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THE USE OF CORRUGATED BOOSTER REFLECTORS FOR SOLAR COLLECTOR FIELDS
Pergamon
PII:
Solar Energy Vol. 65, No. 6, pp. 343–351, 1999 1999 Elsevier Science Ltd S 0 0 3 8 – 0 9 2 X ( 9 9 ) 0 0 0 0 9 – 2 All rights reserved. Printed in Great Britain 0038-092X / 99 / $ - see front matter
www.elsevier.com / locate / solener
THE USE OF CORRUGATED BOOSTER REFLECTORS FOR SOLAR COLLECTOR FIELDS ,† ¨ ¨ MATS RONNELID* and BJORN KARLSSON**
¨ *Solar Energy Research Center, EKOS, Dalarna University College, S-781 88 Borlange, Sweden ¨ ¨ **Vattenfall Utveckling AB, Alvkarleby Laboratory, S-814 26 Alvkarleby, Sweden Received 11 December 1997; accepted 14 January 1999 Communicated by J. GORDON
Abstract—The use of booster reflectors in front of solar collectors is an established technique for increasing the irradiation onto solar collectors. By using corrugated instead of flat booster reflectors it is possible to increase the annual irradiation onto the collector plane, thereby maximising the annual output from the collector–reflector arrangement. The paper includes a description of a ray tracing program which calculates the annual optical performance of a collector–booster reflector system with different V-corrugated reflectors. Calculations based on Swedish solar radiation data show that the use of a booster reflector with varying V-corrugations along the reflector, instead of a flat booster reflector, can increase the annual reflected direct radiation on to the collector by 10%. This is estimated to result in a 3% increase in the annual collector output. The ray-tracing calculations are compared with measurements of the reflection characteristics of single V-shaped reflector arrangements. 1999 Elsevier Science Ltd. All rights reserved.
1. INTRODUCTION
Construction of large solar collector fields is an established way of generating heat for district heating and seasonal storage. In these fields, the collectors are placed in rows behind one other. The collector rows must be far enough apart to avoid one row shading the next one. Therefore, a fraction of the radiation falling on the area covered by the collector field will hit the ground between the rows. At high latitudes, as in Sweden (latitude 558N–688N), the annual mean solar altitude angle will be fairly low. Thus the ground area covered by the collector field will be 2–2.5 times the area of the solar collector apertures. This means that a large percentage of the solar radiation that falls on the site is received by the ground between the rows of collectors, thus reducing the annual field efficiency based on site area to half, or less than half, of the efficiency based on the collector aperture area. One method of increasing the output from solar collector fields is to use booster reflectors between the collector rows. Properly installed booster reflectors will reflect a large portion of the radiation that normally falls on the ground between the collector rows onto the collector aperture, see Fig. 1a. The possible benefit of using †
Author to whom correspondence should be addressed. Tel.: 146-23-778712; fax: 146-23-778701; e-mail: [email protected]
booster reflectors has been pointed out by several authors, e.g. Tabor (1966); Seitel (1975); Grassie and Sheridan (1977); Larson (1980) and Faiman and Zemel (1988). For latitude 608N, an annual performance increase of . 30% has been reported by using flat booster reflectors in front of solar collectors (Perers and Karlsson, 1993). Recent studies have shown that the use of corrugated booster reflectors can increase the annual output from the solar collectors compared
Fig. 1. Booster reflectors for solar collectors. Trajectory of meridian rays for different reflector surfaces; (a) flat reflectors. (b) corrugated reflectors. The tilt angles of the collector and reflector in (a) are typical for Swedish conditions. 343
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¨ M. Ronnelid and B. Karlsson
to the case with flat booster reflectors (Perers et ¨ al., 1994; Ronnelid et al., 1994). Meridian rays (i.e. radiation incident from the south on east– west aligned collector rows) reflected in the booster reflector will be directed towards the collector base if the reflector has a proper linear corrugation perpendicular to the collector as in Fig. 1b. By using corrugated instead of flat booster reflectors it is therefore possible to direct some of the radiation that would otherwise have been reflected over the collector on to the collector plane. It is possible to use projection angles to analyse the performance of a flat symmetrical booster reflector in front of a solar collector. For a southfaced solar collector equipped with a flat booster reflector only the profile angle (Duffie and Beckman, 1991) or the east–west vertical angle (Hollands, 1971) needs to be known to calculate the reflection of the direct radiation onto the collector plane. This is possible since the collector–reflector system is symmetrical in the east–west direction, and therefore only the radiation component from the south contributes to the irradiation on the collector plane. If the booster reflector has a non-flat surface structure, which is the case with the V-corrugated reflector, the calculation of the reflected radiation is more complicated. The calculation cannot be reduced to a two-dimensional problem by the use of profile angles since the reflector normals are directed out of the meridian plane. Radiation incident from the south will therefore be reflected out from the meridian plane, as illustrated in Fig. 1b. For high corrugation angles the radiation may also be multiply reflected before it leaves the reflector. Therefore each incident ray has to be traced individually through the system by vector calculations to determine if it reaches the collector aperture. 2. RAY TRACING PROGRAM
A ray-tracing program has been developed to calculate the optical performance of collectors with corrugated booster reflectors. The collector rows have a tilt angle ac 5 458 towards the horizon and are assumed to be infinitely long in the east–west direction. The linear corrugated structure of the reflectors is assumed to be symmetrically V-corrugated, with a corrugation angle b, defined in Fig. 2. Other parameters are the reflector tilt (ar ), the relative reflector width (LR ) and the specular reflectance ( r ). The collector width is assumed to be one length unit.
Fig. 2. Corrugation angle for the reflectors.
