Abstract

To predict the energetic effectiveness of a tubular light guide accurately, a theoretically founded approach has to be used rather than any empirical approximation. The computed illuminance below a light guide can become inaccurate if neither Fresnel’s equations nor realistic optical path lengths in a cupola are taken into consideration. It is shown that incorporation of both of them into a theoretical model results in lowered luminous flux below the light guide. Assumption of directionally independent transmission coefficient leads to average errors in luminous fluxes of about 10%. The peak errors are typically higher and correspond to lightbeams crossing a hemispherical top dome near its circular base. The solution concept used in this paper can improve predictions of energetic effectiveness for tubular light guides under diffuse daylight conditions.

© 2013 Optical Society of America

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References

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  1. J. T. Kim and G. Kim, “Overview and new developments in optical daylighting systems for building a healthy indoor environment,” Build. Environ. 45, 256–269 (2010).
    [CrossRef]
  2. M. Al-Marwaee and D. Carter, “Tubular guidance systems for daylight: achieved and predicted installation performances,” Appl. Energy 83, 774–788 (2006).
    [CrossRef]
  3. B. I. Ismail, “Design and performance of a transportable hemispherical solar still,” Renew. Energy 34, 145–150 (2009).
    [CrossRef]
  4. D. Jenkins, T. Muneer, and J. Kubie, “A design tool or predicting the performances of light pipes,” Energy Build. 37, 485–492 (2005).
    [CrossRef]
  5. M. A. Wilkinson, “Natural lighting under translucent domes,” Light. Res. Technol. 24, 117–126 (1992).
    [CrossRef]
  6. A. Laouadi and M. R. Atif, “Prediction models of optical characteristics for domed skylights under standard and real sky conditions,” in 7th International IBPSA Conference (IBPSA, 2001), pp. 1101–1108.
  7. M. Kocifaj, “Overcast sky luminance is dependent on the physical state of the atmosphere below cloud level,” Light. Res. Technol. 42, 149–159 (2010).
    [CrossRef]
  8. S. Chirarattananon, V. D. Hien, P. Chaiwiwatworakul, and P. Chirarattananon, “Simulation of transmission of daylight through cylindrical light pipes,” J. Sustain. Energ. Environ. 1, 97–103 (2010).
  9. R. Kittler, “Universal modelling of daylight climates for design purposes,” Architect. Sci. Rev. 42, 75–78 (1999).
    [CrossRef]
  10. J. T. Houghton, The Physics of Atmospheres (Cambridge University, 1986).
  11. J. M. Bennet, “Polarized light,” in Handbook of Optics, M. Bass and V. N. Mahajan, eds. (McGraw-Hill, 2009), Vol. 1.
  12. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
  13. M. Kocifaj and F. Kundracik, “Luminous intensity solid of tubular light guide and its characterization using asymmetry parameter,” Sol. Energy 85, 2003–2010 (2011).
    [CrossRef]

2011 (1)

M. Kocifaj and F. Kundracik, “Luminous intensity solid of tubular light guide and its characterization using asymmetry parameter,” Sol. Energy 85, 2003–2010 (2011).
[CrossRef]

2010 (3)

M. Kocifaj, “Overcast sky luminance is dependent on the physical state of the atmosphere below cloud level,” Light. Res. Technol. 42, 149–159 (2010).
[CrossRef]

S. Chirarattananon, V. D. Hien, P. Chaiwiwatworakul, and P. Chirarattananon, “Simulation of transmission of daylight through cylindrical light pipes,” J. Sustain. Energ. Environ. 1, 97–103 (2010).

J. T. Kim and G. Kim, “Overview and new developments in optical daylighting systems for building a healthy indoor environment,” Build. Environ. 45, 256–269 (2010).
[CrossRef]

2009 (1)

B. I. Ismail, “Design and performance of a transportable hemispherical solar still,” Renew. Energy 34, 145–150 (2009).
[CrossRef]

2006 (1)

M. Al-Marwaee and D. Carter, “Tubular guidance systems for daylight: achieved and predicted installation performances,” Appl. Energy 83, 774–788 (2006).
[CrossRef]

2005 (1)

D. Jenkins, T. Muneer, and J. Kubie, “A design tool or predicting the performances of light pipes,” Energy Build. 37, 485–492 (2005).
[CrossRef]

1999 (1)

R. Kittler, “Universal modelling of daylight climates for design purposes,” Architect. Sci. Rev. 42, 75–78 (1999).
[CrossRef]

1992 (1)

M. A. Wilkinson, “Natural lighting under translucent domes,” Light. Res. Technol. 24, 117–126 (1992).
[CrossRef]

Al-Marwaee, M.

