Abstract

Fixed-mirror solar concentrators (FMSCs) use a static reflector and a moving receiver. They are easily installable on building roofs. However, for high-concentration factors, several flat mirrors would be needed. If curved mirrors are used instead, high-concentration levels can be achieved, and such a solar concentrator is called a curved-slats fixed-mirror solar concentrator (CSFMSC), on which little information is available. Herein, a methodology is proposed to characterize the CSFMSC using 3D ray-tracing tools. The CSFMSC shows better optical characteristics than the FMSC, as it needs fewer reflector segments for achieving the same concentration and optical efficiency.

© 2013 Optical Society of America

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References

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  1. IEA, “Technology roadmap: solar heating and cooling” (2012).
  2. J. M. Gordon and M. Jeffrey, Solar Energy the State of the Art: ISES Position Papers (James & James, 2001).
  3. W. G. Steward and F. Kreith, “Stationary concentrating reflector cum tracking absorber solar energy collector: optical design characteristics,” Appl. Opt. 14, 1509–1512 (1975).
    [CrossRef]
  4. M. F. El-Refaie, “Performance analysis of the stationary-reflector/tracking-absorber solar collector,” Appl. Energy 28, 163–189 (1987).
    [CrossRef]
  5. M. F. El-Refaie, “Performance analysis of the stationary-reflector/tracking-absorber solar collector,” Energy Convers. Manag. 29, 111–127 (1989).
    [CrossRef]
  6. J. L. Russell, E. P. DePlomb, and R. K. Bansal, “Principles of the fixed mirror solar concentrator,” 139–145 (1974).
  7. R. L. Bansal, “Theoretical analysis of fixed mirror solar concentrator,” Ph.D. thesis (Arizona State University, 1974).
  8. G. H. Eggers and J. L. Russell, “The FMSC collector subsystem for the Sandia Solar Total Energy Facility,” in Solar Cooling and Heating: Architectural, Engineering, and Legal Aspects; Proceedings of the Forum (Hemisphere Publishing, 1978), pp. 255–271.
  9. V. E. Dudley and R. M. Workhoven, “Summary report: concentrating solar collector test results: Collector Module Test Facility (CMTF). January–December 1978,” SAND78-0977 (1979).
  10. R. Pujol Nadal and V. Martínez Moll, “Optical analysis of the fixed mirror solar concentrator by forward ray-tracing procedure,” J. Sol. Energy Eng. 134, 031009 (2012).
  11. W. R. McIntire, “Factored approximations for biaxial incident angle modifiers,” Sol. Energy 29, 315–322 (1982).
    [CrossRef]
  12. D. Chemisana, A. Coronas, J. López-Villada, J. I. Rosell, and C. Lodi, “Building integration of concentrating systems for solar cooling applications,” Appl. Therm. Eng. 50, 1472–1479 (2013).
    [CrossRef]
  13. J. A. Duffie and W. Beckman, Solar Engineering of Thermal Processes (Wiley, 1991).
  14. R. Pujol Nadal, “Comportamiento óptico y térmico de un concentrador solar lineal con reflector estacionario y foco móvil,” Ph.D. thesis (University of Balearic Islands, 2012), http://hdl.handle.net/10803/84115 .
  15. V. Balasubramanian and G. Sankarasubramanian, “Stretched tape design of fixed mirror solar concentrator with curved mirror elements,” Sol. Energy 51, 109–119 (1993).
    [CrossRef]
  16. V. Martínez Moll, R. Pujol Nadal, A. Moià Pol, and H. Schwiger, “Analysis of a stationary parabolic linear concentrator with tracking absorber,” in 13th International Symposium on Concentrated Solar Power and Chemical Energy Technologies (2006).
  17. D. Buie, C. J. Dey, and S. Bosi, “The effective size of the solar cone for solar concentrating systems,” Sol. Energy 74, 417–427 (2003).
    [CrossRef]
  18. T. Tesfamichael and E. Wäckelgård, “Angular solar absorptance of absorbers used in solar thermal collectors,” Appl. Opt. 38, 4189–4197 (1999).
    [CrossRef]
  19. A. Rabl, P. Bendt, and H. W. Gaul, “Optimization of parabolic trough solar collectors,” Sol. Energy 29, 407–417 (1982).
    [CrossRef]
  20. A. Fernández-García, E. Zarza, L. Valenzuela, and M. Pérez, “Parabolic-trough solar collectors and their applications,” Renew. Sust. Energ. Rev. 14, 1695–1721 (2010).
    [CrossRef]
  21. G. Zhu, “Study of the optical impact of receiver position error on parabolic trough collectors,” J. Sol. Energy Eng. 135, 031021 (2013).
    [CrossRef]
  22. M. Rönnelid, B. Perers, and B. Karlsson, “On the factorisation of incidence angle modifiers for CPC collectors,” Sol. Energy 59, 281–286 (1997).
    [CrossRef]