The reflectance is assumed to be constant, independent of angle of incidence and polarisation. These simplifications will have a minor influence on the results since the reflectance of aluminium, which is the most common reflector material, is almost constant except for very large angles of incidence. The incidence angle dependence of the collector is however more pronounced. Therefore the radiation incident onto the collector plane is weighted by an incident angle dependence function of the optical efficiency of the collector (given by Souka and Safwat, 1966):
S
1 K(u ) 5 1 2 b 0 ]] 2 1 cos(u )
D
(1)
where u is the angle of incidence on the collector plane and b o is the incidence angle modifier coefficient which is assumed to be a positive number. For large u, Eq. (1) becomes negative. To avoid this
S
D
1 K(u ) 5 0 when b 0 ]] 2 1 . 1 . cos(u )
(2)
End effects caused by finite collector or reflector length are neglected by assuming the collector (and reflector) to be infinitely long. This causes an error in the calculation of the irradiation reflected towards the collector. In many applications, however, the collectors are installed in long rows, where the length of the collector row is much larger than the collector width. If the collector rows are long enough, typically$10 times the collector width, the error caused by assuming infinite collector lengths can be kept within a few percent (Perers and Karlsson, 1993). The angle of incidence of the solar radiation is defined by the two angles, us and ue , which are the projected incidence angles onto the vertical planes extending from north to south and from east to west respectively, see Fig. 3. These angles are measured relative to the zenith direction. For each angle of incidence, 200 rays were traced through the collector–reflector arrangement. Calculations were performed for 2400 different angles of incidence in order to get a clear picture of the
The use of corrugated booster reflectors for solar collector fields
Fig. 3. Projected incidence angles for solar radiation.
acceptance function over the entire angular interval of interest. The width of the corrugations ( y o in Fig. 2) can also be varied. A very small y o , typically less than 1 / 1000 of the reflector length, is assumed to minimise the edge effects of the corrugated reflectors. No major changes in the acceptance behaviour will occur if the width of the corrugations is varied. Calculations for a specific collector–reflector geometry with an optical performance described by r and b 0 will give a two-dimensional acceptance function F(us , ue ) for the complete collector– reflector system. For calculating the long-term performance of this system, the annual sky distribution of the solar radiation also has to be known. Therefore the calculated acceptance function for radiation from all parts of the sky has to be compared with real irradiation data in order to calculate the amount of direct irradiation that hits the collector plane annually. For these calculations, solar radiation data from Stockholm (latitude 59.48N) 1986 was used. It was originally given in hourly averages, but was later processed with the TRNSYS solar radiation processor (TRNSYS, 1992) in order to generate 6 minute data values and a more homogeneous distribution of direct solar radiation over different parts of the sky. For each generated value of direct radiation, the mean projection angles us and ue during the period were calculated and summarised into a matrix of us and ue . The summarised matrix for irradiation data for one year was multiplied with the matrix describing the acceptance function. This gives a value which represents the annual useful irradiation from direct radiation that reaches a unit-area of the collector aperture. The word ‘useful’ is used to emphasise that the incidence angle performance of the collector has already been taken into account by the use of Eqns (1) and (2). The useful irradiation that
345
reaches the collector is therefore less than the total irradiation that reaches the collector since no optical losses, due to non-normal incidence of the radiation, are taken into account in the latter case. Although both the direct and diffuse radiation will contribute to the irradiation on the collectors, only the direct component was used in the calculations. Calculations show that more than 60% of the total annual irradiation on a 458 tilted, southfacing collector in mid-Sweden during 1983– 1991 was direct radiation. Since thermal collectors preferably work during clear weather conditions, the amount of direct radiation during collector operation is about 75% of the total irradiation on the collector (Perers, 1998). Furthermore, if we assume that the diffuse radiation is isotropic, the introduction of corrugations in the reflector surface will not change the irradiation distribution from diffuse radiation on the collector plane. The only difference is a slightly reduced mean intensity in the collector plane due to multiple reflection losses when large corrugation angles are used. The error introduced by only taking the direct irradiation into account in the calculations is therefore small, and is neglected in this study. 3. RESULTS
Fig. 4 shows the annual increase of useful direct irradiation onto the collector plane for collectors equipped with corrugated booster reflectors with specular reflectance. In this example
Fig. 4. Annual increase of useful direct irradiation onto a collector when it is equipped with a corrugated booster reflector. Geometry assumed is: ac 5458, ar 5208, LR 52.0. Optical parameters are b o 50.2 and r 50.60–0.90. Radiation data from Stockholm, 1986. Annual irradiation on the collector without a booster reflector is calculated to 977 kWhm 22 year 21 and the annual output is around 300 kWhm 22 .
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¨ M. Ronnelid and B. Karlsson
the following inputs are assumed: ac 5458, ar 5 208, LR 52.0, b o 50.2 and r 50.60–0.90. The described geometry of the collector–reflector arrangement is what has been predicted to be near optimum for Swedish conditions at latitude 608N (Perers, 1995). As discussed later, the shape of the curves in Fig. 4 is due to the angular distribution of the direct solar radiation, and therefore the booster efficiency will be strongly dependent on reflector geometry. It can be seen in Fig. 4 that the increase in annual useful direct irradiation on the collector is 8% larger if a corrugated booster reflector with small corrugation angles ( b ¯108) is used, instead of a flat booster reflector ( b 508). In Fig. 5 the angular distribution of the annual direct radiation for Stockholm is plotted in a diagram with the projection angles us and ue as coordinates. In the figure it is shown that most of the irradiation comes from a rather narrow band located at 308,us ,458 and 2608,ue ,608. This band represents the summer irradiation with positive values for ue in the mornings and negative values for ue in the evenings. Fig. 6 shows the ratio between the annual increase of useful direct irradiation on the collector when a corrugated booster reflector with b 5 108 is used, and the annual increase when a flat reflector with the same length and tilt is used. The shaded area shows from which part of the sky the corrugated reflector works better than the flat reflector. The improvement achieved by using corrugated reflectors is pronounced for large east– west components of the solar radiation where the corrugated reflector increases the irradiation onto the collector by .10% compared to a flat reflector. If Fig. 6 is compared to Fig. 5 it can be seen
Fig. 5. Angular distribution of the annual direct irradiation on a horizontal surface for Stockholm (latitude 59.48N). Radiation data from 1986.
Fig. 6. Ratio between the annual increase of useful direct irradiation on the collector when a corrugated booster reflector with b 5108 is used, and the annual increase when a flat reflector with the same length and tilt is used. r 50.8. Geometry given in the caption to Fig. 4.
that the incident angles for which this happens correspond to morning and afternoon solar radiation during the summer period. If a reflector with corrugation angleb 5308 is used instead, this reflector will work better than a flat reflector only during a few hours around noon when uue u is small and when us ,558, as illustrated in Fig. 7. During summer the corrugated reflector will reflect less radiation towards the collector than a flat reflector when uue u.208. This large
Fig. 7. Ratio between the annual increase of useful direct irradiation on the collector when a corrugated booster reflector with b 5308 is used, and the annual increase when a flat reflector with the same length and tilt is used. r 50.8. Geometry given in the caption to Fig. 4.
