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Optimal position of flat plate reflectors of solar thermal collector
Energy and Buildings 45 (2012) 161–168
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Optimal position of flat plate reflectors of solar thermal collector Ljiljana T. Kostic´ ∗ , Zoran T. Pavlovic´ Department of Physics, Faculty of Science and Mathematics, University of Niˇs, PO Box 224, 18 000 Niˇs, Serbia
a r t i c l e
i n f o
Article history: Received 15 July 2011 Received in revised form 18 October 2011 Accepted 31 October 2011 Keywords: Solar thermal collector Flat plate reflector Energy efficiency
a b s t r a c t In this paper the results of the influence of position of the flat plate reflectors made of Al sheet on thermal efficiency of solar thermal collector with spectrally selective absorber are presented. Analytical and experimental results on determination of the optimal position of flat plate solar reflectors during the day time over the whole year period are shown. Both numerical calculation and experimental measurements indicate that optimal angle position of the bottom reflector is the lowest (5◦ ) in December and the highest (38◦ ) in June for collector fixed at ˇ = 45◦ position. The thermal efficiency of thermal collector without reflectors and with reflectors in optimal position has been determined. Though the thermal efficiency of thermal collector decreases slightly with the solar radiation intensity, the total thermal energy generated by thermal collector with reflectors in optimal position is significantly higher than total thermal energy generated by thermal collector without reflectors. These results show the positive effect of reflectors made of Al sheet and there is an energy gain in the range 35–44% in the summer period for thermal collector with reflectors, which is expected to reduce the cost pay back time. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Solar energy could be one of primary sources of energy because it is ecologically clean and is freely available to everyone over the long time periods. The most common use of solar energy includes its transformation in either thermal energy by means of thermal collectors or in electrical energy by means of photovoltaic collectors. Wide utilization of thermal and photovoltaic solar collectors in modern buildings has become the subject of extensive research [1–3]. Thermal collectors that are built-in as integral facade or roof elements of modern buildings are particularly interesting. They can be used for heating the sanitary water in private houses, blocks of flats, tourist objects, hospitals, schools and other buildings. Flat solar radiation reflectors can be mounted on thermal collector in order to obtain higher thermal efficiency. The amount of direct light gathered by combination of reflector and flat-plate collector has been analyzed by McDaniels et al. more than 35 years ago [4]. The calculations were done allowing variable reflector and collector orientation angles, variable latitude and arbitrary sun hour angle away from solar noon. At the same time, Seitel explored the use of diffuse and specular flat reflectors to enhance the performance of flat-plate solar collectors by means of Fortran routines, which optimize the size, shape and placement of reflector and collector [5]. Also, the mathematical model to simulate the performance of flat-plate collector–reflector systems was
∗ Corresponding author. Tel.: +381 18 533 014; fax: +381 18 533 014. ´ E-mail address: [email protected] (L.T. Kostic). 0378-7788/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2011.10.059
analyzed by Grassie and Sheridan [6]. The model was used to predict the annual performance of a water heating system with several values of the reflector angle. The problems of energy performance of flat-plate collector–reflector systems were also investigated in works of Dang [7] and Arata and Geddes [8]. A model for the calculation of incident solar radiation from flat- and CPC-shaped external reflectors onto the flat plate solar collector arrays was developed by Perers and Karlsson [9]. Also, Perers et al. [10] studied intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations. Another analytical model has been developed and used to determine solar irradiation on flat collectors augmented with planar reflectors by Bollentin and Wilk [11]. The use of corrugated booster reflectors for solar collector fields was considered by Ronnelid and Karlsson [12]. They have shown that by using the corrugated instead of flat booster reflectors it was possible to increase the annual irradiation onto the collector plane, thereby maximizing the annual output from the collector–reflector arrangement. Hussein et al. [13] gave a theoretical analysis of the instantaneous, daily and yearly enhancement in solar energy collection of a tilted flatplate solar collector augmented by a plane reflector. The shadow effect due to the reflector on the collector was considered in the analysis. Tripanagnostopoulos et al. [14] constructed and tested the flat plate solar collectors with colored absorbers for water heating applications. The study included collectors in their typical form with the protective glazing, and also collectors without glazing. In order to overcome the high thermal losses of the unglazed
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Nomenclature Aa a C e ES ET Gdif Gdif col Gdif sky Gdir col Gh Gin Gnet col
Gref r1 Gref r2 Gref gr Gtot col ˙ m N r R Ta Ti To Vw T ˛ ˛1 ˛2 ˇ s ı ε T th z Al g ω
collector surface area (m2 ) absorption coefficient concentration factor the root mean square deviation (◦ ) total solar radiation energy during the day (Wh) total generated thermal energy during the day (Wh) diffuse solar radiation on horizontal surface (W m−2 ) total diffuse solar radiation (W m−2 ) sky-diffuse solar radiation (W m−2 ) direct solar radiation on collector surface (W m−2 ) global solar radiation on horizontal surface (W m−2 ) global solar incident radiation (W m−2 ) net incoming solar radiation on the collector surface without the additional solar input from reflected solar radiation from reflectors (W m−2 ) reflected solar radiation from bottom reflector which reached the collector surface (W m−2 ) reflected solar radiation from upper reflector which reached the collector surface (W m−2 ) reflected solar radiation from the ground (W m−2 ) total solar radiation on the collector surface (W m−2 ) water mass flow rate (kg s−1 ) number of day in year coefficient of correlation reflectance ambient air temperature (◦ C) water input temperature (◦ C) water output temperature (◦ C) wind speed (m s−1 ) temperature difference (K) solar altitude angle (◦ ) angle between bottom reflector and horizontal plane (◦ ) angle between upper reflector and vertical plane (◦ ) collector tilted plane angle (◦ ) solar azimuth angle (◦ ) declination angle of the sun (◦ ) emittance latitude of the location of thermal collector (◦ ) total daily thermal efficiency thermal efficiency solar zenith angle when a surface is facing the south (◦ ) reflectance from Al sheet ground reflectance sun hour angle (◦ )
collectors and the low optical efficiency of the colored absorbers, they used flat booster reflectors. The additional solar radiation input from the reflectors increased the thermal energy output of the collectors, thus improving their performance. Hellstrom et al. [15] investigated the impact of optical and thermal properties on the performance of flat plate solar collectors. The collector parameters were determined with theoretically based calculated program verified from laboratory measurements. Inclusion of external booster reflectors increases the expected annual output depending on reflector material. In order to obtain the irradiance distribution on the absorber, different simulation models for flat mirror concentrators were developed by Pancotti [16]. Carboni and Montanari [17] proposed a quantitative approach able to forecast the profitability of the introduction of domestic
Fig. 1. Schematic diagram of the thermal collector with flat solar radiation reflectors.
solar thermal systems operating in parallel with the most common systems for heating domestic sanitary water. The approach was developed by analyzing the most common system for heating sanitary water from both the engineering and economic points of view. At the same time, the technical-economic solutions related to the most commercialized solar heating systems and their compatibility with the most common traditional heating systems was studied. The theoretical analysis of a solar thermal collector with flat plate top reflector was presented by Tanaka [18]. He predicted the daily solar radiation absorbed on an absorbing plate of the collector throughout the year, which varied considerably with the inclination of both the collector and reflector, and was slightly affected by the ratio of the reflector and collector length. The investigations described in this paper were performed on thermal collectors with and without flat plate solar radiation reflectors, and the goal was to determine optimal position of reflector plate for the given position of collector. First, we will present an analytical model for determination of the optimal position of aluminium sheet made flat plate solar reflector for inclination (tilt angle) of thermal collector of 45◦ , during the day time over the whole year period. The theoretical results obtained by analytical model will be then shown to be in good agreement with experimental data. The thermal efficiencies of solar thermal collectors without reflectors and with reflectors in optimal position have been determined as well. 2. Analytical model Model was developed for a thermal collector with tilt angle fixed at 45◦ . The south-directed collector was mounted at the rooftop of the Faculty of Science and Mathematics building (43◦ 19 N, 21◦ 54 E), University of Nis, Serbia. Two aluminium sheet made flat plate solar reflectors of the same size as the collector were mounted on the collector, as shown in Fig 1. In a model that we propose here the total solar radiation Gtot col on the thermal collector surface with tilted plane angle ˇ is the sum of the direct radiation on collector surface Gdir col , the reflected radiation from bottom reflector which reached the collector surface Gref r1 with tilted plane angle ˛1 , the reflected radiation from upper reflector which reached the collector surface Gref r2 with tilted plane angle ˛2 , and the total diffuse radiation Gdiff col , i.e. Gtot
col
= Gdir
col
+ Gref
r1
+ Gref
r2
+ Gdif
col ,
(1)
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where [19]: Gdir
col
= Gin · sin(˛ + ˇ).
