Pergamon PII: SOO38-092X(96)00061-8

Solar Energy Vol. 57, No. 2, pp. 93-109, 1996 Copyright 0 1996 Elsevier Science Ltd

Printed in Great Britain. All rights reserved 0038-092X/96 $15.00+0.00

EXPERIMENTAL INVESTIGATION OF HEAT LOSSES FROM LOW-CONCENTRATING NON-IMAGING CONCENTRATORS

MATS RONNELID* and BJORN KARLSSON** *Solar Energy Research Centec, Dalarna University, S-78188 Borlange, Sweden

and **Vattenfall Utveckhng AB, Alvkarlebylaboratoriet, S-81426 Alvkarleby, Sweden

(Communicated by Brian Norton)

Abstract-Heat loss measurements have been performed on a V-trough collector model with concentration ratio 1.56 and with flat absorbers consisting of five parallel reflector troughs aligned east-west. The collector was tilted 45”. Depending on the similarity in geometry between V-troughs and compound parabolic concentrators, the results should in general be valid also for low-concentrating CPCs. The absorbers were heated electrically and the heat losses were calculated from the input power to the absorber surface. Several geometrical and material properties that affect the heat losses from the collector were investigated. It is concluded that the use of transparent insulation, such as Teflon@ films, in low-concentrat- ing solar collectors can reduce the heat losses substantially. The reflector emittance in the infrared has an impact on the heat losses. Use of highly emitting reflectors instead of low-emitting reflectors increases the overall heat losses by about 5-S%. The conversion of experimentally measured heat losses into heat losses for real collectors and practical material considerations is discussed. Copyright 0 1996 Elsevier Science Ltd.

1. INTRODUCTION

The development of large area collectors for district heating has been one main area of solar collector development in Sweden since the mid 1980s. One possible way of constructing collec- tors with high annual performance is to use internal reflectors inside the collector, since a reduced absorber area implies reduced heat losses. The optimal choice of reflectors is Compound Parabolic Concentrators (CPCs) which are ideal since they reach the thermo- dynamic limit of concentration (Welford and Winston, 1989).

Several studies have been performed on the heat losses from CPC- and trough-like solar collectors during the last two decades. Among the studies done on concentrators with planar absorbers, are theoretical calculations of radia- tive and convective heat losses in CPC-collec- tors by Rabl (1976) and calculations by use of finite element technique by Abdel-Khalik ef al. (1978). V-troughs have been studied by Meyer et al. (1982), who used an interferometric tech- nique to determine the convective heat flow inside the reflector cavities. The use of transpar- ent insulation in the form of convection supres- sion films or glazing in CPC-collectors with flat absorbers has been studied by Tatara and Thodos (1984) and Fasulo et al. (1987).

The heat losses in CPC-collectors with non- evacuated tubular absorbers have also been studied both numerically by Hsieh ( 1981), Chew

et al. (1989) and by Eames and Norton (1993a) and experimentally, e.g. by Chew et al. (1988) and Eames and Norton (1993b). For further reading, a review of the state-of-the-art up to 1991 in optical and thermal analysis of CPC- collectors by Norton et al. (1991) is recommended.

The present study is a complement to the previous studies. It investigates how different material properties, such as optical and thermal properties of reflectors and transparent insula- tion, and geometrical arrangements affect the overall heat losses of CPC-collectors with flat- plate absorbers. By measuring the heat losses from an electrically heated collector model, it is possible to change materials and geometry in the model, and thereby study how this changes the overall heat losses from the collector. If the collector model consists of several linear reflec- tor troughs, it is also possible to study how the different troughs thermally affect each other if they are not ideally insulated from each other.

Section 2 describes the experimental set-up which was used. In Section 3 the results of the performed measurements are given and briefly discussed. At the end of this section all measure- ments are summarised in Table 2. In Section 4 we discuss how the heat losses measured in the laboratory can be converted to values for a real solar collector. In Section 5, some practical material considerations are given. In Section 6, the application of the results to other concentra- tor geometries than the one with a one-sided

93

94 M. Rdnnelid and B. Karlsson

flat absorber is discussed. Finally, the main conclusions are summarised in Section 7.

2. EXPERIMENTAL SET-UP

The hot box used for the heat loss measure- ments was built up by blocks of polystyrene with an average thickness of about 400 mm. It is shown in Fig. l(a). This thickness was chosen to reduce the influence of back- and side-heat losses on the total heat losses. In the front side of the box there was a cavity where the model of the collector was built up with absorber surface, reflectors and transparent insulation, and the hot box was covered with a glazing of 6 mm acrylic plastic. The glazing was held to the front side of the hot box by a wooden frame and pressed tightly to the hot box front in order to avoid air leakage from the collector cavity to the ambient air. The bottom of the cavity was covered with a hard mineral wool sheet of 20 mm to protect the polystyrene from melting when the absorber surface was heated. The hot box was tilted 45” relative to the horizontal. This tilt is in accordance with the collector tilts that are normal for use in Swedish climatic conditions.

The collector model was built up by 0.5 mm thick TeknoTerm aluminium absorbers which have an individual width of 142 mm. In all measurements the absorbers were aligned paral- lel with the horizontal, as shown in Fig. l(b). This corresponds to an east-west (EW) align- ment in a real south-facing collector.

The absorbers were electrically heated by a heating foil glued to the back side of the absorb- ers which was fed by variable DC source. In the collector mode with internal reflectors, five

120-l 40

absorbers were used which were parallel coupled according to Fig. 2. The resistance of each foil was measured individually and was almost equal to 40 Q at room temperature, with a small temperature dependence. Therefore, by feeding the absorbers with an electric current, all five absorbers will be heated by the same power. The absorber temperature was measured at five equally spaced points with thermocouples riv- etted on the absorber. In the middle of the collector near thermocouple 13 in Fig. 2, two additional thermocouples recorded the absorber temperature to get the temperature gradient over the absorber.

The different reflectors used as internal reflec- tors in the collector model mostly had a flat shape. This means that the cavities formed by the reflectors had a traditional V-trough shape. Flat reflectors were used instead of CPC-shaped reflectors because they were easier to manufacture in the laboratory scale. As illustrated in Fig. 3, the difference between the

Hot box top

Hot box bottom I

Fig. 2. Electrical connection of absorbers in the V-trough solar collector model. The numbers refer to the thermo-

couples, marked x in the Figure.

cover

(4 lb) Fig. 1. (a) Geometry of hot box used for heat loss measurements. Distances in mm. (b) Side view of a hot

box equipped with a single-glazed V-trough solar collector model.

Experimental investigation of heat losses from low-concentrating non-imaging concentrators 95

Fig. 3. Geometry of V-trough and CPC-trough used for heat loss measurements.

V-trough-shape and the CPC-shape suggested for a real collector is very small, and the differ- ence in heat losses should therefore be negligible. In some of the experiments (see Section 3.3.1), the real CPC-shape of the reflectors was used. The geometric concentration C of the used concentrators was in $1 cases C = 1.56X, which corresponds to a CPC-concentrator with accep- tance angle 35” and a truncation degree of 0.4.