2013 (2)

D. Chemisana, A. Coronas, J. López-Villada, J. I. Rosell, and C. Lodi, “Building integration of concentrating systems for solar cooling applications,” Appl. Therm. Eng. 50, 1472–1479 (2013).
[CrossRef]

G. Zhu, “Study of the optical impact of receiver position error on parabolic trough collectors,” J. Sol. Energy Eng. 135, 031021 (2013).
[CrossRef]

2012 (1)

R. Pujol Nadal and V. Martínez Moll, “Optical analysis of the fixed mirror solar concentrator by forward ray-tracing procedure,” J. Sol. Energy Eng. 134, 031009 (2012).

2010 (1)

A. Fernández-García, E. Zarza, L. Valenzuela, and M. Pérez, “Parabolic-trough solar collectors and their applications,” Renew. Sust. Energ. Rev. 14, 1695–1721 (2010).
[CrossRef]

2003 (1)

D. Buie, C. J. Dey, and S. Bosi, “The effective size of the solar cone for solar concentrating systems,” Sol. Energy 74, 417–427 (2003).
[CrossRef]

1999 (1)

1997 (1)

M. Rönnelid, B. Perers, and B. Karlsson, “On the factorisation of incidence angle modifiers for CPC collectors,” Sol. Energy 59, 281–286 (1997).
[CrossRef]

1993 (1)

V. Balasubramanian and G. Sankarasubramanian, “Stretched tape design of fixed mirror solar concentrator with curved mirror elements,” Sol. Energy 51, 109–119 (1993).
[CrossRef]

1989 (1)

M. F. El-Refaie, “Performance analysis of the stationary-reflector/tracking-absorber solar collector,” Energy Convers. Manag. 29, 111–127 (1989).
[CrossRef]

1987 (1)

M. F. El-Refaie, “Performance analysis of the stationary-reflector/tracking-absorber solar collector,” Appl. Energy 28, 163–189 (1987).
[CrossRef]

1982 (2)

W. R. McIntire, “Factored approximations for biaxial incident angle modifiers,” Sol. Energy 29, 315–322 (1982).
[CrossRef]

A. Rabl, P. Bendt, and H. W. Gaul, “Optimization of parabolic trough solar collectors,” Sol. Energy 29, 407–417 (1982).
[CrossRef]

1975 (1)

Balasubramanian, V.

V. Balasubramanian and G. Sankarasubramanian, “Stretched tape design of fixed mirror solar concentrator with curved mirror elements,” Sol. Energy 51, 109–119 (1993).
[CrossRef]

Bansal, R. K.

J. L. Russell, E. P. DePlomb, and R. K. Bansal, “Principles of the fixed mirror solar concentrator,” 139–145 (1974).

Bansal, R. L.

R. L. Bansal, “Theoretical analysis of fixed mirror solar concentrator,” Ph.D. thesis (Arizona State University, 1974).

Beckman, W.

J. A. Duffie and W. Beckman, Solar Engineering of Thermal Processes (Wiley, 1991).

Bendt, P.

A. Rabl, P. Bendt, and H. W. Gaul, “Optimization of parabolic trough solar collectors,” Sol. Energy 29, 407–417 (1982).
[CrossRef]

Bosi, S.

D. Buie, C. J. Dey, and S. Bosi, “The effective size of the solar cone for solar concentrating systems,” Sol. Energy 74, 417–427 (2003).
[CrossRef]

Buie, D.

D. Buie, C. J. Dey, and S. Bosi, “The effective size of the solar cone for solar concentrating systems,” Sol. Energy 74, 417–427 (2003).
[CrossRef]

Chemisana, D.