(2)
The reflected radiation from bottom reflector Gref r1 with tilted plane angle ˛1 and the reflected radiation from upper reflector Gref r2 with tilted plane angle ˛2 are defined as: Gref
r1
= A1 · Gin · sin · sin(˛ − ˛1 );
= ˇ + 2 · ˛1 − ˛,
(3)
Gref
r2
= A1 · Gin · sin · cos(˛ + ˛2 );
= ˛ + 2 · ˛2 − ˇ,
(4)
The angles and are indicated in Fig. 1. The total diffuse radiation on the thermal collector is the sum of the sky-diffuse radiation Gdif sky and the reflected radiation from the ground Gref gr [19]: Gdif
col
= Gdif
sky
+ Gref
gr
= Gdif ·
1 + cos ˇ 1 − cos ˇ + g · Gh · . 2 2 (5)
In the above expressions, ˛ is solar altitude angle, Gin is global solar incident radiation, Al is Al sheet reflectance, Gdif is diffuse radiation on horizontal surface, Gh is global solar radiation on horizontal surface, and g is ground reflectance (ground albedo 0.2 without snow, 0.6 with snow). The solar zenith angle when a surface is facing the south is given as [19]: cos z = cos( − ˇ) · cos ı · cos ω + sin( − ˇ) · sin ı,
(6)
where ı is declination angle of the sun and it is function of a number of the day N in year [19]:
ı = 23.45◦ · sin 360◦ ·
284 + N 365
,
sin ˛ = cos · cos ı · cos ω + sin · sin ı,
The experiment has been conducted in Solar Energy Laboratory of the Faculty of Science and Mathematics, University of Niˇs, Serbia, in 2008 and 2009. The climate of the Niˇs area is moderate and continental, with an average temperature of 11.2 ◦ C during the year. The warmest month of the year is July, with the average temperature of 21.2 ◦ C. The coldest month is January, averaging at 0.2 ◦ C. There are 123 days with rain and 43 days with snow. The average daily solar global radiation is 4200 Wh/m2 .
(7)
(8)
and solar azimuth angle is given as [19]: sin · cos ı · cos ω − cos · sin ı . cos ˛
(9)
The analytical model is given by expressions Eqs. (1)–(9). The total solar radiation on the collector, Gtot col = F(˛, ˇ, ˛1 , ˛2 , , , ω, ı, Gin , Gdif , Gh , , N), is a complex function of several parameters. In order to determine optimal position ˛1 of the reflector it is necessary to find the extreme value of this function, i.e. to solve the following equation: ∂Gtot col =0 ∂˛1
3. Experiment
and where is latitude of the location of thermal collector and ω is sun hour angle. Solar altitude angle is determined by [19]:
cos s =
Fig. 2. Schematic diagram of the cross section of thermal collector: (1) flat reflectors, (2) glass, (3) spectrally selective absorber, (4) aluminium support, (5) copper tubes, (6) thermal insulation, (7) box.
(10)
Analytical methods to solve this equation are too complicated and do not lead to practical solution. Instead, the equation was solved numerically under the assumptions that ˛2 = const = 0◦ and solar position at zenith. The zenith solar position was assumed because the solar radiation intensity in that case is maximum, while its variation with time remains rather small over relatively long period (about 2 h). An appropriate software program was created to calculate the dependence of solar radiation on the collector, Gtot col , as a function of reflector tilt angle ˛1 , declination angle ı, latitude , south-directed thermal collector tilt angle ˇ, and number of the day in a year N. Optimal tilt angle of bottom reflector ˛1 max at solar zenith for each day N in the year was determined by numerical calculations of Gtot col (˛1 ). The optimal angle of bottom reflector ˛1 max and its change as the function of a number of days N in year was calculated for a given tilted plane angle ˇ of thermal collector, latitude and declination angle of the sun ı.
3.1 System description Measurements have been performed on thermal collector with and without flat plate solar radiation reflectors. Thermal collector has been produced by NISSAL Co., Niˇs, Serbia. Schematic diagram of the cross section of thermal collector with flat solar radiation reflectors is given in Fig. 2. Thermal collector (dimensions 1.37 m × 0.72 m, surface area 0.986 m2 ) was made of electrolitically colored anodized aluminium box, thermal insulation from mineral wool, spectrally selective absorber, aluminium on the back and protective glass on the front side. Spectrally selective absorber is composed of interconnected aluminium sheets with copper tubes installed in the bottom. In this collector Al/Al2 O3 -Ni spectrally selective absorber with absorption coefficient a = 0.9 and emittance ε = 0.2 has been used. Spectrally selective absorber was made by electrolitically coloring of aluminium sheets in nickel sulfate solution. Anodic oxidation of Al sheets was done in phosphoric acid solution. The thermal collector was mounted on the metal support made of bottom (fixed) and upper (movable) part thus enabling tilting of the collector in relation to the horizontal plane of 0–90◦ . Thermal collector in this experiment has been kept in a position angle of 45◦ in relation to the horizontal plane and has been south oriented. In order to get more thermal energy, two Al sheet made flat plate reflectors (actual chemical composition was Al (99.99%)/Fe (0.01%)), whose dimensions were 1.37 m × 0.72 m, have been mounted on thermal collector with the changeable position in relation to thermal collector. In order to obtain the highest solar radiation intensity on thermal collector, positions of the bottom and upper reflectors have been changed and optimal position of reflectors have been determined so as to obtain maximal concentration of solar radiation intensity. Schematic diagram of the system, which has been used for determination of the thermal characteristics of solar thermal collector, is given in Fig. 3.
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Fig. 4. Reflectance from Al sheet: (1) total, (2) diffuse, (3) specular. Fig. 3. Schematic diagram of the system for the determination of thermal characteristics of solar thermal collector: (1) hot water storage, (2) pump, (3) valves, (4) Kamstrup-Multical 401 calorimeter, (5) thermal collector, (6) MINI-KLA device with single-crystalline silicon solar cell as the sensor, (7) meteorological station DAVIS Vantage PRO, (8) computer.
