to achieve in an environmental chamber. Temperature differences between floor and roof, windows and solar simulator, induce natural convection. Green and Cruz Costa measured the wind speed by cup anemometers, a measuremen'
0.8-~
)
25
(lOb)
the collector elficiency (7 =
t.e.ma,,
uw(m/s)
06
,
I model error of ( a ~ = 0.012 ) proves the test approach. The results are in agreement with the values of 0.87 for ( F R a ) a n d 19.4 W / m 2 K for (FRUL) measured by Svendsen [ 7 ] for a wind speed level of 2 m/s. Both the large values of ( q ) and (c4) reflect the bending of the fluid tubes of the FAFCO-collector. In comparison to the flat metal absorber, the effective heat exchanging area is enhanced. Multiple reflection improves the optical elficiency.
2
.
3
Fig. 6. Optical efficiency (/"Rc~)and heat loss coefficient (/~R/-:L ) of a compact rubber absorber arc determined indoors in dependence of wind speed (u,) [ 37 ];
,..:/0. 0, 1 (I..RL..t.)={13.0±2. 6
u. l W (m/s/) l m2K '
assuming 0.5 m/s for the first entry.
270
H. ~OLTAU
device which has a response threshold between 0.3 m/s and 1 m/s. Assuming a minimum wind speed of about 0.5 m/s seems to be more reasonable. 4.3 Comparison with alternate test approache.s The test procedures for uncovered solar collectors which have been accepted as national standards are the American standard ASHRAE 96-1980 [ 5 ] and the Austrian norm ONORM M 7724[6]. Astonishingly, these two handle the thermal performance of uncovered collectors rather superficially. The ASHRAE standard[5] adopts almost completely the recommendations of covered flat-plate collectors. It disregards the Iongwave radiation exchange between sky and collector and the wind-dependence of the system parameters. The Austrian norm[6] presents a two-stage indoor test. The method refers to the mean fluid temperature. Equation (9) may be regarded as test model, yet, the influence of longwave radiation is untreated. In the first run the optical efficiency ( F ' a ) is determined. The air-stream is parallel to the plate. The flow speed is fixed. For the second run a cover plate is mounted a distance or'0.1 m above the absorber surface. The airstream is directed through the channel. The heat loss factor (F'UL) is determined for three different wind speed values. As visualized in Fig. 7a, ignoring the wind dependence of the optical efficiency (F'a) is an approximation only, especially for low-cost uncovered collectors where moderate internal heat transfer coefficients (hi) are common. The experimental investigation of the Centre d'Energetique in Valbonne (France)[8] shows that same feature. The usefulness of the so-determined parameter value ( F ' Ut) for the prediction of the energy yield in the open air is uncertain. The canalization of the airstream changes the value of the heat loss coefficient and its dependence on wind speed. The alternate test ideas discussed in the following consider the Iongwave radiation exchange and the wind dependence of the collector parameters. The Danish test draft [ 7 ] as proposed by Svendsen from the Thermal Insulation Laboratory of the Technical University is restricted to uncovered fully wetted solar collectors. Svendsen abstains from the linearization of the longwave radiation term (eqn (2)). The energy balance of the collector is formulated in two nonlinear equations in dependence of the mean absorber plate and fluid temperature. The collector performance is characterized by the forced convection heat transfer coefficient (hrc) of the top surface and the internal heat transfer coefficient (h+) between fluid and plate, as well as by the shortwave absorptance (a) and the longwave emissivity (+), which are determined by optical methods of a collector sample, The transfer coefficients are estimated from heat loss measurements performed at various wind speed levels. The average absorber plate temperature is measured by a radiation thermometer; the mean fluid temperature is evaluated as the arithmetical mean of inlet and outlet.
The field of application for the test is restricted; collector arrays made of flexible pipes or any tubes spaced by fins are hard to evaluate, as an eflbctivc fin efficiency factor is not provided. On the other hand, the linearization of the Iongwave radiation term is very precise, as described in section 2.1, allowing for the direct determination of either (F'a) and (F'Ut) or (kR~) and (F~UI). The standard proposals of France [ 8 ] and the Collector and System Testing Group of the European Community (CSTG)[9] differ from the one in hand in three relevant points: 1. The test model refers to the mean fluid temperature. According to the present nomenclature it is
- ( F ' b l , ) ( T , , - 7~) (11) where (T,,) is the mean fluid temperature and ( F ' ) is the collector efficiency factor. The determination of the mean fluid temperature, which is not specified in the paper, may give rise to difficulties, as outlined in section 2.1. 2. All the parameter values are determined under steady state conditions. The restriction to stationary conditions is rigorous though not necessary, as set out in section 3.3. 3. A model for the wind dependence of the collector parameters is not provided. The collector efficiency is determined and displayed for two different levels of wind speed (2 m/s and 6 m/s (CSTG)) requiring a wind generator for indoor and outdoor testing. By the wind generator, uniform and definite wind field conditions with high average velocities are aimed at, independently of weather and location. The effort is large. An average flow velocity of 6 m/s will be difficult to achieve. Experiments which have been performed in the Netherlands[20] demonstrate the lasting influence of the natural wind field. The specification of the relevant flow parameters (as turbulence intensity, eddy size and flow pattern ) and their comparison with natural conditions are not included. 5. CONCI,USION AND FUTURE WORK The test procedure described in the paper has been used successfully for the determination of the thermal performance of diverse unglazed collector types, indoors and outdoors. The comparison with alternate approaches emphasizes its characteristics, as summarized in the introduction. The linear context between the collector parameters and the wind speed above the collector array has been proven within the range of 1 m/s up to 4 m / s . Now, a round robin test of the comparability of the test results has to be performed. The following issues are of special interest: I. Experience with plastics collectors made of flexible separate pipes is missing so far.
Thermal performance of uncovered solar collectors
271
c~J t.o 0.9 0.8
-
-
0.7
h,
= 200
WIm2K
h, = 100 W/m2K
o.6 0.5
I
I
i
~
#
2
3
1,
h~ =
5
EO
W/m2K
uw (re~s]
(a)
l r**Tfttaj_r ' r,
1
~F'ULJ zo :
0.,1 t
2
4
(b)
6
=
Cf
Fig. 7. ( a ) The collector efficiency factor (F') as a function ofwind speed (u,), in dependence of the internal heat transfer coefficient (hi)" (b) the variation of the fluid temperature (Tf) in dependence of the dwell time (td) and the specific fluid capacity (cf).
2. The collector mounting instructions have to be formulated precisely: Most unglazed collectors are not backside insulated. They do not exist in modules. The spacing of pipe collectors is arbitrary, and the energy yield is a function of the solar absorptivity and the heat conductivity of the base plate material. 3. The dependence of the optical efficiency on the incident angle of the solar radiation is unsettled, especially for pipe and strip collectors. 4. The variance in the wind field quantities is a major source of uncertainty in the estimated parameter values. The specification of the average wind speed and the turbulence intensity is a first approximation only. Supplementing the values of the directional turbulence and the average eddy size improves our knowledge. At the University of Munich diverse products of plastic and rubber collectors will be tested next year, including the measurement of diffuse and direct solar irradiation. The characterization of the wind field in the urban environment and its impact on the heat loss of a fiat plate within an accuracy of 1 W / m 2 K is the content of a running project. The simulation of a natural wind field in an environmental chamber is investigated in cooperation with Harrison at the Canadian National Solar Test Facility.
