Abstract

A blackbody cavity is developed for continuously measuring the temperature of molten steel, which consists of a cylindrical outer tube with a flat bottom, a coaxial inner tube, and an aperture diaphragm. The ray-tracing approach based on the Monte Carlo method was applied to calculate the effective emissivity for the isothermal cavity with the diffuse walls. And the dependences of the effective emissivity on the inner tube relative length were calculated for various inner tube radii, outer tube lengths, and wall emissivities. Results indicate that the effective emissivity usually has a maximum corresponding to the inner tube relative length, which can be explained by the impact of the inner tube relative length on the probability of the rays absorbed after two reflections. Thus, these results are helpful to the optimal design of the blackbody cavity.

© 2014 Optical Society of America

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References

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  1. Z. Xie, Y. Ci, H. J. Meng, and H. Zhang, “Development of continuous temperature measuring sensor for liquid steel based on blackbody cavity,” Chin. J. Scientific Instrum. 26, 446–448, 456 (2005).
  2. S. M. Zhao, G. H. Mei, J. Zhang, and Z. Xie, “Finite element analysis of composite structure continuous temperature-measuring sensor for liquid steel,” J. Northeast. Univ. Nat. Sci. 133, 926–929 (2012).
  3. S. M. Zhao, G. H. Mei, J. Sun, W. Yang, and Z. Xie, “Estimation of effective diffusion coefficient of gaseous species in MgO-C refractories by shrinking core model,” ISIJ Int. 52, 1186–1195 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (2)

S. M. Zhao, G. H. Mei, J. Zhang, and Z. Xie, “Finite element analysis of composite structure continuous temperature-measuring sensor for liquid steel,” J. Northeast. Univ. Nat. Sci. 133, 926–929 (2012).

S. M. Zhao, G. H. Mei, J. Sun, W. Yang, and Z. Xie, “Estimation of effective diffusion coefficient of gaseous species in MgO-C refractories by shrinking core model,” ISIJ Int. 52, 1186–1195 (2012).
[CrossRef]

2010 (1)

A. V. Prokhorov and L. M. Hanssen, “Effective emissivity of a cylindrical cavity with an inclined bottom: II. Non-isothermal cavity,” Metrologia 47, 33–46 (2010).
[CrossRef]

2005 (1)

Z. Xie, Y. Ci, H. J. Meng, and H. Zhang, “Development of continuous temperature measuring sensor for liquid steel based on blackbody cavity,” Chin. J. Scientific Instrum. 26, 446–448, 456 (2005).

2004 (2)

A. V. Prokhorov and L. M. Hanssen, “Effective emissivity of a cylindrical cavity with an inclined bottom: I. Isothermal cavity,” Metrologia 41, 421–431 (2004).
[CrossRef]

S. R. Meier, R. I. Joseph, and S. K. Antiochos, “Radiation characteristics of a high-emissivity cylindrical-spherical cavity with obscuration,” J. Opt. Soc. Am. A 21, 104–112 (2004).
[CrossRef]

2002 (1)

1998 (2)

A. V. Prokhorov, “Monte Carlo method in optical radiometry,” Metrologia 35, 465–471 (1998).
[CrossRef]

J. Ishii, M. Kobayashi, and F. Sakuma, “Effective emissivities of black-body cavities with grooved cylinders,” Metrologia 35, 175–180 (1998).
[CrossRef]

1995 (1)

M. J. Ballico, “Modelling of the effective emissivity of a graphite tube black body,” Metrologia 32, 259–265 (1995).
[CrossRef]

1992 (1)

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

1985 (1)

1984 (1)

H. P. Chen, T. Q. Li, S. R. Chen, and Z. X. Chu, “Calculation of effective surface emissivity of square cavities,” Chin. J. IR Res. 3, 166–171 (1984).

1980 (2)

S. R. Chen, Z. X. Chu, and H. P. Chen, “Precise calculation of the integrated emissivity of baffled blackbody cavities,” Metrologia 16, 69–72 (1980).
[CrossRef]

A. Ono, “Calculation of the directional emissivities of cavities by the Monte Carlo method,” J. Opt. Soc. Am. 70, 547–554 (1980).
[CrossRef]

1976 (1)

1975 (1)

1974 (1)

1973 (1)

1964 (1)

J. R. Howell and M. Perlmutter, “Monte Carlo solution of thermal transfer through radiant media between gray walls,” Heat Transfer 86, 116–122 (1964).
[CrossRef]

Antiochos, S. K.

Ballico, M. J.

M. J. Ballico, “Modelling of the effective emissivity of a graphite tube black body,” Metrologia 32, 259–265 (1995).
[CrossRef]

Bedford, R. E.

Chen, H. P.