3.2. Measuring equipment Total, diffuse and specular reflectance from Al sheet has been measured by means of a Beckman UV/VIS/NIR 5240 Spectrophotometer with integrating sphere. For the measurement of solar radiation intensity on thermal collector surface MINI-KLA device (Ingenieurburo Mencke & Tegtmeyer) has been used. This device has a single-crystalline silicon solar cell as the sensor. Measurements have been performed by an hour with solar cell in the middle of thermal collector. An automatic meteorological station DAVIS Vantage PRO has been used for the measurement of meteorological parameters, such as the ambient temperature Ta , the wind speed Vw , etc. All meteorological data have been registered in 10-min intervals. Heated water was brought to the hot water storage by means of circulation pump (Fig. 3). Electrical thermometers with Pt-100 temperature sensors have been used for the measurements of input and output temperature from the collector and water temperature in hot water storage, whereas the Kamstrup-Multical 401 calorimeter has been used for measurements of the thermal energy obtained in hot water storage and for the water mass flow rate. Hot water from the hot water storage has been drained out every morning, and the storage has been again filled with cold water. Heating of water in the storage during the day has been continuously monitored in the period from 8:00 to 17:00 h. Water temperature in storage has been measured at the end of the day.
Measurements of the total solar radiation on thermal collector with reflectors in optimal position have been performed by an hour in the period from 8:00 to 17:00 h in certain points along the x and y axes of the Cartesian coordinate system, where origin was at the centre of the thermal collector surface. Measurement results of the total solar radiation from 8:00 to 17:00 h (typical day 26 June 2009) along the x and y axes are given in Figs. 5 and 6, respectively. It can be seen that the distribution of the total solar radiation on thermal collector surface was almost uniform, which is of importance for applications of thermal collectors with reflectors in the buildings. Measurements have been done in 2009 for different days. The total solar radiation intensity (Gtot col ) on thermal collector surface in the sun peak was measured for different positions of reflectors. As already mentioned, the period of solar position at zenith was chosen for measurements because of maximum solar radiation and its small variations with time, which were the most favorable experimental conditions. The zenith solar position is favorable for measuring the intensity of solar radiation on thermal collector at different tilt angles ˛1 of the bottom reflector, as well as for experimental determination of Gtot col max as a function of the optimal position ˛1 of the bottom reflector. Typical results for the change of total solar radiation intensity (Gtot col ) on thermal collector surface measured during the sun peak on 21 June 2009 depending on the positions of reflectors are shown
4. Results and discussion 4.1. Optimal position First, we investigated total, diffuse and specular reflectance from the flat solar radiation reflector made of Al sheet in the wavelength range of 350–750 nm, and results are shown in Fig. 4. As can be seen, the total, diffuse and specular reflectance from flat solar radiation reflectors made of Al sheet in VIS region were 0.65–0.82, 0.52–0.61, and 0.13–0.21, respectively. The diffuse reflectance from Al sheet was higher then specular reflectance and it considerably influenced the distribution of the total solar radiation on thermal collector surface.
Fig. 5. Distribution of the total solar radiation on thermal collector surface along axes x.
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Fig. 6. Distribution of the total solar radiation on thermal collector surface along axes y.
in Fig. 7, where ˛1 denotes the angle between bottom reflector and horizontal plane, and ˛2 denotes the angle between upper reflector and vertical plane. Net incoming solar radiation on the thermal collector surface without the additional solar input from reflected solar radiation from reflectors in the sun peak for this day was Gnet col = 922 W/m2 . As can be seen in the figure, optimal position of the bottom reflector on the above date was at the angle of 38◦ when the top reflector was kept at 0◦ angular position. The values of the optimal positions of upper and bottom reflectors for given tilted plane angle ˇ = 45◦ in the sun peak have also been determined by means of the analytical model represented by Eqs. (1)–(10). These values change during the year with variations of declination angle ı of the sun. A comparison between numerical and experimental findings for optimal position of the bottom reflector (for upper reflector ˛2 = 0◦ ) during the year is shown in Fig. 8 and Table 1. As can be seen, the maximum calculated value of optimal angle position of bottom reflector was 37.78◦ , and was obtained on June 21 (Summer Solstice), when the declination angle was at its maximum 23.45◦ , whereas the minimum calculated value was 5.12◦ , obtained on December 22 (Winter Solstice), when the declination angle was at its minimum −23.45◦ . It also can be seen that the experimental
Fig. 8. A change of optimal position ˛1 max of bottom reflector during the year in the sun peak: (1) solid line-calculated analytical data, (2) squares-experimental data.
value of optimal position of the bottom reflector reached the maximum angle value of 38◦ in June, and decreased to 5◦ in December. The coefficient of correlation (r) of numerical calculated data and experimental data for optimal angle of bottom reflector during the year in the sun peak can be calculated by using the relation [20]: n
n r=
Xi Yi −
n n Xi
Yi
n 2 n 2 , n n n X 2 − X × n Y2− Y i=1
i=1
i
i=1
i=1
i
i
i=1
(11)
i
i=1
i=1
and the root mean square deviation (RMSD = e) can be calculated by using the expression [20]:
e=
n (X i=1 i
n
− Yi )2
(12)
,
where Xi denotes numerically calculated data of optimal angle of bottom reflector, Yi denotes experimental data of optimal angle of bottom reflector during the year, and n is the number of experimental data. Table 1 Calculated (Xi ) and measured (Yi ) values of optimal angle ˛1max of bottom reflector during the year in the sun peak.
Fig. 7. A change of total solar radiation Gtot col on thermal collector surface depending on reflectors position in the sun peak: (1) without upper reflector, (2) ˛2 = 20◦ , (3) ˛2 = 10◦ and (4) ˛2 = 0◦ .
Number of day in year (N)
Xi (◦ )
41 68 86 100 106 130 139 155 167 183 194 211 230 258 274 288 317 355
11.34 18.18 23.19 26.99 28.52 33.77 35.26 37.11 37.78 37.64 36.85 34.57 30.73 23.36 18.79 14.93 8.42 5.12
Yi (◦ ) 8 16 20 24 28 34 36 38 38 38 36 34 30 24 20 16 8 5
ei = Xi − Yi (◦ ) 3.34 2.18 3.19 2.99 0.52 −0.23 −0.74 −0.89 −0.22 −0.36 0.85 0.57 0.73 −0.64 −1.21 −1.07 0.42 0.12
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Fig. 10. A change of the total generated thermal energy during the day by thermal collector: (1) without reflectors, (2) with reflectors in optimal position. Fig. 9. A change of solar radiation on thermal collector during the typical day: (1) without reflectors Gnet col , (2) with reflectors in optimal position Gtot col .
The coefficient of correlation and the root mean square deviation for our data given in Table 1, as calculated by means of Eqs. (11) and (12), were r = 0.992 and e = 1.521◦ , respectively. Root mean square deviation was mainly the consequence of the shift of mechanical components for changing the tilted plane angle of reflectors. The good agreement between numerical and experimental data, which was demonstrated above, allowed us to predict reliable values for optimal position of reflectors for different collector tilted plane angles. A change in total solar radiation on thermal collector surface without and with reflectors in optimal position during the day (typical day 21 June 2009) is shown in Fig. 9. The concentration factor (C) of solar radiation intensity has been calculated based on the measurement results for the total solar radiation on the thermal collector surface with reflectors Gtot col and net incoming solar radiation on the collector surface without the additional solar input from reflected solar radiation from reflectors Gnet col during the day: C=
Gtot Gnet
col
,
(13)
col
where Gnet col is defined by: Gnet
col
= Gdir
col
+ Gdif
col .