Acknowledgments--The development of the test procedure is based essentially on the successful cooperation within the team of Task Ill from the Solar Heating and Cooling Programme of the International Energy Agency. Special thanks are due to B. Rogers, B. Wood, S. Harrison, J. Keller, and W. Spirkl. and to S. Klein.
REFERENCES
1. ASHRAE Standard 93-1986, Methods of testing--to determine the thermal performance ~f solar collectors. ASHRAE Publications, New York. USA. 2. R. Croy, tteating of swimming pool water in l,auenau, In Tagung,shericht yore 7. lnternationah'n Stmnen[i~rton. DGS, Frankfurt, Germany, p. 728 ( 1990L 3. U. Rehrmann, Heating of swimming pool water in Spenge, In Tagungsbericht vom 7, lnternattonalen Sonnetllbrum. DGS, Frankfurt, Germany, p. 734 ( 1990L 4. H. Soltau, A recommended test method for determining the thermal performance of uncovered solar collectors, 1988, lEA Task III Working Document, Ludwig-Maximilians-University, Munich (Germany), In B. A. Rogers, H. Sollau and B. D. Wood, The characterization of solar collector thermal performance. Techn. Rep. No. SEU-IEATr2 (in press). 5. ASHRAE Standard 96-1980, Methods ~ftesting--to determine the thermal performance o f unglazed .fiat-plate liquid-type solar collectors. ASHRAE Publications, New York, USA. 6. ONORM M 7724, Uncovered plastic solar collectors: A
272
H. SOL'IAtJ
test procedure to determine conversion ./actor. heat loss and gain coefficient. Osterreichisches Normungsinstitut, Wien, Austria ( 1987 ). 7. S. Svendsen, Performance of umx~vered solar coUectors. Technical Report 85-17, Thermal Insulation Laboratory-Technical University, Copenhagen. Denmark ( 1985 ). 8. M. Gschwind and J. Robert, Unglazed solar collectors testing, Technical Report, ARMINES--Center of Energy, Valbonne, France ( 1987 ). 9. European Solar Collector and Systems Testing Group,
23. 24.
25.
Recommendations ~)r perfi~rmance and durabilit)' tests of solar collectors and water heating s),stems. Technical Report, Joint Research Center. Ispra, Italy (1989). 10. S.J. Harrison, D. McClenahan, and V. H. Nielsen, Testing unglazed solar collector thermal performance, In Proceedings of the ISES Solar World Congress. Kobe, Japan, pp. 736-741 (1989). 11. H. Soltau, The thermal perlormance (~[uncovered collectors. Fortschrittsberichte der VDI-Zeitschriften, Reihe 6: Energietechnik, VDI-Verlag, Diisseldorf. Germany ( 1989 ). 12. H. Soltau, The thermal performance of uncovered collectors, In Proc. ~f the ISES Solar World Congress Hamburg, Germany, (1987). 13. J. A. Dut~e and W. A. Beckman, Solar engineering qf thermalpr~'esses. John Wiley & Sons, New York ( 1980 ). 14. The ~PPkT pvrgo,neter. Technical data. The Eppley Lab. Inc., Newporl, RI (1987). 15. J. W. Enz. J. C. Klink, and D. G. Baker, Solar radiation effects on pyrgeometer performance, Journal ~lApplied Meteorolog.v 14, 1297-1302 ( 1975 ). 16. B. Albrecht, M. Poellot, and S. K. Cox, Procedures for improving pyrgeometer measurements, Journal o[Applied Meteorology 16, 188 ( 1977 ). 17. D. I. Wardle and L. J. B. McArthur, Ground level mon-
itoring of long-wave irradiance with the Eppley pvrgeometer. Technical Report ARD-87-2. Atmospheric Envi18. 19.
20.
2 I.
ronment Service--Environment Canada, ASES (1986 ). P. Berdahl and R. Fromberg, The thermal radiance of clear skies, Solar Energy 29, 299-314 (1982). C. U. D~ike, A new model ~f the pyrradiometer type ~f Schulze, Technical Report 126, Deutscher Wetterdienst-Selbstverlag, Offenbach, Germany (I 972). J. Havinga and A. J. Th.M. Wijsman, Characterization of uncovered solar coUectors, IEA Task Ill Working Document, Technisch Physische Dienst, Delft, Netherlands ( November 1985 ). J. Keller, Characterization of the thermal performance of uncovered solar collectors by parameters including the dependence on wind velocity, humidity and infrared sky radiation as well as on solar irradiance, In Proceedings ~I
the Second Workshop on Solar Assisted Heat Pumps with Ground Coupled Storage, Vienna, Austria ( May 1985 ). 22. G. Angermeier, R. Pitz-Paal, and H. Soltau, The wind
26.
27.
dependent heat transfer coefficient of uncovered collector's, In Proc. of the ISES Solar World Congress. Hamburg, Germany (1987). L. C. Burmeister, Convective heat tran,~,r. John Wiley & Sons, New York (1983). F. L. Test, R. C. Lessmann, and A. Johary, Heat transfer during wind flow over rectangular bodies in the natural environment, J. of Heat TransJer, Trans. t)f ,4SME 103, 262-267 ( 1981 ). E. M. Sparrow and K. K. Tien, Forced convetion heat transfer at an inclined and yawed plate--application to solar collectors, J. of Heat Transfer. Trans. of ASME 99, 507-512 (1977). H. Soltau and G. Angermeier, Modelling the heat transfer of a fiat plate in the highly turbulent wind field of an urban environment, In Proc. of the 9th ItlTC Congress. Jerusalem, Israel, pp. 151 - 156 (1990). H. Hopfenziz, An experimental and theoretical investi-
gation on the effk'ct offree-stream turbulence and pressure gradients on a turbulent boundary layer. Fortschrittsber28.
29.
30.
31.
32.
33.
34. 35.
