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Research Papers

Shape Optimized Heliostats Using a Tailored Stiffness Approach

[+] Author and Article Information
Li Meng

ASME Student Member
Department of Precision Instruments
and Mechanology,
Tsinghua University,
Beijing 100084, China;
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: mengl04@gmail.com

Zheng You

Professor
Department of Precision Instruments
and Mechanology,
Tsinghua University,
Beijing 100084, China
e-mail: yz-dpi@mail.tsinghua.edu.cn

A. F. M. Arif

Professor
Member of ASME
Department of Mechanical Engineering,
King Fahd University of Petroleum & Minerals,
Dhahran 31261, Saudi Arabia
e-mail: afmarif@kfupm.edu.sa

Steven Dubowsky

Professor
ASME Fellow
Department of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: dubowsky@mit.edu

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received November 6, 2012; final manuscript received September 29, 2013; published online November 26, 2013. Assoc. Editor: Markus Eck.

J. Sol. Energy Eng 136(2), 021017 (Nov 26, 2013) (9 pages) Paper No: SOL-12-1300; doi: 10.1115/1.4025827 History: Received November 06, 2012; Revised September 29, 2013

In central receiver systems, the ideal reflective shape of a heliostat is a section of a paraboloid that adapting with the sun's angle and the mirror's location in the field. Deviation from this shape leads to optical astigmatism that increases the spot size on the receiver aperture, which eventually causes higher energy loss and lower conversion efficiency. However, it is challenging to implement the ideal shape by conventional design and manufacturing methods. In this paper, a novel compliant heliostat design methodology is proposed. By tailoring the two dimensional stiffness profile of a square plate, the paraboloid shape can be formed by a simple, low-cost mechanism with concentrated moment loads on the corners of the plate. The static optimized shapes, which can be easily realized by adjusting the loads according to the locations during heliostat assembly on the site, are suggested as approximations of the ideal shapes. Analytical models were developed in detail for the methodology. Numerical analysis consists of finite element analysis, optical ray tracing, and optimization. The numerical results illustrate that the performance of the shape optimized heliostats using tailored stiffness approach is close to the ideal shapes, providing substantial improvement in optical efficiency and reduction in spot size comparing to the flat mirrors. Furthermore, experiments on a prototype heliostat mechanism with a honeycomb-sandwich panel were conducted to validate the effectiveness of this low-cost shaping approach.

Copyright © 2014 by ASME
Topics: Design , Mirrors , Shapes , Stiffness
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Figures

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Fig. 1

Compliant heliostat mechanism

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Fig. 2

A simple optical model of a heliostat and receiver system

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Fig. 3

The ideal heliostat paraboloid

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Fig. 5

Heliostat mechanism

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Fig. 4

Concept of a cable tensioned heliostat mounted on its tracker

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Fig. 9

Errors between the tailored-stiffness heliostat shape and the ideal paraboloid; units: μm

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Fig. 12

Photograph of the deformation experiment

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Fig. 13

Honeycomb-sandwich panel

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Fig. 14

Contour plots of analytical surface deformation; units: mm

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Fig. 8

FEA deformation of the tailored-stiffness heliostat; units: m

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Fig. 17

Reflected points on the receiver aperture plane for honeycomb-sandwich panel; units: mm

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Fig. 7

Reference field configuration

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Fig. 10

Normalized flux distribution on the receiver aperture plane for the tailored-stiffness heliostat; units: m

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Fig. 11

Normalized flux distribution on the receiver aperture plane for the flat heliostat; units: m

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Fig. 15

Experimental deformation of the honeycomb-sandwich panel; units: mm

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Fig. 16

Experimental deformation of the steel sheet; units: mm

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Fig. 18

Normalized flux distribution on the receiver aperture plane for honeycomb-sandwich panel; units: m

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Fig. 6

Heliostat stiffness design

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