(14)
The concentration factor (C) of solar radiation intensity was 1.5 for this day. Also average value of the concentration factor was approximately 1.5 in the summer period (June–September). 4.2. Thermal analysis Thermal analysis was performed for collector without reflectors and with reflectors in optimal position. The thermal efficiency th of the solar thermal collector can be determined from following expression: th =
˙ p (To − Ti ) mc , Aa Gtot col
(15)
˙ = dm/dt is water mass flow rate, cp is water specific heat where m (4180 J kg−1 K−1 ), Ti is water input temperature and To is water output temperature, whereas Aa is the collector surface area [19,21]. The variation of thermal efficiency th relative to the water input temperature Ti , the ambient temperature Ta and the total incoming solar radiation intensity Gtot col is determined experimentally
as a function of the ratio T/Gtot col , where T = Ti − Ta . The function th = f(T/Gtot col ) is used for the performance determination of thermal collectors. Total daily thermal efficiency T is defined by: T =
ET , ES
(16)
where ET (Wh) is the total generated thermal energy during the day by thermal collector and ES (Wh) is the total incoming solar radiation energy during the day on thermal collector. Thermal performance of solar thermal system with reflectors depends on the water input temperature (Ti ), ambient temperature (Ta ), net incoming solar radiation intensity (Gnet col ) and the concentration factor (C). The total generated thermal energy during the day by thermal collector without reflectors and with reflectors in optimal position has been measured in the period March–October 2009. Changes of the total generated thermal energy during the day from 8:00 to 17:00 h by thermal collector with reflectors in optimal position and without reflectors for typical day (21 June 2009) in the summer period are shown in Fig. 10. Measurements during this day have shown that total generated thermal energy has increased by 41% in thermal collector with reflectors in optimal position compared to thermal collector without reflectors. The increase of total thermal energy obtained by thermal collector with reflectors in optimal position during the summer period varied in the range 35–44% and it was dependent on the meteorological parameters, such as the ambient temperature Ta , the wind speed Vw , solar radiation G, etc. The total daily thermal efficiency T has been determined on the basis of measurement results for the total generated thermal energy during the day by thermal collector (ET ) and the total incoming solar radiation energy during the day on thermal collector (ES ). The value of the total daily thermal efficiency for thermal collector with reflectors in optimal position is lower then thermal efficiency of thermal collector without reflectors. For C = 1.5, decrease of total daily thermal efficiency for thermal collector with reflectors in optimal position varies in the range 4–10% during the summer period. The changes of water input temperature and water output temperature during the day in thermal collector without reflectors and with reflectors in optimal position is given in Fig. 11. The water input temperature Ti and water output temperature To during the day in thermal collector with reflectors in optimal position are higher than water input and output temperature in thermal collector without reflectors. Also the temperature
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significantly higher than total thermal energy generated by thermal collector without reflectors. 5. Conclusion
Fig. 11. A change of water input temperature (1) and water output temperature (2) in thermal collector during the day without reflectors and water input temperature (3) and water output temperature (4) in thermal collector during the day with reflectors in optimal position.
difference T0 − Ti between output and input temperature in thermal collector with reflectors in optimal position is higher than temperature difference in thermal collector without reflectors. Thermal efficiency th of thermal collector as a function of T/Gtot col operating values for the same day (21 June 2009) is shown in Fig. 12. These results have been calculated for average ˙ = 0.02 kg/s, net wind speed Vw = 0.3 m/s, water mass flow rate m incoming solar radiation intensity Gnet col = 922 W/m2 and ambient temperature Ta = 28 ◦ C. It can be seen that thermal efficiency th of thermal collector with reflectors in optimal position was lower than thermal efficiency of PV/Thermal collector without reflectors. The results have shown that thermal efficiency th to great extent depends on the ambient temperature and solar radiation. Though the thermal efficiency of thermal collector decreased slightly with the solar radiation intensity, i.e. the thermal efficiency of thermal collector with reflectors was lower than that of thermal collector without reflectors, the total thermal energy generated by thermal collector with reflectors in optimal position was
Fig. 12. Thermal efficiency th of thermal collector: (1) without reflectors, (2) with reflectors in optimal position.
In this paper the solar thermal collector with spectrally selective absorber with and without flat solar radiation reflectors has been considered. The changes of optimal positions of reflectors during the year have been determined analytically and experimentally for collector fixed at ˇ = 45◦ position in order to obtain the maximum concentration of solar radiation intensity. Both numerical calculation and experimental measurements indicated that optimal angle position of the bottom reflector was the lowest (5◦ ) in December and the highest (38◦ ) in June. Systematically good agreement between numerical and experimental data during the year has been found, which allowed us to predict reliable values for optimal position of reflectors for different collector tilted plane angle. Average value of the concentration factor in the summer period (June–September) was approximately 1.5. For this period the increase of total thermal energy obtained by thermal collector with reflectors in optimal position varied in the range 35–44%. The results have shown the positive effect of reflectors made of Al sheet and, considering the additional cost of about 15% for the reflectors, there was an average energy gain of about 40% in the summer period for thermal collector with reflectors. This energy gain is expected to reduce the cost pay back time, and the model proposed in this paper could be useful to determine optimal positions of thermal collectors (with or without reflectors) as integral facade or roof elements in modern buildings. Acknowledgement The authors gratefully acknowledge the support from Ministry of Science of the Republic of Serbia through Project No. TR32026. References [1] H. Gunerhan, A. Hepbasli, Exergetic modeling and performance evaluation of solar water heating systems for building applications, Energy and Buildings 39 (2007) 509–516. [2] A.F. Miguel, Constructal design of solar energy-based systems for buildings, Energy and Buildings 40 (2008) 1020–1030. [3] C.D. Corbin, Z.J. Zhai, Experimental and numerical investigation on thermal and electrical performance of a building integrated photovoltaic-thermal collector system, Energy and Buildings 42 (2010) 76–82. [4] D.K. McDaniels, D.H. Lowndes, H. Mathew, J. Reynolds, R. Gray, Enhanced solar energy collection using reflector-solar thermal collector combinations, Solar Energy 17 (1975) 277–283. [5] S.C. Seitel, Collector performance enhancement with flat reflectors, Solar Energy 17 (1975) 291–295. [6] S.L. Grassie, N.R. Sheridan, The use of planar reflectors for increasing the energy yield of flat-plate collectors, Solar Energy 19 (1977) 663–668. [7] A. Dang, Collector, collector-reflector systems-an analytical and practical study, Energy Conversion and Management 26 (1986) 33–39. [8] A.A. Arata, R.W. Geddes, Combined collector–reflector systems, Energy 11 (1986) 621–630. [9] B. Perers, B. Karlsson, External reflectors for large solar collector arrays, simulation model and experimental results, Solar Energy 51 (1993) 327–337. [10] B. Perers, B. Karlsson, M. Bergkvist, Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations, Solar Energy 53 (1994) 215–226. [11] J.W. Bollentin, R.D. Wilk, Modeling the solar irradiation on flat plate collectors augmented with planar reflectors, Solar Energy 55 (1995) 343–354. [12] M. Ronnelid, B. Karlsson, The use of corrugated booster reflectors for solar collectors fields, Solar Energy 65 (1999) 343–351. [13] H.M.S. Hussein, G.E. Ahmad, M.A. Mohamad, Optimization of operational and design parameters of plane reflector-tilted flat plate solar collector systems, Energy 25 (2000) 529–542. [14] Y. Tripanagnostopoulos, M. Souliotis, T.H. Nousia, Solar collectors with colored absorbers, Solar Energy 68 (2000) 343–356. [15] B. Hellstrom, M. Adsten, P. Nostell, B. Karlsson, E. Wackelgard, The impact of optical and thermal properties on the performance of flat plate solar collectors, Renewable Energy 28 (2003) 331–344.
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[16] L. Pancotti, Optical simulation model for flat mirror concentrators, Solar Energy Materials and Solar Cells 91 (2007) 551–559. [17] C. Carboni, R. Montanari, Solar thermal systems: advantages in domestic integration, Renewable Energy 33 (2008) 1364–1373. [18] H. Tanaka, Solar thermal collector augmented by flat plate booster reflector: optimum inclination of collector and reflector, Applied Energy 88 (2011) 1395–1404.