The reflector temperature was measured in the middle of the central reflector trough, near measuring point 13 in Fig. 2. On each of the two reflectors surrounding the absorber, the temperature was measured at three points with different distances from the glazing. These meas- urements were performed with thermocouples that were glued with a heat conducting paste on the back side of the reflectors. In the same way the temperature of the acrylic glazing was measured at a point exactly above point 13 in Fig. 2 by thermocouples glued on the inner and outer surface of the acrylic cover. The air temperature in the laboratory was measured by two independent thermocouples. All the thermo- couples measured with an uncertainty of +o.l”c.

For comparing the heat losses from collectors with internal reflectors with standard flat plate collectors, measurements were also performed on a flat plate collector model which was built up in the same hot box frame. This model consisted of eight absorbers which were parallel coupled in the same way as for the model with internal reflectors.

For each measurement, the voltage T/ and the resistance R was read by a universal instrument. From this the input power to the absorber could be calculated as

p=;.

In thermal equilibrium, this input power equals the total heat losses U from the collector model in the hot box:

P = UAAT (2)

where A is the collector model aperture area and

AT = Tabs - T, (3) with T, = surrounding air temperature. The tem- perature dependent U value for the collector model is calculated by combining eqns ( 1 )-( 3)

U(AT) = V2

RA(T,, - T,)’ (4)

The temperature varies over the absorber surface, with lower temperatures near the edges of the collector caused by increased heat losses through the edge insulation. In a real applica- tion in a large collector field, the collector surface is typically lo-180 m2 (Wilson et al., 1989), and the influence of edge effects should be much smaller than in the case of the hot box. Therefore, the absorber temperature Tabs in the hot box was defined as the mean temperature of the most central temperature sensors. For the case with the collector model with internal reflectors this means that Tabs = (T7 + T, + T9 + Ti2 + T13 + T14 + T17 + T’, + T’,)/9 where the subscripts refer to the thermocouples indi- cated in Fig. 2. By only using the most central temperatures in defining the absorber temper- ature, the influence of edge effects is minimised. This is possible because all parts of the absorber surface are fed with the same power. For the case with the flat plate collector model with eight absorbers, the absorber temperature was defined as the mean temperature of six temper- atures in the middle of the hot box.

The hot box reaches thermal steady state conditions 7-10 h after the heating starts. However, the laboratory environment could change during the day by fluctuations in the indoor temperature and by air circulation caused by the air conditioning system running during day-time in the house, see Fig. 4. Therefore the readings were always done early in the morning, after a night with uniform laboratory climate. For the measurements with real CPC-shaped reflector surfaces, a data- logger was installed which automatically made the readings every hour. The U value was then defined as the mean U value for the 7 h between 11.00 p.m. and 6.00 a.m.

As the thermocouples were in good thermal contact with the absorbers the maximum error for the mean absorber temperature was esti- mated to approximately 0.1%. The relative uncertainty of the U value calculations was estimated to a few percent. However, since we

96 M. Rbnnelid and B. Karlsson

. . . Absorber temperature - - -Ambient temperature

o Calculated U-value 3.1 _-.- . .._ I.---.../ __..___ j __..... _ 50

February 12-13, 1994 l-45

0 12 24 36 40 Noon Midnight Noon

Hour

Fig. 4. Example of calculated U values for different hours during a 48 h period starting at midnight.

are comparing the U value calculated for different collector geometries and different absorber temperatures from temperatures mea- sured with the same thermocouples all the time, the relative error while comparing two measure- ments should be small. As indicated in Fig. 4, the fluctuation of the calculated U value is c l%, except for the afternoon values which are not used for this study.

Since the hot box was built up using poly- styrene, the measurements were restricted to absorber temperatures 590°C. This is equal to temperature differences Tabs - T, < 70°C. This is a restriction of the measurement equipment, but these temperatures cover most of the temper- ature range that is of practical interest for flat plate and non-evacuated CPC-collectors.

All infrared properties of the materials involved in the measurements were calculated by measuring the near normal specular reflec- tance, or transmittance, with a Perkin-Elmer infrared spectrometer. Except for the black- painted reflector surface discussed in Section 3.3,

all reflectors used had a high degree of specular reflectance in the visible range. Since the ratio between the wavelength and surface roughness increases for increased wavelength, the diffuse part of the reflectance decreases when the wave- length increases. It is therefore assumed that the diffuse reflectance is negligible for long wave- lengths corresponding to heat radiation in the range < 100°C. The emittance and transmit- tance in the infrared region is summarised in Table 1 and was calculated by assuming a black- body curve at 70°C as reference.

3. RESULTS OF THE MEASUREMENTS

A total of 20 different solar collector arrange- ments, involving different geometries and different materials, were investigated with the hot box technique. All models involving internal reflectors had the same reflector geometry with a geometrical concentration ratio C = 1.56X and a reflector height of 12 cm over the absorber.

The heat losses for each arrangement were measured at 3-6 different temperature levels to get a true picture of the temperature dependence of the heat losses. A regression line was calcu- lated according to

u = u0 + U,(T,,, - T,) (5)

which is a convenient way to express the heat loss coefficient in solar collectors (Cooper and Dunkle, 1981). However, the convection part of the heat losses is proportional to a power of temperature difference AT which is different from unity. This is an effect which can be dominant for small AT, and the experiments therefore show that a linear approximation of the heat losses according to eqn (5) is not appropriate for temperature differences when AT = (7& - T,) < 15°C. Measurements of the heat losses when AT< 15°C are therefore excluded in the diagrams presented in this sec-

Table 1. Measured values of near normal emittance and transmittance of materials involved in the experi- mental investigation. A temperature of 343 K is assumed. Values for the laboratory environment and the

black oainted absorber are estimated values.

Sample Emittance Transmittance

Pure aluminium Polyethene-coated aluminium foil Black painted aluminium foil Anodised aluminium 3M 5400 Scotchcall reflector foil Sun Strip absorber Acrylic cover (6 mm) FEP Teflon film (25.4 pm) Black painted absorber (estimated) Laboratory environment (estimated)

0.04 _ 0.04 _ 0.93 _ 0.74 _ 0.75 _ 0.20 _ 0.94 0.002 0.53 0.42 0.9 1.00 _

Experimental investigation of heat losses from low-concentrating non-imaging concentrators 97

tion. This is also reasonable since solar collec- tors of the CPC-type most often work with absorber temperatures Tabs > T, + 15°C.

3.1. Air space between reflector and glazing Heat loss measurements were performed with

different air gaps between the reflectors and the acrylic cover. In the first measurement, the cover was put directly against the top of the reflectors so that five separate reflector cavities were formed without allowing any air to flow between the cavities. This was repeated with the acrylic cover lifted to create air gaps of 1 and 2 cm between the cover and the reflectors.

acrylic barriers were inserted in the five reflector cavities. The barriers were made of 2 mm thick acrylic sheets which were cut to the right width and placed in the cavities parallel with the absorber, at varying distances from the outer glazing. The acrylic sheets were kept in place by their own weight. The distance between the reflector tops and the outer glazing was 2 cm.

