# Mathematical modelling and analysis of variation in surface of solar Scheffler concentrator for seasonal variations

VIT University

^{1}07 Apr 2016-pp 78-83

TL;DR: In this paper, the seasonal tracking variation in the parabola curvature was calculated and the maximum depth of the 7m2 concentrator for equinox, summer and winter solstice was 0.227m, 0.223m and 0.229m respectively.

Abstract: Solar concentrators are extensively tested as an alternative for conventional thermal sources. Scheffler concentrators is proving to be very effective in medium temperature applications as it has advantage of easy manufacturing and tracking. Though manufacturing is easy, it is complex to design for any required area of the reflector. The work here is an attempt to make the design process simpler. The seasonal tracking variation in the parabola curvature was calculated. It shows that variation in vertical curvature from the equinox position to summer solstice is 22.4% while that for winter solstice is −18.2% and that in horizontal curvature for summer solstice is −22.6% and for winter solstice is 13.2%. Also, variation in the curvatures of the crossbars were studied and it is found that the variation during equinox and seasonal extremes vary from 7.6% to 16.6%. The maximum depth of the 7m2 concentrator for equinox, summer and winter solstice is 0.227m, 0.223m and 0.229m respectively.

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TL;DR: In this paper, the authors present important developments of small point-focusing concentrator in the past decade, which refers to the parabolic dish concentrator, the point-focus Fresnel lens, and the Scheffler reflector.

Abstract: The technology of small point-focusing concentrator of solar energy has been developing rapidly in recent years owing to its compact structure and high collecting efficiency. This report presents important developments of small point-focusing concentrator in the past decade. This kind of solar concentrator refers to the parabolic dish concentrator, the point-focusing Fresnel lens, and the Scheffler reflector. Technological advances of these concentrators and the related performances have been presented. There are three main mirror fabrication technologies for dish concentrator, which are high polishing metal, silver-glass mirror and vacuum-membrane. Polymethyl methacrylate is widely used as material in Fresnel lens. Many scholars have proposed new lens shape to improve the uniformity of focusing. The Scheffler reflector has a characteristic of fixed focus, but its design parameters are not perfect so current research focuses on the theoretical calculation of the mirror. In addition, typical applications of the small point-focusing concentrator in photovoltaic system, solar thermal system, solar chemical system, and day-lighting system are summarized. Upon listing the important publications in open literature, a category of main applications of such kind of solar collector is provided based on the working characteristics of the system.

21 citations

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TL;DR: In this paper, the authors present a complete description of the design principle and construction details of an 8m2 surface area Scheffler concentrator with respect to equinox (solar declination) by selecting a specific lateral part of a paraboloid.

98 citations

### "Mathematical modelling and analysis..." refers background or methods in this paper

...Whereas axis parallel to east-west direction is used to adjust seasonal variations [3]....

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...Standing and laying are the two configurations of the Scheffler depending on its orientation with absorber [3]....

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TL;DR: In this paper, a new mathematical model for estimating the intercept factor of a Scheffler-type solar concentrator (STSC) based on the geometric and optical behaviour of the concentrator in Cartesian coordinates was developed and applied to determine the technical feasibility of attaching the STSC to a 3-kWe Stirling engine.

65 citations

### "Mathematical modelling and analysis..." refers background in this paper

...Slope of parabola is calculated such that it corresponds to the required height of the absorber [4, 7]....

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...The seasonal adjustments consists of rotation of symmetrical axis of parabola by declination,δ about Scheffler focus such that its axis will still be parallel to the incoming rays [4]....

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27 May 2015TL;DR: In this paper, the effect of the variations of rim angles was found to cause variations in the size of the focal image of Scheffler reflectors in two axes, and these variations differ among these axes.

Abstract: Our purpose is to help projects of receivers for Scheffler concentrators in order to avoid losses of energy at the entrance of thermal radiation absorbers. The Scheffler concentrator is a paraboloidal solar concentrator that works in a two axes track system and, thus, maintains the focal image fixed in its stopped absorber with the variation of the solar declination and azimuth. The image formed by Scheffler concentrator is presented. The reflector geometry is defined by a lateral section of a paraboloid and its reflector has elliptical profile. At equinox, these rim angles are approximately 49.6 and 109.6 degrees from the paraboloid axis. However the tracking system for adjusting to the variation in solar declination causes a change in these rim angles. An analysis of the effect of these variations over the image of the focus, the aperture area to the Sun, and the concentration ratio is performed. The effect of the variations of rim angles was found to cause variations in the size of the focal image of Scheffler reflectors in two axes, and these variations differ among these axes. Were also found that the aperture area can vary twice, and, the concentration ratio, once during the year.

5 citations

### "Mathematical modelling and analysis..." refers background in this paper

...Slope of parabola is calculated such that it corresponds to the required height of the absorber [4, 7]....

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