D. Chemisana, A. Coronas, J. López-Villada, J. I. Rosell, and C. Lodi, “Building integration of concentrating systems for solar cooling applications,” Appl. Therm. Eng. 50, 1472–1479 (2013).
[CrossRef]

Coronas, A.

D. Chemisana, A. Coronas, J. López-Villada, J. I. Rosell, and C. Lodi, “Building integration of concentrating systems for solar cooling applications,” Appl. Therm. Eng. 50, 1472–1479 (2013).
[CrossRef]

DePlomb, E. P.

J. L. Russell, E. P. DePlomb, and R. K. Bansal, “Principles of the fixed mirror solar concentrator,” 139–145 (1974).

Dey, C. J.

D. Buie, C. J. Dey, and S. Bosi, “The effective size of the solar cone for solar concentrating systems,” Sol. Energy 74, 417–427 (2003).
[CrossRef]

Dudley, V. E.

V. E. Dudley and R. M. Workhoven, “Summary report: concentrating solar collector test results: Collector Module Test Facility (CMTF). January–December 1978,” SAND78-0977 (1979).

Duffie, J. A.

J. A. Duffie and W. Beckman, Solar Engineering of Thermal Processes (Wiley, 1991).

Eggers, G. H.

G. H. Eggers and J. L. Russell, “The FMSC collector subsystem for the Sandia Solar Total Energy Facility,” in Solar Cooling and Heating: Architectural, Engineering, and Legal Aspects; Proceedings of the Forum (Hemisphere Publishing, 1978), pp. 255–271.

El-Refaie, M. F.

M. F. El-Refaie, “Performance analysis of the stationary-reflector/tracking-absorber solar collector,” Energy Convers. Manag. 29, 111–127 (1989).
[CrossRef]

M. F. El-Refaie, “Performance analysis of the stationary-reflector/tracking-absorber solar collector,” Appl. Energy 28, 163–189 (1987).
[CrossRef]

Fernández-García, A.

A. Fernández-García, E. Zarza, L. Valenzuela, and M. Pérez, “Parabolic-trough solar collectors and their applications,” Renew. Sust. Energ. Rev. 14, 1695–1721 (2010).
[CrossRef]

Gaul, H. W.

A. Rabl, P. Bendt, and H. W. Gaul, “Optimization of parabolic trough solar collectors,” Sol. Energy 29, 407–417 (1982).
[CrossRef]

Gordon, J. M.

J. M. Gordon and M. Jeffrey, Solar Energy the State of the Art: ISES Position Papers (James & James, 2001).

Jeffrey, M.

J. M. Gordon and M. Jeffrey, Solar Energy the State of the Art: ISES Position Papers (James & James, 2001).

Karlsson, B.

M. Rönnelid, B. Perers, and B. Karlsson, “On the factorisation of incidence angle modifiers for CPC collectors,” Sol. Energy 59, 281–286 (1997).
[CrossRef]

Kreith, F.

Lodi, C.

D. Chemisana, A. Coronas, J. López-Villada, J. I. Rosell, and C. Lodi, “Building integration of concentrating systems for solar cooling applications,” Appl. Therm. Eng. 50, 1472–1479 (2013).
[CrossRef]

López-Villada, J.

D. Chemisana, A. Coronas, J. López-Villada, J. I. Rosell, and C. Lodi, “Building integration of concentrating systems for solar cooling applications,” Appl. Therm. Eng. 50, 1472–1479 (2013).
[CrossRef]

Martínez Moll, V.

R. Pujol Nadal and V. Martínez Moll, “Optical analysis of the fixed mirror solar concentrator by forward ray-tracing procedure,” J. Sol. Energy Eng. 134, 031009 (2012).

V. Martínez Moll, R. Pujol Nadal, A. Moià Pol, and H. Schwiger, “Analysis of a stationary parabolic linear concentrator with tracking absorber,” in 13th International Symposium on Concentrated Solar Power and Chemical Energy Technologies (2006).

McIntire, W. R.

W. R. McIntire, “Factored approximations for biaxial incident angle modifiers,” Sol. Energy 29, 315–322 (1982).
[CrossRef]

Moià Pol, A.