An aluminium laminate consisting of 9 pm aluminium on a polyester base, covered with a 2-3 pm low-emitting polyethene lacquer, was used as a reflector. The laminate was glued on a triangular form that was cut out from polysty- rene blocks. By using the thin laminate in this experiment, the heat conduction through the mirrors was minimised and as a result the heat transport by conduction from one reflector cavity to a nearby cavity should be small.

The same reflectors as in Section 3.1 were used-aluminium laminated foil on polystyrene base. As a result of the thin reflector foil, the heat leakage by conduction through the reflec- tors between the two parts of the reflector cavities separated by the acrylic sheet should be small.

As seen in Fig. 6, the insertion of acrylic sheets in the collector with internal reflectors reduce the U value by roughly 0.5-0.7 W mm2 K-’ compared to a collector without transparent insulation. The heat losses are smallest for acrylic sheets near the absorber. The difference in U value between placing the acrylic sheet on top of the reflectors and near the absorber, is of the order of 0.1 W mm2 K-‘.

As illustrated in Fig. 5, the difference in heat losses in the three cases is small. A tendency to increased heat losses for larger air gaps between the reflector and cover for larger temperature differences can be seen weakly, and is probably explained by an increased air flow between the reflector troughs when the temperature differ- ence is increasing and air gaps are non-zero. However, this effect is small and almost negli- gible in the temperature range investigated.

3.2. Transparent insulation

It should be mentioned that a similar study by Tatara and Thodos (1984) measured the heat losses in a vertically oriented CPC with C = 4X by use of acrylic plates at different distances between the absorber and the cover. They reported that the convective heat transfer rate was increasing for the acrylic sheet near the absorber. However, unlike the present study they used highly conductive reflectors made of 0.379 mm aluminium, which probably caused substantial heat transfer rates between the two cavities separated by the acrylic plate.

3.2.1. Diflerent distance between absorber and 3.2.2. Using diferent transparent insulation transparent insulation. To investigate the possi- material. A practical and commonly used bility of decreasing the heat losses by introduc- transparent insulation in solar collectors is ing transparent insulation into the collector, Teflon@ film. This material has a high thermal

1 distance reflector

0 10 20 30 40 50 60 70 Temperature difference (%)

Fig. 5. Heat losses from a 1.56X V-trough collector model with different spacing between reflector and glazing. Right picture shows a principal drawing of the set-up.

M. Rbnnelid and B. Karlsson

+ V-trough, reference -+ -teflon, 12 cm - * -acrylic, 12 cm

3 f--Q- - acrvlic, 9 cm I 1 I

1 I --Q--a&k, 6 cm

+- acrylic, 3.5 cm

reflector

10 20 30 40 50 60 70 60 d=distance Temperature difference (“C)

Fig. 6. Heat losses from a 1.56X V-trough collector model with transparent insulation at different distances from the absorber. Results from a V-trough collector model without additional convection barrier are

shown as a reference. Right picture shows a principal drawing of the set-up.

stability up to 2OO”C, it has a light weight and a high solar transmittance (r,,, = 0.96). Measurements were therefore performed on a V-trough model with a 25.4 pm FEP-Teflon film (DuPont) placed on the reflector tops, with a 2 cm air gap between the Teflon and the outer glazing. As seen in Fig. 6, the use of Teflon film as transparent insulation results in an increase of the U value of less than 0.1 W m-* K-r in the heat losses compared to when acrylic sheets are used. This depends on the fact that Teflon is partly transparent for IR-radiation (rIR = 0.42) while the acrylic sheet is almost opaque for IR-radiation (r ,k z 0.002). Higher IR-trans- parency increases the heat losses since the radia- tive part of the heat losses between the absorber and outer glazing is increased.

This difference in heat losses when using transparent insulation with different tiR values should be smaller if the absorber emittance is smaller than the actual case in the experiments, where E = 0.20. For non-selective absorbers, the importance of secondary glazing with low rIR increases.

3.3. Rejector emittance

Investigation of the impact of the reflector emittance on the heat losses was done for the two cases with and without a Teflon film as transparent insulation on top of the reflectors. After the measurements in Section 3.2, the low- emitting aluminium laminate was painted dull black which increased the emittance from E = 0.04 to E = 0.93. From a thermal point of view, the only change done by this was a change of

the reflector emittance since all other parts of the collector model were the same.

Early calculations of the impact of the reflec- tor emittance on the heat losses in CPC-collec- tors done by Rabl (1976) showed that the reflector emittance had no (or negligible) impact on the heat losses from the collector. In Rabl’s model for the heat losses, the radiative and convective heat losses from the absorber were treated as separate parts, independent of each other. For the radiative part, an effective emit- tance serf was calculated for the radiative inter- action between the absorber and the cover, and it was found that s,rf was almost independent of the reflector emittance. While calculating the convection losses from the absorber to the cover, the interaction with the reflector walls was neglected, and the convective heat losses were calculated by using correlations for natural con- vection from flat surfaces. However, the results seen in Fig. 7 show that the use of high-emitting reflectors cause an increase in the U value of the order 0.15-0.2 W m-* K-r, compared with the use of low-emitting reflectors in the collector.

To understand the measured difference in heat losses when the reflector emittance is changed, we must look in more detail at the temperature distribution inside the reflector cavity. The wall temperature was measured at 10 locations around a section in the centre of the middle trough of the hot box model, as indicated in Fig. 8. In the Figure the direction of the convec- tion flow inside the reflector cavity is also indicated. This was visually examined by inject- ing smoke through a thin tube that was stuck

Experimental investigation of heat losses from low-concentrating non-imaging concentrators 99

- + - Black foil, &=0.93 --g Aluminium foil, ES 0.04 -O -Black foil + teflon

1.5* 0 10 20 30 40 50 60 70 60

Temperature difference (“C)

Fig. 7. Heat losses from a 1.56X V-trough model using reflector surfaces with different IR-emittance. Measurements were performed with and without Teflon film as transparent

insulation.

0.795

0.360

0.562

Fig. 8. Definition of the loci around the enclosure of the V-trough used in the experiments. The locations of thermo- couples for temperature measurements are indicated with stars. The arrow inside the cavity shows the direction of the

convection flow.

into the cavity through the side insulation of the hot box.