36. 37.
ichte der VDI-Zeitschriften, Reihe 7: StriJmungstechnik, VDI-Verlag, Diisseldorf, Germany (1984). McCormick, F. L. Test, and R. C. Lessmann, The effect of free-stream turbulence on heat transfer from a rectangular prism, J. ~f lh,at Transfer. Trans. ~f ASME 106, 268-275 (1984). P. K. Maciejewski and R. J. Moffat, A correlation for boundary, layer heat transfer accounting for free stream turbulence, In Pr~'. ~f the 9th IHTC Congress. Jerusalem, Israel, pp. 303-308 (1990). E. M. Sparrow, J. W. Ramsey, and E. A. Mass, Effect of finite width on heat transfer and fluid flow about an inclined rectangular plate, J. of Heat Transfer. Trans. of ASME 101, 199-204 (1979). A. J. de Ron, Dynamic modelling and verification of a flat-plate solar collector, Solar Energy 24, 117-127 (1980). R. Kliippel, A. de Nobrega, R. Sizmann, and W. Sch61kopf, Measurement of characteristic solar collector parameters in transient operation, In Proceedings of the ISES Solar World Congress. Montreal, Canada, p. 874 ( 1983 ). M. Emmery and B. A. Rogers, On a solar collector thermal performance test method for use in variable conditions, Solar l-nerg.v 33, I 17-123 ( 1984 ). lloe~ch Energy Absorber. Technical data, ESTEL Siegerlandwerke AG, Kreuztal, Germany ( 1983 ). I. N. Bronstein and K. A. Semendjajew, Pocket-book (~f mathematics. Teubner Verlagsgesellschaft, Leipzig, Germany (1979). 77u' t':.IFCO Solar .~vstem. Technical Data. FAFCO S.A., Biel, Switzerland (1990). A. A. Green and J. Cruz Costa, The influence of wind on unglazed solar collectors, In ('ommunica~'oes do 4. ('ongr(,,ss(~ lh(;rico de Energia Solar. Porto, Portugal { 1988).
0038-(~-12X/92 $5.(10 ~ .(J0 Cop~,nghl (c 1992 Pergamon Press I.Id
TESTING THE THERMAL PERFORMANCE OF UNCOVERED SOLAR COLLECTORS H. SOI/FAU* Department of Physics of the Ludwig-Maximilians-University,8{K)0MiJnchen 40, Germany Abstracl--A proposal tbr an international standard. "Io Determine the Thermal Performanceof Uncovered Collectors," is presented. Test particulars as the measurement of the Iongwavcradiation and the characterization of the wind field determining the convective losses of the absorber surface are discussed, both for indoor and outdoor conditions. The model includes testing under unsteady conditions. A comparison with alternate test approaches is performed. Experimental results arc presented.
I. I N T R O D U C I ' I O N
4. The collector performance is characterized by four (or five) parameter values. They are determined by Testing the thermal performance of glazed fiat-plate calorimetric measurements in a linear fit procedure. solar collectors at low temperature is well established. 5. Indoor and outdoor testing are considered. The For example, the ASHRAE test standard 93 [ 1] is used fundamentals of the experimental set-up and proworldwide. Such test methods developed for glazed cedure are adapted to the ASHRAE standard 9311] collectors cannot be applied to uncovered solar collecto simplify the implementation in existing laborators, however, because they do not specify the influence tories. of the longwave sky irradiation and the external wind 6. Unsteady weather conditions are admitted by field on the collector efficiency. The thermal performodelling the average energy yield over a reasonably mance of uncovered collectors is highly sensitive to long time period of about 1 h. both those effects, as the following examples illustrate: The collector model and the test procedure are pre• An uncovered collector may loose 150 W / m "~ through thermal radiation on a clear and sunny day sented in section 2. Section 3. I examines the Iongwave radiation measurement, and section 3.2 the characand 0 W / m 2 in a cloudy period. terization of the convective losses, for both indoor and • The energy yield of an unglazed collector exposed to an average wind speed of 1 m/s or 4 m/s, above outdoor testing. Testing under transient conditions is the collector surface, may differ by 50%, on a sunny discussed in section 3.3. The detailed guidelines for the day. The influence of wind speed is increased as the test conditions, the instrumentation, the numerical contribution of solar radiation to the energy yield is determination of the system parameters, and the repreduced. (This point is especially relevant if the un- resentation of the test results are expounded elsecovered collector is operated below ambient tem- where[4], and will not be repeated here. They were perature, e.g., if it is used as the low temperature worked out in cooperation with the team of Task 111 heat source of a heat pump system.) The dependence from the Solar Heating and Cooling Programme ofthe of the collector efficiency on wind speed is sum- International Energy Agency (lEA). Section 4 contains a comparison with the American [ 5 ] and the Austrian marized in Fig. I. Hence, for determining the thermal performance standard[6] and the test ideas of Svendsen[7], of uncovered solar collectors a new standard has to be France[ 8] and the European Community [9]. The test developed. The actual interest is large. Already, heating procedure has been examined indoors and outdoors, of swim ming pool water by large-area low-cost uncov- at the National Solar Test Facility of Canada [ 10 ] and ered collectors made of rubber or plastic materials is the University of Munich. The experimental results economically competitive. The costs of the solar energy are displayed. Conclusions are drawn in section 5 resulting in an outlook for future projects. range between 0.06 and 0.07 DM/kWh[2.3]. This paper presents and discusses a test method having the following features: 2. T I l E S T A N D A R D P R O P O S A L I. The energy yield of the collector is evaluated by a model resembling the Hottel-Whillier-Bliss equa2.1 The model tion. In the test procedure the energy yield of the un2. The longwave sky irradiation is part of the radiation covered collector is evaluated by a model which corbalance. 3. The optical efficiency and the heat loss factor are responds to the Hottel-Whillier-Bliss (HWB) equation of a flat-plate solar collector [I 1,12 ]: modelled as linear functions of the average wind speed above the collector array. ' ISES member. 263
264
H, SOl.TAt I
rl -
ity (~) of 0.9. its value is 5.0 W/m2K, when averaged over the permissible operation range) The dependence on ambient or collector temperature is neglected. The resulting error can be estimated by a standard deviation of 0.4 W / m2K. 3. The overall heat loss coefficient ( Ut ) contains the longwave radiation coefficient (h~,), wind induced forced convection (hf~) and conduction losses through insulation (hod):
n 1,5 m/,s
0.8 - ~
o ZSm/g ~ + 3 . 5 r n / s
o,4
Ul = hi, + hrs. + h c d .
a;r JL 0
I 0
I o.ot
0,02
|--0.03
Fig. 1. The efficiency of an uncovered solar collector
speed (u~) on its surface. The presenteddata refer to a collector made of polypropylenetubes with a diameter of 6 mm[ 36]. operated by a flow rate of 250 I/hm:[10].
All variables are averaged over the collector area (A) and a time period (At) which is chosen in dependence of the weather dynamics: l h is a reasonable value, where
(2 = ( m c ) ( T , -
T,)
The state of the art in modelling combined forced and natural convection is contradictory [ 11]. Hence, the test procedure is restricted to wind velocities above 0.3 m/s, where the influence of the natural convection becomes negligible. 4. Forced convection is the dominant contribution to the heat loss. The heat transfer coefficient (hfc) ranges between 3 W/m2K and 60 W/m2K depending on the wind field conditions. The consequent variation of the heat removal factor (FR), which is a function of(UL), is considerable. Figure 2 gives an illustration. In eqn ( 1) the optical efficiency ( k R a ) and the heat loss factor (FRUL) are both modelled as linear functions of the average wind speed (uw) above the collector array (l~a)
= cj - c2u,,
(FRUt.) = c3 + c4u~,.
