a test procedure to determine optical characteristics of solar concentrator

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SESI JOURNAL Vol. 20 No. 1 & 2 June- December, 2010

A Test Procedure for Determining Optical Characteristics of a Dish Concentrator and its

Implementation on a Scheffler Dish

C. A. Kinjavdekar, V. P. Muley, S. B. Kedare and J. K. NayakDepartment of Energy Science and Engineering

IIT Bombay, Powai, Mumbai 400076, India

Abstract: To rate and compare the performance of different types of concentrators, a common basis of testing is desirable. This helps in the design and performance prediction of not only concentrator, but also a complete system. The method consists of optical (Focus Test) and thermal (Performance Test) characterisation of concentrator. This communication presents the Focus Test and its implementation on Scheffler dish concentrator. The test provides the size of the focus, the total solar radiation concentrated, its distribution and concentration ratio. This information is useful in the design of receiver shape and the choice of material.

IntroductionVarious types of solar concentrators have been reported in literature (Duffie Beckman, 2006 and Rabl, 1985). Generally, concentrators with tracking mechanism are widely preferred as they give higher energy output. Scheffler dish (Solar Bruecke, 2009) is one of such tracking concentrator; which consists of a set of mirror reflectors arranged in paraboloidal shape, focusing radiation onto the receiver. Overall performance of the solar dish concentrator system depends on the optical as well as thermal performance.

The optical performance of the reflector depends on the flux distribution in the focal region and physical parameters such as reflector geometry, mirror quality, concentration ratio of the collector, and effect of tracking system. Rabl et al. (1980) reported that measurement of the flux distribution is essential for designing the receiver shape and material to evacuate the concentrated solar power. The analysis of the flux distribution can also be useful for comparing different solar concentrators on the basis of their optical performance (Johnston, 1998).

Various methods for optical characterisation of dish concentrator are reported in literature. But most of the methods are very expensive and have specific applications (Wendelin and Grossman, 1995). A simple and indirect optical characterization method called ‘focus test’, has therefore been proposed by Sharma (2005). It is based on temperature measurement in the focal plane of

SESI JOURNAL© 2009 Solar Energy Society of IndiaVol. 20 No. 1 & 2 June - December, 2010

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the solar dish concentrator and hence to estimate the flux concentrated. This is used to find out characteristic parameters like focus size, total input solar power and local concentration ratio of the dish concentrator. Sharma et al. (2005) have implemented this procedure on a paraboloidal type of dish concentrator, called ARUN 160 (Kedare et al., 2006)

In this paper, the experiments based on the above mentioned test procedure for optical characterization are reported for Scheffler dish concentrator (Aap: 9.5 m2) and the results are discussed. While basic principle proposed by Sharma et al. is followed, a change in focus plate arrangement is suggested and implemented far more accurately. Besides, the estimation of temperature distribution on the focus plate is carried out more rigorously by measuring temperature at a large number of points on the plate. Two approaches, viz., (1) isotherm method and (2) area element method, for analysing the temperature distribution on focus plate, have been evaluated from the point of view of their suitability and convenience for characterisation of focus.

Scheffler dish (Fig. 1) consists of mirror reflectors arranged in paraboloidal shape and is mounted on an axis parallel to the polar axis of the earth. It reflects the incident solar radiation in a fixed direction notwithstanding the motion of the sun and thus has a fixed focus close to ground. It is mainly used for large scale community cooking. Characterisation of such dish concentrator is essential in order to predict its performance over entire operating range. Also accurate optical characterisation is essential for thermal performance characterisation. The characterization of optical performance and detection of optical losses play an important role in improving optical efficiency of the concentrator, which is defined as the ratio of input solar energy captured by the reflector to the input solar energy. In order that the results of experimental investigations are appreciated, the theoretical basis of the method is explained to start with (Sharma et al., 2005)

Fig. 1 :Sketch of a typical Scheffler dish

Kitchen wall

Secondaryreflcctor

Cooking pot

Reflecto

r

Theory of Focus TestA target plane is selected in front of the receiver of a dish concentrator. It is chosen very close to the mouth of the receiver, typically at a distance of 1/4th of the diameter of the receiver. A thin flat metal plate with known emissivity and thermal conductivity is mounted in the target plane such that solar radiation reflected from the dish would be concentrated on one side (front) of the plate. The opposite

KinjavdeKar, Muley, Kedare and nayaK

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side (back) of the plate is insulated. The heat loss from the target plate would be due to conduction through the back surface and convection and radiation from the front surface.