The use of corrugated booster reflectors for solar collector fields
Fig. 8. Ratio between the annual increase of useful direct irradiation on the collector when a corrugated booster reflector with b 5608 is used, and the annual increase when a flat reflector with the same length and tilt is used. r 50.8. Geometry given in the caption to Fig. 4.
angular interval for which a corrugated reflector performs worse than a flat reflector explains the minimum at b 5308 in Fig. 4. When the corruga-
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tion angle b 5608, the corrugated reflector will not perform as well as the flat reflector during the hours around noon but will be better than the flat reflector during summer morning and afternoon hours (308,uue u ,608). This is illustrated in Fig. 8. On the whole, a reflector withb 5608 will be slightly better at reflecting radiation onto the collector than a reflector with b 5308. This explains the local maximum at b ¯608 in Fig. 4. The local maximum around b ¯608 suggests that it may be possible to use standard trapezoidal aluminium sheets for booster reflector applications, since these sheets are composed of reflector surfaces that are either flat or have a fairly large corrugation angle, as illustrated in Fig. 9. A solar collector field with such booster reflectors is shown in Fig. 10, and was installed at the hospital ¨ in Osthammar near Uppsala, Sweden during the summer 1994. The total collector area in this installation is 150 m 2 . Evaluation of this field shows that the output is similar to the expected output from a solar collector field with flat booster ¨ reflectors (Broms and Henfridsson, 1994). For this installation a flat reflector ( b 508) or preferably a slightly corrugated reflector ( b ¯108) would have been better, as indicated in Fig. 4.
Fig. 9. Example of a commercially available trapezoidal aluminium sheet (Gazell AB) used as booster reflector in the solar ¨ collector installation at the hospital in Osthammar, Sweden and in a number of systems in Sweden and Denmark.
¨ Fig. 10. The solar collector field in Osthammar, Sweden, with three rows of collectors and trapezoidal corrugated booster reflectors between the collector rows.
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¨ M. Ronnelid and B. Karlsson
However, a trapezoidal reflector has a much higher mechanical strength which makes the reflector much easier and cheaper to install compared to flat or slightly corrugated reflectors that are mechanically much weaker. Therefore a corru¨ gated reflector of the type used in Osthammar seems to be optimal when both optical properties and cost are taken into account. The decreased annual performance for booster reflectors with large corrugation angles as depicted in Fig. 4, depends to a large extent on the increased number of reflections for radiation reflected in these reflectors. Fig. 11 shows the average number of reflections vs. b for reflected direct radiation which reaches the collector. Due to multiple reflection losses the performance of the reflectors with large-angle corrugations decreases more than linearly with its reflectivity, as illustrated in Fig. 4, and a reduced reflectivity due to dirt and dust will therefore be more serious for larger corrugation angles. Fig. 12 shows the annual incident useful irradiation on the collector from direct radiation reflected in different parts of the reflector. It is seen that for the lower part of the reflector, when LR is small, a flat reflecting surface is preferred for maximising the annual irradiation onto the collector, while a reflecting surface with small corrugations is preferred for the upper part of the reflector. As an example we assume the lower 37.5% of the reflector to be flat, and the upper 62.5% to be corrugated with b 5108. With this arrangement the annual reflected irradiation from direct radiation onto the collector will be 171 kWhm 22 compared to 155 kWhm 22 if only flat reflector surfaces are used. This is an increase of
Fig. 12. Annual incident useful irradiation on the collector from direct radiation reflected in different parts of the reflector. The reflector width is measured from the edge of the reflector near the collector base (LR 50) to the upper part of the reflector (LR 52.0). The width of the collector51.0. Radiation data from Stockholm 1986. r 50.8.
16 kWhm 22 or 10% of the reflected direct radiation. It should be pointed out that Fig. 12 shows the incident irradiation on the collector from reflected direct radiation, while Fig. 4 shows the increase of irradiation onto the collector when booster reflectors are used, compared with a case without booster reflectors. When calculating the latter, one has to take into account that some direct radiation from low solar altitude angles will not reach the collector since it is shaded by the booster reflector. If all the energy from different parts of the reflector for a certain corrugation angle in Fig. 12 is added together, a larger value than indicated in Fig. 4 is obtained because shading of the collector by the booster reflector is included in Fig. 4. 4. VALIDATION OF RAY TRACING CALCULATIONS
Fig. 11. Mean number of reflections in the corrugated booster reflector for direct radiation incident on the collector plane. Geometry given in the caption to Fig. 4. Radiation data from Stockholm 1986.
The ray tracing calculations have been compared with measurements to validate the calculation procedure. The experimental set-up shown in Fig. 13 consisted of two reflector slats, each 5350 cm, which were formed to a V-shape, defined by the corrugation angle in Fig. 2. The reflector arrangement was tilted towards a screen representing the collector plane, and the image from the sun reflected by the V-shaped reflectors towards the screen was photographed. The shape and the intensity of the image was compared with calculations made with the ray tracing program.
The use of corrugated booster reflectors for solar collector fields
349
Fig. 13. Photograph of the image of the reflectors in the solar collector plane of direct solar radiation reflected in three different reflector arrangements, representing V-corrugations of 08, 198 and 108. July 3, solar time 2.15 p.m., latitude 60.68N.
Fig. 13 shows the reflected images in the collector plane from three different reflector arrangements, representing from the left, corrugation angles of 08, 198 and 108 respectively. Part of the reflectors are seen at the bottom of the photograph. The dark areas which divide the reflection images arise from marks on the reflectors which were made to allow calculation of the extension of the images. The image arising from the 198 corrugation in
the middle of Fig. 13 can be compared with the calculated image in Fig. 14. In Fig. 14, each dot represents one ray that has been reflected by the V-shaped reflectors. Both the measurement and the calculation are for a south-facing collector– reflector geometry where ac 5458, ar 5208, latitude560.68N, date5July 3 and solar time5 2.15 p.m. It should be noted that the middle image line from the 198 corrugation set-up in Fig. 14 and the corresponding line in Fig. 13 arise from multiple reflections in the V-shaped reflectors. The agreement between Fig. 13 and 14 as well as other geometries investigated validate the calculation procedure used in the ray tracing calculations. 5. DISCUSSION
Fig. 14. Calculated dispersion image from reflection in a 198 corrugation on the collector plane. Each dot represents one ray which has been randomly distributed onto the corrugation. The rays are incident from a direction corresponding to the sun position on July 3, solar time 2.15 p.m., latitude 60.68N. The collector plane is assumed to be directed south and reflector length51. Geometries used are b 5198, ac 5458 and ar 5208.
