Caustic and its use in designing optimal absorber shapes for 2D concentrators

Harald Ries; Wolfgang Spirkl

doi:10.1117/12.216969

21 August 1995 Caustic and its use in designing optimal absorber shapes for 2D concentrators

Harald Ries, Wolfgang Spirkl

Proceedings Volume 2538, Nonimaging Optics: Maximum Efficiency Light Transfer III; (1995) https://doi.org/10.1117/12.216969
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

The caustic of a set of edge rays is defined as the set of intersection points of adjacent edge rays. For a body having a smooth differentiable contour, the caustic of its edge rays coincides with the contour of the body. Therefore one would assume that by calculating the caustic of the edge rays as they are produced by a 2D concentrator such as a trough, the optimal shape for the absorber, e.g. the minimal surface absorber capable of intercepting all rays, should also coincide with the shape of the caustic. We show that this conjecture is not valid in general, but only if the caustic indeed forms a closed smooth curve. For parabolic trough systems, the caustic intersects and forms closed domains for half rim angles of around 60 degrees and 120 degrees. In both cases the contour is not smooth. Therefore the optimal shape is not given by the domain enclosed by the caustic. We present a general recipe of how to construct minimum surface absorbers for given caustics in 2D and apply this to the case of trough parabolic concentrators. We show practical absorber shapes for parabolic troughs with various rim angles. The optimal contour depends discontinuously on the rim angle. The area of the optimum shape for a rim angle of 90 degrees is 0.72 of the area of the smallest cylindric absorber capable of intersecting all rays.

Citation Download Citation

Harald Ries and Wolfgang Spirkl "Caustic and its use in designing optimal absorber shapes for 2D concentrators", Proc. SPIE 2538, Nonimaging Optics: Maximum Efficiency Light Transfer III, (21 August 1995); https://doi.org/10.1117/12.216969

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