Abstract

For technical reasons, large three-dimensional compound parabolic concentrators (CPC’s) are often built from facets with either no or only one-dimensional curvature. We analyze CPC approximations made with various numbers of axial and circumferential subdivisions. Incident radiation within half-angles of 10° and 30° is considered. The reflectivity of the mirrors is assumed to be 90% or 95%. The performance of faceted concentrators can be significantly improved by optimization as compared with heuristic CPC approaches. The highest increase in transmission that we observed was 19% greater as compared with that of a heuristic CPC approximation. The shapes of the optimized concentrators differ from that of a classic CPC, and most of the optimized concentrators are longer than a classic CPC. For practical concentrators with a small number of facets, the optimized geometry provides better performance than a heuristic approximation of the CPC shape.

© 2000 Optical Society of America

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References

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  1. A. Rabl, “Optical and thermal properties of compound parabolic concentrators,” Sol. Energy 18, 497–511 (1976).
    [CrossRef]
  2. A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, Oxford, 1985).
  3. W. T. Welford, R. Winston, High Collection Non-Imaging Optics (Academic, New York, 1989).
  4. N. Shatz, J. Bortz, “An inverse engineering perspective on nonimaging optical design,” in Nonimaging Optics: Maximum Efficiency Light Transfer III, R. Winston, ed., Proc. SPIE2538, 136–156 (1995).
  5. U. Schöffel, “Optimierung von Endkonzentratoren für solare Hochflussdichteanwendungen,” Ph.D. dissertation (Ludwig-Maximilians-Universität München, Munich, Germany, 1995).
  6. R. Winston, “Nonimaging optics,” Sci. Am. 264, 76–81 (1991).
    [CrossRef]
  7. H. Ries, W. Spirkl, R. Winston, “The cone and the trumpet concentrators in the light of the general edge-ray theorem,” in Nonimaging Optics: Maximum Efficiency Light Transfer III, R. Winston, ed., Proc.2538, 10–15 (1995).
  8. R. Buck, M. Abele, J. Kunberger, T. Denk, P. Heller, R. Lüpfert, “Receiver for solar-hybrid gas turbine and combined cycle systems,” J. Phys. IV 9, 537–544 (1999).
  9. I. Levy, M. Epstein, “Design and operation of a high-power secondary concentrator,” J. Phys. IV 9, 574–580 (1999).
  10. H. Ries, A. Kribus, J. Karni, “Non-isothermal receivers,” J. Sol. Energy Eng. 117, 259–261 (1995).
    [CrossRef]
  11. P. Doron, A. Kribus, “Receiver partitioning: a performance boost for high-temperature solar applications,” in Proceedings of the 8th Symposium on Solar Thermal Concentrating Technologies, M. Böhmer, M. Becker, eds. (Deutsche Forschungsanstalt für Luft- und Raumfahrt, Cologne, Germany, 1996), pp. 627–629.
  12. A. Kribus, P. Doron, J. Karni, R. Rubin, E. Taragan, S. Duchan, “Multi-stage solar receivers: the route to high temperature,” presented at the International Solar Energy Society World Congress, Jerusalem, Israel, 4–9 July 1999.
  13. A. Gray, Modern Differential Geometry of Curves and Surfaces (CRC Press, Boca Raton, Fla., 1994), Sec. 14.5.
  14. A. Timinger (Optics & Energy Consulting, Stoeberlstrasse 68, D-80686 Munich, Germany), W. Spirkl, A. Kribus, H. Ries are preparing a manuscript to be called “Optimized secondary concentrators for a partitioned central receiver system.”
  15. C. F. Gerald, P. O. Wheatly, Applied Numerical Analysis (Addison-Wesley, Reading, Mass., 1994).
  16. H. Ries, “Thermodynamic limitations of the concentrations of electromagnetic radiation,” J. Opt. Soc. Am. 72, 380–385 (1982).
    [CrossRef]
  17. W. Spirkl, A. Timinger, H. Ries, A. Kribus, J. Muschaweck, “Asymmetrical cone-type secondary concentrators for Fresnel type reflectors in solar towers,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 86–93 (1997).
  18. Advanced System Analysis Program (ASAP) (Breault Research Organization, Tucson, Ariz., 1997).

