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Research Papers

Explicit Analytical Expression for Solar Flux Distribution on an Undeflected Absorber Tube of Parabolic Trough Concentrator Considering Sun-Shape and Optical Errors

[+] Author and Article Information
Sourav Khanna

Department of Energy Science and Engineering,
Indian Institute of Technology Bombay,
Powai, Mumbai 400076, India
e-mail: sourav.khanna1@gmail.com

Vashi Sharma

Centre for Energy and Environment,
Malaviya National Institute of Technology,
J.L.N. Marg,
Jaipur 302017, India

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received July 13, 2015; final manuscript received November 22, 2015; published online December 22, 2015. Assoc. Editor: Dr. Akiba Segal.

J. Sol. Energy Eng 138(1), 011010 (Dec 22, 2015) (10 pages) Paper No: SOL-15-1215; doi: 10.1115/1.4032122 History: Received July 13, 2015; Revised November 22, 2015

The absorber tube of the parabolic trough receives the concentrated sun-rays only on the portion facing the reflector. It leads to nonuniformity in the temperature of absorber tube. Thus, the material of tube expands differentially and the tube experiences compression and tension in its different parts. It leads to bending of the tube and the glass cover can be broken. The bending can be reduced by (i) reducing the circumferential nonuniformity in absorber's temperature (using material of high thermal conductivity) and (ii) reducing the nonuniformity in solar flux distribution (using appropriate rim angle of trough). In most of the available studies, Monte Carlo Ray Tracing software has been used to calculate the distribution of solar flux and few studies have used analytical approach. In the present work, an explicit analytical expression is derived for finding the distribution of solar flux accounting for the sun-shape and optical errors. Using it, the design calculations can be carried out in significantly lesser time and lesser computational effort. The explicit expression is also useful in validating the results computed by softwares. The methodology has been verified with the already reported results. The effects of optical errors, rim angle, and aperture width of trough on the solar flux distribution and total flux availability for absorber tube have also been studied. From the calculations, it is found that for Schott 2008 PTR70 receiver (absorber tube with 70 mm outer diameter), 126 deg, 135 deg, and 139 deg, respectively, are the appropriate rim angles corresponding to minimum circumferential nonuniformity in solar flux distribution for 3 m, 6 m, and 9 m aperture width of trough. However, 72 deg, 100 deg, and 112 deg, respectively, are the appropriate rim angles corresponding to the maximum solar flux at absorber tube for 3 m, 6 m, and 9 m aperture width of trough. Considering both the circumferential nonuniformity and the total solar flux availability, 100 deg, 120 deg, and 130 deg, respectively, are the best rim angles.

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References

Figures

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Fig. 1

Cross-sectional view of the system

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Fig. 2

Availability of the sun-rays on the surface of absorber tube

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Fig. 3

Calculation of w(θ): (a) θshd < θθrim and θrim≤ 90 deg, (b) 90 deg < θ < 180 deg and θrim≤ 90 deg, and (c) θrim < θ≤180 deg and θrim > 90 deg

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Fig. 4

Surface of absorber tube intercepting reflected energy from any arbitrary point of trough

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Fig. 6

Distribution of the local concentration ratio

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Fig. 7

Distribution of solar flux on absorber tube for various values of optical errors

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Fig. 8

Distribution of solar flux for various values of rim angle keeping trough's aperture-width fixed as 5.76 m and absorber's outer diameter as 70 mm

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Fig. 9

Variation in total solar flux at absorber tube with trough's rim angle keeping trough's aperture-width fixed as 5.76 m and absorber's outer diameter as 70 mm

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Fig. 10

Distribution of solar flux for various values of aperture width of trough keeping trough's rim angle fixed as 120 deg and absorber's outer diameter as 70 mm

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Fig. 11

Variation in total solar flux at absorber tube with aperture width of trough keeping trough's rim angle fixed as 120 deg and absorber's outer diameter as 70 mm

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Fig. 12

Geometry of parabola

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