V. Martínez Moll, R. Pujol Nadal, A. Moià Pol, and H. Schwiger, “Analysis of a stationary parabolic linear concentrator with tracking absorber,” in 13th International Symposium on Concentrated Solar Power and Chemical Energy Technologies (2006).

Perers, B.

M. Rönnelid, B. Perers, and B. Karlsson, “On the factorisation of incidence angle modifiers for CPC collectors,” Sol. Energy 59, 281–286 (1997).
[CrossRef]

Pérez, M.

A. Fernández-García, E. Zarza, L. Valenzuela, and M. Pérez, “Parabolic-trough solar collectors and their applications,” Renew. Sust. Energ. Rev. 14, 1695–1721 (2010).
[CrossRef]

Pujol Nadal, R.

R. Pujol Nadal and V. Martínez Moll, “Optical analysis of the fixed mirror solar concentrator by forward ray-tracing procedure,” J. Sol. Energy Eng. 134, 031009 (2012).

V. Martínez Moll, R. Pujol Nadal, A. Moià Pol, and H. Schwiger, “Analysis of a stationary parabolic linear concentrator with tracking absorber,” in 13th International Symposium on Concentrated Solar Power and Chemical Energy Technologies (2006).

R. Pujol Nadal, “Comportamiento óptico y térmico de un concentrador solar lineal con reflector estacionario y foco móvil,” Ph.D. thesis (University of Balearic Islands, 2012), http://hdl.handle.net/10803/84115 .

Rabl, A.

A. Rabl, P. Bendt, and H. W. Gaul, “Optimization of parabolic trough solar collectors,” Sol. Energy 29, 407–417 (1982).
[CrossRef]

Rönnelid, M.

M. Rönnelid, B. Perers, and B. Karlsson, “On the factorisation of incidence angle modifiers for CPC collectors,” Sol. Energy 59, 281–286 (1997).
[CrossRef]

Rosell, J. I.

D. Chemisana, A. Coronas, J. López-Villada, J. I. Rosell, and C. Lodi, “Building integration of concentrating systems for solar cooling applications,” Appl. Therm. Eng. 50, 1472–1479 (2013).
[CrossRef]

Russell, J. L.

J. L. Russell, E. P. DePlomb, and R. K. Bansal, “Principles of the fixed mirror solar concentrator,” 139–145 (1974).

G. H. Eggers and J. L. Russell, “The FMSC collector subsystem for the Sandia Solar Total Energy Facility,” in Solar Cooling and Heating: Architectural, Engineering, and Legal Aspects; Proceedings of the Forum (Hemisphere Publishing, 1978), pp. 255–271.

Sankarasubramanian, G.

V. Balasubramanian and G. Sankarasubramanian, “Stretched tape design of fixed mirror solar concentrator with curved mirror elements,” Sol. Energy 51, 109–119 (1993).
[CrossRef]

Schwiger, H.

V. Martínez Moll, R. Pujol Nadal, A. Moià Pol, and H. Schwiger, “Analysis of a stationary parabolic linear concentrator with tracking absorber,” in 13th International Symposium on Concentrated Solar Power and Chemical Energy Technologies (2006).

Steward, W. G.

Tesfamichael, T.

Valenzuela, L.

A. Fernández-García, E. Zarza, L. Valenzuela, and M. Pérez, “Parabolic-trough solar collectors and their applications,” Renew. Sust. Energ. Rev. 14, 1695–1721 (2010).
[CrossRef]

Wäckelgård, E.

Workhoven, R. M.

V. E. Dudley and R. M. Workhoven, “Summary report: concentrating solar collector test results: Collector Module Test Facility (CMTF). January–December 1978,” SAND78-0977 (1979).

Zarza, E.

A. Fernández-García, E. Zarza, L. Valenzuela, and M. Pérez, “Parabolic-trough solar collectors and their applications,” Renew. Sust. Energ. Rev. 14, 1695–1721 (2010).
[CrossRef]

Zhu, G.