Two examples of measured temperatures in the V-trough model with the same temperature difference between the absorber and the ambient are seen in Fig. 9. It is seen that the reflector temperature is lower in the case with high- emitting reflectors compared to the case with low-emitting reflectors, which is caused by the increased radiation losses from the reflectors to the cover. This decreased reflector temperature causes an increased temperature difference between the reflector and the absorber. It is therefore reasonable to assume that this in turn causes an increased convection flow over the absorber. Therefore, the increased heat losses in the case with high-emitting reflectors can be

0 low emitting reflectors ( ~.=0.04) 0 high emitting reflectors ( a= 0.96)

60~

cover I _I

absorber

lower upper reflector reflector I I , 1

0 0,2 0,4 0,6 0,8 1 Position around enclosure

Fig. 9. Example of local temperatures inside the 1.56X V-trough cavity when reflectors with different emittance are used. The positions around the enclosure are defined in

Fig. 8.

explained by a coupling of the radiation- and convection-mode of heat transfer inside the reflector cavity, and cannot be adequately explained by treating radiation and convection separately.

3.3.1. Coupling between rejector and absorber emittance. The impact of the reflector emittance on the heat losses is dependent on the absorber emittance. When absorber emittance increases, the radiation from the absorber to the reflector increases, which increases the reflector temper- ature. This neutralises to a large extent the difference in reflector temperature for low-s and high-c: reflectors, and the reflector emittance should therefore have less importance for the heat losses from the absorber when non-selective absorbers are used.

Experiments were performed with real reflec- tor surfaces and CPC-shaped reflectors with reflector foils glued on a foamglass mould. The CPC-shape is shown in Fig. 3. A low-emitting aluminium laminate (E = 0.04) on a 75 pm thick polyester base was glued with silicon on the foamglass. As a high-emitting reflector, 3M Scotchcall 5400 reflector foil with an acrylic top (E = 0.75) was adhered to the foamglass by the taped back side which is available as a commer- cial product. As the methods of gluing the reflector foils to the foam and the way the reflector foils are built up differ, there will be a difference in conduction heat resistance for the CPCs with the different reflector materials. Especially for large temperature differences, the 3M 5400-foil had a tendency to loosen from the mould, which caused the geometry of the reflec- tor trough to change from the ideal CPC form.

In the experiment two different absorber types

100 M. Rijnnelid and B. Karlsson

were used, which thermally represented a very good selective absorber and a non-selective absorber. The low-emitting absorber was made by winding bare aluminium with E = 0.04 around the electrically heated sun strip absorb- ers. The high-emitting absorber was created by painting these aluminium absorbers with a dull black paint with an estimated emittance of E = 0.9.

Figure 10 illustrates that the increase in heat losses due to increased absorber emittance is larger when low-emitting reflectors are used instead of high-emitting reflectors. While the U value increases 1.1 W m-’ K-r when low-emit- ting reflectors are used and the absorber surface is changed from low-emitting to high-emitting, the increase in U value is 0.9 W m-’ K-r if high-emitting reflectors are used and the same change in absorbers is done. This shows that a decrease in absorber emittance is more impor- tant when the reflector is low-emitting than if the reflector is high-emitting.

3.4. ReJector conductivity

3.4.1. Rejlector thickness. The introduction of highly conductive reflectors in a collector of the type examined in this study will increase the heat losses from the collector. This is because a highly conductive reflector will decrease the heat resistance from the absorber to the cover, which in turn causes an increased heat transfer coefh- cient between the absorber and the cover.

Measurements were made on collector models both with and without Teflon film as a trans- parent insulation on top of the reflectors. Two different reflectors were tested; the aluminium

---t Ea= 0.9, Er = 0.04 + Ea = 0.9, Er = 0.75 --[3-m Ea = 0.04, &r = 0.75 --B-- Ea= 0.04, &r = 0.04

3,5,

1,59 10 20 30 40 50 60 70

Temperature difference (72)

Fig. 10. Heat losses from a CPC-trough model with reflec- tors and absorbers with different emittance.

laminate with E = 0.04 and aluminium thickness of 0.009 mm, and a 0.5 mm thick aluminium reflector with a low-emitting aluminium lami- nate glued on the surface to give the same reflector emittance.

The thick aluminium reflector was bent to a triangular shape. This means that a thermal contact existed between the right reflector in one trough with the left reflector in the next trough since the two reflectors are formed from the same aluminium sheet. The reflectors were placed with their lower part touching the absorber so as to give as good a thermal contact with the absorber as possible. The triangular cavities formed by the thick reflectors were uninsulated.

The results from the four measurements are presented in Fig. 11. The measurements show that the drawback with high conductive reflec- tors is much more dominant in a single-glazed collector (0.3 W me2 K-r increase in heat loss coefficient) than in a collector with addi- tional transparent insulation (0.15 W m-’ K-r increase in heat loss coefficient). This is easily understood from the fact that the Teflon film also works as an insulation barrier for the additional heat transfer from the absorber to the cover caused by an increased reflector conductivity.

The measurement with high conductive reflectors was repeated, but with the triangular cavities formed by the bent aluminium sheet filled with mineral wool insulation. However,

* -0.5mm aluminum sheet, no teflon -0.009 mm aluminum laminate, no teflon --e--0.5 mm aluminum sheet, with teflon ---Q--- 0.009 mm aluminium laminate, with teflon

3’59

L5, 0 10 20 30 40 50 60 70

Temperature difference (“C)

Fig. 11. Heat losses from a 1.56X V-trough model using aluminium reflectors (E = 0.04) with different thicknesses. Measurements were performed with and without Teflon film as transparent insulation between the reflectors and the

cover.

Experimental investigation of heat losses from low-concentrating non-imaging concentrators 101

this caused no measurable change in overall heat losses.

3.4.2. EfSect of air gap between absorber and rej?ector. In early literature on CPC-collectors it has often been recommended that an air gap should be introduced between the absorber and reflector to block the heat conduction from the absorber to the reflector and thereby minimise the heat loss. Measurements on the V-trough configuration were therefore performed compar- ing arrangements with 0.5 mm anodised alumin- ium reflectors (E = 0.74) with and without a 3 mm air gap, created by small acrylic spacers, between the absorber and reflector. In the con- figuration without an air gap, the reflectors were placed as close to the absorber as possible. In both measurements, a Teflon film was used as transparent insulation between the reflectors and the cover.

As seen in Fig. 12, the decrease in heat loss is only in the order of 0.03 W mm2 K-’ when the air gap is introduced, which is surprisingly small, bearing in mind the high heat conductivity of aluminium compared with air.

To understand this we look at the temper- atures in the reflector walls for the two cases with high- and low-conducting reflectors with low-emitting surfaces, shown in Fig. 13. In the case with thick reflectors, the increased conduc- tivity tends to smooth out the temperature in the reflectors which then have a much lower temperature gradient compared to the case with thin reflectors. This effect increases the temper- ature difference between the absorber and the upper reflector, and we can therefore assume an increased convection flow from the absorber to the upper reflector.

