Abstract

In this paper we present a method for designing ideal and optimal 2-D concentrators when the collector is placed inside a dielectric tube for the particular case of a bifacial collector. The method, based on the extreme ray principle of design, avoids the use of differential equations by means of a proper application of Fermat's principle. One advantage of these concentrators is that they allow the size to be small compared with classical CPCs.

© 1983 Optical Society of America

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References

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  1. R. Winston, Sol. Energy 16, 89 (1974).
    [CrossRef]
  2. W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).
  3. M. Collares-Pereira, A. Rabl, R. Winston, Appl. Opt. 16, 2677 (1977).
    [CrossRef] [PubMed]
  4. R. Winston, W. T. Welford, J. Opt. Soc. Am. 68, 289 (1978).
    [CrossRef]
  5. A. Luque, Sol. Cells 3, 355 (1981).
    [CrossRef]
  6. A. Luque, A. Cuevas, J. M. Ruiz, Sol. Cells 2, 151 (1980).
    [CrossRef]
  7. H. Hottel, “Radiant Heat Transmission,” in Heat Transmission, W. H. McAdams, Ed. (McGraw-Hill, New York, 1954).
  8. See, for example, A. Rabl, Sol. Energy 18, 93 (1976).
    [CrossRef]
  9. A. Rabl, Sol. Energy 19, 215 (1977).
    [CrossRef]

1981 (1)

A. Luque, Sol. Cells 3, 355 (1981).
[CrossRef]

1980 (1)

A. Luque, A. Cuevas, J. M. Ruiz, Sol. Cells 2, 151 (1980).
[CrossRef]

1978 (1)

1977 (2)

1976 (1)

See, for example, A. Rabl, Sol. Energy 18, 93 (1976).
[CrossRef]

1974 (1)

R. Winston, Sol. Energy 16, 89 (1974).
[CrossRef]

Collares-Pereira, M.

Cuevas, A.

A. Luque, A. Cuevas, J. M. Ruiz, Sol. Cells 2, 151 (1980).
[CrossRef]

Hottel, H.

H. Hottel, “Radiant Heat Transmission,” in Heat Transmission, W. H. McAdams, Ed. (McGraw-Hill, New York, 1954).

Luque, A.

A. Luque, Sol. Cells 3, 355 (1981).
[CrossRef]

A. Luque, A. Cuevas, J. M. Ruiz, Sol. Cells 2, 151 (1980).
[CrossRef]

Rabl, A.

M. Collares-Pereira, A. Rabl, R. Winston, Appl. Opt. 16, 2677 (1977).
[CrossRef] [PubMed]

A. Rabl, Sol. Energy 19, 215 (1977).
[CrossRef]

See, for example, A. Rabl, Sol. Energy 18, 93 (1976).
[CrossRef]

Ruiz, J. M.

A. Luque, A. Cuevas, J. M. Ruiz, Sol. Cells 2, 151 (1980).
[CrossRef]

Welford, W. T.

R. Winston, W. T. Welford, J. Opt. Soc. Am. 68, 289 (1978).
[CrossRef]

W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).

Winston, R.

R. Winston, W. T. Welford, J. Opt. Soc. Am. 68, 289 (1978).
[CrossRef]

M. Collares-Pereira, A. Rabl, R. Winston, Appl. Opt. 16, 2677 (1977).
[CrossRef] [PubMed]

R. Winston, Sol. Energy 16, 89 (1974).
[CrossRef]

W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Sol. Cells (2)

A. Luque, Sol. Cells 3, 355 (1981).
[CrossRef]

A. Luque, A. Cuevas, J. M. Ruiz, Sol. Cells 2, 151 (1980).
[CrossRef]

Sol. Energy (3)

R. Winston, Sol. Energy 16, 89 (1974).
[CrossRef]

See, for example, A. Rabl, Sol. Energy 18, 93 (1976).
[CrossRef]

A. Rabl, Sol. Energy 19, 215 (1977).
[CrossRef]

Other (2)

W. T. Welford, R. Winston, The Optics of Nonimaging Concentrators (Academic, New York, 1978).

H. Hottel, “Radiant Heat Transmission,” in Heat Transmission, W. H. McAdams, Ed. (McGraw-Hill, New York, 1954).

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Figures (7)

Fig. 1
Fig. 1

Relative position of the source and the entry aperture of the concentrator. X0 is a point of the mirror generated by a first-reflected extreme ray, and Xi is generated by a first-refracted extreme ray.

Fig. 2
Fig. 2

Dielectric tube and collector; d determines their relative position.

Fig. 3
Fig. 3

Concentrator and its source. Also shown is the trajectory of four extreme rays.

Fig. 4
Fig. 4

Detail of the part of the mirror that is generated by nonordinary extreme rays.

Fig. 5
Fig. 5

ITC of ϕ = 30° and n = 1.5 compared with an equivalent CPC.

Fig. 6
Fig. 6

Geometry of an ITC whose end points of the mirror are generated by nonordinary extreme rays.

Fig. 7
Fig. 7

Ideal and optimal concentrator for a tubular collector placed concentrically in the dielectric tube. When the quotient of both radii is n, the entire mirror is outside the dielectric, and its shape is the same as that of a CPC designed as if the dielectric tube were the collector.

Equations (15)

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E = 2 ( A B ¯ A B ¯ ) = 2 ( A B ¯ A B ¯ ) .
E = 2 ( A B ¯ A B ¯ ) = 4 n W ,
[ T Y T ] = T T ,
l = [ A X 0 P ] = [ A T ] + [ T Y ] + [ Y X 0 P ] = [ A T ] + [ T Y T ] + [ T X 0 P ] = [ A T ] + T T + [ T X 0 P ] .
[ T X 0 P ] = T T + [ T X 0 P ] .
l = [ A T ] + T T + [ T X 0 P ] .
E = 2 R [ ϕ m + ϕ π 2 + cos ( ϕ m ϕ ) ] .
2 R [ ϕ m + ϕ π 2 + cos ( ϕ m ϕ ) ] = 4 n W .
G F ¯ + F B + n B P ¯ = n B E ¯ + n E P ¯ = n B P ¯ + 2 n W , G F ¯ + F B = 2 n W ,
P c = A c T 4 σ ,
σ = 2 π 5 n 2 K 4 15 c 0 2 h 3 = σ 0 n 2 ,
E c = π n 2 A c .
E t = π n A c .
r 1 = r 0 n ( 1 S z 2 1 ( S z / n ) 2 ) 1 / 2 ,
P l = 1 n A c T 4 σ 0 n 2 = 2 π r n T 4 σ 0 = 2 π R T 4 σ 0 .

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