= energy yield of the collector system per square meter aperture area a shortwave solar irradiance in collector plane L = relative longwave sky irradiance (see eqn [2], below) shortwave absorptivity of the absorber Iongwave emissivity (absorptivity) of the absorber Ta ambient temperature ~ = exit temperature of the fluid Ti= inlet temperature of the fluid U|. overall heat loss coefficient F.= heat removal factor rnc= heat capacity rate of fluid. Equation (1) differs from the conventional HWB model [ 13 ] in the following ways: I. The insolation is not diminished by the transmittance of the cover. 2, The balance between the absorbed Iongwave sky irradiance (tL*) and the radiation of the collector plate (feTe) is included in the relative longwave sky irradiance (L) and the heat loss of the plate, as follows:
(3)
(4a) (4b)
The model, as presented in eqns ( 1 through 4), achieves an overall precision of 10% of the average energy yield: The characterization of the wind field by the average wind speed is a first order approximation. The nonlinear error due to the wind dependence of the heat removal factor is limited to 3%. The dynamic error is controlled by a correct choice of the averaging time period (At), as outlined in section 3.3. Equation ( 1) is designed as a test and simulation model. It refers to the inlet instead of the mean temperature of the fluid. The accuracy of the prediction is enhanced if the same effective parameters are used in test and simulation. The experimental determination of the mean fluid temperature may raise difficulties. The linear approximation by the measured values of the exit and the inlet fluid temperature, which is generally used for covered solar collectors, is less accurate if transferred to uncovered collectors with a heat loss coefficient of about 20 W/m2K, as illustrated in Fig. 7b. 2.2 T h e test p r o c e d u r e The values ofthe parameter coefficients {G, J = 1,4 } and the system parameter ( ~ ) characterize the collec-
~L* - , a T ~ = t ( L * - oT*~) - ( t t r T ~ - ,aT**) t L - hl~( Tp - T~).
(2)
The heat transfer coefficient (h~,) is part of the overall heat loss coefficient (UE). Assuming an emissiv-
The operation temperature T of the heat transfer fluid is restricted to 278K<(T+7~)/2<308K
and
IT-T,I
<20K.
Thermal performance of uncovered solar collectors
265
r ut j w
(FR~,)
m2 K
" =
.85 y x~
~1¢
16
.75
1l,.
x
txx
lg
x x
12.
It w
J
.65
i
,
Uw Im/s) '~
1
2
3
z,
uw (m/s) 70
0
i
1
2
3
Fig. 2. The dependence of the collector parameters (FRa) (left) and (FRL"L) (right) on the wind speed (u,) is linear with a good approach to accuracy. The data have been recorded outdoors for a metal energy roof with a fiat surface and broad fins, operated by a flow rate of 50 l/hm:.
tor thermal performance. They are determined in the test. The energy yield ( 0 ) of the system is recorded as a function of the meteorological input variables (G, L*, Ta, u,) and the inlet temperature of the fluid (T,). The relative longwave sky irradiance (L) is calculated from (L*) and (T,). The heat capacity rate (rhc) is set in agreement with the manufacturers' recommendations. All quantities are averaged over the time period (At ~ 1 h) and the collector area (A). Using eqns ( 1) and (4), the parameter values { cj } are then estimated from the test data in a joint linear fit procedure. An ordinary least-squares method may be used to minimize the average deviation (a 2) between modelled and measured energy values: 1
(r2 =-
N-4
N
~ (O~,p.i - Qmod.,)2 ~ minimum. (5) t=l
Of course, the quality of the parameter values is related to the variance of the input data, which is specified in the test instructions. Generally, in outdoor testing, a continuous measurement over two to three days yields a good data basis. A minimum number of 10 data points is required for indoor tests. The test proposal suggests the independent determination of the parameter ( ~ ) by photospectrometry. In most cases the ratio will amount to about 0.95. Estimation on the basis of the calorimetric data is possible using nonlinear fit procedures provided the Iongwave sky irradiance varied sufficiently during the test. The test method is intended to apply to small flatplate uncovered collector arrays. It has been validated up to a maximum size of 12 m 2. The mounting of the system is arbitrary. However, it is preferable to build up the collector array directly on a well-insulated roof construction with a white surface with a low heat conductivity. Testing backside-ventilated collectors is very much dependent on the actual topology and the wind direction.
3. TEST
PARTICULARS
3. I Measuring the longwave radiation The longwave sky irradiance (L*) of the hemispherical field of view of the collector is measured in the collector plane using a pyrgeometer or a combination of a pyrradiometer and a pyranometer. Currently, only the Eppley PIR pyrgeometer [ 14 ] is available. It measures the longwave radiation with a wavelength (k) larger than 3 tzm by a method comparable to that ofa pyranometer. The temperature difference between the body of the instrument and the surface of a black receiver which is sheltered from shortwave irradiance by a coated silicon dome is the relevant signal. To obtain reliable data of the Iongwave irradiance by the Eppley pyrgeometer the following modifications are necessary: I. The dome of the pyrgeometer should be ventilated by an airstream with a volume of at least 25 m3/ h[15]. 2. The compensation for the longwave radiation emitted by the body of the instrument (aTe,d,) is performed electrically by a battery circuit. It should be replaced by digital calculation. The body temperature (Tt~y) is determined by a thermistor attached to the housing close to the cold junction of the thermopile [ 16 ]. The calibration procedure in the Eppley laboratory presupposes identity of the dome and the body temperature of the instrument. Yet, by absorption of shortwave irradiance the dome temperature is enhanced. The error in measurement is less than before 1979 when Eppley changed the dome material from KRS5 to silicon. Differences between dome and body temperature up to 2 K for G = 800 W / m 2 were measured, corresponding to an error in the longwave irradiance of about 20 W / m 2. For a more precise measurement the following actions are necessary: A small thermistor is attached to the lower edge o f the dome. The recorded value represents a first approximation of the dome temperature. The thermopile
H. SOLTAU
266
output (t5V) is then corrected by the difference between body and dome temperature, that is, L* = c,,SV+ aT~,d~ + c'o(Tt,,e~ - 7)om~),
(6)