The result from the ray tracing calculations can be used for calculating the impact on collector performance by using corrugated reflectors. For the calculation we assume a collector tilted 458 to the south and defined by a zero loss efficiency described by F9 (ta )50.8, a heat loss coefficient at an operating temperature of 708C described by F9 UL 53.5 W m 22 K 21 and an incidence angle dependence described by Eqn (1) with b 0 50.2. Perers (1995) has shown that collectors of this type, mounted in rows in a collector field, will give an annual output of 300 kWhm 22 in a Stockholm climate without booster reflectors and approximately 425 kWhm 22 with flat booster reflectors with the geometry discussed in chapter 3. The calculations also show that the increase in annual collector output by using booster reflectors
¨ M. Ronnelid and B. Karlsson
350
can be said to be approximately the additional irradiation from the reflector multiplied by the optical efficiency F9 (ta ) of the collector (Perers, 1998). If the reflected direct irradiation on the collector is increased by 10% due to an optimally corrugated reflector, the annually incident radiation on the collector will be increased by 16 kWhm 22 compared with a collector and flat reflector. Taking the optical efficiency into account, it can be assumed that the annual collector output is increased by 13 kWhm 22 . This corresponds to a 3% increase in the annual collector output compared to if a flat reflector is used.
Dr. Bengt Perers for critical reading of the manuscript.
NOMENCLATURE
bo F9 UL F(us , ue ) F9 (ta ) LR
6. CONCLUSIONS
The annual amount of direct radiation on the collector plane can be increased by replacing flat booster reflectors by corrugated booster reflectors with the corrugations perpendicular to the collector. Based on Swedish radiation data, the calculations show that small corrugation angles around 108 are most favourable. This results in an annual reflected direct radiation on the collector which is approximately 8% greater than for a collector with a flat reflector with optimal geometry for Swedish conditions at latitude 608N. Booster reflectors with corrugation angles of b ¯608 work almost as well as flat reflectors if the specular reflectance is high. For low specular reflectance, multiple reflection in the booster reflectors with large corrugation angles considerably reduces the annual reflected irradiation incident on the collector aperture. The advantage of corrugated booster reflectors is greatest for the upper part of the booster reflector. An optimal combination with a flat reflector surface near the collector base and a corrugated reflector at the upper part of the booster reflector increases the effective reflectance by a factor of 1.10 for direct radiation. The annual increase of irradiation onto the collector plane when flat or corrugated reflectors are used is dependent on the distribution of available radiation across the sky. Thus the result is dependent on latitude, climate and geometry. The optimal corrugated booster reflector for increasing the irradiation on a solar collector therefore depends on the installation site. This study has been financed by the Swedish National Energy Administration, Swedish Council for Building Research and Vattenfall AB. The authors want to thank Ms. Anna Liberg for help with the measurements and Dr. Arne Roos and
K(u ) yo
ac ar b u ue
us
r DP
incident angle modifier coefficient collector heat loss coefficient including collector efficiency factor, 22 21 Wm K acceptance function for the reflector– collector system zero loss efficiency for direct radiation at normal incidence relative reflector width (collector width51 length unit) incident angle modifier for direct radiation relative corrugation width (collector width51 length unit) collector tilt angle, degrees reflector tilt angle, degrees corrugation angle (defined in Fig. 2), degrees angle of incidence, degrees projection angle for projection of sun position vector in a vertical plane directed east–west (west positive), degrees projection angle for projection of sun position vector in a vertical plane directed north–south (south positive), degrees specular reflectance annual increase of useful direct irradiation, kWhm 22 year 21
REFERENCES ¨ ¨ Broms G. and Henfridsson U. (1994). Utvardering av Sol¨ ¨ varmesystemet vid Osthammars Sjukhus ( Evaluation of the ¨ solar heating system at Osthammar hospital), Vattenfall ¨ Utveckling AB, Alvkarlebylaboratoriet, Sweden VU-V 94, In Swedish. Duffie J. A. and Beckman W. A. (1991). Solar Engineering of Thermal Processes, Vol. 2, Wiley Interscience, New York. Faiman D. and Zemel A. (1988) Low-profile solar water heaters: The mirror booster problem revisited. Solar Energy 40, 385–390. Grassie S. L. and Sheridan N. R. (1977) The use of planar reflectors for increasing the energy yield of flat plate collectors. Solar Energy 19, 663–668. Hollands K. G. T. (1971) A concentrator for thin film solar cells. Solar Energy 13, 149–163. Larson D. C. (1980) Optimization of flat plate collectors – flat mirror systems. Solar Energy 24, 203–207. Perers B. and Karlsson B. (1993) External reflectors for large collector arrays, simulation model and experimental results. Solar Energy 51, 327–337.
The use of corrugated booster reflectors for solar collector fields Perers B., Karlsson B. and Bergkvist M. (1994) Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations. Solar Energy 53, 215–226. Perers B. (1995). Optical modelling of solar collectors and booster reflectors under nonstationary conditions, Ph D Thesis, Department of Technology, Uppsala University, Sweden, ISBN 91-554-3496-7. Perers B. (1998). Personal communication. ¨ Ronnelid M., Perers B. and Karlsson B. 1994. Optical properties of nonimaging concentrators with corrugated reflectors. In Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XIII, Proc. SPIE,
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Wittwer V., Granquist C.G. and Lampert C.M. (Eds), 2255, pp. 595–602. Seitel S. C. (1975) Collector performance enhancement with flat reflectors. Solar Energy 17, 291–295. Souka A. F. and Safwat H. H. (1966) Optimum orientations for the double exposure flat-plate collector and its reflectors. Solar Energy 10, 170–174. Tabor H. (1966) Mirror boosters for solar collectors. Solar Energy 10, 111–118. TRNSYS 5.1 (1992). A Transient Simulation Program for Solar Energy Systems. Solar Energy Laboratory, University of Wisconsin.
