Abstract

For both linear and point-focus Fresnel reflectors, we present a new type of ideal nonimaging secondary concentrator, the tailored edge-ray concentrator, that can closely approach the thermodynamic limit of concentration. For large rim-angle heliostat fields, practical-sized secondaries with shapes that should be relatively easy to fabricate can achieve concentrations substantially above those of compound parabolic concentrators. This superiority stems from designing so as to accommodate the particular flux from the heliostat field. The edge-ray principle used for generating the new secondary dictates a heliostat tracking strategy that is different from the conventional one but is equally easy to implement.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 2, pp. 22–28;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 4, pp. 54–62;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 5, pp. 84–91, 95–97;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 6, pp. 99–114;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 7, pp. 124–125;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 10, pp. 192–199;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), App. A, pp.223–228.
  2. A. Rabl, “Comparison of solar concentrators,” Sol. Energy 18, 93–111 (1976).
    [CrossRef]
  3. R. Winston, W. T. Welford, “Design of nonimaging concentrators as second stages in tandem with image-forming first stage concentrators,” Appl. Opt. 19, 347–351 (1980).
    [CrossRef] [PubMed]
  4. A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, New York, 1985), Chap. 7, pp. 173–182, 190–193.
  5. D. Feuermann, J. M. Gordon, “Analysis of a two-stage linear Fresnel reflector solar concentrator,” ASME J. Sol. Energy Eng. 113, 272–279 (1991).
    [CrossRef]
  6. J. J. Bartel, P. E. Skvarna, “10-MWe solar thermal central receiver pilot plant,” ASME J. Sol. Energy Eng. 106, 50–58 (1984).
    [CrossRef]
  7. D. Borgese, G. Dinelli, J. J. Faure, J. Gretz, G. Schober, “Euroleios, the 1-MW(el) helioelectric power plant of the European community program,” ASME J. Sol. Energy Eng. 106, 66–77 (1984).
    [CrossRef]
  8. W. Grasse, M. Becker, “Central receiver system (CRS) in the small solar power systems project (SSPS) of the International Energy Agency (IEA),” ASME J. Sol. Energy Eng. 106, 59–65 (1984).
    [CrossRef]
  9. T. Hirono, T. Horigome, “A 1-MWe central receiver type solar thermal electric power pilot plant,” J. Sol. Energy Sci. Eng. 106, 90–97 (1984).
    [CrossRef]
  10. J. O'Gallagher, R. Winston, “Test of a ‘trumpet’ secondary concentrator with a paraboloidal dish primary,” Sol. Energy 36, 37–44 (1986).
    [CrossRef]
  11. D. Suresh, J. O'Gallagher, R. Winston, “Thermal and optical performance test results for compound parabolic concentrators (CPCs),” Sol. Energy 44, 257–270 (1990).
    [CrossRef]
  12. R. B. Bannerot, C. L. Laurence, “A design method for optimizing collector systems for small solar central receivers,” ASME J. Sol. Energy Eng. 102, 240–247 (1980).
    [CrossRef]
  13. F. J. Collado, J. A. Turègano, “Calculation of the annual thermal energy supplied by a defined heliostat field,” Sol. Energy 42, 149–165 (1989).
    [CrossRef]

1991 (1)

D. Feuermann, J. M. Gordon, “Analysis of a two-stage linear Fresnel reflector solar concentrator,” ASME J. Sol. Energy Eng. 113, 272–279 (1991).
[CrossRef]

1990 (1)

D. Suresh, J. O'Gallagher, R. Winston, “Thermal and optical performance test results for compound parabolic concentrators (CPCs),” Sol. Energy 44, 257–270 (1990).
[CrossRef]

1989 (1)

F. J. Collado, J. A. Turègano, “Calculation of the annual thermal energy supplied by a defined heliostat field,” Sol. Energy 42, 149–165 (1989).
[CrossRef]

1986 (1)

J. O'Gallagher, R. Winston, “Test of a ‘trumpet’ secondary concentrator with a paraboloidal dish primary,” Sol. Energy 36, 37–44 (1986).
[CrossRef]