[19] J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes, third ed., John Wiley & Sons, New York, 2006. [20] D.D. Wackerly, W. Mendenhall III, R.L. Scheaffer, Mathematical Statistics with Applications, 7th Edition, Thomson-Brooks/Cole, Belmont CA, 2008. [21] J.F. Kreider, F. Kreith, Solar Energy Handbook, McGraw-Hill Book Company, New York, 1981.
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Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Optimal position of flat plate reflectors of solar thermal collector Ljiljana T. Kostic´ ∗ , Zoran T. Pavlovic´ Department of Physics, Faculty of Science and Mathematics, University of Niˇs, PO Box 224, 18 000 Niˇs, Serbia
a r t i c l e
i n f o
Article history: Received 15 July 2011 Received in revised form 18 October 2011 Accepted 31 October 2011 Keywords: Solar thermal collector Flat plate reflector Energy efficiency
a b s t r a c t In this paper the results of the influence of position of the flat plate reflectors made of Al sheet on thermal efficiency of solar thermal collector with spectrally selective absorber are presented. Analytical and experimental results on determination of the optimal position of flat plate solar reflectors during the day time over the whole year period are shown. Both numerical calculation and experimental measurements indicate that optimal angle position of the bottom reflector is the lowest (5◦ ) in December and the highest (38◦ ) in June for collector fixed at ˇ = 45◦ position. The thermal efficiency of thermal collector without reflectors and with reflectors in optimal position has been determined. Though the thermal efficiency of thermal collector decreases slightly with the solar radiation intensity, the total thermal energy generated by thermal collector with reflectors in optimal position is significantly higher than total thermal energy generated by thermal collector without reflectors. These results show the positive effect of reflectors made of Al sheet and there is an energy gain in the range 35–44% in the summer period for thermal collector with reflectors, which is expected to reduce the cost pay back time. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Solar energy could be one of primary sources of energy because it is ecologically clean and is freely available to everyone over the long time periods. The most common use of solar energy includes its transformation in either thermal energy by means of thermal collectors or in electrical energy by means of photovoltaic collectors. Wide utilization of thermal and photovoltaic solar collectors in modern buildings has become the subject of extensive research [1–3]. Thermal collectors that are built-in as integral facade or roof elements of modern buildings are particularly interesting. They can be used for heating the sanitary water in private houses, blocks of flats, tourist objects, hospitals, schools and other buildings. Flat solar radiation reflectors can be mounted on thermal collector in order to obtain higher thermal efficiency. The amount of direct light gathered by combination of reflector and flat-plate collector has been analyzed by McDaniels et al. more than 35 years ago [4]. The calculations were done allowing variable reflector and collector orientation angles, variable latitude and arbitrary sun hour angle away from solar noon. At the same time, Seitel explored the use of diffuse and specular flat reflectors to enhance the performance of flat-plate solar collectors by means of Fortran routines, which optimize the size, shape and placement of reflector and collector [5]. Also, the mathematical model to simulate the performance of flat-plate collector–reflector systems was
∗ Corresponding author. Tel.: +381 18 533 014; fax: +381 18 533 014. ´ E-mail address: [email protected] (L.T. Kostic). 0378-7788/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2011.10.059
analyzed by Grassie and Sheridan [6]. The model was used to predict the annual performance of a water heating system with several values of the reflector angle. The problems of energy performance of flat-plate collector–reflector systems were also investigated in works of Dang [7] and Arata and Geddes [8]. A model for the calculation of incident solar radiation from flat- and CPC-shaped external reflectors onto the flat plate solar collector arrays was developed by Perers and Karlsson [9]. Also, Perers et al. [10] studied intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations. Another analytical model has been developed and used to determine solar irradiation on flat collectors augmented with planar reflectors by Bollentin and Wilk [11]. The use of corrugated booster reflectors for solar collector fields was considered by Ronnelid and Karlsson [12]. They have shown that by using the corrugated instead of flat booster reflectors it was possible to increase the annual irradiation onto the collector plane, thereby maximizing the annual output from the collector–reflector arrangement. Hussein et al. [13] gave a theoretical analysis of the instantaneous, daily and yearly enhancement in solar energy collection of a tilted flatplate solar collector augmented by a plane reflector. The shadow effect due to the reflector on the collector was considered in the analysis. Tripanagnostopoulos et al. [14] constructed and tested the flat plate solar collectors with colored absorbers for water heating applications. The study included collectors in their typical form with the protective glazing, and also collectors without glazing. In order to overcome the high thermal losses of the unglazed
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Nomenclature Aa a C e ES ET Gdif Gdif col Gdif sky Gdir col Gh Gin Gnet col
Gref r1 Gref r2 Gref gr Gtot col ˙ m N r R Ta Ti To Vw T ˛ ˛1 ˛2 ˇ s ı ε T th z Al g ω
collector surface area (m2 ) absorption coefficient concentration factor the root mean square deviation (◦ ) total solar radiation energy during the day (Wh) total generated thermal energy during the day (Wh) diffuse solar radiation on horizontal surface (W m−2 ) total diffuse solar radiation (W m−2 ) sky-diffuse solar radiation (W m−2 ) direct solar radiation on collector surface (W m−2 ) global solar radiation on horizontal surface (W m−2 ) global solar incident radiation (W m−2 ) net incoming solar radiation on the collector surface without the additional solar input from reflected solar radiation from reflectors (W m−2 ) reflected solar radiation from bottom reflector which reached the collector surface (W m−2 ) reflected solar radiation from upper reflector which reached the collector surface (W m−2 ) reflected solar radiation from the ground (W m−2 ) total solar radiation on the collector surface (W m−2 ) water mass flow rate (kg s−1 ) number of day in year coefficient of correlation reflectance ambient air temperature (◦ C) water input temperature (◦ C) water output temperature (◦ C) wind speed (m s−1 ) temperature difference (K) solar altitude angle (◦ ) angle between bottom reflector and horizontal plane (◦ ) angle between upper reflector and vertical plane (◦ ) collector tilted plane angle (◦ ) solar azimuth angle (◦ ) declination angle of the sun (◦ ) emittance latitude of the location of thermal collector (◦ ) total daily thermal efficiency thermal efficiency solar zenith angle when a surface is facing the south (◦ ) reflectance from Al sheet ground reflectance sun hour angle (◦ )
collectors and the low optical efficiency of the colored absorbers, they used flat booster reflectors. The additional solar radiation input from the reflectors increased the thermal energy output of the collectors, thus improving their performance. Hellstrom et al. [15] investigated the impact of optical and thermal properties on the performance of flat plate solar collectors. The collector parameters were determined with theoretically based calculated program verified from laboratory measurements. Inclusion of external booster reflectors increases the expected annual output depending on reflector material. In order to obtain the irradiance distribution on the absorber, different simulation models for flat mirror concentrators were developed by Pancotti [16]. Carboni and Montanari [17] proposed a quantitative approach able to forecast the profitability of the introduction of domestic
Fig. 1. Schematic diagram of the thermal collector with flat solar radiation reflectors.
