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Technical Briefs

Resolved Order of Scattering for the Solution of Radiative Transfer Equation

[+] Author and Article Information
Liangyu Wang

e-mail: wly621@yahoo.com

Meredith B. Colket

United Technologies Research Center,
East Hartford, CT 06117

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received March 5, 2012; final manuscript received August 9, 2012; published online March 20, 2013. Assoc. Editor: Robert D. Tzou.

J. Heat Transfer 135(4), 044503 (Mar 20, 2013) (3 pages) Paper No: HT-12-1085; doi: 10.1115/1.4023259 History: Received March 05, 2012; Revised August 09, 2012

The solution of the radiative transfer equation (RTE) becomes complicated when the participating medium is scattering and/or the boundary walls are reflecting. To reduce the complexity, the resolved order of scattering (ROS) formulation described in this paper separates the radiative intensities being solved by RTE into a series of intensities corresponding to different orders of the scattering and reflection events. The resulting equation of transfer for each order of radiative intensity is not only much simpler to solve but also represents the physical scattering/reflection processes that are hidden in the original full RTE. The ROS formulation provides a mathematically rigorous and elegant means of solving RTE for strong scattering media with or without reflecting boundaries. Sample calculations are presented for a droplet-laden, 3D enclosure with strong anisotropic scattering.

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References

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Wang, L., Hall, R. J., and Colket, M. B., “Photon Monte Carlo Simulation of Interactions of Water Mist With Fire Radiation,” (to be published).

Figures

Grahic Jump Location
Fig. 1

Floor to Ceiling Transmissivity in 3D droplet-laden enclosure with hot floor. The enclosure is 1.25 m on each side with droplets of effective diameter D32 = 75 μm at a volume fraction of 5 × 10−5. There are 100 × 100 × 100 = 106 spatial grid points and 8 × 12 = 96 discrete FVM ray directions. The droplets, enclosure gas, and sidewalls are assumed to be cool with the floor radiating as a 1200 K black body.

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