M. Al-Marwaee and D. Carter, “Tubular guidance systems for daylight: achieved and predicted installation performances,” Appl. Energy 83, 774–788 (2006).
[CrossRef]

Atif, M. R.

A. Laouadi and M. R. Atif, “Prediction models of optical characteristics for domed skylights under standard and real sky conditions,” in 7th International IBPSA Conference (IBPSA, 2001), pp. 1101–1108.

Bennet, J. M.

J. M. Bennet, “Polarized light,” in Handbook of Optics, M. Bass and V. N. Mahajan, eds. (McGraw-Hill, 2009), Vol. 1.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Carter, D.

M. Al-Marwaee and D. Carter, “Tubular guidance systems for daylight: achieved and predicted installation performances,” Appl. Energy 83, 774–788 (2006).
[CrossRef]

Chaiwiwatworakul, P.

S. Chirarattananon, V. D. Hien, P. Chaiwiwatworakul, and P. Chirarattananon, “Simulation of transmission of daylight through cylindrical light pipes,” J. Sustain. Energ. Environ. 1, 97–103 (2010).

Chirarattananon, P.

S. Chirarattananon, V. D. Hien, P. Chaiwiwatworakul, and P. Chirarattananon, “Simulation of transmission of daylight through cylindrical light pipes,” J. Sustain. Energ. Environ. 1, 97–103 (2010).

Chirarattananon, S.

S. Chirarattananon, V. D. Hien, P. Chaiwiwatworakul, and P. Chirarattananon, “Simulation of transmission of daylight through cylindrical light pipes,” J. Sustain. Energ. Environ. 1, 97–103 (2010).

Hien, V. D.

S. Chirarattananon, V. D. Hien, P. Chaiwiwatworakul, and P. Chirarattananon, “Simulation of transmission of daylight through cylindrical light pipes,” J. Sustain. Energ. Environ. 1, 97–103 (2010).

Houghton, J. T.

J. T. Houghton, The Physics of Atmospheres (Cambridge University, 1986).

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Ismail, B. I.

B. I. Ismail, “Design and performance of a transportable hemispherical solar still,” Renew. Energy 34, 145–150 (2009).
[CrossRef]

Jenkins, D.

D. Jenkins, T. Muneer, and J. Kubie, “A design tool or predicting the performances of light pipes,” Energy Build. 37, 485–492 (2005).
[CrossRef]

Kim, G.

J. T. Kim and G. Kim, “Overview and new developments in optical daylighting systems for building a healthy indoor environment,” Build. Environ. 45, 256–269 (2010).
[CrossRef]

Kim, J. T.

J. T. Kim and G. Kim, “Overview and new developments in optical daylighting systems for building a healthy indoor environment,” Build. Environ. 45, 256–269 (2010).
[CrossRef]

Kittler, R.

R. Kittler, “Universal modelling of daylight climates for design purposes,” Architect. Sci. Rev. 42, 75–78 (1999).
[CrossRef]

Kocifaj, M.

M. Kocifaj and F. Kundracik, “Luminous intensity solid of tubular light guide and its characterization using asymmetry parameter,” Sol. Energy 85, 2003–2010 (2011).
[CrossRef]

M. Kocifaj, “Overcast sky luminance is dependent on the physical state of the atmosphere below cloud level,” Light. Res. Technol. 42, 149–159 (2010).
[CrossRef]

Kubie, J.

D. Jenkins, T. Muneer, and J. Kubie, “A design tool or predicting the performances of light pipes,” Energy Build. 37, 485–492 (2005).
[CrossRef]

Kundracik, F.

M. Kocifaj and F. Kundracik, “Luminous intensity solid of tubular light guide and its characterization using asymmetry parameter,” Sol. Energy 85, 2003–2010 (2011).
[CrossRef]

Laouadi, A.

A. Laouadi and M. R. Atif, “Prediction models of optical characteristics for domed skylights under standard and real sky conditions,” in 7th International IBPSA Conference (IBPSA, 2001), pp. 1101–1108.

Muneer, T.