Consider a small strip of radius ‘r’ and width ‘dr’ in the plate as shown in Fig. 2. Neglecting the heat capacity effect of the strip compared to other terms at steady state, the energy balance for this strip can be written as,

Fig. 2 : A typical strip on focus plate

Absorbed energy = Energy loss by conduction + Energy loss by convection + Energy loss by re-radiation

(1)

The conduction loss consists of two parts, heat conduction from one strip to the neighbouring strips and the heat conduction through the insulation provided on the back side of the plate. Sharma et al. (2005) reported that the heat loss due to conduction from a strip to neighbouring strips is negligible as compared to the convection and radiation loss terms. This is acceptable as long as the plate is thin and the convection and radiation components are order of magnitude higher than conduction loss component. The heat loss by conduction through the insulation consists of conduction through the insulation and then convection to ambient air from the outside surface of the insulation. The convective resistance is very small compared to the conductive resistance and hence can be neglected. Thus Eq. (1) can be written as

(2)

where Φc(r) solar flux at a distance ‘r’ from the center of the focus, W/m2 h convective heat transfer coefficient of the focus plate, W/m2K Tr temperature of the strip at radius ‘r’ from the center of the focus, K Tamb ambient temperature, K ki thermal conductivity of the insulation, W/m-K L thickness of the insulation layer, m σ Stefan-Boltzmann constant, W/m2K4

A Test Procedure for Determining Optical Characteristics of a Dish Concentrator and its Implementation on a Scheffler Dish

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є emissivity of the plateα absorptance of the plate for solar radiation

The convective heat transfer coefficient of the annular strip of the plate can be calculated from the following correlation, assuming annular symmetry for temperature distribution.

h = (Nu ka) / D (3)

with Nu = 0.56 (GrPr cos θi ) (1/4) for 105 < (Gr*Pr*cos θi ) <1011

whereka thermal conductivity of air, W/mK D characteristics length of the plate, mθi inclination of the flat plate with the vertical, degGr Grashof Number = [g β (Tavgstrip – Tamb ) D

3 ] / ν2

Pr Prandtl number = ν/αtg acceleration due to gravity, m/s2

Tavgstrip temperature of the annular strip under consideration, KTamb ambient temperature, Kν kinematic viscosity, m2/sβ coefficient of volume expansion, K-1

αt thermal diffusivity, m2/s

This is valid for 0° < θi < 89°. In case of Scheffler dish, θi happens to be non-zero constant depending on its location. The air properties required for the above correlation are calculated at the mean temperature given by ( Tavgstrip + Tamb ) / 2.

It may be noted that the front side of target plate mostly sees the reflector of the dish; it also sees a part of the surrounding ground and a very small fraction of the sky. Consequently, the ambient temperature, instead of the sky temperature, is used in the radiation term of Eq. (2). This is a reasonably good assumption.

Equation (2) suggests that the solar flux distribution at focal region of the concentrator can be estimated if the temperature distribution is measured. Thus a grid of thermocouples fixed on the entire focus plate would provide a means of estimating the flux distribution. Two approaches can be considered for estimating solar flux distribution, namely, (i) isotherm method and (ii) area element method (Kinjavdekar, 2009).

Isotherm methodBased on the temperatures recorded, isotherms can be plotted adopting linear interpolation technique. The area of the focus plate thus gets divided into a number of strips; the temperature of each strip can be taken as the average of temperatures of neighbouring isotherms. The area of each strip is also calculated. The average temperature of the whole plate (Tavg,plate) is calculated by taking the area-weighted average. The convective heat transfer coefficient is calculated based on this average plate temperature and assumed to be constant for the entire plate. The convective and radiative losses are then calculated for each strip using respective area and average strip temperature. These along with the conduction heat loss from the back surface of the plate can be used in Eq. (2) to get the solar flux falling on a strip. It may be mentioned that the area on the focus plate, which lies outside the area


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covered by the thermocouple grid may be neglected. The method gives a good visualisation of the temperature distribution on the focus plate and

hence can be very useful for collector and receiver design.

