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Research Papers: Radiative Heat Transfer

Equation-Solving DRESOR Method for Radiative Transfer in an Absorbing–Emitting and Isotropically Scattering Slab With Diffuse Boundaries

[+] Author and Article Information
Wang Guihua

State Key Laboratory of Coal Combustion,
Huazhong University of Science and Technology,
Wuhan 430074, P. R. China

Zhou Huaichun

State Key Laboratory of Control and Simulation of Power System and Generation Equipment,
Department of Thermal Engineering,
Tsinghua University,
Beijing 100084, P. R. China
e-mail: hczh@mail.tsinghua.edu.cn

Cheng Qiang

State Key Laboratory of Coal Combustion,
Huazhong University of Science and Technology,
Wuhan 430074, P. R. China
e-mail: chengqiang@mail.hust.edu.cn

Wang Zhichao

State Key Laboratory of Coal Combustion,
Huazhong University of Science and Technology, Wuhan 430074, P. R. China

1,2Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 3, 2011; final manuscript received July 12, 2012; published online October 10, 2012. Assoc. Editor: He-Ping Tan.

J. Heat Transfer 134(12), 122702 (Oct 10, 2012) (10 pages) doi:10.1115/1.4007205 History: Received November 03, 2011; Revised July 12, 2012

The distribution of ratios of energy scattered by the medium or reflected by the boundary surface (DRESOR) method can provide radiative intensity with high directional resolution, but also suffers the common drawbacks of the Monte Carlo method (MCM), i.e., it is time-consuming and produces unavoidable statistical errors. In order to overcome the drawbacks of the MCM, the so-called equation-solving DRESOR (ES-DRESOR) method, an equation-solving method to calculate the DRESOR values differently from the MCM used before, was proposed previously. In this method, a unit blackbody emission is supposed within a small zone around a specified point, while there is no emission elsewhere in a plane-parallel, emitting, absorbing, and isotropically scattering medium with transparent boundaries. The set of equations for the DRESOR values based on two expressions for the incident radiation was set up and solved successfully. In this paper, the ES-DRESOR method is extended to a one-dimensional system with diffusely reflecting boundaries. The principle and formulas are given. Several examples with different parameters are taken to examine the performance of the proposed method. The results showed that all the DRESOR values obtained using the ES-DRESOR method agree well with those got using MCM. The average relative error for the intensity obtained by the ES-DRESOR method is 9.446 × 10−6, lower by over 1 order of magnitude than the 2.638 × 10−4 obtained by the MCM under the same conditions. More importantly, the CPU time for computing the DRESOR values, which ranges from several hundred seconds to several thousand seconds using the MCM, is reduced to 0.167 s using the ES-DRESOR method. The computation time is shortened by about 3 orders of magnitude. The overall performance of the ES-DRESOR method is excellent.

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Figures

Grahic Jump Location
Fig. 1

Physical geometry and 1D discrete grids

Grahic Jump Location
Fig. 2

The flowchart of the calculation of the DRESOR values

Grahic Jump Location
Fig. 3

Comparison of the DRESOR values got by the MCM and the ES-DRESOR method. (a) Rds(0, j), with ε1 = ε2 = 0.5, τL = 1.0, ω = 0.2; (b) Rds(101, j), with ε1 = ε2 = 0.5, τL = 1.0, ω = 0.2; (c) Rds(0, j), with ε1 = 0.3, ε2 = 0.7, τL = 1.0, ω = 0.5; (d) Rds(101, j), with ε1 = 0.3, ε2 = 0.7, τL = 1.0, ω = 0.5.

Grahic Jump Location
Fig. 4

(a) All DRESOR values, Rds(i, j), by the MCM with ε1 = 0.8, ε2 = 0.1, τL = 3.0, ω = 0.5; (b) relative errors of Rds(i, j) by the ES-DRESOR method compared with those by the MCM, where the average relative error is 0.43% and the maximum error is less than 5%

Grahic Jump Location
Fig. 5

Distribution of intensity obtained by the ES-DRESOR method when Tw = 800 K, Tm = 1000 K, τL = 2, ω = 0.6, ε1 = 0.2 and ε2 = 0.4

Grahic Jump Location
Fig. 6

Relative errors for the intensity got by the two methods with ε1 = 0.2, ε2 = 0.4, τL = 2, ω = 0.6. (a) MCM and (b) ES-DRESOR method.

Grahic Jump Location
Fig. 7

Comparison of peak DRESOR values, Rds(i, i), got by the MCM and the ES-DRESOR method with ε1 = 0.2, ε2 = 0.4, τL = 2, ω = 0.6

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