G. Zhu, “Study of the optical impact of receiver position error on parabolic trough collectors,” J. Sol. Energy Eng. 135, 031021 (2013).
[CrossRef]

Appl. Energy (1)

M. F. El-Refaie, “Performance analysis of the stationary-reflector/tracking-absorber solar collector,” Appl. Energy 28, 163–189 (1987).
[CrossRef]

Appl. Opt. (2)

Appl. Therm. Eng. (1)

D. Chemisana, A. Coronas, J. López-Villada, J. I. Rosell, and C. Lodi, “Building integration of concentrating systems for solar cooling applications,” Appl. Therm. Eng. 50, 1472–1479 (2013).
[CrossRef]

Energy Convers. Manag. (1)

M. F. El-Refaie, “Performance analysis of the stationary-reflector/tracking-absorber solar collector,” Energy Convers. Manag. 29, 111–127 (1989).
[CrossRef]

J. Sol. Energy Eng. (2)

R. Pujol Nadal and V. Martínez Moll, “Optical analysis of the fixed mirror solar concentrator by forward ray-tracing procedure,” J. Sol. Energy Eng. 134, 031009 (2012).

G. Zhu, “Study of the optical impact of receiver position error on parabolic trough collectors,” J. Sol. Energy Eng. 135, 031021 (2013).
[CrossRef]

Renew. Sust. Energ. Rev. (1)

A. Fernández-García, E. Zarza, L. Valenzuela, and M. Pérez, “Parabolic-trough solar collectors and their applications,” Renew. Sust. Energ. Rev. 14, 1695–1721 (2010).
[CrossRef]

Sol. Energy (5)

M. Rönnelid, B. Perers, and B. Karlsson, “On the factorisation of incidence angle modifiers for CPC collectors,” Sol. Energy 59, 281–286 (1997).
[CrossRef]

W. R. McIntire, “Factored approximations for biaxial incident angle modifiers,” Sol. Energy 29, 315–322 (1982).
[CrossRef]

V. Balasubramanian and G. Sankarasubramanian, “Stretched tape design of fixed mirror solar concentrator with curved mirror elements,” Sol. Energy 51, 109–119 (1993).
[CrossRef]

A. Rabl, P. Bendt, and H. W. Gaul, “Optimization of parabolic trough solar collectors,” Sol. Energy 29, 407–417 (1982).
[CrossRef]

D. Buie, C. J. Dey, and S. Bosi, “The effective size of the solar cone for solar concentrating systems,” Sol. Energy 74, 417–427 (2003).
[CrossRef]

Other (9)

V. Martínez Moll, R. Pujol Nadal, A. Moià Pol, and H. Schwiger, “Analysis of a stationary parabolic linear concentrator with tracking absorber,” in 13th International Symposium on Concentrated Solar Power and Chemical Energy Technologies (2006).

J. A. Duffie and W. Beckman, Solar Engineering of Thermal Processes (Wiley, 1991).

R. Pujol Nadal, “Comportamiento óptico y térmico de un concentrador solar lineal con reflector estacionario y foco móvil,” Ph.D. thesis (University of Balearic Islands, 2012), http://hdl.handle.net/10803/84115 .

IEA, “Technology roadmap: solar heating and cooling” (2012).

J. M. Gordon and M. Jeffrey, Solar Energy the State of the Art: ISES Position Papers (James & James, 2001).

J. L. Russell, E. P. DePlomb, and R. K. Bansal, “Principles of the fixed mirror solar concentrator,” 139–145 (1974).

R. L. Bansal, “Theoretical analysis of fixed mirror solar concentrator,” Ph.D. thesis (Arizona State University, 1974).

G. H. Eggers and J. L. Russell, “The FMSC collector subsystem for the Sandia Solar Total Energy Facility,” in Solar Cooling and Heating: Architectural, Engineering, and Legal Aspects; Proceedings of the Forum (Hemisphere Publishing, 1978), pp. 255–271.

V. E. Dudley and R. M. Workhoven, “Summary report: concentrating solar collector test results: Collector Module Test Facility (CMTF). January–December 1978,” SAND78-0977 (1979).

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Figures (14)

Fig. 1.
Fig. 1.

θt and θl are the transverse and longitudinal angles that are the projected incidence angles on the two reference planes perpendicular to and along the axis of the collector, respectively. θi is the incident angle.

Fig. 2.
Fig. 2.