Area element methodArea element method is essentially a numerical method. It eliminates the linear interpolation of temperatures for isotherm plotting and thus is a faster method for calculating flux on the focus plate. In this method, each thermocouple is assumed to represent the temperature of a finite area element of d1 by d2 (Fig. 3). It is assumed that the thermocouple represents the average temperature of the respective area element. The average temperature of the plate is calculated based on the values of all temperature points. The convective and radiative losses are then calculated for all area elements. It may be mentioned that each thermocouple is assumed to be representing same amount of area. The area of the focus plate, lying outside the area covered by the thermocouple grid, is neglected. This method is very simple, fast and easily programmable. A good visualisation of the flux distribution on the focus plate can be obtained by using computing software like MATLAB.

Fig. 3 : A typical element area on focus plate

By applying Eq. (2) over the entire focus area (Af), the total radiation concentrated on the target plane Φ can be calculated as,

( )1

i=nr Ac i i

i=φ = Φ ∑

(4)

where Ai is the area of ith strip for isotherm method or the area of ith element for area element method.

The optical concentration ratio (CR) of the concentrator can be calculated as,

CR = Φ / Af Ibn (5) where Af is the aperture area of the dish.


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Thus the flux distribution on the plate can be determined by measuring the temperature distribution on the focus plate and hence, the total concentrated solar flux and concentration ratio of the concentrator can be calculated. Individual strip losses can also be used to estimate the local concentration ratios. This method is implemented on a Scheffler dish concentrator.

Experimental Set-upThe set-up consists of a metal plate (material: mild steel, size: 750 mm x 750 mm; thickness: 3 mm) mounted in front of the receiver (in a plane parallel to the focal plane) and is called as focus plate. To ensure that the plate receives all the reflected radiation from the reflectors, it is made about 20 % larger than the receiver size of the dish. A set of thermocouples are attached to the back side of the plate and are arranged in the form of grid with a spacing of about 75 mm (Fig. 3). Thus 49 thermocouples are fixed with a grid of 7x7. Thermocouples are held in contact with the plate by using an assembly made up of aluminium holder and bolts as shown in Fig. 4. Ceramic rings are used close to the beads of thermocouples to protect the sleeve from high temperature. A thin layer of cement, which can withstand high temperature and conduct heat is used to fix the bead onto the focus plate. A layer of glass wool insulation (50 mm thick) is provided over the thermocouples to minimize heat losses. The front side of the plate is coated with the special paint called Pyropaint, which does not peel off at high temperature and the emissivity of the plate remains constant throughout the experiment. It may be mentioned that, Sharma (2005) did not insulate the focus plate so that heat losses took place from both sides of the plate. On the other hand, in the current arrangement, the back side of the plate is insulated so that the estimation of losses from the plate using its temperature measurement is more accurate. Besides, no paint was used on the front side of the focus plate by Sharma (2005).

Fig. 4 : Typical thermocouple assembly

Instrumentation used for focus test consists of Pyrheliometer for solar irradiance measurement, anemometer for wind speed measurement, and K-type thermocouples for temperature measurement. The thermocouples were calibrated in the range of 300 to 1000oC.

Experimental Procedure The focus plate is mounted at the desired place and the concentrator is focused onto it. The


(b) Plan view

(a) Section view

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measuring instruments are mounted properly and the data are logged onto a computer by using data acquisition modules. The concentrator is focused manually to start with and then its automatic tracking mechanism takes over for continuous tracking during the complete testing period. The test is carried out around solar noon and the measurements are made when the temperature records show steady values for about 25 minutes since the time constant of the focus plate is estimated to be about 12 minutes (Kinjavdekar, 2009). Temperature measurements are recorded at every 1 minute interval while the solar irradiance and wind speed measurements are recorded at every 5 minutes. While experiments have been carried out for a number of days and such measurements are made, the results of a typical day are discussed in a greater detail in the next section.

