Abstract

The collection properties of generalized nonimaging radiation concentrators are studied for the case of geometrical optics. The second law of thermodynamics is applied to a concentrator located at the center of a cavity radiation source. It is shown that for three-dimensional concentrators the concentration C and the angular acceptance α(θ,ϕ) obey the relation l=Cθ=0π/2ϕ=02ππ1α(θ,ϕ)cosθsinθdθdϕ. For cylindrical concentrators, the concentration and angular acceptance α(θ) obey the relation l=Cπ/2π/2(1/2)α(θ)cosθdθ. These relationships are shown to reduce to those previously known for the special case of ideal concentrators.

© 1977 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Winston, “Principles of solar concentrators of a novel design,” Solar Energy 16, 89–95 (1974).
    [Crossref]
  2. A. Rabl, “Comparison of solar concentrators,” Solar Energy 18, 93–111 (1976).
    [Crossref]
  3. R. Winston, “Light collection within the framework of geometrical optics,” J. Opt. Soc. Am. 60, 245–247 (1970).
    [Crossref]
  4. R. Hinterberger and R. Winston, “Efficient light coupler for threshold Čerenkov counters,” Ref. Sci. Instrum. 37, 1094–1095 (1966).
    [Crossref]
  5. R. E. Jones, “Optical properties of cylindrical elliptic concentrators,” Proceedings of Solar World Conference (International Solar Energy Society, Orlando, Fla., 1977), Sec. 36, p. 21–24.

1976 (1)

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

1974 (1)

R. Winston, “Principles of solar concentrators of a novel design,” Solar Energy 16, 89–95 (1974).
[Crossref]

1970 (1)

1966 (1)

R. Hinterberger and R. Winston, “Efficient light coupler for threshold Čerenkov counters,” Ref. Sci. Instrum. 37, 1094–1095 (1966).
[Crossref]

Hinterberger, R.

R. Hinterberger and R. Winston, “Efficient light coupler for threshold Čerenkov counters,” Ref. Sci. Instrum. 37, 1094–1095 (1966).
[Crossref]

Jones, R. E.

R. E. Jones, “Optical properties of cylindrical elliptic concentrators,” Proceedings of Solar World Conference (International Solar Energy Society, Orlando, Fla., 1977), Sec. 36, p. 21–24.

Rabl, A.

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

Winston, R.

R. Winston, “Principles of solar concentrators of a novel design,” Solar Energy 16, 89–95 (1974).
[Crossref]

R. Winston, “Light collection within the framework of geometrical optics,” J. Opt. Soc. Am. 60, 245–247 (1970).
[Crossref]

R. Hinterberger and R. Winston, “Efficient light coupler for threshold Čerenkov counters,” Ref. Sci. Instrum. 37, 1094–1095 (1966).
[Crossref]

J. Opt. Soc. Am. (1)

Ref. Sci. Instrum. (1)

R. Hinterberger and R. Winston, “Efficient light coupler for threshold Čerenkov counters,” Ref. Sci. Instrum. 37, 1094–1095 (1966).
[Crossref]

Solar Energy (2)

R. Winston, “Principles of solar concentrators of a novel design,” Solar Energy 16, 89–95 (1974).
[Crossref]

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

Other (1)

R. E. Jones, “Optical properties of cylindrical elliptic concentrators,” Proceedings of Solar World Conference (International Solar Energy Society, Orlando, Fla., 1977), Sec. 36, p. 21–24.

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 (5)

FIG. 1
FIG. 1

Geomtery for three-dimensional concentrator at the center of a large spherical blackbody radiation cavity. The optical axis is labelled 0.

FIG. 2
FIG. 2

Geometry for cylindrical concentrator at the center of a cylindrical blackbody radiation cavity. The optical axis is denoted by the line 0.

FIG. 3
FIG. 3

For each dielectric filled cylindrical concentrator, the shaded area illustrates the region of the primary aperture where direct radiation from the absorber element dA2 suffers total internal reflection.

FIG. 4
FIG. 4

Geometry for considering total internal reflections in a cylindrical concentrator filled with a transparent medium. The normal to dA2 is denoted by the line N.

FIG. 5
FIG. 5

Angular acceptance curves for two typical concentrators, each with C = 5. The compound parabolic concentrator CPC is a well known ideal concentrator. The comparable elliptic concentrator EC is made by truncating the appropriate ellipse such that the slope and position of the end points of the reflector curves are the same as for those of the CPC. The data shown are from Ref. 5.

Tables (1)

Tables Icon

TABLE I Results of numerical ray tracing for the angular acceptance of an elliptic concentrator with C = 5.

Equations (31)

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

C sin 2 θ c = 1 ,
C sin θ c = 1 .
d E = I cos β d Ω d S ,
d E = π 1 σ T 4 cos β d Ω d S .
d E a = π 1 σ T 4 α ( θ , ϕ ) R 2 A 1 cos θ d S .
E a = π 1 σ T 4 A 1 θ = 0 π / 2 ϕ = 0 2 π α ( θ , ϕ ) cos θ sin θ d θ d ϕ .
E e = σ T 2 4 A 2 .
1 = C θ = 0 π / 2 ϕ = 0 2 π π 1 α ( θ , ϕ ) cos θ sin θ d θ d ϕ ,
d E = π 1 σ T 4 d S cos β r 2 d 1 d z cos ψ ,
d E = π 1 σ T 4 d 1 R 1 d S cos θ cos 2 β d β .
E a = 1 2 σ T 4 d 1 R 1 d S cos θ .
E a / L = 1 2 σ T 4 d 1 π / 2 π / 2 α ( θ ) cos θ d θ ,
E a / L = σ T 2 4 d 2 ,
l = C π / 2 π / 2 1 2 α ( θ ) cos θ d θ ,
ψ c = sin 1 ( 1 / n ) .
θ = 0 θ c ϕ = 0 2 π π 1 σ T 4 cos θ d Ω d A 2 < d E e < θ = 0 π / 2 ϕ = 0 2 π π 1 σ T 4 cos θ d Ω d A 2 .
σ 0 T 4 d 2 < ( E e / L ) < n 2 σ 0 T 4 d 2 ,
1 < C θ = 0 π / 2 ϕ = 0 2 π α ( θ , ϕ ) cos θ sin θ d θ d ϕ < n 2 .
d E = π 1 σ T 4 cos ψ d Ω d A 2 ,
cos ψ = cos β cos ϕ
d Ω = ρ d β d z cos ϕ / ( ρ 2 + z 2 ) .
d Ω = d β cos ϕ d ϕ .
n 2 σ 0 T 4 d A 2 π ψ c ψ c cos β d β π / 2 π / 2 cos 2 ϕ d ϕ d E e < n 2 σ 0 T 4 d A 2 π π / 2 π / 2 cos β d β π / 2 π / 2 cos 2 ϕ d ϕ .
n σ 0 T 4 d 2 E e / L < n 2 σ T 4 d 2 .
n C θ = 0 π / 2 ϕ = 0 2 π α ( θ , ϕ ) cos θ sin θ d θ d ϕ < n 2 .
1 = C θ = 0 θ c ϕ = 0 2 π π 1 cos θ sin θ d θ d ϕ ,
1 = C sin 2 θ ,
1 = C θ c θ c 1 2 cos θ d θ ,
1 = C sin θ c ,
C θ 1 θ 2 α ( θ ) cos θ d θ = 1 C sin θ 1 .
θ 1 θ 2 α ( θ ) cos θ d θ i = 1 n 1 1 2 [ α ( θ i ) cos θ i + α ( θ i + 1 ) cos θ i + 1 ] ( θ i + 1 θ i ) ,