In Fig. 13 we also see that the temperature

+ -0.5 mm aluminum sheet -e-O.5 mm aluminum sheet with 3 mm air gap

-c 2,8--

“E 2. *,6-:

3 F

2,4--

3 2,2--

2 I 6 1’0 2’0 3’0 4’0 5’0 66 7’0

Temperature difference (“C)

Fig. 12. Heat losses from a 1.56X V-trough using 0.5 mm anodised aluminium reflectors with and without a 3 mm air gap between the reflector and absorber. Measurements were performed with a Teflon film as transparent insulation

between the reflectors and the cover.

0 Aluminium laminate (0.009 mm) Aluminium sheet (0.5 mm)

I cover

+ absorber

0 lower upper reflector reflector

Position around enclosure

Fig. 13. Example of local temperatures inside the 1.56X V-trough cavity when reflectors with different conductivity are used. The position around the enclosure is defined in Fig. 8. A Teflon film was placed between the reflector and

the cover.

difference between the reflectors on both sides of the absorber is smoothed out in the case with high conductive reflectors. The small temper- ature difference between the lower and upper reflector in the high-conducting reflector case is explained by heat conduction from one reflector cavity to another by the upper part of the reflectors. By this, the lower reflector in a reflec- tor cavity is heated by the upper reflector in the cavity below. In Fig. 14 we see the middle temperatures of the five absorbers used in the hot box measurements on V-trough configura- tions with thin and thick reflectors. The strong temperature gradient in the case with high con- ductive reflectors is seen clearly, showing that heat is transported from the lower part to the upper part of the collector.

One explanation for the increased heat losses for cases with reflectors with higher conductivity is therefore that the reflectors are heated by

o^ 8. I I I 1 I 00 I I , >- ._ 6 -1 --e-Thick reflector (0.5 mm)

: --e--Thin reflector (0.009 mm)

0 0,2 094 0,6 0,8 1 Distance from bottom of the hot box (m)

Fig. 14. Temperature distribution of the absorbers when thin and thick reflectors are used in the V-trough model. In the measurements, the mean absorber temperature was

~66°C over ambient temperature.

102 M. Rbnnelid and B. Karlsson

convection and conduction from nearby reflec- tors in thermal contact, and not necessarily mainly by metallic conduction of heat direct from the absorber. However, we should bear in mind that although the absorber and reflector were in near contact in this experiment, a perfect thermal contact was not achieved because of irregularities in the reflector surface and absorber edge that are always present in stan- dard materials. If the thermal contact between the absorber and the reflector were perfect, the expected role of the reflector as a conductive cooling fin should be much larger.

3.5. Comparison withpat plate collectors The heat losses from the different V-trough

and CPC-collector models were compared with the heat losses from two flat plate collector models.

1. Flat plate collector model with 11.5 cm distance between the absorber and the cover.

2. Flat plate collector model with 11.5 cm distance between the absorber and the cover and a 25.4pm FEP-Teflon film placed 4 cm below the cover.

The flat plate models consisted of eight paral- lel absorbers. The absorbers and the cover were identical as in the V-trough measurements. The results from these measurements are shown in Fig. 15(a) together with V-trough measurements using low-emitting aluminium laminate as a reflector. These V-trough measurements were selected since they had the lowest heat losses, except for the measurements on V-troughs with acrylic plastics as transparent insulation. The latter were not taken into account since they were assumed to be of less practical interest.

We see that a single-glazed flat plate collector has approximately 0.3-0.4 W m-’ K-i higher heat losses than the corresponding V-trough. If we compare collectors with a Teflon film as transparent insulation, the heat losses for the flat plate case are approximately 0.2 W mm2 K-’ higher than the V-trough case.

The reflectors in the V-trough and CPC- collector models work as convection suppres- sion devices which minimise the air movement from the lower part to the upper part of the absorber surface. Since the hot box measure- ments are performed with constant power input to all absorbers, this leads to an increased temperature gradient, shown in Fig. 16, over the entire absorber surface in the flat plate case,

-o- Flat plate collector - -e- - V-trough collector with

thin reflectors (0.009 mm)

0 0,2 0,4 0,6 0,8 1 1,2 Distance from bottom of the hot box (m)

Fig. 16. Temperature distribution of the absorbers for a V-trough collector model and a flat plate collector model, both with Teflon film as transparent insulation. Mean

absorber temperature z 57°C.

* Flat plate - 4 -V-trou h -E -Fiat 9 p ate with teflon

A. . V-trough with teflon

o- ou 0 1020304050607080 0 1020304050607080

Temperature difference (“C) Temperature difference (“C)

a b

Fig. 15. (a) Heat losses from 1.56X V-trough with thin, low-emitting reflectors and flat plate collector models with and without Teflon. (b) Results from (a) recalculated with eqn (12) for compensating differences

in insulation and front heat loss coefficient between laboratory collectors and real collectors.

Experimental investigation of heat losses from low-concentrating non-imaging concentrators 103

since the air can move from the lower part of the collector cavity to the upper part.

In Table 2, all presented measurements in Section 3 are summarised. A U value for a temperature difference between the absorber and the ambient of 50°C are calculated from the regression lines obtained for each series of measurements. The absolute error of the tabled U value can be estimated to +_O.l W me2 Km2. The relative error between the different measure- ments should be smaller, since the same measurement devices have been used for all measurements.

losses through the back and side insulation of the hot box. The front heat losses are dependent on the heat transfer coefficient inside the reflector cavity from the absorber to the glazing (hutvity) and the heat transfer coefficient from the glazing to the ambient (h,,,). Using the concept of thermal resistance (Duffie and Beckman, 1991), the front heat loss coefficient can be expressed as

1 1 U lab,front = R lab,cavity + hb,w = 1 1

~ -

h lab,cavity + hab,w

(7)

4. CONVERSION OF LABORATORY MEASUREMENT TO OUTDOOR

CONDITIONS

The heat loss coefficient measured in the laboratory is not identical to the heat loss coefficient for a collector at real working condi- tions. First of all the geometry, insulation and ambient climate is different for the hot box and a real collector, but this can be taken into account by a simple formula, derived below. For the laboratory collector, we could put up a heat balance based on the back and front heat loss coefficient

where &ab.cavity stands for the heat resistance between the absorber and the cover and R,ab,w stands for the heat resistance between the cover and the ambient. This gives an expression of the total heat loss coefficient from the hot box:

1 Ulab = 1 1 + Ulab,back. (8)

~ -

h lab,cavity + hab,w

A similar expression can be put up for the heat loss coefficient for a real collector:

Ulab = Ulab,front + Ulab,back (6)

1 U real = 1 1 + Ureal.back. (9)

h reaLcavity + hrea,,w

where Uiab is the total heat loss coefficient for the A shift from the laboratory to the real envi- hot box and &,&,& is the coefficient for the heat ronment will change the heat transfer coefficient

Table 2. Summary of collector model parameter. All models, except numbers 1 l-14 and 19-20 were using a V-trough reflector shape with C = 1.56X. The results are divided into five sub-groups, referring to Sections 3.1-3.5 respectively. For

more details, see the text.