where (co) is the calibration coefficient provided by Eppley laboratories and (co) is a correction factor. The Canadian Atmospheric Environment Service suggests[ 17 ] a correction proportional to the shortwave irradiance (G). To avoid dynamic errors averaging over time periods (At > 10 min) is necessary. Unfortunately, up to now no official calibration facility considers the influence of shortwave irradiance on the pyrgeometer performance and determines the correction factor. From a series of sun and shade experiments Berdahl and Fromberg[18] concluded a value of I I W/mZK for (c'o), in agreement with a calculated estimate of 12 W/m2K. Wardle and MeArthur [ 17 ] found a response of 0.026 W / m" per I W / m 2 shortwave solar irradiation. Provided the longwave sky irradiation is determined as given in eqn (6), an accuracy of about 5 W / m 2 in the hourly value of (L*) was observed. The principle of measurement of a pyrradiometer is equivalent to that of a pyrgeometer. In this case the dome covering the receiver consists of a material which is transparent to long- and shortwave irradiation (.3 tam < ;~ < 60 #m). The pyrradiometer allows determination of the longwave sky irradiance by comparison with a pyranometer output. Indoor testing with a solar simulator ( ~ 6 0 0 K) requires a pyrradiometer, as the sensitive wavelength range of the pyrgeometer is insufficient. The analysis of the pyrradiometer was less satisfactory. The relative error of the Iongwave radiation measurement is large, corresponding to the dominant contribution of shortwave radiation. The dynamic error of the pyrradiometer is substantial [ 19 ]. 3.2 Spec(l.ving the convective losses Corresponding to the physical effects which control the magnitude of the convective losses, the average velocity ( I ), the dynamics (2), and the topology (3) of the wind field on the collector surface, the experimental demands on the flow field are specified. Aiming at collector parameters which are representative for real operating conditions, the discussion is oriented by the properties of the natural wind field. The guidelines represent a first approach based upon present knowledge. The test method abstains from artificial wind generation in the open air. That effort is large[20]. The characterization of the flow field is not simplified, for example, the specification of the turbulence intensity cannot be avoided: Outdoors, the influence of the natural wind field persists. Indoors, the size of the collectors and the environmental chamber differ from classical wind tunnel dimensions. The flow field is turbulent and inhomogenous. 1. In the test procedure the collector parameters (FROt) and (FRU~) are correlated with the magnitude of
the average wind speed (u,~) on the collector surface. A linear model is a good approach, as the data entries in Fig. 2 illustrate. Depending on the surface structure, the heat loss coefficient varies between 30% and 50%, and the optical efficiency changes by about 5% per 1 m/s increase in wind speed. The wind speed is measured at several representative points in the collector plane a distance of 0.1 m above the absorber surface, that is, in the free-stream region outside the local boundary layer. As pictorially demonstrated by Keller [ 21 ], determining the wind speed in front of or significantly above the collector array involves a host of uncertainties, depending on the various nearby surroundings and the wind direction. 2(a). Testing is performed under turbulent flow conditions, indoors and outdoors. Under real operating conditions the collector is exposed to a flow field that is highly variable and turbulent: At the ground level of an urban environment the wind field is characterized by turbulence intensities between 35% and 55% and rapid and significant changes in the local flow direction [22 ]. The effect of the free-stream turbulence is large: the forced convection heat transfer coefficient of a fiat plate is enhanced by about 100°,* compared to wind tunnel studies where the oncoming flow is relatively undisturbed. Figure 3 compares experimental values to the classical solution for undisturbed parallel flow conditions[ 23]. The data have been recorded outdoors, at the collector test facility of the University of Munich ( LMU ), shown in Fig. 4. The open air measurements of Test et a1.[24] show the same magnitude. Also eqn (3) in Fig. 3, which is advised by Duffle and Beckman[13 ], represents a reasonable correlation model with regard to turbulent flow conditions. The formula has given rise to several critical publications (see, e.g., Sparrow and Tien [ 25 ]). It is validated by our data. As a consequence of Fig. 3 the test procedure requires testing under turbulent flow conditions so that outdoor and indoor testing is equivalent and a systematic deviation in the predicted energy yield is avoided. 2(b). The magnitude of the free-stream turbulence is quantified and reported with the test results. The scatter of the data and the correlation models in Fig. 3 indicate the variation of the heat transfer rate with the turbulence properties. Yet, so far no uniform standard model between the forced convection heat transfer coefficient of a fiat plate and turbulent free-stream conditions exists. For the present the turbulence intensity (Tu) is suggested as a reference quantity. It is defined as the relative variance (a~,) of the wind speed magnitude:
Tu = a~.__r.-. Uw
(7)
Thermal performance of uncovered solar collectors
20f
~ (41 ~hfc(W/m2K)
#
~
•
x
..x
,,
~
Z ~d~ ?~.,,/,¢
/
,o....... •
5 L .....
0.5
~
~[3)
x×
oo2o'L2'o, enwronmenf
~
~
/undlsfurbed pacollel .fl°w (I]
/ ......
/ 1,o
,
2,0
uw~/s_j ]
, 3,0
Fig. 3. The con~ective heat transli:r coe|ficient of a flat plate is significantl.~influenced by frcc-strcam turbulence: ( I ) Undisturbed flow. K,~rmfin equation (/,.h,, - 3.5 m)" h~ = 5.0 u~ o8 W/m:K. ( 2 ) l c s t et aL[24] (outdoors); hie
(m/s)
(8.6 ÷ 2.7
u~ ') W/m:K. U.qSS
(3) Dulfie and Beckman[13];
(5.7' 3,8 ( m/s ) ) W/m:K (4) Outdoor mcasurements //~
]lt~.
3. The influence ofthe average wind field topology on the heat transfer coefficient (hfc) is much less for a finite plate than the effect of the free-stream turbulence. That is the conclusion of a detailed experimental investigation of Sparrow et al.[ 30]" for comparison, the numerical results have been transferred to the average wind speed on the collector surface by S o l t a u [ l l ] . The local variance of the flow velocity is restricted to a standard deviation of _+1 m/s.
/
;/"
/ /~/
•
~,~x
267
"
(IMU I. data entries denoted by (×). best tit: hr¢
9.3
u~ .8 W/m-'K.
(m/s)
A m i n i m u m value o f ( T u > 20%) is required during testing. Recently, promising results have been achieved at Munich [ 26 ]. The heat transfer coefficient of a flat plate has been measured outdoors as a function of statistical wind field parameters. The correlation with a parameternamed directional turbulence has been most successful. It quantifies the turbulence by the angular velocity of the local flow direction. It is easily measured by a wind vane. It reduces the scattering of the data to the uncertainty in measurement. 2(c). While the free-stream turbulence is an inherent characteristic of the natural environment, indoor testing requires auxiliary structures for its generation. Grids usually provide low levels of turbulence (Tu < 10%). Vertical three-edged profiled bars used by Hopfenziz[27] lead to a value of about 10%. McCormick et a/.[28] propose horizontal slats reaching a turbulence level of 30% to 40%. Maciejewski and Moffat placed a flat heat flux plate in the margin of a free jet and found turbulence intensities between 20% and 60%[29]. The environmental chamber of the Canadian National Solar Test Facility provides turbulence intensities between 20% and 30%, the generation of which is described in section 4.2.