1999 (2)

R. Buck, M. Abele, J. Kunberger, T. Denk, P. Heller, R. Lüpfert, “Receiver for solar-hybrid gas turbine and combined cycle systems,” J. Phys. IV 9, 537–544 (1999).

I. Levy, M. Epstein, “Design and operation of a high-power secondary concentrator,” J. Phys. IV 9, 574–580 (1999).

1995 (1)

H. Ries, A. Kribus, J. Karni, “Non-isothermal receivers,” J. Sol. Energy Eng. 117, 259–261 (1995).
[CrossRef]

1991 (1)

R. Winston, “Nonimaging optics,” Sci. Am. 264, 76–81 (1991).
[CrossRef]

1982 (1)

1976 (1)

A. Rabl, “Optical and thermal properties of compound parabolic concentrators,” Sol. Energy 18, 497–511 (1976).
[CrossRef]

Abele, M.

R. Buck, M. Abele, J. Kunberger, T. Denk, P. Heller, R. Lüpfert, “Receiver for solar-hybrid gas turbine and combined cycle systems,” J. Phys. IV 9, 537–544 (1999).

Bortz, J.

N. Shatz, J. Bortz, “An inverse engineering perspective on nonimaging optical design,” in Nonimaging Optics: Maximum Efficiency Light Transfer III, R. Winston, ed., Proc. SPIE2538, 136–156 (1995).

Buck, R.

R. Buck, M. Abele, J. Kunberger, T. Denk, P. Heller, R. Lüpfert, “Receiver for solar-hybrid gas turbine and combined cycle systems,” J. Phys. IV 9, 537–544 (1999).

Denk, T.

R. Buck, M. Abele, J. Kunberger, T. Denk, P. Heller, R. Lüpfert, “Receiver for solar-hybrid gas turbine and combined cycle systems,” J. Phys. IV 9, 537–544 (1999).

Doron, P.

A. Kribus, P. Doron, J. Karni, R. Rubin, E. Taragan, S. Duchan, “Multi-stage solar receivers: the route to high temperature,” presented at the International Solar Energy Society World Congress, Jerusalem, Israel, 4–9 July 1999.

P. Doron, A. Kribus, “Receiver partitioning: a performance boost for high-temperature solar applications,” in Proceedings of the 8th Symposium on Solar Thermal Concentrating Technologies, M. Böhmer, M. Becker, eds. (Deutsche Forschungsanstalt für Luft- und Raumfahrt, Cologne, Germany, 1996), pp. 627–629.

Duchan, S.

A. Kribus, P. Doron, J. Karni, R. Rubin, E. Taragan, S. Duchan, “Multi-stage solar receivers: the route to high temperature,” presented at the International Solar Energy Society World Congress, Jerusalem, Israel, 4–9 July 1999.

Epstein, M.

I. Levy, M. Epstein, “Design and operation of a high-power secondary concentrator,” J. Phys. IV 9, 574–580 (1999).

Gerald, C. F.

C. F. Gerald, P. O. Wheatly, Applied Numerical Analysis (Addison-Wesley, Reading, Mass., 1994).

Gray, A.

A. Gray, Modern Differential Geometry of Curves and Surfaces (CRC Press, Boca Raton, Fla., 1994), Sec. 14.5.

Heller, P.

R. Buck, M. Abele, J. Kunberger, T. Denk, P. Heller, R. Lüpfert, “Receiver for solar-hybrid gas turbine and combined cycle systems,” J. Phys. IV 9, 537–544 (1999).

Karni, J.

H. Ries, A. Kribus, J. Karni, “Non-isothermal receivers,” J. Sol. Energy Eng. 117, 259–261 (1995).
[CrossRef]

A. Kribus, P. Doron, J. Karni, R. Rubin, E. Taragan, S. Duchan, “Multi-stage solar receivers: the route to high temperature,” presented at the International Solar Energy Society World Congress, Jerusalem, Israel, 4–9 July 1999.

Kribus, A.