solar thermal systems operating in parallel with the most common systems for heating domestic sanitary water. The approach was developed by analyzing the most common system for heating sanitary water from both the engineering and economic points of view. At the same time, the technical-economic solutions related to the most commercialized solar heating systems and their compatibility with the most common traditional heating systems was studied. The theoretical analysis of a solar thermal collector with flat plate top reflector was presented by Tanaka [18]. He predicted the daily solar radiation absorbed on an absorbing plate of the collector throughout the year, which varied considerably with the inclination of both the collector and reflector, and was slightly affected by the ratio of the reflector and collector length. The investigations described in this paper were performed on thermal collectors with and without flat plate solar radiation reflectors, and the goal was to determine optimal position of reflector plate for the given position of collector. First, we will present an analytical model for determination of the optimal position of aluminium sheet made flat plate solar reflector for inclination (tilt angle) of thermal collector of 45◦ , during the day time over the whole year period. The theoretical results obtained by analytical model will be then shown to be in good agreement with experimental data. The thermal efficiencies of solar thermal collectors without reflectors and with reflectors in optimal position have been determined as well. 2. Analytical model Model was developed for a thermal collector with tilt angle fixed at 45◦ . The south-directed collector was mounted at the rooftop of the Faculty of Science and Mathematics building (43◦ 19 N, 21◦ 54 E), University of Nis, Serbia. Two aluminium sheet made flat plate solar reflectors of the same size as the collector were mounted on the collector, as shown in Fig 1. In a model that we propose here the total solar radiation Gtot col on the thermal collector surface with tilted plane angle ˇ is the sum of the direct radiation on collector surface Gdir col , the reflected radiation from bottom reflector which reached the collector surface Gref r1 with tilted plane angle ˛1 , the reflected radiation from upper reflector which reached the collector surface Gref r2 with tilted plane angle ˛2 , and the total diffuse radiation Gdiff col , i.e. Gtot
col
= Gdir
col
+ Gref
r1
+ Gref
r2
+ Gdif
col ,
(1)
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163
where [19]: Gdir
col
= Gin · sin(˛ + ˇ).
(2)
The reflected radiation from bottom reflector Gref r1 with tilted plane angle ˛1 and the reflected radiation from upper reflector Gref r2 with tilted plane angle ˛2 are defined as: Gref
r1
= A1 · Gin · sin · sin(˛ − ˛1 );
= ˇ + 2 · ˛1 − ˛,
(3)
Gref
r2
= A1 · Gin · sin · cos(˛ + ˛2 );
= ˛ + 2 · ˛2 − ˇ,
(4)
The angles and are indicated in Fig. 1. The total diffuse radiation on the thermal collector is the sum of the sky-diffuse radiation Gdif sky and the reflected radiation from the ground Gref gr [19]: Gdif
col
= Gdif
sky
+ Gref
gr
= Gdif ·
1 + cos ˇ 1 − cos ˇ + g · Gh · . 2 2 (5)
In the above expressions, ˛ is solar altitude angle, Gin is global solar incident radiation, Al is Al sheet reflectance, Gdif is diffuse radiation on horizontal surface, Gh is global solar radiation on horizontal surface, and g is ground reflectance (ground albedo 0.2 without snow, 0.6 with snow). The solar zenith angle when a surface is facing the south is given as [19]: cos z = cos( − ˇ) · cos ı · cos ω + sin( − ˇ) · sin ı,
(6)
where ı is declination angle of the sun and it is function of a number of the day N in year [19]:
ı = 23.45◦ · sin 360◦ ·
284 + N 365
,
sin ˛ = cos · cos ı · cos ω + sin · sin ı,
The experiment has been conducted in Solar Energy Laboratory of the Faculty of Science and Mathematics, University of Niˇs, Serbia, in 2008 and 2009. The climate of the Niˇs area is moderate and continental, with an average temperature of 11.2 ◦ C during the year. The warmest month of the year is July, with the average temperature of 21.2 ◦ C. The coldest month is January, averaging at 0.2 ◦ C. There are 123 days with rain and 43 days with snow. The average daily solar global radiation is 4200 Wh/m2 .
(7)
(8)
and solar azimuth angle is given as [19]: sin · cos ı · cos ω − cos · sin ı . cos ˛
(9)
The analytical model is given by expressions Eqs. (1)–(9). The total solar radiation on the collector, Gtot col = F(˛, ˇ, ˛1 , ˛2 , , , ω, ı, Gin , Gdif , Gh , , N), is a complex function of several parameters. In order to determine optimal position ˛1 of the reflector it is necessary to find the extreme value of this function, i.e. to solve the following equation: ∂Gtot col =0 ∂˛1
3. Experiment
and where is latitude of the location of thermal collector and ω is sun hour angle. Solar altitude angle is determined by [19]:
cos s =
Fig. 2. Schematic diagram of the cross section of thermal collector: (1) flat reflectors, (2) glass, (3) spectrally selective absorber, (4) aluminium support, (5) copper tubes, (6) thermal insulation, (7) box.
(10)
Analytical methods to solve this equation are too complicated and do not lead to practical solution. Instead, the equation was solved numerically under the assumptions that ˛2 = const = 0◦ and solar position at zenith. The zenith solar position was assumed because the solar radiation intensity in that case is maximum, while its variation with time remains rather small over relatively long period (about 2 h). An appropriate software program was created to calculate the dependence of solar radiation on the collector, Gtot col , as a function of reflector tilt angle ˛1 , declination angle ı, latitude , south-directed thermal collector tilt angle ˇ, and number of the day in a year N. Optimal tilt angle of bottom reflector ˛1 max at solar zenith for each day N in the year was determined by numerical calculations of Gtot col (˛1 ). The optimal angle of bottom reflector ˛1 max and its change as the function of a number of days N in year was calculated for a given tilted plane angle ˇ of thermal collector, latitude and declination angle of the sun ı.
3.1 System description Measurements have been performed on thermal collector with and without flat plate solar radiation reflectors. Thermal collector has been produced by NISSAL Co., Niˇs, Serbia. Schematic diagram of the cross section of thermal collector with flat solar radiation reflectors is given in Fig. 2. Thermal collector (dimensions 1.37 m × 0.72 m, surface area 0.986 m2 ) was made of electrolitically colored anodized aluminium box, thermal insulation from mineral wool, spectrally selective absorber, aluminium on the back and protective glass on the front side. Spectrally selective absorber is composed of interconnected aluminium sheets with copper tubes installed in the bottom. In this collector Al/Al2 O3 -Ni spectrally selective absorber with absorption coefficient a = 0.9 and emittance ε = 0.2 has been used. Spectrally selective absorber was made by electrolitically coloring of aluminium sheets in nickel sulfate solution. Anodic oxidation of Al sheets was done in phosphoric acid solution. The thermal collector was mounted on the metal support made of bottom (fixed) and upper (movable) part thus enabling tilting of the collector in relation to the horizontal plane of 0–90◦ . Thermal collector in this experiment has been kept in a position angle of 45◦ in relation to the horizontal plane and has been south oriented. In order to get more thermal energy, two Al sheet made flat plate reflectors (actual chemical composition was Al (99.99%)/Fe (0.01%)), whose dimensions were 1.37 m × 0.72 m, have been mounted on thermal collector with the changeable position in relation to thermal collector. In order to obtain the highest solar radiation intensity on thermal collector, positions of the bottom and upper reflectors have been changed and optimal position of reflectors have been determined so as to obtain maximal concentration of solar radiation intensity. Schematic diagram of the system, which has been used for determination of the thermal characteristics of solar thermal collector, is given in Fig. 3.
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Fig. 4. Reflectance from Al sheet: (1) total, (2) diffuse, (3) specular. Fig. 3. Schematic diagram of the system for the determination of thermal characteristics of solar thermal collector: (1) hot water storage, (2) pump, (3) valves, (4) Kamstrup-Multical 401 calorimeter, (5) thermal collector, (6) MINI-KLA device with single-crystalline silicon solar cell as the sensor, (7) meteorological station DAVIS Vantage PRO, (8) computer.