No s. s, Second glazing Reflector UL (W m-2 K-l)

thickness (AT= 50°C) Comment

6 7 8 9

10 11 12 13 14 15 16 17

18

19 20

0.20 0.20 0.20 0.20 0.20

0.20 0.20 0.20 0.20 0.20 0.90 0.90 0.04 0.04 0.20 0.20 0.20

0.20

0.20 0.20

0.04 0.04 0.04

8:Zl 0.04 0.04 0.04 0.93 0.93 0.04 0.75 0.75 0.04 0.04 0.04 0.74

0.74

none 9m 2.63 none 9m 2.67 none 9w 2.68 Teflon, 25 pm 9w 2.11 Acrylic, 2 mm 9w 2.04

Acrylic, 2 mm 9m 2.02 Acrylic, 2 mm 9m 1.98 Acrylic, 2 mm 9pm 1.95 none 9m 2.77 Teflon 9m 2.25 none 9w 3.28 none -1Opm 3.11 Teflon -lOfilm 2.11 Teflon 9pm 2.02 none 0.5 mm 2.97 Teflon 0.5 mm 2.25 Teflon 0.5 mm 2.45

none 3.23 Teflon 2.36

0.5 mm 2.43

0 cm air space reflector-cover 1 cm air space reflector-cover 2 cm air space reflector-cover Teflon on reflector tops Acrylic on reflector tops, 12 cm from absorber Acrylic 9 cm from absorber Acrylic 6 cm from absorber Acrylic 3.5 cm from absorber

CPC-shaped reflectors CPC-shaped reflectors CPC-shaped reflectors CPC-shaped reflectors

No air gap between absorber and reflector 3 mm air gap between absorber and reflector Flat plate model Flat plate model

104 M. Riinnelid and B. Karlsson

h, because of the effect of wind and the effective sky temperature not being equal to the ambient temperature, which in turn will change the temperature of the glazing. Although the heat transfer coefficient for the collector cavity hcavity is temperature dependent, the shift in glazing temperature is so small that we can approximate the heat transfer coefficient for the laboratory collector and a real collector to be equal:

h lab,cavity = real,cavity . h (10)

Combining eqns (8)-( 10) we can therefore estimate the heat loss coefficient for a real collector from the measured laboratory collec- tor:

1 u real = 1 1 1 -_-

UIab - Ulab,back + hrea,,w hab,w

+v real,back. (11)

By covering the front of the hot box with insulation with a known thickness and thermal conductivity and measuring the heat losses, the back loss coefficient was estimated to Ur.&,&,& = 0.3 W me2 K-l. This is surprisingly high taking into account the thickness of the polystyrene insulation, but can be explained by a large heat transfer from the sides of the cavity in the hot box through the front part of the side insulation of the hot box. A realistic back loss coefficient for a large real collector could be estimated to 0.6 W m-’ K-r. The heat transfer coefficient for the front glazing in the laboratory was calcu- lated to hlab,w = 9+1 Wm-2K-‘, while for a real collector we assume hrea,,w = 20 W mm2 K-’ to be a reasonable choice, as suggested by Rabl (1985) for a modest, windy, summer climate. These values give an expression for the heat loss coefficient for a real collector:

1 u real =

1 1 1 u -03+20-9 lab .

+ 0.6 (W mm2 K-l). (12)

The U values obtained in the laboratory for flat plate collectors and V-trough collectors in Fig. 15(a) is recalculated to real collector condi- tions according to eqn (12) and shown in Fig. 15(b). We see that using eqn (12) causes an increased difference between the heat loss coefficients between two collectors in a real environment compared to a difference in heat

loss coefficients between two collectors mea- sured by hot box technique in a laboratory environment with lower front loss coefficient. Therefore, the relative profit of decreasing the heat loss coefficient by a certain technique esti- mated by laboratory measurements is a slight underestimation of what may be possible for real collectors.

Also a high temperature gradient over the absorber surface as for the flat plate case in Fig. 16 introduces an uncertainty in the heat loss calculation. Since the heat loss coefficient is temperature dependent, the calculation of lJ from a mean temperature for the whole absorber surface leads to an underestimation of the heat loss coefficient. The temperature gradient over the absorber surface is larger for the cases with flat plate collectors and V-trough collectors with highly conductive reflectors compared to the V-trough collectors with low-conducting reflec- tors. Therefore the difference in heat losses between the two former cases and the last is larger than predicted by the heat loss calculation based on an absorber mean temperature in this study. The difference is however small. Earlier hot box measurements on the heat losses from flat plate collector models by Hellstrom et al. (1989) have shown that the heat losses from the model where the absorber surface was heated with constant power all over the surface were about 2.5% larger than the case where the absorber was held at a constant temperature.

It should also be noted that the absorber mean temperature defined in our experiments is the absorber plate mean temperature, while the heat loss coefficients for solar collectors often are referring to the temperature difference between the fluid mean temperature in the col- lector and the ambient temperature. Since the plate temperature in a real collector is larger than the fluid temperature and the heat loss coefficient is temperature dependent, care has to be taken while comparing heat loss coeffi- cients measured by the hot box technique with heat loss coefficients derived from collector test procedures.

A more dominant difference between experi- mental and real heat loss coefficients is the effect of absorbed solar radiation in the reflectors in real collectors. The absorbed radiation will raise the reflector temperature and thereby affect the heat loss coefficient by changed radiation and convection modes inside the reflector cavity (Rabl, 1985). Field measurements on a real CPC-collector (Ronnelid et al., 1996) have

Experimental investigation of heat losses from low-concentrating non-imaging concentrators 105

shown more than 10% lower U,-value for the CPC-collector than predicted by hot box meas- urements. Therefore the heat loss coefficients derived from indoor experiments and eqn (12) should be seen as the higher limitations of the real heat loss coefficient. In principle the effect of absorbed solar radiation in the reflectors on the heat loss coefficient can be studied by the hot box technique if the reflectors are heated by e.g. a heating foil glued on the back side of the reflectors. This is planned to be done in a future project.

If the reflectors are low-emitting in the infra- red, this absorbed radiation will be kept in the reflector and raise the reflector temperature at thermal equilibrium. However, if the reflectors are high-emitting in the infrared, a large portion of the absorbed solar radiation will be emitted to the cover because of the high view factor between the reflector and cover compared with the view factor between the reflector and absorber. Since one explanation of the high heat losses in the case of high-emitting reflectors seems to be the large temperature difference between the absorber and the reflectors, we can assume that the difference in heat losses if low-e or high-e reflectors are used is increased by the impact of absorption of solar radiation. The measured difference in heat losses from collectors with the two reflector types made with the hot box technique should therefore be seen as a lower bound of the impact of reflector emittance on the heat losses.

Differences in heat loss coefficients for labora- tory measurements and real collectors also arise from the fact that the heat flux direction is different in the two cases (Rockendorf et al., 1993). However, the relative difference in heat losses from the hot box measurements for different configurations when the same basic geometry is used tells us how the overall heat losses are affected by different material proper- ties in the collector. Therefore the relative change in heat losses (in percent) for the meas- urements when different materials are used is assumed to be approximately valid for outdoor collector performance.