3.3. Unsteady weather conditions Outdoor testing confronts us with arbitrarily varying weather conditions. For a precise evaluation of the energy yield a test model is required which considers the time variation of the input variables and the collector dynamics, that is, the heat capacities of the absorber plate (co) and the heat transfer fluid (Cr). Such a test model is less straightforward than the model given in eqn ( 1 )[31-33]. This test method avoids the problem by restricting the analysis to the average energy yield over a reasonable time period. The argument is: Provided the heat capacity rate (thc) is nearly constant, the collector can be treated as a linear system with a high accuracy. The nonlinear error in the energy yield due to a correlated change in the wind speed and the solar irradiation or the ambient temperature is small. It can be estimated to be about 3%[11]. The dynamic error (AQ) of a linear system due to the neglect of the heat capacities is a function of the difference between the initial and final state of the system only. It is independent of the time course of the input variables. Hence, the relative dynamic error ( A Q / O A t ) of the energy yield decreases with the length of the measurement period (At). For small uncovered collector arrays with a m a x i m u m size of about 10 m 2 made by conventional materials as metal or plastic, averaging the data over I h or 30 up to 100 times the fluid dwell time limits the error to 3% [ 11,12 ]. The simple equation AQ = (% + cr) × ( T i ( A t ) +2 T e ( A t ) - Ti(0) +2 T~(0))
(8)
provides a reasonable approximation, where (Ti(t)) and (Te(t)) are the inlet and the outlet temperature at time (t), respectively. 4. INSPECrlON OF THE TEST PROCEDURE The standard proposal has been investigated at the Canadian National Solar Test Facility ( N S T F ) and at the collector test facility of the University of Munich ( L M U ) . In Canada four different compact plastic absorbers have been tested indoors, under definite conditions in an environmental chamber. In Munich the calorimetric parameters of a metal energy roof have been determined by outdoor measurements over two days. The optical parameters ( a ) and (~) were deter-
268
H. SOI.TAU
Fig. 4. A 10 m 2 energy roof is tested at the outdoor collector test facility of the LMU.
mined independently by means of a Beckman spectrometer. The measurement result is in agreement with the data given by the manufacturer ( ( ~ )
f (FR/-:t) = /(9.5 --+ 0.9) +
llv. I W
=
(2.8 _+ 0.4) ( m / s ) J 0.95 _+ 0.01 ~.
with covariance matrix cov(c'j, c'~)
!
The results are promising, in the outdoor test the model error amounts to 9 W / m 2, or 5% ofthe average energy yield. In the indoor experiment an accuracy of 0.01 is achieved in the collector efficiency. 4.1. Outdoor test
At the outdoor collector test facility of the L M U a small array (A = 3.5 × 3.5 m 2) of four uncovered solar collectors has been tested. The metal absorber [ 34 ] has backside insulated parallel tubes with a fiat cross section and broad fins covering about two-thirds of its surface. The fin efficiency factor is high. The collector array is operated by a 30% Antifrogen-N-water mixture and a flow rate of 50 I / h m 2. The collectors are mounted on an artificial roof construction tilted 45 ° to south. The longwave irradiance is measured by a modified Eppley pyrgeometer in the collector plane. Five cup anemometers for wind speed measurement are mounted a distance of 0. l m above the collector surface, as illustrated in Fig. 4. Wind vanes are used for the determination of the directional turbulence. The estimation of the system parameters on the basis of a two-day measurement period in June with moderate cloudiness yields ( F R a ) = {(.83 + 0.2) - (.03 - .01 ) u(--~s) }
(9h)
(9a)
1.00
.
.
.
.
.
.
.
.
.
+0.96
1.00
......
+0.69
-0.66
1.00
• .-
+0.70
-0.75
-0.96
1.00.
All data are averaged over the collector array and a 20 rain period. The wind speed varied between 1.0 m / s and 3. I m/s. A turbulence intensity of 45% was measured as was a directional turbulence of 10°/s. The test results are pictured in Fig. 5. They agree with estimated values of a large number of data ( N = 150) within their standard deviation. The average model error accounts to 9 W / m 2 or 5% of the mean energy yield. 4.2 Indoor test At the environmental chamber of the NSTF, Harrison et a/.[10] investigated four different compact plastic collectors. Included is the FAFCO-collectot [ 36 ]. It consists of parallel polypropylene tubes with a diameter of 6 m m which are welded against each other. It is operated by a flow rate of 250 l / h m 2. An array of about 3 m 2 is mounted on a built-up section of roof tilted 60 ° to the floor. Uniform radiation is produced by a Vortek argon arc lamp. Chamber and air temperature are controlled by means of an air conditioning system. As the argon lamp is mounted outside
Thermal performance of uncovered solar collectors
269
/ ~.. ,~O~)%(F.,'
0,8~
(1) N = 20
18 _
(2) N = 150
"~.~,
///.7~_.36
~
.//Z/-
//.//~/////I"(HN 20 =
0,75
-~"~'~'~~'~ \\
o,650
I
1
1
2
UW (nVs)
-
(lJ "~(2)
-
I
1
3
4
/:~//"
(2) N=150
/~,/'//
10 0
/,
J
1
2
(a)
IuWtm/s) I 3 4 (b)
Fig. 5. (a) Optical efficiency (Faa). and (b) heat loss coefficient (FRUt.) of a metal absorber type as a function of wind speed (u,,), as determined outdoors in a two-day measurement period in June (N = 20). The results agree within the standard deviation (a) with estimated values of a large number of data (N = 150). the chamber, a vanishing relative Iongwave irradiance (L ~ 0) is achieved. The wind generator system creates a flow field upstream parallel to the collector surface with a stagnation line at its lower end. Hot sensor anemometers measure the wind speed each 0.3 m, a distance of0.15 m above the test area. The average wind velocity varies from 1.5 m / s to 3.5 m/s. The local variance is 0.5 m / s between the lower and the upper end of the plate. The ventilators are located 3 m downstream of the collector array. Turbulence intensities between 20% and 30% are generated by horizontal bars in front of the main ventilators and by the development of the free jet in the surrounding air. A moderate level of directional turbulence of about 6 ° / s is concluded from a preliminary paper vane test. The test shows significant wind dependence of the collector parameters; the results for the FAFCO-collector are (FRcO =
(FRUL) =
The
fly, 1
(10.2 + 4 . 7
influence on
Q/(. +
(10a)
0 . 8 8 -- .03 ( m / s ) J
u(---~s)}~-3-~. W
The linear dependence of the collector parameters on wind speed has been proved up to 3.5 m/s. It is challenged in the conclusions of Green and Cruz Costa[37] who conducted an indoor test at a 2 m 2 compact absorber area made of an EPDM rubber material. The collector is backside insulated. Figure 6 shows the test results. The value of the heat loss coefficient registrated at zero wind speed (Ut. > 15 W / m 2 K ) is large. A vanishing flow velocity is difficult to achieve in an environmental chamber. Temperature differences between floor and roof, windows and solar simulator, induce natural convection. Green and Cruz Costa measured the wind speed by cup anemometers, a measuremen'
0.8-~
)
25
(lOb)
the collector elficiency (7 =
t.e.ma,,
uw(m/s)
06
,
I model error of ( a ~ = 0.012 ) proves the test approach. The results are in agreement with the values of 0.87 for ( F R a ) a n d 19.4 W / m 2 K for (FRUL) measured by Svendsen [ 7 ] for a wind speed level of 2 m/s. Both the large values of ( q ) and (c4) reflect the bending of the fluid tubes of the FAFCO-collector. In comparison to the flat metal absorber, the effective heat exchanging area is enhanced. Multiple reflection improves the optical elficiency.
2
.
3
Fig. 6. Optical efficiency (/"Rc~)and heat loss coefficient (/~R/-:L ) of a compact rubber absorber arc determined indoors in dependence of wind speed (u,) [ 37 ];
,..:/0. 0, 1 (I..RL..t.)={13.0±2. 6
u. l W (m/s/) l m2K '
assuming 0.5 m/s for the first entry.
