Abstract

An algorithm based on the Monte Carlo method is described that permits the precise calculation of radiant emission characteristics of nonisothermal blackbody cavities for use as standard sources in radiometry, photometry, and radiation thermometry. The algorithm is realized for convex axisymmetric specular-diffuse cavities formed by three conical surfaces. The numerical experiments provide estimates of normal effective emissivities of cylindrical blackbody cavities with flat or conical bottoms for various axisymmetric temperature distributions on the cavity walls.

© 1995 Optical Society of America

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References

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  1. Y. Ohwada, “Mathematical proof of an extended Kirchhoff law for a cavity having directional-dependent characteristics,” J. Opt. Soc. Am. A 5, 141–145 (1988).
    [CrossRef]
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    [CrossRef]
  3. R. E. Bedford, C. K. Ma, “Emissivities of diffuse cavities. II: Isothermal and nonisothermal cylindro-cones,” J. Opt. Soc. Am. 65, 565–572 (1975).
    [CrossRef]
  4. R. E. Bedford, C. K. Ma, “Emissivities of diffuse cavities. III. Isothermal and nonisothermal double cones,” J. Opt. Soc. Am. 66, 724–730 (1976).
    [CrossRef]
  5. R. E. Bedford, C. K. Ma, Z. Chu, Y. Sun, S. Chen, “Emissivities of diffuse cavities. 4. Isothermal and nonisothermal cylindro-inner-cones,” Appl. Opt. 24, 2971–2980 (1985).
    [CrossRef] [PubMed]
  6. Y. Ohwada, “Evaluation of effective emissivities of nonisothermal cavities,” Appl. Opt. 22, 2322–2325 (1983).
    [CrossRef] [PubMed]
  7. J. S. Redgrove, K. H. Berry, “Emissivity of a cylindrical blackbody cavity having diffuse and specular components of reflectivity with a correction term for nonisothermal conditions,” High Temp. High Pressures 15, 1–11 (1983).
  8. F. O. Bartell, W. L. Wolf, “Cavity radiator theory,” Infrared Phys. 16, 13–26 (1976).
    [CrossRef]
  9. A. Ono, “Calculation of the directional emissivities of cavities by the Monte Carlo method,” J. Opt. Soc. Am. 70, 547–554 (1980).
    [CrossRef]
  10. R. P. Heinisch, E. M. Sparrow, N. Shamsundar, “Radiant emission from baffled conical cavities,” J. Opt. Soc. Am. 63, 152–158 (1973).
    [CrossRef]
  11. V. I. Sapritsky, A. V. Prokhorov, “Calculation of the effective emissivities of specular-diffuse cavities by the Monte Carlo method,” Metrologia 29, 9–14 (1992).
    [CrossRef]
  12. R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 2nd ed. (McGraw-Hill, New York, 1981).
  13. U. Kienitz, “Infrarot-Strahlungsmeßverfahren zue berührungslosen Bestimmung von Temperature und Oberflächen-emissionenseigenschaften,” Wiss. Z. Tech. Univ. Dresden 35, 30–32 (1986).

1992

V. I. Sapritsky, A. V. Prokhorov, “Calculation of the effective emissivities of specular-diffuse cavities by the Monte Carlo method,” Metrologia 29, 9–14 (1992).
[CrossRef]

1988

1986

U. Kienitz, “Infrarot-Strahlungsmeßverfahren zue berührungslosen Bestimmung von Temperature und Oberflächen-emissionenseigenschaften,” Wiss. Z. Tech. Univ. Dresden 35, 30–32 (1986).

1985

1983

Y. Ohwada, “Evaluation of effective emissivities of nonisothermal cavities,” Appl. Opt. 22, 2322–2325 (1983).
[CrossRef] [PubMed]

J. S. Redgrove, K. H. Berry, “Emissivity of a cylindrical blackbody cavity having diffuse and specular components of reflectivity with a correction term for nonisothermal conditions,” High Temp. High Pressures 15, 1–11 (1983).

1980

1976

1975

1974

1973

Bartell, F. O.

F. O. Bartell, W. L. Wolf, “Cavity radiator theory,” Infrared Phys. 16, 13–26 (1976).
[CrossRef]

Bedford, R. E.

Berry, K. H.

J. S. Redgrove, K. H. Berry, “Emissivity of a cylindrical blackbody cavity having diffuse and specular components of reflectivity with a correction term for nonisothermal conditions,” High Temp. High Pressures 15, 1–11 (1983).

Chen, S.

Chu, Z.

Heinisch, R. P.

Howell, J. R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 2nd ed. (McGraw-Hill, New York, 1981).

Kienitz, U.

U. Kienitz, “Infrarot-Strahlungsmeßverfahren zue berührungslosen Bestimmung von Temperature und Oberflächen-emissionenseigenschaften,” Wiss. Z. Tech. Univ. Dresden 35, 30–32 (1986).

Ma, C. K.

Ohwada, Y.

Ono, A.

Prokhorov, A. V.

V. I. Sapritsky, A. V. Prokhorov, “Calculation of the effective emissivities of specular-diffuse cavities by the Monte Carlo method,” Metrologia 29, 9–14 (1992).
[CrossRef]

Redgrove, J. S.

J. S. Redgrove, K. H. Berry, “Emissivity of a cylindrical blackbody cavity having diffuse and specular components of reflectivity with a correction term for nonisothermal conditions,” High Temp. High Pressures 15, 1–11 (1983).

Sapritsky, V. I.

V. I. Sapritsky, A. V. Prokhorov, “Calculation of the effective emissivities of specular-diffuse cavities by the Monte Carlo method,” Metrologia 29, 9–14 (1992).
[CrossRef]

Shamsundar, N.