5. PRACTICAL MATERIAL

CONSIDERATIONS

5.1. Rejector emittance In Section 3.3. we have seen that the IR

emittance of the reflectors had an impact on the overall heat losses in collectors with internal

reflectors, where a low-emitting reflector results in lower heat losses. An untreated metallic reflector surface, like aluminium with an IR-spectrum shown in Fig. 17(a) or silver, has a high reflectance and thus a low emittance in the infrared region. An untreated reflector surface is however not desirable to be used in solar collectors, since moisture and pollution will deteriorate the reflectance as time goes on. It is therefore preferable to cover the reflector surface with a protective layer which is transparent enough to keep a high reflectance in the solar spectrum and strong enough to protect the reflector from deterioration by impact from the environment.

Aluminium reflectors can be anodised to create a relatively thick and strong aluminium oxide layer as protective coating. Although the reflectance in the solar spectrum is almost unchanged by this layer, the reflectance is drasti- cally reduced in the infrared because of the absorption of radiation in the Al,O,-layer in the region lo-30 pm, which is shown in Fig. 17(b). This leads to a high emittance in the temperature region around 0-300°C which is the working temperature for solar thermal appli- cations. The reflector can also be protected by adding an outer surface of glass or plastics and thus creating a second surface reflector. Most of the used coatings have, like the acrylic- covered reflector film in Fig. 17(c), strong absorption of radiation in the infrared, which thus give the reflector a high emittance in the IR-range. However, if we instead use a plastic coating like polyethene in Fig. 17(d), the build-up of the molecules with only carbon and hydrogen in the chemical structure leads to much less absorption in IR, with only small absorption in the region 3-6 pm. This absorp- tion occurs at a wavelength which is too short to affect the emittance for thermal radiation in the region around 100°C and thus this coating can be used to create a second surface reflector with low emittance in the infrared region.

The low-emitting reflector laminate used in the reported measurements has a coating of a polyethene lacquer of a few micrometres. This reflector foil is commercially available for about $2 rnb2 (Eriksson, 1995). A drawback with this material is however the poor heat resistance of the lacquer, which gets soft at temperatures above 100°C. The reflectors can thus be dam- aged if the collectors reach stagnation temper- atures. Also the polyester back side of the aluminium laminate can cause problems as it

106 M. Riinnelid and B. Karlsson

10 20 30 40 50 Wavelength (pm)

a

8 098

ti 0,6

go,4

do,2

0 10 20 30 4’0 5’0 Wavelength ( pm)

C

Wavelength ( p m) b

0 - 1 I I I I I I I 0 10 20 30 40 50

Wavelength (CL m) d

Fig. 17. Reflectance spectrum in the infrared for different commercially available reflector materials: (a) pure aluminium; (b) anodised aluminium; (c) 3M Scotchcall 5400 foil covered with acrylic; (d) aluminium

foil with polyethene cover.

starts to shrink at 150-160°C. However, if the reflector is not exposed to external tensions, the reflector should not be damaged for temper- atures below approximately 140°C. Much care must therefore be taken when mounting such reflectors in collectors, such as introducing an airgap between the reflector and the absorber to prevent thermal damage of the reflectors during stagnation.

5.2. Transparent insulation materials From an economic point of view, a convection

barrier near the absorber reduces the material cost since less transparent insulation material is needed. At the same time a glazing near the absorber leads to a decreased optical efficiency for the collector since this results in larger reflection losses caused by an increased angle of incidence than a glazing on top of the reflectors (Rabl, 1976). A transparent insulation on top of the reflectors is also probably easier to install. Taking all this into account, transparent insula- tion near the glazing in CPC-collectors with flat absorbers is probably preferable.

The introduction of transparent insulation can lower the heat losses from collectors with internal reflectors substantially. FEP-Teflon film seems to be a good choice because of its high

thermal stability and high transmittivity for solar radiation. The price is also reasonably low, about $8 m-‘. The use of Teflon film in ordinary flat plate collectors is standard in many countries in order to get a high temperature collector with good performance at working temperatures around 70-90°C. Some problems are however coupled with the use of Teflon films. Inappropriate installation or tension can cause tears which grow with time and drastically reduce the performance of the collector (Wennerholm, 1994). However, tensioning the film is necessary, since the film may otherwise adhere to the cover or the absorber of the collector. If the Teflon film sticks to a selective absorber, the drawback is double, since the collector in practice turns into a single-glazed collector with high heat losses. The selectivity of the absorber is also destroyed since the emittance of Teflon is E = 0.53.

In a CPC-collector, the Teflon can be put into the collector without too much tension, since the film can rest on the reflector tops. This also keeps the necessary distance between the film and the absorber to prevent adherence of the Teflon to the absorber. Much care must however be taken while manufacturing the reflectors, so the upper reflector edges are

Experimental investigation of heat losses from low-concentrating non-imaging concentrators 107

not sharp. For minimising the risk of break- ing the film, a film thickness of 25.4 pm is recommended.

5.3. Rejector conductivity

As shown in Section 3.4, thick reflectors in collectors will increase the heat losses. However, if a transparent insulation between the reflectors and the cover is used, the effect of the increased reflector conductivity is much smaller and this concept may be optimal, depending on perfor- mance and manufacturing costs. While thin reflectors demand a hard foam to get the proper shape, thick and self-supporting reflectors can be easier and cheaper to manufacture. The material cost may also be smaller for thick reflectors, since the air space between the reflec- tors between two absorbers does not need to be insulated.

6. APPLICATION OF RESULTS TO OTHER CONCENTRATOR GEOMETRIES

This study has concerned only one type of concentrator geometry, which is relevant for low-concentrating CPCs with flat one-sided absorbers. This geometry was chosen because of its applicability for use in the collectors built on the Long Ground Based (LGB) concept, see Rdnnelid et al. (1996). However, for many ther- mal applications, other concentrator geometries are interesting, e.g. concentrators with tubular absorbers or fin-like absorbers which are illumi- nated on both sides, because these reduce back losses and material requirement.

Although the geometries for different concen- trators can differ substantially from each other, we can assume that many of the thermal effects described in this article will also appear if other geometries are studied. However, if more precise results are required for other geometries, new measurements or calculations have to be made.

The use of transparent insulation between the reflectors and the cover will reduce the heat losses in all concentrating configurations since an additional thermal resistance for the heat flow between the absorber and cover is intro- duced. We can therefore assume that the effect of transparent insulation in other concentrator geometries will be similar to that reported.

We expect that the reflector emittance also has an effect on the overall heat losses in other geometries since the use of high-emitting reflec- tors implies a reduced reflector temperature, independent of the absorber geometry. In addi- tion, it has been shown that the effect of the

reflector emittance on the heat losses is a com- bined radiation-convection effect, and the con- vection heat transfer is of course dependent on the geometry of the reflector cavity and on the absorber shape. Therefore the result from this study is not directly convertible to other concen- trator geometries.