1984 (4)

J. J. Bartel, P. E. Skvarna, “10-MWe solar thermal central receiver pilot plant,” ASME J. Sol. Energy Eng. 106, 50–58 (1984).
[CrossRef]

D. Borgese, G. Dinelli, J. J. Faure, J. Gretz, G. Schober, “Euroleios, the 1-MW(el) helioelectric power plant of the European community program,” ASME J. Sol. Energy Eng. 106, 66–77 (1984).
[CrossRef]

W. Grasse, M. Becker, “Central receiver system (CRS) in the small solar power systems project (SSPS) of the International Energy Agency (IEA),” ASME J. Sol. Energy Eng. 106, 59–65 (1984).
[CrossRef]

T. Hirono, T. Horigome, “A 1-MWe central receiver type solar thermal electric power pilot plant,” J. Sol. Energy Sci. Eng. 106, 90–97 (1984).
[CrossRef]

1980 (2)

R. B. Bannerot, C. L. Laurence, “A design method for optimizing collector systems for small solar central receivers,” ASME J. Sol. Energy Eng. 102, 240–247 (1980).
[CrossRef]

R. Winston, W. T. Welford, “Design of nonimaging concentrators as second stages in tandem with image-forming first stage concentrators,” Appl. Opt. 19, 347–351 (1980).
[CrossRef] [PubMed]

1976 (1)

A. Rabl, “Comparison of solar concentrators,” Sol. Energy 18, 93–111 (1976).
[CrossRef]

Bannerot, R. B.

R. B. Bannerot, C. L. Laurence, “A design method for optimizing collector systems for small solar central receivers,” ASME J. Sol. Energy Eng. 102, 240–247 (1980).
[CrossRef]

Bartel, J. J.

J. J. Bartel, P. E. Skvarna, “10-MWe solar thermal central receiver pilot plant,” ASME J. Sol. Energy Eng. 106, 50–58 (1984).
[CrossRef]

Becker, M.

W. Grasse, M. Becker, “Central receiver system (CRS) in the small solar power systems project (SSPS) of the International Energy Agency (IEA),” ASME J. Sol. Energy Eng. 106, 59–65 (1984).
[CrossRef]

Borgese, D.

D. Borgese, G. Dinelli, J. J. Faure, J. Gretz, G. Schober, “Euroleios, the 1-MW(el) helioelectric power plant of the European community program,” ASME J. Sol. Energy Eng. 106, 66–77 (1984).
[CrossRef]

Collado, F. J.

F. J. Collado, J. A. Turègano, “Calculation of the annual thermal energy supplied by a defined heliostat field,” Sol. Energy 42, 149–165 (1989).
[CrossRef]

Dinelli, G.

D. Borgese, G. Dinelli, J. J. Faure, J. Gretz, G. Schober, “Euroleios, the 1-MW(el) helioelectric power plant of the European community program,” ASME J. Sol. Energy Eng. 106, 66–77 (1984).
[CrossRef]

Faure, J. J.

D. Borgese, G. Dinelli, J. J. Faure, J. Gretz, G. Schober, “Euroleios, the 1-MW(el) helioelectric power plant of the European community program,” ASME J. Sol. Energy Eng. 106, 66–77 (1984).
[CrossRef]

Feuermann, D.

D. Feuermann, J. M. Gordon, “Analysis of a two-stage linear Fresnel reflector solar concentrator,” ASME J. Sol. Energy Eng. 113, 272–279 (1991).
[CrossRef]

Gordon, J. M.

D. Feuermann, J. M. Gordon, “Analysis of a two-stage linear Fresnel reflector solar concentrator,” ASME J. Sol. Energy Eng. 113, 272–279 (1991).
[CrossRef]

Grasse, W.

W. Grasse, M. Becker, “Central receiver system (CRS) in the small solar power systems project (SSPS) of the International Energy Agency (IEA),” ASME J. Sol. Energy Eng. 106, 59–65 (1984).
[CrossRef]

Gretz, J.