D. Jenkins, T. Muneer, and J. Kubie, “A design tool or predicting the performances of light pipes,” Energy Build. 37, 485–492 (2005).
[CrossRef]

Wilkinson, M. A.

M. A. Wilkinson, “Natural lighting under translucent domes,” Light. Res. Technol. 24, 117–126 (1992).
[CrossRef]

Appl. Energy (1)

M. Al-Marwaee and D. Carter, “Tubular guidance systems for daylight: achieved and predicted installation performances,” Appl. Energy 83, 774–788 (2006).
[CrossRef]

Architect. Sci. Rev. (1)

R. Kittler, “Universal modelling of daylight climates for design purposes,” Architect. Sci. Rev. 42, 75–78 (1999).
[CrossRef]

Build. Environ. (1)

J. T. Kim and G. Kim, “Overview and new developments in optical daylighting systems for building a healthy indoor environment,” Build. Environ. 45, 256–269 (2010).
[CrossRef]

Energy Build. (1)

D. Jenkins, T. Muneer, and J. Kubie, “A design tool or predicting the performances of light pipes,” Energy Build. 37, 485–492 (2005).
[CrossRef]

J. Sustain. Energ. Environ. (1)

S. Chirarattananon, V. D. Hien, P. Chaiwiwatworakul, and P. Chirarattananon, “Simulation of transmission of daylight through cylindrical light pipes,” J. Sustain. Energ. Environ. 1, 97–103 (2010).

Light. Res. Technol. (2)

M. Kocifaj, “Overcast sky luminance is dependent on the physical state of the atmosphere below cloud level,” Light. Res. Technol. 42, 149–159 (2010).
[CrossRef]

M. A. Wilkinson, “Natural lighting under translucent domes,” Light. Res. Technol. 24, 117–126 (1992).
[CrossRef]

Renew. Energy (1)

B. I. Ismail, “Design and performance of a transportable hemispherical solar still,” Renew. Energy 34, 145–150 (2009).
[CrossRef]

Sol. Energy (1)

M. Kocifaj and F. Kundracik, “Luminous intensity solid of tubular light guide and its characterization using asymmetry parameter,” Sol. Energy 85, 2003–2010 (2011).
[CrossRef]

Other (4)

A. Laouadi and M. R. Atif, “Prediction models of optical characteristics for domed skylights under standard and real sky conditions,” in 7th International IBPSA Conference (IBPSA, 2001), pp. 1101–1108.

J. T. Houghton, The Physics of Atmospheres (Cambridge University, 1986).

J. M. Bennet, “Polarized light,” in Handbook of Optics, M. Bass and V. N. Mahajan, eds. (McGraw-Hill, 2009), Vol. 1.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

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Figures (9)

Fig. 1.
Fig. 1.

Local coordinates of the cupola and an incident light beam.

Fig. 2.
Fig. 2.

Errors in luminous fluxes computed for all applicable solar altitudes and for three sky types.

Fig. 3.
Fig. 3.

Relative illuminance at the cupola base assuming CIE Standard Overcast Sky (on the left) and Unit Sky (on the right).

Fig. 4.
Fig. 4.

Relative illuminance at the cupola base assuming CIE Standard Clear Sky and various sun altitudes: 18.5° (on the left), 42° (in the middle), and 65.5° (on the right).

Fig. 5.
Fig. 5.

Relative diffuse illuminance measured along southern–northern axes below the cupola. Various sky types are considered. The sun altitudes are (from left to right): 18.5°, 42°, and 65.5°.

Fig. 6.
Fig. 6.

The model luminance distribution computed for CIE Standard Clear Sky and for Bratislava (capital of Slovakia) on May 7th at 9:00 AM. The exterior illuminance comprises only the diffuse light component.

Fig. 7.
Fig. 7.

The illuminance distribution on the light-tube base. The exterior illuminance is computed for sky type 12 assuming only the diffuse illuminance. The system parameters are as follows: (cupola: thickness h=4mm, transmission coefficient for normal beams=0.89, the volume attenuation coefficient νil=30m1); (tube: radius R=0.16m, length=2m, internal reflectance=0.934). Here, the average cosine is a cosine-weighted integral of luminance function below a light guide [13].

Fig. 8.
Fig. 8.