H. P. Chen, T. Q. Li, S. R. Chen, and Z. X. Chu, “Calculation of effective surface emissivity of square cavities,” Chin. J. IR Res. 3, 166–171 (1984).

S. R. Chen, Z. X. Chu, and H. P. Chen, “Precise calculation of the integrated emissivity of baffled blackbody cavities,” Metrologia 16, 69–72 (1980).
[CrossRef]

Chen, S. R.

R. E. Bedford, C. K. Ma, Z. X. Chu, and S. R. Chen, “Emissivities of diffuse cavities 4: Isothermal and nonisothermal cylindro-inner-cones,” Appl. Opt. 24, 2971–2980 (1985).
[CrossRef]

H. P. Chen, T. Q. Li, S. R. Chen, and Z. X. Chu, “Calculation of effective surface emissivity of square cavities,” Chin. J. IR Res. 3, 166–171 (1984).

S. R. Chen, Z. X. Chu, and H. P. Chen, “Precise calculation of the integrated emissivity of baffled blackbody cavities,” Metrologia 16, 69–72 (1980).
[CrossRef]

Chu, Z. X.

R. E. Bedford, C. K. Ma, Z. X. Chu, and S. R. Chen, “Emissivities of diffuse cavities 4: Isothermal and nonisothermal cylindro-inner-cones,” Appl. Opt. 24, 2971–2980 (1985).
[CrossRef]

H. P. Chen, T. Q. Li, S. R. Chen, and Z. X. Chu, “Calculation of effective surface emissivity of square cavities,” Chin. J. IR Res. 3, 166–171 (1984).

S. R. Chen, Z. X. Chu, and H. P. Chen, “Precise calculation of the integrated emissivity of baffled blackbody cavities,” Metrologia 16, 69–72 (1980).
[CrossRef]

Ci, Y.

Z. Xie, Y. Ci, H. J. Meng, and H. Zhang, “Development of continuous temperature measuring sensor for liquid steel based on blackbody cavity,” Chin. J. Scientific Instrum. 26, 446–448, 456 (2005).

Gao, K. M.

K. M. Gao and Z. Xie, Theory and Technology of Infrared Radiation Temperature Measurement (Northeastern University, 1989).

Hanssen, L. M.

A. V. Prokhorov and L. M. Hanssen, “Effective emissivity of a cylindrical cavity with an inclined bottom: II. Non-isothermal cavity,” Metrologia 47, 33–46 (2010).
[CrossRef]

A. V. Prokhorov and L. M. Hanssen, “Effective emissivity of a cylindrical cavity with an inclined bottom: I. Isothermal cavity,” Metrologia 41, 421–431 (2004).
[CrossRef]

Heinisch, R. P.

Howell, J. R.

J. R. Howell and M. Perlmutter, “Monte Carlo solution of thermal transfer through radiant media between gray walls,” Heat Transfer 86, 116–122 (1964).
[CrossRef]

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (Taylor and Francis, 2002), Vol. 4.

Ishii, J.

J. Ishii, M. Kobayashi, and F. Sakuma, “Effective emissivities of black-body cavities with grooved cylinders,” Metrologia 35, 175–180 (1998).
[CrossRef]

Joseph, R. I.

Kobayashi, M.

J. Ishii, M. Kobayashi, and F. Sakuma, “Effective emissivities of black-body cavities with grooved cylinders,” Metrologia 35, 175–180 (1998).
[CrossRef]

Li, T. Q.

H. P. Chen, T. Q. Li, S. R. Chen, and Z. X. Chu, “Calculation of effective surface emissivity of square cavities,” Chin. J. IR Res. 3, 166–171 (1984).

Ma, C. K.

Mei, G. H.

S. M. Zhao, G. H. Mei, J. Zhang, and Z. Xie, “Finite element analysis of composite structure continuous temperature-measuring sensor for liquid steel,” J. Northeast. Univ. Nat. Sci. 133, 926–929 (2012).

S. M. Zhao, G. H. Mei, J. Sun, W. Yang, and Z. Xie, “Estimation of effective diffusion coefficient of gaseous species in MgO-C refractories by shrinking core model,” ISIJ Int. 52, 1186–1195 (2012).
[CrossRef]

Meier, S. R.

Meng, H. J.

Z. Xie, Y. Ci, H. J. Meng, and H. Zhang, “Development of continuous temperature measuring sensor for liquid steel based on blackbody cavity,” Chin. J. Scientific Instrum. 26, 446–448, 456 (2005).

Ono, A.

Pahl, R. J.

Perlmutter, M.

J. R. Howell and M. Perlmutter, “Monte Carlo solution of thermal transfer through radiant media between gray walls,” Heat Transfer 86, 116–122 (1964).
[CrossRef]

Porkhorov, A. V.