H. Ries, A. Kribus, J. Karni, “Non-isothermal receivers,” J. Sol. Energy Eng. 117, 259–261 (1995).
[CrossRef]

W. Spirkl, A. Timinger, H. Ries, A. Kribus, J. Muschaweck, “Asymmetrical cone-type secondary concentrators for Fresnel type reflectors in solar towers,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 86–93 (1997).

A. Kribus, P. Doron, J. Karni, R. Rubin, E. Taragan, S. Duchan, “Multi-stage solar receivers: the route to high temperature,” presented at the International Solar Energy Society World Congress, Jerusalem, Israel, 4–9 July 1999.

A. Timinger (Optics & Energy Consulting, Stoeberlstrasse 68, D-80686 Munich, Germany), W. Spirkl, A. Kribus, H. Ries are preparing a manuscript to be called “Optimized secondary concentrators for a partitioned central receiver system.”

P. Doron, A. Kribus, “Receiver partitioning: a performance boost for high-temperature solar applications,” in Proceedings of the 8th Symposium on Solar Thermal Concentrating Technologies, M. Böhmer, M. Becker, eds. (Deutsche Forschungsanstalt für Luft- und Raumfahrt, Cologne, Germany, 1996), pp. 627–629.

Kunberger, J.

R. Buck, M. Abele, J. Kunberger, T. Denk, P. Heller, R. Lüpfert, “Receiver for solar-hybrid gas turbine and combined cycle systems,” J. Phys. IV 9, 537–544 (1999).

Levy, I.

I. Levy, M. Epstein, “Design and operation of a high-power secondary concentrator,” J. Phys. IV 9, 574–580 (1999).

Lüpfert, R.

R. Buck, M. Abele, J. Kunberger, T. Denk, P. Heller, R. Lüpfert, “Receiver for solar-hybrid gas turbine and combined cycle systems,” J. Phys. IV 9, 537–544 (1999).

Muschaweck, J.

W. Spirkl, A. Timinger, H. Ries, A. Kribus, J. Muschaweck, “Asymmetrical cone-type secondary concentrators for Fresnel type reflectors in solar towers,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 86–93 (1997).

Rabl, A.

A. Rabl, “Optical and thermal properties of compound parabolic concentrators,” Sol. Energy 18, 497–511 (1976).
[CrossRef]

A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, Oxford, 1985).

Ries, H.

H. Ries, A. Kribus, J. Karni, “Non-isothermal receivers,” J. Sol. Energy Eng. 117, 259–261 (1995).
[CrossRef]

H. Ries, “Thermodynamic limitations of the concentrations of electromagnetic radiation,” J. Opt. Soc. Am. 72, 380–385 (1982).
[CrossRef]

W. Spirkl, A. Timinger, H. Ries, A. Kribus, J. Muschaweck, “Asymmetrical cone-type secondary concentrators for Fresnel type reflectors in solar towers,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 86–93 (1997).

H. Ries, W. Spirkl, R. Winston, “The cone and the trumpet concentrators in the light of the general edge-ray theorem,” in Nonimaging Optics: Maximum Efficiency Light Transfer III, R. Winston, ed., Proc.2538, 10–15 (1995).

A. Timinger (Optics & Energy Consulting, Stoeberlstrasse 68, D-80686 Munich, Germany), W. Spirkl, A. Kribus, H. Ries are preparing a manuscript to be called “Optimized secondary concentrators for a partitioned central receiver system.”

Rubin, R.

A. Kribus, P. Doron, J. Karni, R. Rubin, E. Taragan, S. Duchan, “Multi-stage solar receivers: the route to high temperature,” presented at the International Solar Energy Society World Congress, Jerusalem, Israel, 4–9 July 1999.

Schöffel, U.

U. Schöffel, “Optimierung von Endkonzentratoren für solare Hochflussdichteanwendungen,” Ph.D. dissertation (Ludwig-Maximilians-Universität München, Munich, Germany, 1995).

Shatz, N.

N. Shatz, J. Bortz, “An inverse engineering perspective on nonimaging optical design,” in Nonimaging Optics: Maximum Efficiency Light Transfer III, R. Winston, ed., Proc. SPIE2538, 136–156 (1995).

Spirkl, W.