PII:
Solar Energy Vol. 65, No. 6, pp. 343–351, 1999 1999 Elsevier Science Ltd S 0 0 3 8 – 0 9 2 X ( 9 9 ) 0 0 0 0 9 – 2 All rights reserved. Printed in Great Britain 0038-092X / 99 / $ - see front matter
www.elsevier.com / locate / solener
THE USE OF CORRUGATED BOOSTER REFLECTORS FOR SOLAR COLLECTOR FIELDS ,† ¨ ¨ MATS RONNELID* and BJORN KARLSSON**
¨ *Solar Energy Research Center, EKOS, Dalarna University College, S-781 88 Borlange, Sweden ¨ ¨ **Vattenfall Utveckling AB, Alvkarleby Laboratory, S-814 26 Alvkarleby, Sweden Received 11 December 1997; accepted 14 January 1999 Communicated by J. GORDON
Abstract—The use of booster reflectors in front of solar collectors is an established technique for increasing the irradiation onto solar collectors. By using corrugated instead of flat booster reflectors it is possible to increase the annual irradiation onto the collector plane, thereby maximising the annual output from the collector–reflector arrangement. The paper includes a description of a ray tracing program which calculates the annual optical performance of a collector–booster reflector system with different V-corrugated reflectors. Calculations based on Swedish solar radiation data show that the use of a booster reflector with varying V-corrugations along the reflector, instead of a flat booster reflector, can increase the annual reflected direct radiation on to the collector by 10%. This is estimated to result in a 3% increase in the annual collector output. The ray-tracing calculations are compared with measurements of the reflection characteristics of single V-shaped reflector arrangements. 1999 Elsevier Science Ltd. All rights reserved.
1. INTRODUCTION
Construction of large solar collector fields is an established way of generating heat for district heating and seasonal storage. In these fields, the collectors are placed in rows behind one other. The collector rows must be far enough apart to avoid one row shading the next one. Therefore, a fraction of the radiation falling on the area covered by the collector field will hit the ground between the rows. At high latitudes, as in Sweden (latitude 558N–688N), the annual mean solar altitude angle will be fairly low. Thus the ground area covered by the collector field will be 2–2.5 times the area of the solar collector apertures. This means that a large percentage of the solar radiation that falls on the site is received by the ground between the rows of collectors, thus reducing the annual field efficiency based on site area to half, or less than half, of the efficiency based on the collector aperture area. One method of increasing the output from solar collector fields is to use booster reflectors between the collector rows. Properly installed booster reflectors will reflect a large portion of the radiation that normally falls on the ground between the collector rows onto the collector aperture, see Fig. 1a. The possible benefit of using †
Author to whom correspondence should be addressed. Tel.: 146-23-778712; fax: 146-23-778701; e-mail: [email protected]
booster reflectors has been pointed out by several authors, e.g. Tabor (1966); Seitel (1975); Grassie and Sheridan (1977); Larson (1980) and Faiman and Zemel (1988). For latitude 608N, an annual performance increase of . 30% has been reported by using flat booster reflectors in front of solar collectors (Perers and Karlsson, 1993). Recent studies have shown that the use of corrugated booster reflectors can increase the annual output from the solar collectors compared
Fig. 1. Booster reflectors for solar collectors. Trajectory of meridian rays for different reflector surfaces; (a) flat reflectors. (b) corrugated reflectors. The tilt angles of the collector and reflector in (a) are typical for Swedish conditions. 343
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¨ M. Ronnelid and B. Karlsson
to the case with flat booster reflectors (Perers et ¨ al., 1994; Ronnelid et al., 1994). Meridian rays (i.e. radiation incident from the south on east– west aligned collector rows) reflected in the booster reflector will be directed towards the collector base if the reflector has a proper linear corrugation perpendicular to the collector as in Fig. 1b. By using corrugated instead of flat booster reflectors it is therefore possible to direct some of the radiation that would otherwise have been reflected over the collector on to the collector plane. It is possible to use projection angles to analyse the performance of a flat symmetrical booster reflector in front of a solar collector. For a southfaced solar collector equipped with a flat booster reflector only the profile angle (Duffie and Beckman, 1991) or the east–west vertical angle (Hollands, 1971) needs to be known to calculate the reflection of the direct radiation onto the collector plane. This is possible since the collector–reflector system is symmetrical in the east–west direction, and therefore only the radiation component from the south contributes to the irradiation on the collector plane. If the booster reflector has a non-flat surface structure, which is the case with the V-corrugated reflector, the calculation of the reflected radiation is more complicated. The calculation cannot be reduced to a two-dimensional problem by the use of profile angles since the reflector normals are directed out of the meridian plane. Radiation incident from the south will therefore be reflected out from the meridian plane, as illustrated in Fig. 1b. For high corrugation angles the radiation may also be multiply reflected before it leaves the reflector. Therefore each incident ray has to be traced individually through the system by vector calculations to determine if it reaches the collector aperture. 2. RAY TRACING PROGRAM
A ray-tracing program has been developed to calculate the optical performance of collectors with corrugated booster reflectors. The collector rows have a tilt angle ac 5 458 towards the horizon and are assumed to be infinitely long in the east–west direction. The linear corrugated structure of the reflectors is assumed to be symmetrically V-corrugated, with a corrugation angle b, defined in Fig. 2. Other parameters are the reflector tilt (ar ), the relative reflector width (LR ) and the specular reflectance ( r ). The collector width is assumed to be one length unit.
Fig. 2. Corrugation angle for the reflectors.
