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Research Papers

Optimal Heat Collection Element Shapes for Parabolic Trough Concentrators

[+] Author and Article Information
Charles L. Bennett

 Lawrence Livermore National Laboratory, Livermore, CA 94550

J. Sol. Energy Eng 130(2), 021008 (Mar 10, 2008) (5 pages) doi:10.1115/1.2888757 History: Received November 08, 2006; Revised December 19, 2007; Published March 10, 2008

For nearly 150years, the cross section of the heat collection tubes used at the focus of parabolic trough solar concentrators has been circular. This type of tube is obviously simple and easily fabricated, but it is not optimal. It is shown in this article that the optimal shape, assuming a perfect parabolic figure for the concentrating mirror, is instead oblong and is approximately given by a pair of facing parabolic segments.

FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

A drawing of the parabolic trough solar concentrating mirror and hot air engine built by John Ericsson in 1883 is shown. Ericsson’s “Sun-motor” was a form of Stirling engine. The heat collection tube at the focus is clearly circular. It is also notable that Ericsson’s trough was not horizontal, and indeed featured a universal joint so that the mirror could be positioned to directly face the sun.

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Figure 2

The shapes of three types of heat collection element profiles are displayed. Each shape has a height to width ratio of 2. The shape labeled “caustic” is a minimal absorber according to the recipe of Ries and Spirkl for a parabolic concentrating mirror having f∕D=0.25. The shape labeled “parabolas” corresponds to segments from a pair of parabolic curves having a common focus at the center of the figures, and is Cobble’s optimal shape. The third shape is a simple rhombus, having a height twice its width.

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Figure 3

An illustration of the effects of surface slope errors on the distribution of reflected sun light is displayed in the x-y plane perpendicular to the parabolic trough longitudinal symmetry axis

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Figure 4

An illustration of the case of a rhombus shaped heat collection element is shown

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Figure 5

Curves of the net thermal power collected are shown as a function of the width of a rhombic heat collection element for various focal length to aperture diameter f∕D ratios. The arrow indicates the value of the FWHM for the reflected solar flux Gaussian distribution assumed.

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Figure 6

Curves of the net thermal power collected are shown as a function of the diameter of a circular heat collection element for various focal length to aperture diameter f∕D ratios. The right hand arrow indicates the absorbing tube diameter to focal length for the LS-3 heat collection elements used in the SEGS plants. The f∕D ratio equals 0.288 for the SEGS mirrors.

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Figure 7

A curve of the net thermal power collected for the rhombic collector with a concentrating mirror having f∕D=0.17 is compared with the curve for the circular tube collector with a concentrating mirror having f∕D=0.20. The height to width ratio is 2.12 for the rhombic collector.

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Figure 8

The fractional absorption as a function of the mean width to focal length ratio is displayed for four different choices for the shape of the profile of the heat collection element. These curves, nonintersecting over the displayed range, are explicitly labeled in the figure. In this case, the reflected sunlight distribution is assumed to have a normal distribution with a rms angular width of 5.3mrad.

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Figure 9

The fractional absorption as a function of the mean width to focal length ratio is displayed for four different choices for the shape of the profile of the heat collection element. These curves, nonintersecting over the displayed range, are explicitly labeled in the figure. In this case, the solar angular distribution is assumed to be completely unaffected by optical aberrations or atmospheric scattering.

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