Research Papers

Comparison-Based Optical Assessment of Hyperboloid and Ellipsoid Reflectors in a Beam-Down Solar Tower System With Linear Fresnel Heliostats

[+] Author and Article Information
Xian Li

NUS Environmental Research Institute,
National University of Singapore,
1 Create Way, CREATE Tower #15-02,
Singapore 138602, Singapore
e-mail: erilx@nus.edu.sg

Meng Lin

Mechanical Engineering,
École polytechnique fédérale de Lausanne,
Lausanne 1015, Switzerland
e-mail: meng.lin@epfl.ch

Yanjun Dai

School of Mechanical Engineering,
Shanghai Jiao Tong University,
800 Dongchuan Road,
Shanghai 200240, China
e-mail: yjdai@sjtu.edu.cn

Chi-Hwa Wang

Department of Chemical and
Biomolecular Engineering,
National University of Singapore,
4 Engineering Drive 4,
Singapore 117585, Singapore
e-mail: chewch@nus.edu.sg

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 October 3, 2016; final manuscript received August 7, 2017; published online September 12, 2017. Assoc. Editor: Marc Röger.

J. Sol. Energy Eng 139(6), 061003 (Sep 12, 2017) (14 pages) Paper No: SOL-16-1434; doi: 10.1115/1.4037742 History: Received October 03, 2016; Revised August 07, 2017

Beam-down concentrating solar tower (BCST) is known for its merits in easy installation and maintenance as well as lower convection heat loss of the central receiver (CR) when comparing to a traditional concentrated solar tower system. A point-line-coupling-focus (PLCF) BCST system using linear Fresnel heliostat (LFH) as the first stage concentrator (heliostat) and hyperboloid/ellipsoid reflector as the tower reflector (TR) is proposed and theoretically analyzed and compared in this paper. Theoretical investigation on the ray concentrating mechanism with two commonly used reflector structures, namely, hyperboloid and ellipsoid, is conducted utilizing Monte Carlo ray-tracing (MCRT) method. The objective of this study is to reveal the achievable optical performance of these types of TRs in the PLCF system considering the effect of LFH tracking errors on TR astigmatism as well as the differences of optical efficiency factors and power transmission in a large-scale biomimetic layout. Results indicate that the ellipsoid system is superior in terms of interception efficiency over the hyperboloid system due to smaller astigmatism at the CR aperture, especially at larger facet tracking error. However, the ellipsoid reflector shows significantly lower TR shading efficiency resulting from the larger TR surface area compared to that of the hyperboloid reflector. The total optical efficiency of the hyperboloid system is always better than that of the ellipsoid system, and this efficiency gap decreases as the ratio ε increases. The hyperboloid TR is proved to be more promising and practical for the PLCF system.

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Grahic Jump Location
Fig. 1

Schematic of the focusing concept of two PLCF systems: (a) the ellipsoid system and (b) the hyperboloid system

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Fig. 2

Schematic of the parameter-based geometric structure of the PLCF systems with ellipsoid and hyperboloid reflectors: (a) the ellipsoid system, (b) the hyperboloid system, and (c) the LFH module

Grahic Jump Location
Fig. 3

Schematic of the parameter-based geometric structure of the 3D CPC

Grahic Jump Location
Fig. 4

Schematic of the geometric and optical structure of a single LFH sun-tracking model: (a) optical structure of the PLCF process, (b) the initial stage, (c) a rotation movement around xm,f-axis (from P-xm,f-ym,f-zm,f to P-xm,s-ym,s-zm,s) with a frame tracking angle βh, and (d) a rotation movement around ym,s-axis (from P-xm,s-ym,s-zm,s to P-xm,t-ym,t-zm,t) with a facet tracking angle βm

Grahic Jump Location
Fig. 5

The coordinates of three LFHs (#1 LFH, #2 LFH, and #3 LFH)

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Fig. 6

Frame tracking angle differences of each facet for an individual LFH as a function of the solar position: (a)–(c) #1 LFH, (d)–(f) #2 LFH, and (g)–(i) #3 LFH

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Fig. 7

Facet tracking angle differences of each facet for an individual LFH as a function of solar position: (a)–(c) #1 LFH, (d)–(f) #2 LFH, and (g)–(i) #3 LFH

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Fig. 8

Facet tracking error of each facet for an individual LFH as a function of solar position: (a)–(c) #1 LFH, (d)–(f) #2 LFH, and (g)–(i) #3 LFH

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Fig. 9

The effect of tracking errors on astigmatism at the lower focal plane with the variation of γ at α = 40 deg and ε = 1.875: (a) the lower focal points of the ID = 1 facet and (b) the variation of Δξ

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Fig. 10

Astigmatism behaviors of hyperboloid and ellipsoid PLCF systems with the variation of facet tracking error Em at ε = 1.875: (a) #2 LFH at α = 80 deg, (b) #2 LFH at α = 40 deg, (c) #3 LFH at α = 80 deg, and (d) #3 LFH at α = 40 deg

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Fig. 11

Comparison of the spot images of the ellipsoid and hyperboloid reflectors: (a) the spot image of the ellipsoid at the lower focal plane, (b) the spot image of the hyperboloid at the lower focal plane, (c) the spot image of the ellipsoid at the exit plane of the CPC, (d) the spot image of the hyperboloid at the exit plane of the CPC, and (e) 1% of 1 × 107 rays transmitted in the PLCF systems removing the spillage rays of TR and CPC

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Fig. 12

Effects of various factors on magnification M for ellipsoid and hyperboloid reflectors: (a) the effect of the ratio ε, (b) the effect of the distance D, (c) the effect of solar azimuth γ, and (d) the effect of the solar altitude α

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Fig. 13

Geometric structure of an individual LFH and a nonuniform layout: (a) the relative structure of a single LFH and a CR and (b) a nonuniform large-scale biomimetic layout

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Fig. 14

The effects of solar position on the optical efficiency factors and power transmission at different values of ratio ε: (a) shading efficiency of TR ηs,TR, (b) efficiency from TR to the exit of CPC (ηitρCPCρTR), (c) total optical efficiency ηo, and (d) power transmission in the PLCF system




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