The reflectance is assumed to be constant, independent of angle of incidence and polarisation. These simplifications will have a minor influence on the results since the reflectance of aluminium, which is the most common reflector material, is almost constant except for very large angles of incidence. The incidence angle dependence of the collector is however more pronounced. Therefore the radiation incident onto the collector plane is weighted by an incident angle dependence function of the optical efficiency of the collector (given by Souka and Safwat, 1966):
S
1 K(u ) 5 1 2 b 0 ]] 2 1 cos(u )
D
(1)
where u is the angle of incidence on the collector plane and b o is the incidence angle modifier coefficient which is assumed to be a positive number. For large u, Eq. (1) becomes negative. To avoid this
S
D
1 K(u ) 5 0 when b 0 ]] 2 1 . 1 . cos(u )
(2)
End effects caused by finite collector or reflector length are neglected by assuming the collector (and reflector) to be infinitely long. This causes an error in the calculation of the irradiation reflected towards the collector. In many applications, however, the collectors are installed in long rows, where the length of the collector row is much larger than the collector width. If the collector rows are long enough, typically$10 times the collector width, the error caused by assuming infinite collector lengths can be kept within a few percent (Perers and Karlsson, 1993). The angle of incidence of the solar radiation is defined by the two angles, us and ue , which are the projected incidence angles onto the vertical planes extending from north to south and from east to west respectively, see Fig. 3. These angles are measured relative to the zenith direction. For each angle of incidence, 200 rays were traced through the collector–reflector arrangement. Calculations were performed for 2400 different angles of incidence in order to get a clear picture of the
The use of corrugated booster reflectors for solar collector fields
Fig. 3. Projected incidence angles for solar radiation.
acceptance function over the entire angular interval of interest. The width of the corrugations ( y o in Fig. 2) can also be varied. A very small y o , typically less than 1 / 1000 of the reflector length, is assumed to minimise the edge effects of the corrugated reflectors. No major changes in the acceptance behaviour will occur if the width of the corrugations is varied. Calculations for a specific collector–reflector geometry with an optical performance described by r and b 0 will give a two-dimensional acceptance function F(us , ue ) for the complete collector– reflector system. For calculating the long-term performance of this system, the annual sky distribution of the solar radiation also has to be known. Therefore the calculated acceptance function for radiation from all parts of the sky has to be compared with real irradiation data in order to calculate the amount of direct irradiation that hits the collector plane annually. For these calculations, solar radiation data from Stockholm (latitude 59.48N) 1986 was used. It was originally given in hourly averages, but was later processed with the TRNSYS solar radiation processor (TRNSYS, 1992) in order to generate 6 minute data values and a more homogeneous distribution of direct solar radiation over different parts of the sky. For each generated value of direct radiation, the mean projection angles us and ue during the period were calculated and summarised into a matrix of us and ue . The summarised matrix for irradiation data for one year was multiplied with the matrix describing the acceptance function. This gives a value which represents the annual useful irradiation from direct radiation that reaches a unit-area of the collector aperture. The word ‘useful’ is used to emphasise that the incidence angle performance of the collector has already been taken into account by the use of Eqns (1) and (2). The useful irradiation that
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reaches the collector is therefore less than the total irradiation that reaches the collector since no optical losses, due to non-normal incidence of the radiation, are taken into account in the latter case. Although both the direct and diffuse radiation will contribute to the irradiation on the collectors, only the direct component was used in the calculations. Calculations show that more than 60% of the total annual irradiation on a 458 tilted, southfacing collector in mid-Sweden during 1983– 1991 was direct radiation. Since thermal collectors preferably work during clear weather conditions, the amount of direct radiation during collector operation is about 75% of the total irradiation on the collector (Perers, 1998). Furthermore, if we assume that the diffuse radiation is isotropic, the introduction of corrugations in the reflector surface will not change the irradiation distribution from diffuse radiation on the collector plane. The only difference is a slightly reduced mean intensity in the collector plane due to multiple reflection losses when large corrugation angles are used. The error introduced by only taking the direct irradiation into account in the calculations is therefore small, and is neglected in this study. 3. RESULTS
Fig. 4 shows the annual increase of useful direct irradiation onto the collector plane for collectors equipped with corrugated booster reflectors with specular reflectance. In this example
Fig. 4. Annual increase of useful direct irradiation onto a collector when it is equipped with a corrugated booster reflector. Geometry assumed is: ac 5458, ar 5208, LR 52.0. Optical parameters are b o 50.2 and r 50.60–0.90. Radiation data from Stockholm, 1986. Annual irradiation on the collector without a booster reflector is calculated to 977 kWhm 22 year 21 and the annual output is around 300 kWhm 22 .
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¨ M. Ronnelid and B. Karlsson
the following inputs are assumed: ac 5458, ar 5 208, LR 52.0, b o 50.2 and r 50.60–0.90. The described geometry of the collector–reflector arrangement is what has been predicted to be near optimum for Swedish conditions at latitude 608N (Perers, 1995). As discussed later, the shape of the curves in Fig. 4 is due to the angular distribution of the direct solar radiation, and therefore the booster efficiency will be strongly dependent on reflector geometry. It can be seen in Fig. 4 that the increase in annual useful direct irradiation on the collector is 8% larger if a corrugated booster reflector with small corrugation angles ( b ¯108) is used, instead of a flat booster reflector ( b 508). In Fig. 5 the angular distribution of the annual direct radiation for Stockholm is plotted in a diagram with the projection angles us and ue as coordinates. In the figure it is shown that most of the irradiation comes from a rather narrow band located at 308,us ,458 and 2608,ue ,608. This band represents the summer irradiation with positive values for ue in the mornings and negative values for ue in the evenings. Fig. 6 shows the ratio between the annual increase of useful direct irradiation on the collector when a corrugated booster reflector with b 5 108 is used, and the annual increase when a flat reflector with the same length and tilt is used. The shaded area shows from which part of the sky the corrugated reflector works better than the flat reflector. The improvement achieved by using corrugated reflectors is pronounced for large east– west components of the solar radiation where the corrugated reflector increases the irradiation onto the collector by .10% compared to a flat reflector. If Fig. 6 is compared to Fig. 5 it can be seen
Fig. 5. Angular distribution of the annual direct irradiation on a horizontal surface for Stockholm (latitude 59.48N). Radiation data from 1986.
Fig. 6. Ratio between the annual increase of useful direct irradiation on the collector when a corrugated booster reflector with b 5108 is used, and the annual increase when a flat reflector with the same length and tilt is used. r 50.8. Geometry given in the caption to Fig. 4.
that the incident angles for which this happens correspond to morning and afternoon solar radiation during the summer period. If a reflector with corrugation angleb 5308 is used instead, this reflector will work better than a flat reflector only during a few hours around noon when uue u is small and when us ,558, as illustrated in Fig. 7. During summer the corrugated reflector will reflect less radiation towards the collector than a flat reflector when uue u.208. This large
Fig. 7. Ratio between the annual increase of useful direct irradiation on the collector when a corrugated booster reflector with b 5308 is used, and the annual increase when a flat reflector with the same length and tilt is used. r 50.8. Geometry given in the caption to Fig. 4.