A. Timinger (Optics & Energy Consulting, Stoeberlstrasse 68, D-80686 Munich, Germany), W. Spirkl, A. Kribus, H. Ries are preparing a manuscript to be called “Optimized secondary concentrators for a partitioned central receiver system.”

H. Ries, W. Spirkl, R. Winston, “The cone and the trumpet concentrators in the light of the general edge-ray theorem,” in Nonimaging Optics: Maximum Efficiency Light Transfer III, R. Winston, ed., Proc.2538, 10–15 (1995).

W. Spirkl, A. Timinger, H. Ries, A. Kribus, J. Muschaweck, “Asymmetrical cone-type secondary concentrators for Fresnel type reflectors in solar towers,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 86–93 (1997).

Taragan, E.

A. Kribus, P. Doron, J. Karni, R. Rubin, E. Taragan, S. Duchan, “Multi-stage solar receivers: the route to high temperature,” presented at the International Solar Energy Society World Congress, Jerusalem, Israel, 4–9 July 1999.

Timinger, A.

W. Spirkl, A. Timinger, H. Ries, A. Kribus, J. Muschaweck, “Asymmetrical cone-type secondary concentrators for Fresnel type reflectors in solar towers,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 86–93 (1997).

A. Timinger (Optics & Energy Consulting, Stoeberlstrasse 68, D-80686 Munich, Germany), W. Spirkl, A. Kribus, H. Ries are preparing a manuscript to be called “Optimized secondary concentrators for a partitioned central receiver system.”

Welford, W. T.

W. T. Welford, R. Winston, High Collection Non-Imaging Optics (Academic, New York, 1989).

Wheatly, P. O.

C. F. Gerald, P. O. Wheatly, Applied Numerical Analysis (Addison-Wesley, Reading, Mass., 1994).

Winston, R.

R. Winston, “Nonimaging optics,” Sci. Am. 264, 76–81 (1991).
[CrossRef]

W. T. Welford, R. Winston, High Collection Non-Imaging Optics (Academic, New York, 1989).

H. Ries, W. Spirkl, R. Winston, “The cone and the trumpet concentrators in the light of the general edge-ray theorem,” in Nonimaging Optics: Maximum Efficiency Light Transfer III, R. Winston, ed., Proc.2538, 10–15 (1995).

J. Opt. Soc. Am. (1)

J. Phys. IV (2)

R. Buck, M. Abele, J. Kunberger, T. Denk, P. Heller, R. Lüpfert, “Receiver for solar-hybrid gas turbine and combined cycle systems,” J. Phys. IV 9, 537–544 (1999).

I. Levy, M. Epstein, “Design and operation of a high-power secondary concentrator,” J. Phys. IV 9, 574–580 (1999).

J. Sol. Energy Eng. (1)

H. Ries, A. Kribus, J. Karni, “Non-isothermal receivers,” J. Sol. Energy Eng. 117, 259–261 (1995).
[CrossRef]

Sci. Am. (1)

R. Winston, “Nonimaging optics,” Sci. Am. 264, 76–81 (1991).
[CrossRef]

Sol. Energy (1)

A. Rabl, “Optical and thermal properties of compound parabolic concentrators,” Sol. Energy 18, 497–511 (1976).
[CrossRef]

Other (12)

A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, Oxford, 1985).

W. T. Welford, R. Winston, High Collection Non-Imaging Optics (Academic, New York, 1989).

N. Shatz, J. Bortz, “An inverse engineering perspective on nonimaging optical design,” in Nonimaging Optics: Maximum Efficiency Light Transfer III, R. Winston, ed., Proc. SPIE2538, 136–156 (1995).

U. Schöffel, “Optimierung von Endkonzentratoren für solare Hochflussdichteanwendungen,” Ph.D. dissertation (Ludwig-Maximilians-Universität München, Munich, Germany, 1995).

H. Ries, W. Spirkl, R. Winston, “The cone and the trumpet concentrators in the light of the general edge-ray theorem,” in Nonimaging Optics: Maximum Efficiency Light Transfer III, R. Winston, ed., Proc.2538, 10–15 (1995).