Siegel, R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 2nd ed. (McGraw-Hill, New York, 1981).

Sparrow, E. M.

Sun, Y.

Wolf, W. L.

F. O. Bartell, W. L. Wolf, “Cavity radiator theory,” Infrared Phys. 16, 13–26 (1976).
[CrossRef]

Appl. Opt.

High Temp. High Pressures

J. S. Redgrove, K. H. Berry, “Emissivity of a cylindrical blackbody cavity having diffuse and specular components of reflectivity with a correction term for nonisothermal conditions,” High Temp. High Pressures 15, 1–11 (1983).

Infrared Phys.

F. O. Bartell, W. L. Wolf, “Cavity radiator theory,” Infrared Phys. 16, 13–26 (1976).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Metrologia

V. I. Sapritsky, A. V. Prokhorov, “Calculation of the effective emissivities of specular-diffuse cavities by the Monte Carlo method,” Metrologia 29, 9–14 (1992).
[CrossRef]

Wiss. Z. Tech. Univ. Dresden

U. Kienitz, “Infrarot-Strahlungsmeßverfahren zue berührungslosen Bestimmung von Temperature und Oberflächen-emissionenseigenschaften,” Wiss. Z. Tech. Univ. Dresden 35, 30–32 (1986).

Other

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 2nd ed. (McGraw-Hill, New York, 1981).

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Figures (11)

Fig. 1
Fig. 1

Cavities to which the calculation is applied.

Fig. 2
Fig. 2

Spectral normal effective emissivities of a cylindrical cavity for the first family of temperature distributions.

Fig. 3
Fig. 3

Spectral normal effective emissivities of a cylindrical cavity for the second family of temperature distributions.

Fig. 4
Fig. 4

Spectral normal effective emissivities of a cylindrical cavity for the third family of temperature distributions.

Fig. 5
Fig. 5

Spectral normal effective emissivities of a cylindrical cavity for the fourth family of temperature distributions.

Fig. 6
Fig. 6

Spectral normal effective emissivities of a cylindrical cavity for the fifth family of temperature distributions.

Fig. 7
Fig. 7

Spectral normal effective emissivities of a cylindrical cavity for the sixth family of temperature distributions.

Fig. 8
Fig. 8

Spectral hemispherical emissivities of a flat specimen of oxidized stainless steel.

Fig. 9
Fig. 9

Spectral normal effective emissivities of a cylindroconical cavity.

Fig. 10
Fig. 10

Spectral normal effective emissivities of a nonisothermal cylindrical cavity for five reference temperatures.

Fig. 11
Fig. 11

Spectral normal effective emissivities of a nonisothermal cylindroconical cavity for five reference temperatures.

Equations (23)

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e 0 ( λ , ξ , ω ) = α e 0 ( λ , ξ , - ω ) = 1 - ρ e 0 ( λ , ξ , - ω ) ,
( λ ) + ρ ( λ ) = 1 ,
D = ρ d ( λ ) ρ ( λ ) ,
L e ( λ , ξ , ω ) = e ( λ , ξ , ω , T 0 ) L BB ( λ , T 0 ) ,
e ( λ , ξ , ω , T 0 ) = e 0 ( λ , ξ , ω ) + Δ e ( λ , ξ , ω , T 0 ) ,
W = ρ ( λ ) W ,
ω = ω - 2 n ( n ω ) ,
F ( ξ ) = ( 1 π ) Ω cos θ ξ d Ω ,
W = ρ ( λ ) [ 1 - F ( ξ ) ] W .
θ = arcsin H θ ,
ϕ = 2 π H ϕ .
x = x + ω x t ,
y = y + ω y t ,
z = z + ω z t
x 2 + y 2 - ( z - z 0 i ) 2 tan 2 ( χ i / 2 ) = 0.
i = 1 with 0 < z < z 1 , = 2 with z 1 < z < z 2 , = 3 with z 2 < z < z 3 .
e ( λ , ξ , ω ) = 1 - ( 1 n n 0 ) i = 1 n j = 1 n 0 i k = 1 m i j ρ k ( λ ) F ( ξ i j k ) × l = 1 k - 1 [ 1 - F ( ξ i j l ) ] ,
L e ( λ , ξ , ω ) = ( λ ) n n 0 i = 1 n j = 1 n 0 i k = 1 m i j ρ k - 1 ( λ ) L BB ( λ , T i j k ) γ i j k ,
e ( λ , ξ , ω , T 0 ) = ( λ ) n n 0 L BB ( λ , T 0 ) i = 1 n j = 1 n 0 i k = 1 m i j ρ k - 1 L BB ( λ , T i j k ) γ i j k .
e 0 ( λ , ξ , ω ) = ( λ ) n n 0 i = 1 n j = 1 n 0 i k = 1 m i j ρ k - 1 ( λ ) γ i j k .
Δ e ( λ , ξ , ω , T 0 ) = ( λ ) n n 0 L BB ( λ , T 0 ) i = 1 n j = 1 n 0 i k = 1 m i j ρ k - 1 ( λ ) × [ L BB ( λ , T i j k ) - L BB ( λ , T 0 ) ] γ i j k .
e ( λ , ξ , ω , T 0 ) = 1 + 1 n n 0 i = 1 n j = 1 n 0 i k = 1 m i j { ρ k - 1 ( λ ) ( λ ) [ L BB ( λ , T i j k ) - L BB ( λ , T 0 ) ] γ i j k L BB ( λ , T i j k ) - ρ ( λ ) F ( ξ i j k ) l = 1 k - 1 [ 1 - F ( ξ i j l ) ] } .
T 0 * = 1 S S T ( ξ ) Q ( ξ ) d S ,

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