It can be noted that Eames and Norton (1993b) have made numerical studies of the heat losses in low-concentrating CPCs with tubular absorbers. Their studies showed that the effect of including long-wave radiation exchange in the calculation has a minor effect on the over- all results.

The heat transfer from absorber to the reflec- tors is dominated by convection. The impact of the reflector thickness on the heat losses is partly independent of the gap between absorber and reflector. Therefore, even if we use concen- trator geometries with little or no contact between absorber and reflector, it is assumed that thick reflectors will increase the temper- ature near the glazing and thus increase the heat losses from the absorber. However, even if we expect the general trend of increased heat losses for increased reflector thickness for most concentrator geometries, this effect is to a large extent a convection dependent process. Each concentrator geometry therefore has to be studied individually to define the size of this effect more precisely.

Finally, it has been shown that small air gaps <2 cm between the reflectors and the cover have a small impact on the overall heat losses from the collector. We do not see any reason why this result should not be valid also for other geometries.

7. CONCLUSIONS

The measured (indoor) heat losses are different from the real (outdoor) ones because of a number of factors. Differences in back losses and front heat transfer coefficients between the laboratory equipment and a real collector make the measured values smaller than would be expected in a real collector. Differences in the absorber temperature profile are another uncer- tainty in converting the measured results to real collectors. However, the relative changes in the heat losses for different materials and geometries in the collector are barely affected, and the trends measured with the laboratory equipment should also be valid for real collectors.

Measurements were mainly performed using a V-trough geometry for the reflectors in the

108 M. Rijnnelid and B. Karlsson

hot box model. However, the difference in the reflector shape used and a real CPC-reflector shape is very small, and the results should therefore also be valid for CPC-collectors. The measurements were restricted to one concen- tration and one tilt angle for the collector. A change in concentration will substantially change the heat losses since the absorber area is inversely proportional to the concentration. The effect of collector tilt should be smaller. The effect of inclination of V-troughs on the average heat transfer rate has been reported by Meyer et aE. (1982) to be at most 5%. Another restriction of the measurements is that measure- ments were performed with the reflector troughs aligned only in an east-west orientation. Recent studies by Collares-Pereira (1994) have shown that the heat losses in CPC-collectors change when the orientation changes from an east-west to a north-south orientation.

Based on the measurements on a C = 1.56X concentrator geometry with a flat, selective absorber aligned east-west and with the collec- tor tilted 45”, and by use of eqn (12) for convert- ing the measured values to outdoor conditions, the following conclusions can be made.

1. Small air gaps up to 2 cm between the reflectors and cover do not change the heat losses noticeably. For large temperature differ- ences >7O”C between the absorber and cover the heat losses may increase for collectors with air gaps between reflectors and cover due to increased air circulation between the reflector troughs.

2. Introduction of transparent insulation into the collector reduces the heat losses significantly. Introduction of a Teflon film between the reflec- tors and the cover causes a heat loss reduction of the order of 20%, or 0.6-0.7 W me2 K-‘, compared to a single-glazed collector with internal reflectors. If an IR-opaque transparent film or sheet is used, the heat losses can be reduced by a few percent further. Placing the transparent insulation near the absorber gives better heat loss suppression than placing the insulation on the reflector tops. The benefit of placing the transparent insulation near the absorber is however doubtful because of decreased optical efficiency caused by increased reflection losses of the incident solar radiation.

3. The reflector emittance has an impact on the heat losses from collectors with internal reflectors. If selective absorbers are used, the use of reflectors with high emittance in the collector can cause a heat loss increase of the order up

to 0.2Wm-‘K-l, compared to when low- emitting reflectors are used. If the absorber is non-selective, the effect of the reflector emittance on the heat losses is reduced. This increase in heat losses for highly emitting reflectors is prob- ably not caused by radiation alone, but has to be explained by a coupling of radiation and convection effects inside the collector cavity.

4. Use of reflectors with high conductivity increases the heat losses. Introduction of an air gap between the reflector and the absorber does not reduce the heat losses significantly. However, an air gap between the absorber and the reflector can be desirable to protect the reflector from damage if the solar collector comes into stagnation, resulting in a high absorber temperature. The increase in heat losses is in the order of 0.2 W m-’ K-’ if a 0.5 mm thick aluminium reflector is used as opposed to a 0.009 mm aluminium reflector for a collector equipped with a Teflon film as transparent insulation. If the collector is single glazed, the difference in heat losses between using the two reflectors should be in the order of 0.5 W mm2 K-‘.

The introduction of transparent insulation and the use of thick reflectors instead of thin will probably affect the heat losses in a similar way in CPC-type concentrators of other con- figurations than the one investigated here. The impact of the reflector emittance on the heat losses in other configurations is however not obvious and further studies have to be carried out in order to quantify the effect.

Acknowledgements-This work has been financed by grants from the Swedish Council for Building Research, Vattenfall Utveckling AB, the research board at the University College Fahm Borlange and the Industrial Liaison Office at Uppsala University. Mats Ronnelid wants to thank Professor Manuel Collares-Pereira, Dr Lars Broman and Dr Heimo Zinko for fruitful discussions during the project.

NOMENCLATURE A area (m’) C concentration ratio d distance (m)

h Isb,cavity heat transfer coefficient from absorber to cover, measured in laboratory (W mm2 K-t)

h lab.w heat transfer coefficient from cover to ambient, measured in laboratory (W me2 K-i)

h rCB,,favity heat transfer coefficient from absorber to cover, measured in outdoor climate (W m-* K-‘)

h rcs,.w heat transfer coefficient from’ cover to ambient, measured in outdoor climate (W rn-’ K-‘)

h, heat transfer coefficient from cover to ambient (Wm ) -2K-I

P power (W) R electric resistance (Q), heat transfer resistance

(m*K W-i)

Experimental investigation of heat losses from low-concentrating non-imaging concentrators 109

R ,ab,cavity heat transfer resistance between absorber and cover, measured in laboratory (m’ K W- ‘)

R ,ab,w heat transfer resistance between cover and ambi- ent, measured in laboratory (m’ K W-‘)

T temperature (“C) T. ambient temperature (“C)

xba absorber temperature (“C) AT temperature difference (“C)

U collector heat loss coefficient (W m-* K-‘) Ulab collector heat loss coefficient, measured in labora-

tory (W mm* K-‘) u ,ab.bacl collector back heat loss coefficient, measured in

laboratory (W mm2 K-’ 1 u lab.front collector front heat loss coefficient, measured in

laboratory (W m-‘K-’ ) V _, collector heat loss coefficient, measured in real

climate (W me2 K-’ ) CJ rcai,bsck collector back loss coefficient, measured in real

climate (W rn-’ Km’) V voltage (V)

Greek letters E emittance

E,~ effective emittance 5 transmittance

~~~~ solar transmittance zIR transmittance for infrared radiation

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