Results and DiscussionBased on the temperature records of the focus plate, the optical characteristics of Scheffler dish concentrator are estimated both by isotherm and area element method. The following values have been used for the calculations:

Emissivity of focus plate (estimated from FTIR measurement) = 0.125• Thermal conductivity of insulation = 0.06 W/m-K• Thickness of insulation = 0.05 m• Absorptivity of focus plate in solar spectrum = 0.875• Figure 5 shows a typical isotherm plot on March 30, 2009; the temperatures (in °C) of different

strips are listed in a column on the right side of the figure. From this plot of isotherms, the temperature

Table 1: Temperature values and mean film temperature

Strip Boundary

Tstrip (°C) Tavgstrip (°C) Area (m2) Tavgplate (°C) Tamb (°C) Tmf (°C)

0 (Centre) 755

331.8 37.1 184.5

1 750 752.5 0.00152 700 725 0.00423 650 675 0.00904 600 625 0.00935 550 575 0.00906 500 525 0.00887 450 475 0.00978 400 425 0.01049 350 375 0.011410 300 325 0.013211 250 275 0.023012 200 225 0.032513 150 175 0.046814 100 125 0.0128

Total Area of Strips 0.2017


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Table 2: Flux and concentration ratio based on isotherm method (Ibn = 701 W/m2)

Flux (W/m2)Strip Conductive

componentConvective component

Radiative component

Total Local CR

N 981.2 4196.9 8883.5 14061.5 20.1M 943.4 4035.6 7960.5 12939.6 18.5L 874.9 3742.3 6467.2 11084.4 15.8K 806.3 3449.0 5192.5 9447.7 13.5J 737.7 3155.6 4113.7 8007.1 11.4I 669.2 2862.3 3209.8 6741.3 9.6H 600.6 2569.0 2460.8 5630.4 8.0G 532.0 2275.7 1847.8 4655.5 6.6F 463.4 1982.4 1353.3 3799.1 5.4E 394.9 1689.1 961.0 3044.9 4.3D 326.3 1395.8 655.6 2377.7 3.4C 257.7 1102.4 423.3 1783.5 2.5B 189.2 809.1 251.4 1249.7 1.8A 120.6 515.8 128.4 764.8 1.1

Total incident power (W): 762.6

Fig. 5 : Isotherm diagram of focus plate (March 30, 2009)


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Element Flux (W/m2)

Local CRNo. Temperature(°C)

Conductive component

Convective component

Radiative component

Total

T18 755 984.46 4076.50 8967.90 14028.87 20.0T25 734 956.34 3960.06 8267.64 13184.03 18.8T19 656 848.63 3514.04 5954.74 10317.41 14.7T26 643 831.00 3441.04 5627.86 9899.90 14.1T24 628 810.60 3356.57 5266.37 9433.54 13.5T32 623 802.91 3324.71 5134.57 9262.18 13.2T17 607 781.21 3234.87 4776.10 8792.18 12.5T33 535 682.21 2824.94 3369.36 6876.51 9.8T31 516 657.09 2720.88 3067.24 6445.21 9.2T27 413 515.02 2132.61 1714.82 4362.44 6.2T20 398 495.25 2050.76 1569.01 4115.03 5.9T23 396 491.99 2037.26 1545.84 4075.10 5.8T11 330 402.20 1665.45 998.47 3066.12 4.4T30 317 383.43 1587.74 904.36 2875.53 4.1T34 314 379.81 1572.71 886.90 2839.41 4.1T12 306 369.25 1529.01 837.44 2735.70 3.9T16 306 368.43 1525.61 833.68 2727.72 3.9T39 302 363.65 1505.82 812.00 2681.47 3.8T38 279 331.22 1371.55 674.92 2377.70 3.4T10 267 315.31 1305.65 613.80 2234.76 3.2T40 261 307.22 1272.16 584.20 2163.59 3.1T13 231 265.84 1100.80 447.40 1814.04 2.6T28 217 246.79 1021.91 392.15 1660.85 2.4T37 212 239.83 993.10 373.11 1606.05 2.3T9 208 234.71 971.89 359.46 1566.06 2.2T15 202 225.88 935.33 336.69 1497.90 2.1T41 197 219.57 909.19 320.96 1449.72 2.1T29 197 218.69 905.57 318.82 1443.08 2.1T22 190 209.65 868.14 297.17 1374.97 2.0T4 186 204.92 848.54 286.20 1339.65 1.9