D. Borgese, G. Dinelli, J. J. Faure, J. Gretz, G. Schober, “Euroleios, the 1-MW(el) helioelectric power plant of the European community program,” ASME J. Sol. Energy Eng. 106, 66–77 (1984).
[CrossRef]

Hirono, T.

T. Hirono, T. Horigome, “A 1-MWe central receiver type solar thermal electric power pilot plant,” J. Sol. Energy Sci. Eng. 106, 90–97 (1984).
[CrossRef]

Horigome, T.

T. Hirono, T. Horigome, “A 1-MWe central receiver type solar thermal electric power pilot plant,” J. Sol. Energy Sci. Eng. 106, 90–97 (1984).
[CrossRef]

Laurence, C. L.

R. B. Bannerot, C. L. Laurence, “A design method for optimizing collector systems for small solar central receivers,” ASME J. Sol. Energy Eng. 102, 240–247 (1980).
[CrossRef]

O'Gallagher, J.

D. Suresh, J. O'Gallagher, R. Winston, “Thermal and optical performance test results for compound parabolic concentrators (CPCs),” Sol. Energy 44, 257–270 (1990).
[CrossRef]

J. O'Gallagher, R. Winston, “Test of a ‘trumpet’ secondary concentrator with a paraboloidal dish primary,” Sol. Energy 36, 37–44 (1986).
[CrossRef]

Rabl, A.

A. Rabl, “Comparison of solar concentrators,” Sol. Energy 18, 93–111 (1976).
[CrossRef]

A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, New York, 1985), Chap. 7, pp. 173–182, 190–193.

Schober, G.

D. Borgese, G. Dinelli, J. J. Faure, J. Gretz, G. Schober, “Euroleios, the 1-MW(el) helioelectric power plant of the European community program,” ASME J. Sol. Energy Eng. 106, 66–77 (1984).
[CrossRef]

Skvarna, P. E.

J. J. Bartel, P. E. Skvarna, “10-MWe solar thermal central receiver pilot plant,” ASME J. Sol. Energy Eng. 106, 50–58 (1984).
[CrossRef]

Suresh, D.

D. Suresh, J. O'Gallagher, R. Winston, “Thermal and optical performance test results for compound parabolic concentrators (CPCs),” Sol. Energy 44, 257–270 (1990).
[CrossRef]

Turègano, J. A.

F. J. Collado, J. A. Turègano, “Calculation of the annual thermal energy supplied by a defined heliostat field,” Sol. Energy 42, 149–165 (1989).
[CrossRef]

Welford, W. T.

R. Winston, W. T. Welford, “Design of nonimaging concentrators as second stages in tandem with image-forming first stage concentrators,” Appl. Opt. 19, 347–351 (1980).
[CrossRef] [PubMed]

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 2, pp. 22–28;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 4, pp. 54–62;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 5, pp. 84–91, 95–97;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 6, pp. 99–114;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 7, pp. 124–125;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 10, pp. 192–199;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), App. A, pp.223–228.

Winston, R.

D. Suresh, J. O'Gallagher, R. Winston, “Thermal and optical performance test results for compound parabolic concentrators (CPCs),” Sol. Energy 44, 257–270 (1990).
[CrossRef]

J. O'Gallagher, R. Winston, “Test of a ‘trumpet’ secondary concentrator with a paraboloidal dish primary,” Sol. Energy 36, 37–44 (1986).
[CrossRef]

R. Winston, W. T. Welford, “Design of nonimaging concentrators as second stages in tandem with image-forming first stage concentrators,” Appl. Opt. 19, 347–351 (1980).
[CrossRef] [PubMed]

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 2, pp. 22–28;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 4, pp. 54–62;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 5, pp. 84–91, 95–97;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 6, pp. 99–114;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 7, pp. 124–125;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 10, pp. 192–199;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), App. A, pp.223–228.