270
H. ~OLTAU
device which has a response threshold between 0.3 m/s and 1 m/s. Assuming a minimum wind speed of about 0.5 m/s seems to be more reasonable. 4.3 Comparison with alternate test approache.s The test procedures for uncovered solar collectors which have been accepted as national standards are the American standard ASHRAE 96-1980 [ 5 ] and the Austrian norm ONORM M 7724[6]. Astonishingly, these two handle the thermal performance of uncovered collectors rather superficially. The ASHRAE standard[5] adopts almost completely the recommendations of covered flat-plate collectors. It disregards the Iongwave radiation exchange between sky and collector and the wind-dependence of the system parameters. The Austrian norm[6] presents a two-stage indoor test. The method refers to the mean fluid temperature. Equation (9) may be regarded as test model, yet, the influence of longwave radiation is untreated. In the first run the optical efficiency ( F ' a ) is determined. The air-stream is parallel to the plate. The flow speed is fixed. For the second run a cover plate is mounted a distance or'0.1 m above the absorber surface. The airstream is directed through the channel. The heat loss factor (F'UL) is determined for three different wind speed values. As visualized in Fig. 7a, ignoring the wind dependence of the optical efficiency (F'a) is an approximation only, especially for low-cost uncovered collectors where moderate internal heat transfer coefficients (hi) are common. The experimental investigation of the Centre d'Energetique in Valbonne (France)[8] shows that same feature. The usefulness of the so-determined parameter value ( F ' Ut) for the prediction of the energy yield in the open air is uncertain. The canalization of the airstream changes the value of the heat loss coefficient and its dependence on wind speed. The alternate test ideas discussed in the following consider the Iongwave radiation exchange and the wind dependence of the collector parameters. The Danish test draft [ 7 ] as proposed by Svendsen from the Thermal Insulation Laboratory of the Technical University is restricted to uncovered fully wetted solar collectors. Svendsen abstains from the linearization of the longwave radiation term (eqn (2)). The energy balance of the collector is formulated in two nonlinear equations in dependence of the mean absorber plate and fluid temperature. The collector performance is characterized by the forced convection heat transfer coefficient (hrc) of the top surface and the internal heat transfer coefficient (h+) between fluid and plate, as well as by the shortwave absorptance (a) and the longwave emissivity (+), which are determined by optical methods of a collector sample, The transfer coefficients are estimated from heat loss measurements performed at various wind speed levels. The average absorber plate temperature is measured by a radiation thermometer; the mean fluid temperature is evaluated as the arithmetical mean of inlet and outlet.
The field of application for the test is restricted; collector arrays made of flexible pipes or any tubes spaced by fins are hard to evaluate, as an eflbctivc fin efficiency factor is not provided. On the other hand, the linearization of the Iongwave radiation term is very precise, as described in section 2.1, allowing for the direct determination of either (F'a) and (F'Ut) or (kR~) and (F~UI). The standard proposals of France [ 8 ] and the Collector and System Testing Group of the European Community (CSTG)[9] differ from the one in hand in three relevant points: 1. The test model refers to the mean fluid temperature. According to the present nomenclature it is
- ( F ' b l , ) ( T , , - 7~) (11) where (T,,) is the mean fluid temperature and ( F ' ) is the collector efficiency factor. The determination of the mean fluid temperature, which is not specified in the paper, may give rise to difficulties, as outlined in section 2.1. 2. All the parameter values are determined under steady state conditions. The restriction to stationary conditions is rigorous though not necessary, as set out in section 3.3. 3. A model for the wind dependence of the collector parameters is not provided. The collector efficiency is determined and displayed for two different levels of wind speed (2 m/s and 6 m/s (CSTG)) requiring a wind generator for indoor and outdoor testing. By the wind generator, uniform and definite wind field conditions with high average velocities are aimed at, independently of weather and location. The effort is large. An average flow velocity of 6 m/s will be difficult to achieve. Experiments which have been performed in the Netherlands[20] demonstrate the lasting influence of the natural wind field. The specification of the relevant flow parameters (as turbulence intensity, eddy size and flow pattern ) and their comparison with natural conditions are not included. 5. CONCI,USION AND FUTURE WORK The test procedure described in the paper has been used successfully for the determination of the thermal performance of diverse unglazed collector types, indoors and outdoors. The comparison with alternate approaches emphasizes its characteristics, as summarized in the introduction. The linear context between the collector parameters and the wind speed above the collector array has been proven within the range of 1 m/s up to 4 m / s . Now, a round robin test of the comparability of the test results has to be performed. The following issues are of special interest: I. Experience with plastics collectors made of flexible separate pipes is missing so far.
Thermal performance of uncovered solar collectors
271
c~J t.o 0.9 0.8
-
-
0.7
h,
= 200
WIm2K
h, = 100 W/m2K
o.6 0.5
I
I
i
~
#
2
3
1,
h~ =
5
EO
W/m2K
uw (re~s]
(a)
l r**Tfttaj_r ' r,
1
~F'ULJ zo :
0.,1 t
2
4
(b)
6
=
Cf
Fig. 7. ( a ) The collector efficiency factor (F') as a function ofwind speed (u,), in dependence of the internal heat transfer coefficient (hi)" (b) the variation of the fluid temperature (Tf) in dependence of the dwell time (td) and the specific fluid capacity (cf).
2. The collector mounting instructions have to be formulated precisely: Most unglazed collectors are not backside insulated. They do not exist in modules. The spacing of pipe collectors is arbitrary, and the energy yield is a function of the solar absorptivity and the heat conductivity of the base plate material. 3. The dependence of the optical efficiency on the incident angle of the solar radiation is unsettled, especially for pipe and strip collectors. 4. The variance in the wind field quantities is a major source of uncertainty in the estimated parameter values. The specification of the average wind speed and the turbulence intensity is a first approximation only. Supplementing the values of the directional turbulence and the average eddy size improves our knowledge. At the University of Munich diverse products of plastic and rubber collectors will be tested next year, including the measurement of diffuse and direct solar irradiation. The characterization of the wind field in the urban environment and its impact on the heat loss of a fiat plate within an accuracy of 1 W / m 2 K is the content of a running project. The simulation of a natural wind field in an environmental chamber is investigated in cooperation with Harrison at the Canadian National Solar Test Facility.
Acknowledgments--The development of the test procedure is based essentially on the successful cooperation within the team of Task Ill from the Solar Heating and Cooling Programme of the International Energy Agency. Special thanks are due to B. Rogers, B. Wood, S. Harrison, J. Keller, and W. Spirkl. and to S. Klein.