Table 3: Flux and concentration ratio based on area element method (Ibn = 701 W/m2)


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Element Flux (W/m2)

Local CRNo. Temperature(°C)

Conductive component

Convective component

Radiative component

Total

T5 179 194.74 806.40 263.43 1264.58 1.8T35 176 190.63 789.39 254.55 1234.58 1.8T21 173 185.82 769.44 244.36 1199.62 1.7T3 172 184.91 765.67 242.47 1193.04 1.7T46 172 184.38 763.48 241.37 1189.22 1.7T8 166 176.93 732.62 226.19 1135.73 1.6T47 165 176.01 728.84 224.36 1129.21 1.6T14 163 173.28 717.54 218.97 1109.80 1.6T45 156 162.72 673.81 198.77 1035.30 1.5T6 155 161.46 668.57 196.43 1026.46 1.5T2 151 155.74 644.87 185.99 986.60 1.4T36 144 146.47 606.50 169.75 922.72 1.3T42 135 133.73 553.76 148.66 836.15 1.2T48 134 133.10 551.14 147.65 831.88 1.2T44 132 129.64 536.80 142.18 808.62 1.2T1 131 129.43 535.94 141.86 807.23 1.2T7 126 121.83 504.50 130.23 756.57 1.1T49 86 66.85 276.82 59.40 403.07 0.6T43 79 56.96 235.85 48.92 341.72 0.5

Total incident power (W): 880.08

Fig. 6 : 3-D plot of concentration ratio


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of strips, the corresponding strip areas and the average plate temperature (Tavg,plate) are calculated as per the procedure outlined in section 2 and are presented in Table 1. At the mean temperature of Tavg,plate and the ambient temperature, the properties of air are taken from standard handbook. Besides, the average wind speed corresponding to the steady state period of the experiment was found to be 1.11 m/s. Based on these data, the convective heat loss coefficient is calculated for different inclinations of the focus plate during the test period. The average convective heat loss coefficient is found to be 5.13 W/m2-K. Accordingly, the corresponding convective heat loss from each strip is estimated. The radiative losses are calculated by using average strip temperature and the corresponding area. The conduction loss from the backside of the plate is estimated. As per the procedure mentioned in section 2, the solar flux, total incident power and concentration ratio are calculated; Table 2 presents such results; the maximum uncertainty in the flux calculations is about 0.1%.

Similarly, the calculations are also made based on area element method (section 2) and the corresponding results of are presented in Table 3 in the order of decreasing element temperature. It may be seen that the total number of area elements in the focus plate (Fig. 3) is quite high compared to the total number of strips of the plate based on isotherm method. Consequently the flux estimation is likely to be more accurate. Besides, it eliminates the procedure of linear interpolation, between two measured values of temperatures, adopted in isotherm method. In addition, the area element method is less tedious than the latter and thus is recommended.

The parameter local optical concentration ratio is used to compare the performance of a dish concentrator on various days. As the term concentration ratio is dimensionless, it gives the optical performance of the concentrator independent of the variation in the solar radiation. Figure 6 represents the 3-D plot of variation of concentration ratios with distance from the centre of the focus plate. The central thermocouple is assumed to be at the origin, thus thermocouple grid is spread over all four quadrants. Figure 7 shows the contour plot of the concentration ratio variation on the focus plate based on area element method. Thus these plots can be used to compare the optical performance of dish concentrator on various days.

