In this article, a new hybrid solution to the radiative transfer equation (RTE) is proposed. Following the modified differential approximation (MDA), the radiation intensity is first split into two components: a “wall” component, and a “medium” component. Traditionally, the wall component is determined using a viewfactor-based surface-to-surface exchange formulation, while the medium component is determined by invoking the first-order spherical harmonics (P1) approximation. Recent studies have shown that although the MDA approach is accurate over a large range of optical thicknesses, it is prohibitive for complex three-dimensional geometry with obstructions, both from a computational efficiency as well as memory standpoint. The inefficiency stems from the use of the viewfactor-based approach for determination of the wall-emitted component. In this work, instead, the wall component is determined directly using the control angle discrete ordinates method (CADOM). The new hybrid method was validated for both two-dimensional (2D) and three-dimensional (3D) geometries against benchmark Monte Carlo results for gray media in which the optical thickness was varied over a large range. In all cases, the accuracy of the hybrid method was found to be within a few percent of Monte Carlo results, and comparable to the solutions of the RTE obtained directly using CADOM. Finally, the new hybrid method was explored for 3D nongray media in the presence of reflecting walls and various scattering albedos. As a noteworthy advantage, irrespective of the conditions used, it was always found to be computationally more efficient than standalone CADOM and up to 15 times more efficient than standalone CADOM for optically thick media with strong scattering.
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November 2012
This article was originally published in
Journal of Heat Transfer
Research-Article
Solution of the Radiative Transfer Equation in Three-Dimensional Participating Media Using a Hybrid Discrete Ordinates: Spherical Harmonics Method
Sandip Mazumder
Sandip Mazumder
1
Fellow ASME
e-mail: mazumder.2@osu.edu
Department of Mechanical and Aerospace Engineering,
e-mail: mazumder.2@osu.edu
Department of Mechanical and Aerospace Engineering,
The Ohio State University Columbus
,OH
43210
1Corresponding author.
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Sandip Mazumder
Fellow ASME
e-mail: mazumder.2@osu.edu
Department of Mechanical and Aerospace Engineering,
e-mail: mazumder.2@osu.edu
Department of Mechanical and Aerospace Engineering,
The Ohio State University Columbus
,OH
43210
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 16, 2011; final manuscript received May 21, 2012; published online September 28, 2012. Assoc. Editor: He-Ping Tan.
J. Heat Transfer. Nov 2012, 134(11): 112702 (12 pages)
Published Online: September 28, 2012
Article history
Received:
May 16, 2011
Revision Received:
May 21, 2012
Citation
Sankar, M., and Mazumder, S. (September 28, 2012). "Solution of the Radiative Transfer Equation in Three-Dimensional Participating Media Using a Hybrid Discrete Ordinates: Spherical Harmonics Method." ASME. J. Heat Transfer. November 2012; 134(11): 112702. https://doi.org/10.1115/1.4007129
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