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

Prokhorov, A. V.

A. V. Prokhorov and L. M. Hanssen, “Effective emissivity of a cylindrical cavity with an inclined bottom: II. Non-isothermal cavity,” Metrologia 47, 33–46 (2010).
[CrossRef]

A. V. Prokhorov and L. M. Hanssen, “Effective emissivity of a cylindrical cavity with an inclined bottom: I. Isothermal cavity,” Metrologia 41, 421–431 (2004).
[CrossRef]

A. V. Prokhorov, “Monte Carlo method in optical radiometry,” Metrologia 35, 465–471 (1998).
[CrossRef]

Sakuma, F.

J. Ishii, M. Kobayashi, and F. Sakuma, “Effective emissivities of black-body cavities with grooved cylinders,” Metrologia 35, 175–180 (1998).
[CrossRef]

Sapritsky, V. I.

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

Shamsundar, N.

Shannon, M. A.

Siegel, R.

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (Taylor and Francis, 2002), Vol. 4.

Sparrow, E. M.

Sun, J.

S. M. Zhao, G. H. Mei, J. Sun, W. Yang, and Z. Xie, “Estimation of effective diffusion coefficient of gaseous species in MgO-C refractories by shrinking core model,” ISIJ Int. 52, 1186–1195 (2012).
[CrossRef]

Xie, Z.

S. M. Zhao, G. H. Mei, J. Sun, W. Yang, and Z. Xie, “Estimation of effective diffusion coefficient of gaseous species in MgO-C refractories by shrinking core model,” ISIJ Int. 52, 1186–1195 (2012).
[CrossRef]

S. M. Zhao, G. H. Mei, J. Zhang, and Z. Xie, “Finite element analysis of composite structure continuous temperature-measuring sensor for liquid steel,” J. Northeast. Univ. Nat. Sci. 133, 926–929 (2012).

Z. Xie, Y. Ci, H. J. Meng, and H. Zhang, “Development of continuous temperature measuring sensor for liquid steel based on blackbody cavity,” Chin. J. Scientific Instrum. 26, 446–448, 456 (2005).

K. M. Gao and Z. Xie, Theory and Technology of Infrared Radiation Temperature Measurement (Northeastern University, 1989).

Yang, W.

S. M. Zhao, G. H. Mei, J. Sun, W. Yang, and Z. Xie, “Estimation of effective diffusion coefficient of gaseous species in MgO-C refractories by shrinking core model,” ISIJ Int. 52, 1186–1195 (2012).
[CrossRef]

Zhang, H.

Z. Xie, Y. Ci, H. J. Meng, and H. Zhang, “Development of continuous temperature measuring sensor for liquid steel based on blackbody cavity,” Chin. J. Scientific Instrum. 26, 446–448, 456 (2005).

Zhang, J.

S. M. Zhao, G. H. Mei, J. Zhang, and Z. Xie, “Finite element analysis of composite structure continuous temperature-measuring sensor for liquid steel,” J. Northeast. Univ. Nat. Sci. 133, 926–929 (2012).

Zhao, S. M.

S. M. Zhao, G. H. Mei, J. Zhang, and Z. Xie, “Finite element analysis of composite structure continuous temperature-measuring sensor for liquid steel,” J. Northeast. Univ. Nat. Sci. 133, 926–929 (2012).

S. M. Zhao, G. H. Mei, J. Sun, W. Yang, and Z. Xie, “Estimation of effective diffusion coefficient of gaseous species in MgO-C refractories by shrinking core model,” ISIJ Int. 52, 1186–1195 (2012).
[CrossRef]

Appl. Opt. (2)

Chin. J. IR Res. (1)

H. P. Chen, T. Q. Li, S. R. Chen, and Z. X. Chu, “Calculation of effective surface emissivity of square cavities,” Chin. J. IR Res. 3, 166–171 (1984).

Chin. J. Scientific Instrum. (1)

Z. Xie, Y. Ci, H. J. Meng, and H. Zhang, “Development of continuous temperature measuring sensor for liquid steel based on blackbody cavity,” Chin. J. Scientific Instrum. 26, 446–448, 456 (2005).

Heat Transfer (1)

J. R. Howell and M. Perlmutter, “Monte Carlo solution of thermal transfer through radiant media between gray walls,” Heat Transfer 86, 116–122 (1964).
[CrossRef]

ISIJ Int. (1)

S. M. Zhao, G. H. Mei, J. Sun, W. Yang, and Z. Xie, “Estimation of effective diffusion coefficient of gaseous species in MgO-C refractories by shrinking core model,” ISIJ Int. 52, 1186–1195 (2012).
[CrossRef]

J. Northeast. Univ. Nat. Sci. (1)

S. M. Zhao, G. H. Mei, J. Zhang, and Z. Xie, “Finite element analysis of composite structure continuous temperature-measuring sensor for liquid steel,” J. Northeast. Univ. Nat. Sci. 133, 926–929 (2012).

