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Research Papers: Radiative Heat Transfer

Equation Solving DRESOR Method for Radiative Transfer in Three-Dimensional Isotropically Scattering Media

[+] Author and Article Information
Zhifeng Huang

School of Power and Mechanical
Engineering,
Wuhan University,
Wuhan, Hubei 430072, China
State Key Laboratory of Coal Combustion,
Huazhong University of Science and Technology,
Wuhan, Hubei 430074, China

Huaichun Zhou

Key Laboratory for Thermal Science
and Power Engineering of
Ministry of Education,
Tsinghua University,
Beijing 10084, China
e-mail: hczh@mail.tsinghua.edu.cn

Guihua Wang

State Key Laboratory of Coal Combustion,
Huazhong University of Science and Technology,
Wuhan, Hubei 430074, China

Pei-feng Hsu

Mechanical and Aerospace
Engineering Department,
Florida Institute of Technology,
Melbourne, FL 32901
School of Mechanical Engineering,
Shanghai Dianji University,
Shanghai 201306, China
e-mail: phsu@fit.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 3, 2012; final manuscript received July 18, 2013; published online June 24, 2014. Assoc. Editor: William P. Klinzing.

J. Heat Transfer 136(9), 092702 (Jun 24, 2014) (11 pages) Paper No: HT-12-1645; doi: 10.1115/1.4025133 History: Received December 03, 2012; Revised July 18, 2013

Distributions of ratios of energy scattered or reflected (DRESOR) method is a very efficient tool used to calculate radiative intensity with high directional resolution, which is very useful for inverse analysis. The method is based on the Monte Carlo (MC) method and it can solve radiative problems of great complexity. Unfortunately, it suffers from the drawbacks of the Monte Carlo method, which are large computation time and unavoidable statistical errors. In this work, an equation solving method is applied to calculate DRESOR values instead of using the Monte Carlo sampling in the DRESOR method. The equation solving method obtains very accurate results in much shorter computation time than when using the Monte Carlo method. Radiative intensity with high directional resolution calculated by these two kinds of DRESOR method is compared with that of the reverse Monte Carlo (RMC) method. The equation solving DRESOR (ES-DRESOR) method has better accuracy and much better time efficiency than the Monte Carlo based DRESOR (original DRESOR) method. The ES-DRESOR method shows a distinct advantage for calculating radiative intensity with high directional resolution compared with the reverse Monte Carlo method and the discrete ordinates method (DOM). Heat flux comparisons are also given and the ES-DRESOR method shows very good accuracy.

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Figures

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Fig. 1

Coordinate system and calculation model for intensity in an arbitrary direction

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Fig. 2

DRESOR values in the case of ω = 0.5, ρ = 0.0, DRESOR method with (a) 10,000 energy bundles, (b) 100,000 energy bundles, (c) 1,000,000 energy bundles, and (d) ES-DRESOR method

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Fig. 3

Hemispherical intensity at the center point of the top wall in the case of ω = 0.8, ρ = 0.5 (a) radiative intensity by the ES-DRESOR method, (b) |IES-DRESOR-IRMC|/IRMC, (c) |IDRESOR-IRMC|/IRMC, and (d) |IDOM-IRMC|/IRMC

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Fig. 4

Dimensionless intensity at coordinate (0, 0, 1.0 m) in the case of ρ = 0.5 with different ω (circle: RMC; square: DRESOR; triangle: ES-DRESOR; cross: DOM)

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Fig. 5

Dimensionless intensity at coordinate (0, 0, 1.0 m) in the case of ω = 0.5 with different ρ (circle: RMC; square: DRESOR; triangle: ES-DRESOR; cross: DOM)

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Fig. 6

Dimensionless heat flux q(x, 0.0, 1.0 m)/(σT04) in the case of ρ = 0.5 with different ω (circle: RMC; square: DRESOR; triangle: ES-DRESOR; cross: DOM)

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Fig. 7

Computation time comparison for DRESOR values between the DRESOR and ES-DRESOR methods in the case of ω = 0.5, ρ = 0.5

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Fig. 8

Computation time comparison for radiative heat flux between the RMC and ES-DRESOR methods in the case of ω = 0.5, ρ = 0.5

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