P. Doron, A. Kribus, “Receiver partitioning: a performance boost for high-temperature solar applications,” in Proceedings of the 8th Symposium on Solar Thermal Concentrating Technologies, M. Böhmer, M. Becker, eds. (Deutsche Forschungsanstalt für Luft- und Raumfahrt, Cologne, Germany, 1996), pp. 627–629.

A. Kribus, P. Doron, J. Karni, R. Rubin, E. Taragan, S. Duchan, “Multi-stage solar receivers: the route to high temperature,” presented at the International Solar Energy Society World Congress, Jerusalem, Israel, 4–9 July 1999.

A. Gray, Modern Differential Geometry of Curves and Surfaces (CRC Press, Boca Raton, Fla., 1994), Sec. 14.5.

A. Timinger (Optics & Energy Consulting, Stoeberlstrasse 68, D-80686 Munich, Germany), W. Spirkl, A. Kribus, H. Ries are preparing a manuscript to be called “Optimized secondary concentrators for a partitioned central receiver system.”

C. F. Gerald, P. O. Wheatly, Applied Numerical Analysis (Addison-Wesley, Reading, Mass., 1994).

W. Spirkl, A. Timinger, H. Ries, A. Kribus, J. Muschaweck, “Asymmetrical cone-type secondary concentrators for Fresnel type reflectors in solar towers,” in Nonimaging Optics: Maximum Efficiency Light Transfer IV, R. Winston, ed., Proc. SPIE3139, 86–93 (1997).

Advanced System Analysis Program (ASAP) (Breault Research Organization, Tucson, Ariz., 1997).

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Figures (9)

Fig. 1
Fig. 1

The available radiation arrives uniformly at the polygonal entrance aperture (a) out of a cone of directions with half opening angle θ a (b).

Fig. 2
Fig. 2

Different kinds of subdivision define the number of facets in the concentrator. The concentrator in (a) has six circumferential and three axial subdivisions. The apertures have the shape of regular hexagons. The axial profile consists of three plane sections connecting the edges of the apertures. In the limiting case of infinite circumferential subdivisions (b) the apertures have the form of circles. The concentrator consists of conic sections. In the limiting case of infinite axial subdivisions (c) the axial profile has the shape of a smooth curve. The concentrator consists of one-dimensional curved facets, the leaves.

Fig. 3
Fig. 3

Transmission efficiency of heuristic CPC approaches with 95% and 90% reflectivity. The curves are shown for 10° and 30° half opening angles. The curves show the transmission of faceted concentrators with 3, 4, 6, and 48 circumferential subdivisions. The lighter horizontal lines show the transmission of a smooth 3D CPC with 10° (dashed) or 30° (solid) nominal half opening angle. Here and in subsequent figures, par. leaves means parabolic leaves.

Fig. 4
Fig. 4

Transmission of the optimized concentrators with 95% and 90% reflectivity. The curves are shown for 10° and 30° half opening angles. The curves show the transmission of faceted concentrators with 3, 4, 6, 12 and 48 circumferential subdivisions. The light horizontal lines show the transmission of a smooth, classic 3D CPC with 10° (dashed) or 30° (solid) nominal half opening angle. At the right the transmission for parabolic leaves as a limiting case of infinite axial subdivisions is shown.

Fig. 5
Fig. 5

Differences in transmission between the optimized concentrators and the heuristic CPC approaches. The curves show the absolute difference between the curves in Figs. 3 and 4.

Fig. 6
Fig. 6

Transmission of the optimized concentrators as a function of the total number of facets. Only the points with highest performance for any given number of facets are shown.

Fig. 7
Fig. 7

Axial profiles of the optimized concentrators with hexagonal apertures for radiation with 30° half opening angle. The profile of a classic CPC is also shown as dashed line curves. For clarity the profiles of the optimized concentrators are shifted outward. Starting at the exit aperture of the CPC (lower end of the dashed curves) and moving outward we show the profiles of the optimized concentrators with 1, 3, 4, and 16 axial subdivisions, and parabolic leaves. The drawing is to scale.

Fig. 8
Fig. 8

Same as Fig. 7 for radiation with 10° half opening angle. The drawing is not to scale.

Fig. 9
Fig. 9

Transmission through 3D textbook CPC’s that are scaled along their axes. The available radiation has a half opening angle of 10°.

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