Appl. Opt. (1)

ASME J. Sol. Energy Eng. (5)

D. Feuermann, J. M. Gordon, “Analysis of a two-stage linear Fresnel reflector solar concentrator,” ASME J. Sol. Energy Eng. 113, 272–279 (1991).
[CrossRef]

J. J. Bartel, P. E. Skvarna, “10-MWe solar thermal central receiver pilot plant,” ASME J. Sol. Energy Eng. 106, 50–58 (1984).
[CrossRef]

D. Borgese, G. Dinelli, J. J. Faure, J. Gretz, G. Schober, “Euroleios, the 1-MW(el) helioelectric power plant of the European community program,” ASME J. Sol. Energy Eng. 106, 66–77 (1984).
[CrossRef]

W. Grasse, M. Becker, “Central receiver system (CRS) in the small solar power systems project (SSPS) of the International Energy Agency (IEA),” ASME J. Sol. Energy Eng. 106, 59–65 (1984).
[CrossRef]

R. B. Bannerot, C. L. Laurence, “A design method for optimizing collector systems for small solar central receivers,” ASME J. Sol. Energy Eng. 102, 240–247 (1980).
[CrossRef]

J. Sol. Energy Sci. Eng. (1)

T. Hirono, T. Horigome, “A 1-MWe central receiver type solar thermal electric power pilot plant,” J. Sol. Energy Sci. Eng. 106, 90–97 (1984).
[CrossRef]

Sol. Energy (4)

J. O'Gallagher, R. Winston, “Test of a ‘trumpet’ secondary concentrator with a paraboloidal dish primary,” Sol. Energy 36, 37–44 (1986).
[CrossRef]

D. Suresh, J. O'Gallagher, R. Winston, “Thermal and optical performance test results for compound parabolic concentrators (CPCs),” Sol. Energy 44, 257–270 (1990).
[CrossRef]

A. Rabl, “Comparison of solar concentrators,” Sol. Energy 18, 93–111 (1976).
[CrossRef]

F. J. Collado, J. A. Turègano, “Calculation of the annual thermal energy supplied by a defined heliostat field,” Sol. Energy 42, 149–165 (1989).
[CrossRef]

Other (2)

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 2, pp. 22–28;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 4, pp. 54–62;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 5, pp. 84–91, 95–97;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 6, pp. 99–114;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 7, pp. 124–125;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), Chap. 10, pp. 192–199;High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989), App. A, pp.223–228.

A. Rabl, Active Solar Collectors and Their Applications (Oxford U. Press, New York, 1985), Chap. 7, pp. 173–182, 190–193.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Schematic 2-D cross section of a Fresnel reflector primary and flat absorber. ℒ is the distance from the absorber to the center of a symmetrically placed heliostat field that subtends a rim half-angle ϕmax. Only seven heliostats are shown for clarity of illustration. Effective solar angle 20s is grossly exaggerated in order to show heliostats and absorber on the same scale.

Fig. 2
Fig. 2

Phase space region (view factor versus spatial extent) occupied by radiation focused onto a flat absorber from (a) a 2-D and (b) a 3-D Fresnel reflector with conventional aiming strategy. Étendue is the area within the curve. Smaller and larger rectangular areas, indicated by broken lines, show the extreme designs for secondary CPC's as discussed in Section 2.

Fig. 3
Fig. 3

Maximum collection efficiency of a rotationally symmetric 3-D device constructed by rotating the corresponding ideal 2-D device as a function of field rim half-angle ϕmax. The ordinate is A abs - min 3 - D - rot / A abs - min 3 - D [see Eq.(14)].

Fig. 4
Fig. 4

Collection efficiency versus field rim half-angle for (a) 2-D and (b) 3-D systems with a CPC secondary concentrator at maximum concentration.

Fig. 5
Fig. 5

Concentration relative to the thermodynamic limit versus field rim half-angle for (a) 2-D and (b) 3-D systems with a CPC secondary concentrator at maximum collection efficiency.