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (1)

Metrologia (7)

S. R. Chen, Z. X. Chu, and H. P. Chen, “Precise calculation of the integrated emissivity of baffled blackbody cavities,” Metrologia 16, 69–72 (1980).
[CrossRef]

J. Ishii, M. Kobayashi, and F. Sakuma, “Effective emissivities of black-body cavities with grooved cylinders,” Metrologia 35, 175–180 (1998).
[CrossRef]

A. V. Prokhorov and L. M. Hanssen, “Effective emissivity of a cylindrical cavity with an inclined bottom: I. Isothermal cavity,” Metrologia 41, 421–431 (2004).
[CrossRef]

A. V. Prokhorov and L. M. Hanssen, “Effective emissivity of a cylindrical cavity with an inclined bottom: II. Non-isothermal cavity,” Metrologia 47, 33–46 (2010).
[CrossRef]

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

A. V. Prokhorov, “Monte Carlo method in optical radiometry,” Metrologia 35, 465–471 (1998).
[CrossRef]

M. J. Ballico, “Modelling of the effective emissivity of a graphite tube black body,” Metrologia 32, 259–265 (1995).
[CrossRef]

Other (2)

K. M. Gao and Z. Xie, Theory and Technology of Infrared Radiation Temperature Measurement (Northeastern University, 1989).

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (Taylor and Francis, 2002), Vol. 4.

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Figures (9)

Fig. 1.
Fig. 1.

Schematic view of continuous temperature measurement system for molten steel (a), cylindrical cavity (b), and cavity formed by two coaxial tubes (c).

Fig. 2.
Fig. 2.

Schematic drawing of a cavity formed by two coaxial tubes.

Fig. 3.
Fig. 3.

Schematic drawing of the ray tracing. The solid and dotted lines represent the direction of an incident ray and the reflected rays, respectively.

Fig. 4.
Fig. 4.

Average effective emissivity as a function of inner tube relative length, Li/Lo, for Ri=0.5, 0.6, 0.7, 0.8, εo=εi=0.85, Ro=1, Lo=4, where (a) without a diaphragm, Ra=Ri and (b) with a diaphragm Ra=0.5Ro.

Fig. 5.
Fig. 5.

Directions of the ray after the first reflection at the central point of the cavity bottom.

Fig. 6.
Fig. 6.

Probability of the rays within β as a function of Li/Lo, where Ri=0.50.8, Ro=1, Ra=0.5Ro, Lo=4, εo=εi.

Fig. 7.
Fig. 7.

Average effective emissivity as a function of inner tube relative length, Li/Lo, for Lo=2, 3, 4, 6, 8, 10, εo=εi=0.85, Ro=1, Ri=0.7, where (a) without a diaphragm, Ra=Ri. (b) With a diaphragm, Ra=0.5Ro.

Fig. 8.
Fig. 8.

Average effective emissivity as a function of inner tube relative length, Li/Lo, for εi=0.55, 0.65, 0.75, 0.85, 0.95, εo=0.85, Ro=1, Ri=0.7, Lo=4, where (a) without a diaphragm, Ra=Ri. (b) With a diaphragm, Ra=0.5Ro.

Fig. 9.
Fig. 9.

Local effective emissivity as a function of the distance from center to edge of the cavity bottom for Li/Lo=0, 0.2, 0.4, 0.6, 0.8, εo=εi=0.85, Ro=1, Ri=0.7, Lo=4, where (a) without a diaphragm Ra=Ri. (b) With a diaphragm, Ra=0.5Ro.

Tables (3)

Tables Icon

Table 1. Characteristic Parameters of the Cylindrical Cavity with Diffuse Walls

Tables Icon

Table 2. Effective Emissivity Distribution Calculated for the Cylindrical Cavity

Tables Icon

Table 3. Average Effective Emissivities for Various Combinations of the Inner Tube Critical Parameters (Outer Tube Parameters: εo=0.85, Lo=4, Ro=1)

Equations (7)

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

ελ,e(λ,Tref,T,ρ)=Lλ(λ,T,ρ)Lλ,bb(λ,Tref),
ελ,e(λ,Tref,T,ρ)=Lλ(λ,T,ρ)c1·{π·λ5[exp(c2/(λTref))1]}1,
εt,e(Tref,T,ρ)=πL(T,ρ)σTref4,
ελ,a=1SaSaελ,e(λ,Tref,T,ρ)dSa,
ψ=arcsinuψ,ϕ=2πuϕ,
εe0=αe0=NαN,
Nα=Nα0+Nα1+Nα2++Nαi+,

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