REFERENCES
1. ASHRAE Standard 93-1986, Methods of testing--to determine the thermal performance ~f solar collectors. ASHRAE Publications, New York. USA. 2. R. Croy, tteating of swimming pool water in l,auenau, In Tagung,shericht yore 7. lnternationah'n Stmnen[i~rton. DGS, Frankfurt, Germany, p. 728 ( 1990L 3. U. Rehrmann, Heating of swimming pool water in Spenge, In Tagungsbericht vom 7, lnternattonalen Sonnetllbrum. DGS, Frankfurt, Germany, p. 734 ( 1990L 4. H. Soltau, A recommended test method for determining the thermal performance of uncovered solar collectors, 1988, lEA Task III Working Document, Ludwig-Maximilians-University, Munich (Germany), In B. A. Rogers, H. Sollau and B. D. Wood, The characterization of solar collector thermal performance. Techn. Rep. No. SEU-IEATr2 (in press). 5. ASHRAE Standard 96-1980, Methods ~ftesting--to determine the thermal performance o f unglazed .fiat-plate liquid-type solar collectors. ASHRAE Publications, New York, USA. 6. ONORM M 7724, Uncovered plastic solar collectors: A
272
H. SOL'IAtJ
test procedure to determine conversion ./actor. heat loss and gain coefficient. Osterreichisches Normungsinstitut, Wien, Austria ( 1987 ). 7. S. Svendsen, Performance of umx~vered solar coUectors. Technical Report 85-17, Thermal Insulation Laboratory-Technical University, Copenhagen. Denmark ( 1985 ). 8. M. Gschwind and J. Robert, Unglazed solar collectors testing, Technical Report, ARMINES--Center of Energy, Valbonne, France ( 1987 ). 9. European Solar Collector and Systems Testing Group,
23. 24.
25.
Recommendations ~)r perfi~rmance and durabilit)' tests of solar collectors and water heating s),stems. Technical Report, Joint Research Center. Ispra, Italy (1989). 10. S.J. Harrison, D. McClenahan, and V. H. Nielsen, Testing unglazed solar collector thermal performance, In Proceedings of the ISES Solar World Congress. Kobe, Japan, pp. 736-741 (1989). 11. H. Soltau, The thermal perlormance (~[uncovered collectors. Fortschrittsberichte der VDI-Zeitschriften, Reihe 6: Energietechnik, VDI-Verlag, Diisseldorf. Germany ( 1989 ). 12. H. Soltau, The thermal performance of uncovered collectors, In Proc. ~f the ISES Solar World Congress Hamburg, Germany, (1987). 13. J. A. Dut~e and W. A. Beckman, Solar engineering qf thermalpr~'esses. John Wiley & Sons, New York ( 1980 ). 14. The ~PPkT pvrgo,neter. Technical data. The Eppley Lab. Inc., Newporl, RI (1987). 15. J. W. Enz. J. C. Klink, and D. G. Baker, Solar radiation effects on pyrgeometer performance, Journal ~lApplied Meteorolog.v 14, 1297-1302 ( 1975 ). 16. B. Albrecht, M. Poellot, and S. K. Cox, Procedures for improving pyrgeometer measurements, Journal o[Applied Meteorology 16, 188 ( 1977 ). 17. D. I. Wardle and L. J. B. McArthur, Ground level mon-
itoring of long-wave irradiance with the Eppley pvrgeometer. Technical Report ARD-87-2. Atmospheric Envi18. 19.
20.
2 I.
ronment Service--Environment Canada, ASES (1986 ). P. Berdahl and R. Fromberg, The thermal radiance of clear skies, Solar Energy 29, 299-314 (1982). C. U. D~ike, A new model ~f the pyrradiometer type ~f Schulze, Technical Report 126, Deutscher Wetterdienst-Selbstverlag, Offenbach, Germany (I 972). J. Havinga and A. J. Th.M. Wijsman, Characterization of uncovered solar coUectors, IEA Task Ill Working Document, Technisch Physische Dienst, Delft, Netherlands ( November 1985 ). J. Keller, Characterization of the thermal performance of uncovered solar collectors by parameters including the dependence on wind velocity, humidity and infrared sky radiation as well as on solar irradiance, In Proceedings ~I
the Second Workshop on Solar Assisted Heat Pumps with Ground Coupled Storage, Vienna, Austria ( May 1985 ). 22. G. Angermeier, R. Pitz-Paal, and H. Soltau, The wind
26.
27.
dependent heat transfer coefficient of uncovered collector's, In Proc. of the ISES Solar World Congress. Hamburg, Germany (1987). L. C. Burmeister, Convective heat tran,~,r. John Wiley & Sons, New York (1983). F. L. Test, R. C. Lessmann, and A. Johary, Heat transfer during wind flow over rectangular bodies in the natural environment, J. of Heat TransJer, Trans. t)f ,4SME 103, 262-267 ( 1981 ). E. M. Sparrow and K. K. Tien, Forced convetion heat transfer at an inclined and yawed plate--application to solar collectors, J. of Heat Transfer. Trans. of ASME 99, 507-512 (1977). H. Soltau and G. Angermeier, Modelling the heat transfer of a fiat plate in the highly turbulent wind field of an urban environment, In Proc. of the 9th ItlTC Congress. Jerusalem, Israel, pp. 151 - 156 (1990). H. Hopfenziz, An experimental and theoretical investi-
gation on the effk'ct offree-stream turbulence and pressure gradients on a turbulent boundary layer. Fortschrittsber28.
29.
30.
31.
32.
33.
34. 35.
36. 37.
ichte der VDI-Zeitschriften, Reihe 7: StriJmungstechnik, VDI-Verlag, Diisseldorf, Germany (1984). McCormick, F. L. Test, and R. C. Lessmann, The effect of free-stream turbulence on heat transfer from a rectangular prism, J. ~f lh,at Transfer. Trans. ~f ASME 106, 268-275 (1984). P. K. Maciejewski and R. J. Moffat, A correlation for boundary, layer heat transfer accounting for free stream turbulence, In Pr~'. ~f the 9th IHTC Congress. Jerusalem, Israel, pp. 303-308 (1990). E. M. Sparrow, J. W. Ramsey, and E. A. Mass, Effect of finite width on heat transfer and fluid flow about an inclined rectangular plate, J. of Heat Transfer. Trans. of ASME 101, 199-204 (1979). A. J. de Ron, Dynamic modelling and verification of a flat-plate solar collector, Solar Energy 24, 117-127 (1980). R. Kliippel, A. de Nobrega, R. Sizmann, and W. Sch61kopf, Measurement of characteristic solar collector parameters in transient operation, In Proceedings of the ISES Solar World Congress. Montreal, Canada, p. 874 ( 1983 ). M. Emmery and B. A. Rogers, On a solar collector thermal performance test method for use in variable conditions, Solar l-nerg.v 33, I 17-123 ( 1984 ). lloe~ch Energy Absorber. Technical data, ESTEL Siegerlandwerke AG, Kreuztal, Germany ( 1983 ). I. N. Bronstein and K. A. Semendjajew, Pocket-book (~f mathematics. Teubner Verlagsgesellschaft, Leipzig, Germany (1979). 77u' t':.IFCO Solar .~vstem. Technical Data. FAFCO S.A., Biel, Switzerland (1990). A. A. Green and J. Cruz Costa, The influence of wind on unglazed solar collectors, In ('ommunica~'oes do 4. ('ongr(,,ss(~ lh(;rico de Energia Solar. Porto, Portugal { 1988).