The illuminance on a working plane situated 2 m below the light guide. The hemispherical dome is clean, showing the volume attenuation coefficient νil=30m1. The left plot (pane 8a) corresponds to the simplified model accepting directionally independent attenuation. The right plot (pane 8b) is obtained for a model that accounts for Fresnel’s optics and different attenuation of beams that propagate cupolas at inclined trajectories.

Fig. 9.
Fig. 9.

The same as in Fig. 8, but for a dirty cupola with volume attenuation coefficient νil=55m1. The left plot is referenced as 9a, while the right plot is 9b.

Tables (2)

Tables Icon

Table 1. Accurate, Approximate, and Relative Luminous Fluxes at the Base of Transparent Hemispherical Cupola with Radius R=0.16m and Absorption Coefficient νil=30m1Three Sky Models (types 1, 5, and 12) Are Simulated for Sun Elevations γs=18.5°, 42°, and 65.5°

Tables Icon

Table 2. Accurate, Approximate and Relative Luminous Fluxes at the Base of Transparent Hemispherical Cupola with Radius R=0.16m and Absorption Coefficient νil=55m1, Used to Simulate Cupolas with Dirty Interfaces

Equations (28)

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cosα=|u·v||u|·|v|=|x1·(x1x0)+y1·(y1y0)+z12|x12+y12+z12·(x1x0)2+(y1y0)2+(z1)2,
u=SP=PS=(x1;y1;z1),v=AP=PA=(x1x0;y1y0;z1).
cosα=|R2x0x1y0y1|RR+r02(x0x1+y0y1),
x0=r0cosϕ0,y0=r0sinϕ0.
x1=Rcosϕ1sinϑ,y1=Rsinϕ1sinϑ,z1=Rcosϑ.
cosα=|Rr0cos(ϕ0ϕ1)sinϑ|R2+r022Rr0cos(ϕ0ϕ1)sinϑ,
sinαsinβ=n2n1.
ρTE=(n1cosαn2cosβn1cosα+n2cosβ)2,
ρTM=(n1cosβn2cosαn1cosβ+n2cosα)2.
ρ=12[(n1cosαn21(n1n2sinα)2n1cosα+n21(n1n2sinα)2)2+(n11(n1n2sinα)2n2cosαn11(n1n2sinα)2+n2cosα)2].
sinα=1[Rr0cos(ϕ0ϕ1)sinϑ]2R2+r022Rr0cos(ϕ0ϕ1)sinϑ.
Y=Rr0cos(ϕ0ϕ1)sinϑR2+r022Rr0cos(ϕ0ϕ1)sinϑ,
ρ(r0,ϕ0,ϕ1,ϑ)=12{2Y22YY2+n221+n2212Y2+2YY2+n221+n221,+Y2(n24+1)2Yn22Y2+n221+n221Y2(n24+1)+2Yn22Y2+n221+n221},
τ(r0,ϕ0,ϕ1,ϑ)=(1ρ(r0,ϕ0,ϕ1,ϑ))2eν1ρ2(r0,ϕ0,ϕ1,ϑ)e2ν,
ν=νilhcosβ
ν=νilhn2cos2α+n221,
La(ϑ,ϕ1)=(φ(ϑ)φ(0°)·f(χ)f(Zs))LZ,
LZ=Dv/Ev[B(sinγs)C(cosγs)D+Esinγs],
LZ=(A1·TV+A2)sinγs+0.7(TV+1)(sinγs)C(cosγs)D+0.04TV.
φ(ϑ)=1+a·e(b/cosϑ),
f(χ)=1+c·(edχedπ/2)+e·cos2χ.
cosχ=cosZscosϑ+sinZssinϑcos(ϕsϕ1),
ED(r0,ϕ0)=ϑ=0π/2ϕ1=02πLa(ϑ,ϕ1)τ(r0,ϕ0,ϕ1,ϑ)cosϑsinϑdϑdϕ1.
EappD(r0,ϕ0)=eνϑ=0π/2ϕ1=02πLa(ϑ,ϕ1)cosϑsinϑdϑdϕ1,
ErelD(r0,ϕ0)=ED(r0,ϕ0)EappD(r0,ϕ0).
ΦD=r0=0Rϕ0=02πED(r0,ϕ0)r0dr0dϕ0.
ΦappD=r0=0Rϕ0=02πEappD(r0,ϕ0)r0dr0dϕ0.
ΦrelD=ΦDΦappD.

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