3.2. Measuring equipment Total, diffuse and specular reflectance from Al sheet has been measured by means of a Beckman UV/VIS/NIR 5240 Spectrophotometer with integrating sphere. For the measurement of solar radiation intensity on thermal collector surface MINI-KLA device (Ingenieurburo Mencke & Tegtmeyer) has been used. This device has a single-crystalline silicon solar cell as the sensor. Measurements have been performed by an hour with solar cell in the middle of thermal collector. An automatic meteorological station DAVIS Vantage PRO has been used for the measurement of meteorological parameters, such as the ambient temperature Ta , the wind speed Vw , etc. All meteorological data have been registered in 10-min intervals. Heated water was brought to the hot water storage by means of circulation pump (Fig. 3). Electrical thermometers with Pt-100 temperature sensors have been used for the measurements of input and output temperature from the collector and water temperature in hot water storage, whereas the Kamstrup-Multical 401 calorimeter has been used for measurements of the thermal energy obtained in hot water storage and for the water mass flow rate. Hot water from the hot water storage has been drained out every morning, and the storage has been again filled with cold water. Heating of water in the storage during the day has been continuously monitored in the period from 8:00 to 17:00 h. Water temperature in storage has been measured at the end of the day.
Measurements of the total solar radiation on thermal collector with reflectors in optimal position have been performed by an hour in the period from 8:00 to 17:00 h in certain points along the x and y axes of the Cartesian coordinate system, where origin was at the centre of the thermal collector surface. Measurement results of the total solar radiation from 8:00 to 17:00 h (typical day 26 June 2009) along the x and y axes are given in Figs. 5 and 6, respectively. It can be seen that the distribution of the total solar radiation on thermal collector surface was almost uniform, which is of importance for applications of thermal collectors with reflectors in the buildings. Measurements have been done in 2009 for different days. The total solar radiation intensity (Gtot col ) on thermal collector surface in the sun peak was measured for different positions of reflectors. As already mentioned, the period of solar position at zenith was chosen for measurements because of maximum solar radiation and its small variations with time, which were the most favorable experimental conditions. The zenith solar position is favorable for measuring the intensity of solar radiation on thermal collector at different tilt angles ˛1 of the bottom reflector, as well as for experimental determination of Gtot col max as a function of the optimal position ˛1 of the bottom reflector. Typical results for the change of total solar radiation intensity (Gtot col ) on thermal collector surface measured during the sun peak on 21 June 2009 depending on the positions of reflectors are shown
4. Results and discussion 4.1. Optimal position First, we investigated total, diffuse and specular reflectance from the flat solar radiation reflector made of Al sheet in the wavelength range of 350–750 nm, and results are shown in Fig. 4. As can be seen, the total, diffuse and specular reflectance from flat solar radiation reflectors made of Al sheet in VIS region were 0.65–0.82, 0.52–0.61, and 0.13–0.21, respectively. The diffuse reflectance from Al sheet was higher then specular reflectance and it considerably influenced the distribution of the total solar radiation on thermal collector surface.
Fig. 5. Distribution of the total solar radiation on thermal collector surface along axes x.
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165
Fig. 6. Distribution of the total solar radiation on thermal collector surface along axes y.
in Fig. 7, where ˛1 denotes the angle between bottom reflector and horizontal plane, and ˛2 denotes the angle between upper reflector and vertical plane. Net incoming solar radiation on the thermal collector surface without the additional solar input from reflected solar radiation from reflectors in the sun peak for this day was Gnet col = 922 W/m2 . As can be seen in the figure, optimal position of the bottom reflector on the above date was at the angle of 38◦ when the top reflector was kept at 0◦ angular position. The values of the optimal positions of upper and bottom reflectors for given tilted plane angle ˇ = 45◦ in the sun peak have also been determined by means of the analytical model represented by Eqs. (1)–(10). These values change during the year with variations of declination angle ı of the sun. A comparison between numerical and experimental findings for optimal position of the bottom reflector (for upper reflector ˛2 = 0◦ ) during the year is shown in Fig. 8 and Table 1. As can be seen, the maximum calculated value of optimal angle position of bottom reflector was 37.78◦ , and was obtained on June 21 (Summer Solstice), when the declination angle was at its maximum 23.45◦ , whereas the minimum calculated value was 5.12◦ , obtained on December 22 (Winter Solstice), when the declination angle was at its minimum −23.45◦ . It also can be seen that the experimental
Fig. 8. A change of optimal position ˛1 max of bottom reflector during the year in the sun peak: (1) solid line-calculated analytical data, (2) squares-experimental data.
value of optimal position of the bottom reflector reached the maximum angle value of 38◦ in June, and decreased to 5◦ in December. The coefficient of correlation (r) of numerical calculated data and experimental data for optimal angle of bottom reflector during the year in the sun peak can be calculated by using the relation [20]: n
n r=
Xi Yi −
n n Xi
Yi
n 2 n 2 , n n n X 2 − X × n Y2− Y i=1
i=1
i
i=1
i=1
i
i
i=1
(11)
i
i=1
i=1
and the root mean square deviation (RMSD = e) can be calculated by using the expression [20]:
e=
n (X i=1 i
n
− Yi )2
(12)
,
where Xi denotes numerically calculated data of optimal angle of bottom reflector, Yi denotes experimental data of optimal angle of bottom reflector during the year, and n is the number of experimental data. Table 1 Calculated (Xi ) and measured (Yi ) values of optimal angle ˛1max of bottom reflector during the year in the sun peak.
Fig. 7. A change of total solar radiation Gtot col on thermal collector surface depending on reflectors position in the sun peak: (1) without upper reflector, (2) ˛2 = 20◦ , (3) ˛2 = 10◦ and (4) ˛2 = 0◦ .
Number of day in year (N)
Xi (◦ )
41 68 86 100 106 130 139 155 167 183 194 211 230 258 274 288 317 355
11.34 18.18 23.19 26.99 28.52 33.77 35.26 37.11 37.78 37.64 36.85 34.57 30.73 23.36 18.79 14.93 8.42 5.12
Yi (◦ ) 8 16 20 24 28 34 36 38 38 38 36 34 30 24 20 16 8 5
ei = Xi − Yi (◦ ) 3.34 2.18 3.19 2.99 0.52 −0.23 −0.74 −0.89 −0.22 −0.36 0.85 0.57 0.73 −0.64 −1.21 −1.07 0.42 0.12
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Fig. 10. A change of the total generated thermal energy during the day by thermal collector: (1) without reflectors, (2) with reflectors in optimal position. Fig. 9. A change of solar radiation on thermal collector during the typical day: (1) without reflectors Gnet col , (2) with reflectors in optimal position Gtot col .
The coefficient of correlation and the root mean square deviation for our data given in Table 1, as calculated by means of Eqs. (11) and (12), were r = 0.992 and e = 1.521◦ , respectively. Root mean square deviation was mainly the consequence of the shift of mechanical components for changing the tilted plane angle of reflectors. The good agreement between numerical and experimental data, which was demonstrated above, allowed us to predict reliable values for optimal position of reflectors for different collector tilted plane angles. A change in total solar radiation on thermal collector surface without and with reflectors in optimal position during the day (typical day 21 June 2009) is shown in Fig. 9. The concentration factor (C) of solar radiation intensity has been calculated based on the measurement results for the total solar radiation on the thermal collector surface with reflectors Gtot col and net incoming solar radiation on the collector surface without the additional solar input from reflected solar radiation from reflectors Gnet col during the day: C=
Gtot Gnet
col
,
(13)
col
where Gnet col is defined by: Gnet
col
= Gdir
col
+ Gdif
col .