Optical principle of the FMSC. The receiver moves along a circular path on the generating circle. The generating circle has a radius R, the focal length is F=2R, and the receiver is positioned by the θf angle. The position angle of the receiver is twice the transversal incidence angle (θf=2θt). The reflector width is W.

Fig. 3.
Fig. 3.

(a) Schematic showing the focal length F, reflector width W, and number of mirrors N. (b) Front view of evacuated tube, where the tube is considered as a receiver.

Fig. 4.
Fig. 4.

CSFMSC reflector with F/W=1.0, N=3, and a geometric concentration of Ca=10. A visualization of the principal rays is shown for normal incidence and for a 45° transversal incidence. The path of the receiver is the same as in the FMSC.

Fig. 5.
Fig. 5.

CSFMSC with five parabolic mirrors (N=5) and with parameters F/W=1.0 and Ca=10. A ray-tracing visualization is shown for transversal incidence angles θt=0° and θt=30°.

Fig. 6.
Fig. 6.

CSFMSC with five parabolic mirrors (N=5) and with parameters F/W=1.0 and Ca=10. A ray-tracing visualization is shown for transversal incidence angles θt=45° and θt=57°. The last one corresponds to the angle limit of the receiver position θf,lim=114° when the receiver intercepts the reflector. In this case, for greater values of θtθt,lim=57°, the receiver remains fixed at θf,lim=114°.

Fig. 7.
Fig. 7.

(a) Optical efficiency at normal incidence as a function of the geometric concentration ratio for different values of F-number (F/W) and N. (b) Optical efficiency at normal incidence as a function of the F-number for N=1.

Fig. 8.
Fig. 8.

Transversal IAM curves depending on the F/W ratio as a function of transversal angle for different Ca and N values.

Fig. 9.
Fig. 9.

Transversal IAM curves depending on the geometric concentration ratio as a function of the transversal angle for different F/W and N values.

Fig. 10.
Fig. 10.

Transversal IAM curves depending on the number of mirrors as a function of the transversal angle for different Ca and F/W values.

Fig. 11.
Fig. 11.

Longitudinal IAM curves for various values of F/W, Ca, and N.

Fig. 12.
Fig. 12.

Analysis of the case of N=1, F/W=3.0, and Ca=3. (a) Factorized IAM, calculated by ray-tracing. (b) Error in the calculation of the energy collected from direct radiation if KK(θt,0)K(0,θl)f(θt,θl) is used instead of K(θt,θl). The values of the error estimators are RMSE=0.0615, MBE=0.0206, MAE=7.68%, and ME=7.55%.

Fig. 13.
Fig. 13.

Analysis of the case of N=7, F/W=1.0, and Ca=24. (a) Factorized IAM, calculated by ray-tracing. (b) Error in the calculation of energy collected from direct radiation if KK(θt,0)K(0,θl)f(θt,θl) is used instead of K(θt,θl). The values of the error estimators are RMSE=0.0109, MBE=0.0035, MAE=3.47%, and ME=1.38%.

Fig. 14.
Fig. 14.

Local distribution of the radiation on the receiver for N=1, 3, 5, and 7 for F/W=1.5 and Ca=15. The longitudinal length of the concentrator was considered to be L=1u.

Tables (1)

Tables Icon

Table 1. Averages of Error Estimators for Comparison of the Factorized IAM and Ray-Tracing IAM

Equations (13)

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

z(x)=(xc1)24c3+c2.
zi=xi24c3,i+c2,i,
2R=c3,i+c2,i.
S=Gb(γρτα)0Kγρτα,
αα0=10.017(1cosθi1)1.8.
K(θt,0)=η(θt,0)η(0,0),
K(0,θl)=η(0,θl)η(0,0),
ΔK=[K(θt,0)K(0,θl)K(θt,θl)]cos(θi).
RMSE=[1NpΔK2]1/2,
MBE=1NpΔK,
MAE=1Np|ΔK|K(θt,θl)cos(θi),
ME=1NpΔKK(θt,θl)cos(θi).
f(θt,θl)={L[R+Rcos(2θt)]tan(θl)L2Rtan(θl)θt<θt,limandθl<75L[R+Rcos(2θt,lim)]tan(θl)L2Rtan(θl)θtθt,limandθl<751θl75,

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