Fig. 6
Fig. 6

Schematic illustration of construction of the TERC and the associated new tracking strategy (see explanation in Section 3). For clarity of illustration, the solar angle is grossly exaggerated to show sufficient detail. Only the RHS construction is shown; the LHS is its mirror image.

Fig. 7
Fig. 7

Phase space region occupied by radiation focused onto a flat absorber from (a) a 2-D and (b) a 3-D Fresnel reflector with the new proposed tracking scheme.

Fig. 8
Fig. 8

Concentration relative to the thermodynamic limit versus relative depth of the TERC secondary (effectively, degree of truncation of the TERC) at maximal collection efficiency for (a) 2-D and (b) 3-D systems. Calculations are for ϕmax = 49.6°. The lower curve represents the contribution of direct hits only; the upper curve is the total contribution from direct and reflected hits.

Fig. 9
Fig. 9

Scale drawing of the truncated TERC designed for ϕmax = 49.6° and maximum collection efficiency with ϕ as high as 40°. The secondary polar (construction) angle is indicated by β, measured from the absorber edge and defined as zero along the absorber.

Fig. 10
Fig. 10

(a) TERC reflector slope and (b) extreme direction versus concentrator polar (construction) angle. The TERC design is for ϕmax = 49.6°.

Fig. 11
Fig. 11

Concentration relative to the thermodynamic limit versus relative depth of the TERC that was designed for ϕmax = 49.6°, an enlarged version of Fig. 8. Note that the lower abscissa is limited to a maximum value of 0.1; this range is used to represent devices of reasonable dimensions. The heliostat field is assumed to be truncated accordingly, so that maximum collection efficiency is ensured. The field rim half-angle is shown on the upper abscissa. Corresponding results for full CPC secondary reflectors are also plotted, by a broken curve, as a function of the field rim half-angle (upper abscissa). Note that this upper abscissa is not to linear scale. This graph permits comparison of the TERC and the CPC.

Fig. 12
Fig. 12

Same as Fig. 11 but for ϕmax = 35°.

Fig. 13
Fig. 13

Scale drawing of the truncated TERC that was designed for ϕmax = 35° and maximum collection efficiency of ϕ as high as 25°. The secondary polar (construction) angle is indicated by β, measured from the absorber edge and defined as zero along the absorber.

Fig. 14
Fig. 14

TERC reflector extreme direction versus concentrator polar angle. The TERC was designed for ϕmsx = 35°.

Tables (1)

Tables Icon

Table 1 Nomenclature

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

E = d ν d x ,
d ν = υ cos ( ϕ ) ,
υ 2 = 2 sin ( θ s ) ,
υ 3 = π sin 2 ( θ s ) .
x = r 2 - D ,
x = π r 2 3 - D ,
E Fresnel 2 - D ( ϕ ) = 2 υ 2 ln [ tan ( π 4 + ϕ 2 ) ] ,
E Fresnel 3 - D ( ϕ ) = 2 π υ 3 2 [ 1 cos ( ϕ ) cos ( ϕ ) ] .
x ( ϕ ) = r , ν ( ϕ ) = 2 sin ( ϕ ) 2 - D ,
x ( ϕ ) = π r | r | , ν ( ϕ ) = π sin ( ϕ ) | sin ( ϕ ) | 3 - D ,
r ( ϕ ) = [ tan ( ϕ ± θ s ) tan ( ϕ ) ] ( for both 2 - D and 3 - D ) .
A abs - min 2 - D ( ϕ ) = E Fresnel 2 - D ( ϕ ) 2 = υ 2 ln [ tan ( π 4 + ϕ 2 ) ] ,
A abs - min 3 - D ( ϕ ) = E Fresnel 3 - D ( ϕ ) π = 2 υ 3 2 [ 1 cos ( ϕ ) cos ( ϕ ) ] .
A abs - min 3 - D - rot = π ( A abs - min 2 - D / 2 ) 2
x ( ϕ ) = { tan ( ϕ ± 2 θ s ) [ tan ( ϕ ) ± α / ] } ,
A
E

Metrics