(14)
The concentration factor (C) of solar radiation intensity was 1.5 for this day. Also average value of the concentration factor was approximately 1.5 in the summer period (June–September). 4.2. Thermal analysis Thermal analysis was performed for collector without reflectors and with reflectors in optimal position. The thermal efficiency th of the solar thermal collector can be determined from following expression: th =
˙ p (To − Ti ) mc , Aa Gtot col
(15)
˙ = dm/dt is water mass flow rate, cp is water specific heat where m (4180 J kg−1 K−1 ), Ti is water input temperature and To is water output temperature, whereas Aa is the collector surface area [19,21]. The variation of thermal efficiency th relative to the water input temperature Ti , the ambient temperature Ta and the total incoming solar radiation intensity Gtot col is determined experimentally
as a function of the ratio T/Gtot col , where T = Ti − Ta . The function th = f(T/Gtot col ) is used for the performance determination of thermal collectors. Total daily thermal efficiency T is defined by: T =
ET , ES
(16)
where ET (Wh) is the total generated thermal energy during the day by thermal collector and ES (Wh) is the total incoming solar radiation energy during the day on thermal collector. Thermal performance of solar thermal system with reflectors depends on the water input temperature (Ti ), ambient temperature (Ta ), net incoming solar radiation intensity (Gnet col ) and the concentration factor (C). The total generated thermal energy during the day by thermal collector without reflectors and with reflectors in optimal position has been measured in the period March–October 2009. Changes of the total generated thermal energy during the day from 8:00 to 17:00 h by thermal collector with reflectors in optimal position and without reflectors for typical day (21 June 2009) in the summer period are shown in Fig. 10. Measurements during this day have shown that total generated thermal energy has increased by 41% in thermal collector with reflectors in optimal position compared to thermal collector without reflectors. The increase of total thermal energy obtained by thermal collector with reflectors in optimal position during the summer period varied in the range 35–44% and it was dependent on the meteorological parameters, such as the ambient temperature Ta , the wind speed Vw , solar radiation G, etc. The total daily thermal efficiency T has been determined on the basis of measurement results for the total generated thermal energy during the day by thermal collector (ET ) and the total incoming solar radiation energy during the day on thermal collector (ES ). The value of the total daily thermal efficiency for thermal collector with reflectors in optimal position is lower then thermal efficiency of thermal collector without reflectors. For C = 1.5, decrease of total daily thermal efficiency for thermal collector with reflectors in optimal position varies in the range 4–10% during the summer period. The changes of water input temperature and water output temperature during the day in thermal collector without reflectors and with reflectors in optimal position is given in Fig. 11. The water input temperature Ti and water output temperature To during the day in thermal collector with reflectors in optimal position are higher than water input and output temperature in thermal collector without reflectors. Also the temperature
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significantly higher than total thermal energy generated by thermal collector without reflectors. 5. Conclusion
Fig. 11. A change of water input temperature (1) and water output temperature (2) in thermal collector during the day without reflectors and water input temperature (3) and water output temperature (4) in thermal collector during the day with reflectors in optimal position.
difference T0 − Ti between output and input temperature in thermal collector with reflectors in optimal position is higher than temperature difference in thermal collector without reflectors. Thermal efficiency th of thermal collector as a function of T/Gtot col operating values for the same day (21 June 2009) is shown in Fig. 12. These results have been calculated for average ˙ = 0.02 kg/s, net wind speed Vw = 0.3 m/s, water mass flow rate m incoming solar radiation intensity Gnet col = 922 W/m2 and ambient temperature Ta = 28 ◦ C. It can be seen that thermal efficiency th of thermal collector with reflectors in optimal position was lower than thermal efficiency of PV/Thermal collector without reflectors. The results have shown that thermal efficiency th to great extent depends on the ambient temperature and solar radiation. Though the thermal efficiency of thermal collector decreased slightly with the solar radiation intensity, i.e. the thermal efficiency of thermal collector with reflectors was lower than that of thermal collector without reflectors, the total thermal energy generated by thermal collector with reflectors in optimal position was
Fig. 12. Thermal efficiency th of thermal collector: (1) without reflectors, (2) with reflectors in optimal position.
In this paper the solar thermal collector with spectrally selective absorber with and without flat solar radiation reflectors has been considered. The changes of optimal positions of reflectors during the year have been determined analytically and experimentally for collector fixed at ˇ = 45◦ position in order to obtain the maximum concentration of solar radiation intensity. Both numerical calculation and experimental measurements indicated that optimal angle position of the bottom reflector was the lowest (5◦ ) in December and the highest (38◦ ) in June. Systematically good agreement between numerical and experimental data during the year has been found, which allowed us to predict reliable values for optimal position of reflectors for different collector tilted plane angle. Average value of the concentration factor in the summer period (June–September) was approximately 1.5. For this period the increase of total thermal energy obtained by thermal collector with reflectors in optimal position varied in the range 35–44%. The results have shown the positive effect of reflectors made of Al sheet and, considering the additional cost of about 15% for the reflectors, there was an average energy gain of about 40% in the summer period for thermal collector with reflectors. This energy gain is expected to reduce the cost pay back time, and the model proposed in this paper could be useful to determine optimal positions of thermal collectors (with or without reflectors) as integral facade or roof elements in modern buildings. Acknowledgement The authors gratefully acknowledge the support from Ministry of Science of the Republic of Serbia through Project No. TR32026. References [1] H. Gunerhan, A. Hepbasli, Exergetic modeling and performance evaluation of solar water heating systems for building applications, Energy and Buildings 39 (2007) 509–516. [2] A.F. Miguel, Constructal design of solar energy-based systems for buildings, Energy and Buildings 40 (2008) 1020–1030. [3] C.D. Corbin, Z.J. Zhai, Experimental and numerical investigation on thermal and electrical performance of a building integrated photovoltaic-thermal collector system, Energy and Buildings 42 (2010) 76–82. [4] D.K. McDaniels, D.H. Lowndes, H. Mathew, J. Reynolds, R. Gray, Enhanced solar energy collection using reflector-solar thermal collector combinations, Solar Energy 17 (1975) 277–283. [5] S.C. Seitel, Collector performance enhancement with flat reflectors, Solar Energy 17 (1975) 291–295. [6] S.L. Grassie, N.R. Sheridan, The use of planar reflectors for increasing the energy yield of flat-plate collectors, Solar Energy 19 (1977) 663–668. [7] A. Dang, Collector, collector-reflector systems-an analytical and practical study, Energy Conversion and Management 26 (1986) 33–39. [8] A.A. Arata, R.W. Geddes, Combined collector–reflector systems, Energy 11 (1986) 621–630. [9] B. Perers, B. Karlsson, External reflectors for large solar collector arrays, simulation model and experimental results, Solar Energy 51 (1993) 327–337. [10] B. Perers, B. Karlsson, M. Bergkvist, Intensity distribution in the collector plane from structured booster reflectors with rolling grooves and corrugations, Solar Energy 53 (1994) 215–226. [11] J.W. Bollentin, R.D. Wilk, Modeling the solar irradiation on flat plate collectors augmented with planar reflectors, Solar Energy 55 (1995) 343–354. [12] M. Ronnelid, B. Karlsson, The use of corrugated booster reflectors for solar collectors fields, Solar Energy 65 (1999) 343–351. [13] H.M.S. Hussein, G.E. Ahmad, M.A. Mohamad, Optimization of operational and design parameters of plane reflector-tilted flat plate solar collector systems, Energy 25 (2000) 529–542. [14] Y. Tripanagnostopoulos, M. Souliotis, T.H. Nousia, Solar collectors with colored absorbers, Solar Energy 68 (2000) 343–356. [15] B. Hellstrom, M. Adsten, P. Nostell, B. Karlsson, E. Wackelgard, The impact of optical and thermal properties on the performance of flat plate solar collectors, Renewable Energy 28 (2003) 331–344.
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