The results of the focus test can be used to select the size of the focus and hence the aperture of the receiver of a dish concentrator. The procedure can be explained as follows. Out of the different values of the temperatures measured on the focus plate, the one with highest

Fig. 7 : Contour plot of concentration ratio


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value is chosen as the centre and concentric circles are drawn around it. Each circular area may enclose a number of area elements (refer Fig. 3) partially or completely depending on the radius chosen. As mentioned earlier, each area element is associated with a constant temperature and hence flux. With a weighted area-average of these elements, the total power incident on a particular area is estimated. Accordingly, the cumulative incident power is estimated as different concentric circles from the centre on the focus plate are considered. Figure 8 shows a plot of the cumulative incident power and the fraction of the total incident power against radius of the circular area of the focus plate. It is seen that the cumulative incident power increases as the radius increases, initially quite rapidly and then slowly. This is as expected. With increase in area around the centre, more and more incident power is accounted. Once the major part of the focus is covered, any further increase does not contribute to the cumulative power significantly.

The designer has the choice to select a particular size of the focus depending on what fraction of the total power is required to be intercepted. For an example, if 95% of the total power is to be intercepted, the aperture of the receiver can be 30 cm in the present dish (Fig. 8). It may be noted that while a larger size of the aperture would intercept higher fraction of the power, it would lead to higher receiver heat loss. Thus a trade-off has to be made in the final

Fig. 8: Variation of cumulative incident power and fraction on the focus plate as a function of radius

receiver design. The focus test results however provide a clear picture as far as the interception of the incident power in the focus region is concerned. This along with the receiver heat loss studies can be used to size the receiver. The magnitude of the incident power can be used as a basis for selecting the material of the receiver.

ConclusionsThe optical characterisation of a solar dish concentrator can be done by carrying out focus test. It provides the size of the focus, the total incident power, its distribution and the concentration ratio.

Two approaches, namely, the isotherm method and the area element method, can be considered for estimating the solar flux and its distribution on the focus plate. The second approach is more accurate and is recommended. The focus test results can be used to find out the focus size and hence


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the aperture of the receiver of a dish. While a larger aperture of the receiver would intercept higher fraction of the incident power, it would result in higher receiver heat loss.

AcknowledgementsThe authors acknowledge the financial support provided by the Ministry of New and Renewable Energy, Government of India, New Delhi for carrying out this work.

References1. Duffie J. and Beckman W., Solar engineering of thermal processes, 2nd edition, John Wiley, New York,

1991.2. Johnston G., ‘Focal region measurements of the 20 m2 tilted dish at Australian National University’, Solar

Energy, 63(2), 117-124, 19983. Kedare S.B., Nayak J.K. and Paranjape A.D., Development, installation and evaluation of large scale

concentrating solar collector for medium temperature industrial thermal applications. Final Report of R&D project no. 15/9/2002-ST, Ministry of New and Renewable Energy, Govt. of India, 2006.

4. Kinjavdekar C. A., ‘Development of Testing Procedure for Solar Dish Concentrators’, M.Tech. Dissertation, Dept of Energy Science and Engineering, IIT, Mumbai, 2009

5. Rabl A., Active Solar Collectors and their Applications, Oxford University press, New York, 1985.6. Rabl A., Gaul H. and Bendt P., ‘Determining the optical quality of focusing collectors without laser ray

tracing’, Journal of Solar Energy Engineering, 102, 128-133, 1980.7. Sharma V.R., ‘Testing of paraboloidal concentrating solar thermal collector’, M.Tech. Dissertation,

Energy Systems Engineering, IIT-Bombay, 20058. Sharma V.R., S. J. Bhosale, S.B. Kedare, J.K.Nayak, ‘A Simple method to determine the optical quality of

paraboloid concentrating solar thermal collector’, SESI Journal, 15(2), pp. 21-27, 20059. Solare Bruecke, 2009, ‘How does a Scheffler reflector work?’, http://www.solare-bruecke.org , Website

accessed on Feb 2, 201010. Wendelin T.J. and Grossman J.W., ‘Comparison of Three Optical Methods for Optical Characterization of

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a test procedure to determine optical characteristics of solar concentrator

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