The use of corrugated booster reflectors for solar collector fields
Fig. 8. Ratio between the annual increase of useful direct irradiation on the collector when a corrugated booster reflector with b 5608 is used, and the annual increase when a flat reflector with the same length and tilt is used. r 50.8. Geometry given in the caption to Fig. 4.
angular interval for which a corrugated reflector performs worse than a flat reflector explains the minimum at b 5308 in Fig. 4. When the corruga-
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tion angle b 5608, the corrugated reflector will not perform as well as the flat reflector during the hours around noon but will be better than the flat reflector during summer morning and afternoon hours (308,uue u ,608). This is illustrated in Fig. 8. On the whole, a reflector withb 5608 will be slightly better at reflecting radiation onto the collector than a reflector with b 5308. This explains the local maximum at b ¯608 in Fig. 4. The local maximum around b ¯608 suggests that it may be possible to use standard trapezoidal aluminium sheets for booster reflector applications, since these sheets are composed of reflector surfaces that are either flat or have a fairly large corrugation angle, as illustrated in Fig. 9. A solar collector field with such booster reflectors is shown in Fig. 10, and was installed at the hospital ¨ in Osthammar near Uppsala, Sweden during the summer 1994. The total collector area in this installation is 150 m 2 . Evaluation of this field shows that the output is similar to the expected output from a solar collector field with flat booster ¨ reflectors (Broms and Henfridsson, 1994). For this installation a flat reflector ( b 508) or preferably a slightly corrugated reflector ( b ¯108) would have been better, as indicated in Fig. 4.
Fig. 9. Example of a commercially available trapezoidal aluminium sheet (Gazell AB) used as booster reflector in the solar ¨ collector installation at the hospital in Osthammar, Sweden and in a number of systems in Sweden and Denmark.
¨ Fig. 10. The solar collector field in Osthammar, Sweden, with three rows of collectors and trapezoidal corrugated booster reflectors between the collector rows.
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¨ M. Ronnelid and B. Karlsson
However, a trapezoidal reflector has a much higher mechanical strength which makes the reflector much easier and cheaper to install compared to flat or slightly corrugated reflectors that are mechanically much weaker. Therefore a corru¨ gated reflector of the type used in Osthammar seems to be optimal when both optical properties and cost are taken into account. The decreased annual performance for booster reflectors with large corrugation angles as depicted in Fig. 4, depends to a large extent on the increased number of reflections for radiation reflected in these reflectors. Fig. 11 shows the average number of reflections vs. b for reflected direct radiation which reaches the collector. Due to multiple reflection losses the performance of the reflectors with large-angle corrugations decreases more than linearly with its reflectivity, as illustrated in Fig. 4, and a reduced reflectivity due to dirt and dust will therefore be more serious for larger corrugation angles. Fig. 12 shows the annual incident useful irradiation on the collector from direct radiation reflected in different parts of the reflector. It is seen that for the lower part of the reflector, when LR is small, a flat reflecting surface is preferred for maximising the annual irradiation onto the collector, while a reflecting surface with small corrugations is preferred for the upper part of the reflector. As an example we assume the lower 37.5% of the reflector to be flat, and the upper 62.5% to be corrugated with b 5108. With this arrangement the annual reflected irradiation from direct radiation onto the collector will be 171 kWhm 22 compared to 155 kWhm 22 if only flat reflector surfaces are used. This is an increase of
Fig. 12. Annual incident useful irradiation on the collector from direct radiation reflected in different parts of the reflector. The reflector width is measured from the edge of the reflector near the collector base (LR 50) to the upper part of the reflector (LR 52.0). The width of the collector51.0. Radiation data from Stockholm 1986. r 50.8.
16 kWhm 22 or 10% of the reflected direct radiation. It should be pointed out that Fig. 12 shows the incident irradiation on the collector from reflected direct radiation, while Fig. 4 shows the increase of irradiation onto the collector when booster reflectors are used, compared with a case without booster reflectors. When calculating the latter, one has to take into account that some direct radiation from low solar altitude angles will not reach the collector since it is shaded by the booster reflector. If all the energy from different parts of the reflector for a certain corrugation angle in Fig. 12 is added together, a larger value than indicated in Fig. 4 is obtained because shading of the collector by the booster reflector is included in Fig. 4. 4. VALIDATION OF RAY TRACING CALCULATIONS
Fig. 11. Mean number of reflections in the corrugated booster reflector for direct radiation incident on the collector plane. Geometry given in the caption to Fig. 4. Radiation data from Stockholm 1986.
The ray tracing calculations have been compared with measurements to validate the calculation procedure. The experimental set-up shown in Fig. 13 consisted of two reflector slats, each 5350 cm, which were formed to a V-shape, defined by the corrugation angle in Fig. 2. The reflector arrangement was tilted towards a screen representing the collector plane, and the image from the sun reflected by the V-shaped reflectors towards the screen was photographed. The shape and the intensity of the image was compared with calculations made with the ray tracing program.
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Fig. 13. Photograph of the image of the reflectors in the solar collector plane of direct solar radiation reflected in three different reflector arrangements, representing V-corrugations of 08, 198 and 108. July 3, solar time 2.15 p.m., latitude 60.68N.
Fig. 13 shows the reflected images in the collector plane from three different reflector arrangements, representing from the left, corrugation angles of 08, 198 and 108 respectively. Part of the reflectors are seen at the bottom of the photograph. The dark areas which divide the reflection images arise from marks on the reflectors which were made to allow calculation of the extension of the images. The image arising from the 198 corrugation in
the middle of Fig. 13 can be compared with the calculated image in Fig. 14. In Fig. 14, each dot represents one ray that has been reflected by the V-shaped reflectors. Both the measurement and the calculation are for a south-facing collector– reflector geometry where ac 5458, ar 5208, latitude560.68N, date5July 3 and solar time5 2.15 p.m. It should be noted that the middle image line from the 198 corrugation set-up in Fig. 14 and the corresponding line in Fig. 13 arise from multiple reflections in the V-shaped reflectors. The agreement between Fig. 13 and 14 as well as other geometries investigated validate the calculation procedure used in the ray tracing calculations. 5. DISCUSSION
Fig. 14. Calculated dispersion image from reflection in a 198 corrugation on the collector plane. Each dot represents one ray which has been randomly distributed onto the corrugation. The rays are incident from a direction corresponding to the sun position on July 3, solar time 2.15 p.m., latitude 60.68N. The collector plane is assumed to be directed south and reflector length51. Geometries used are b 5198, ac 5458 and ar 5208.
The result from the ray tracing calculations can be used for calculating the impact on collector performance by using corrugated reflectors. For the calculation we assume a collector tilted 458 to the south and defined by a zero loss efficiency described by F9 (ta )50.8, a heat loss coefficient at an operating temperature of 708C described by F9 UL 53.5 W m 22 K 21 and an incidence angle dependence described by Eqn (1) with b 0 50.2. Perers (1995) has shown that collectors of this type, mounted in rows in a collector field, will give an annual output of 300 kWhm 22 in a Stockholm climate without booster reflectors and approximately 425 kWhm 22 with flat booster reflectors with the geometry discussed in chapter 3. The calculations also show that the increase in annual collector output by using booster reflectors
¨ M. Ronnelid and B. Karlsson
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can be said to be approximately the additional irradiation from the reflector multiplied by the optical efficiency F9 (ta ) of the collector (Perers, 1998). If the reflected direct irradiation on the collector is increased by 10% due to an optimally corrugated reflector, the annually incident radiation on the collector will be increased by 16 kWhm 22 compared with a collector and flat reflector. Taking the optical efficiency into account, it can be assumed that the annual collector output is increased by 13 kWhm 22 . This corresponds to a 3% increase in the annual collector output compared to if a flat reflector is used.
Dr. Bengt Perers for critical reading of the manuscript.
NOMENCLATURE
bo F9 UL F(us , ue ) F9 (ta ) LR
6. CONCLUSIONS
The annual amount of direct radiation on the collector plane can be increased by replacing flat booster reflectors by corrugated booster reflectors with the corrugations perpendicular to the collector. Based on Swedish radiation data, the calculations show that small corrugation angles around 108 are most favourable. This results in an annual reflected direct radiation on the collector which is approximately 8% greater than for a collector with a flat reflector with optimal geometry for Swedish conditions at latitude 608N. Booster reflectors with corrugation angles of b ¯608 work almost as well as flat reflectors if the specular reflectance is high. For low specular reflectance, multiple reflection in the booster reflectors with large corrugation angles considerably reduces the annual reflected irradiation incident on the collector aperture. The advantage of corrugated booster reflectors is greatest for the upper part of the booster reflector. An optimal combination with a flat reflector surface near the collector base and a corrugated reflector at the upper part of the booster reflector increases the effective reflectance by a factor of 1.10 for direct radiation. The annual increase of irradiation onto the collector plane when flat or corrugated reflectors are used is dependent on the distribution of available radiation across the sky. Thus the result is dependent on latitude, climate and geometry. The optimal corrugated booster reflector for increasing the irradiation on a solar collector therefore depends on the installation site. This study has been financed by the Swedish National Energy Administration, Swedish Council for Building Research and Vattenfall AB. The authors want to thank Ms. Anna Liberg for help with the measurements and Dr. Arne Roos and
K(u ) yo
ac ar b u ue
us
r DP
incident angle modifier coefficient collector heat loss coefficient including collector efficiency factor, 22 21 Wm K acceptance function for the reflector– collector system zero loss efficiency for direct radiation at normal incidence relative reflector width (collector width51 length unit) incident angle modifier for direct radiation relative corrugation width (collector width51 length unit) collector tilt angle, degrees reflector tilt angle, degrees corrugation angle (defined in Fig. 2), degrees angle of incidence, degrees projection angle for projection of sun position vector in a vertical plane directed east–west (west positive), degrees projection angle for projection of sun position vector in a vertical plane directed north–south (south positive), degrees specular reflectance annual increase of useful direct irradiation, kWhm 22 year 21
REFERENCES ¨ ¨ Broms G. and Henfridsson U. (1994). Utvardering av Sol¨ ¨ varmesystemet vid Osthammars Sjukhus ( Evaluation of the ¨ solar heating system at Osthammar hospital), Vattenfall ¨ Utveckling AB, Alvkarlebylaboratoriet, Sweden VU-V 94, In Swedish. Duffie J. A. and Beckman W. A. (1991). Solar Engineering of Thermal Processes, Vol. 2, Wiley Interscience, New York. Faiman D. and Zemel A. (1988) Low-profile solar water heaters: The mirror booster problem revisited. Solar Energy 40, 385–390. Grassie S. L. and Sheridan N. R. (1977) The use of planar reflectors for increasing the energy yield of flat plate collectors. Solar Energy 19, 663–668. Hollands K. G. T. (1971) A concentrator for thin film solar cells. Solar Energy 13, 149–163. Larson D. C. (1980) Optimization of flat plate collectors – flat mirror systems. Solar Energy 24, 203–207. Perers B. and Karlsson B. (1993) External reflectors for large collector arrays, simulation model and experimental results. Solar Energy 51, 327–337.
The use of corrugated booster reflectors for solar collector fields Perers B., Karlsson B. and Bergkvist M. (1994) Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations. Solar Energy 53, 215–226. Perers B. (1995). Optical modelling of solar collectors and booster reflectors under nonstationary conditions, Ph D Thesis, Department of Technology, Uppsala University, Sweden, ISBN 91-554-3496-7. Perers B. (1998). Personal communication. ¨ Ronnelid M., Perers B. and Karlsson B. 1994. Optical properties of nonimaging concentrators with corrugated reflectors. In Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XIII, Proc. SPIE,
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Wittwer V., Granquist C.G. and Lampert C.M. (Eds), 2255, pp. 595–602. Seitel S. C. (1975) Collector performance enhancement with flat reflectors. Solar Energy 17, 291–295. Souka A. F. and Safwat H. H. (1966) Optimum orientations for the double exposure flat-plate collector and its reflectors. Solar Energy 10, 170–174. Tabor H. (1966) Mirror boosters for solar collectors. Solar Energy 10, 111–118. TRNSYS 5.1 (1992). A Transient Simulation Program for Solar Energy Systems. Solar Energy Laboratory, University of Wisconsin.