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Research Papers: Radiative Heat Transfer

Ray Effect Mitigation Through Reference Frame Rotation

[+] Author and Article Information
John Tencer

Sandia National Laboratories,
1515 Eubank SE,
Albuquerque, NM 87123
e-mail: jtencer@sandia.gov

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 3, 2015; final manuscript received May 20, 2016; published online June 14, 2016. Assoc. Editor: Laurent Pilon.

J. Heat Transfer 138(11), 112701 (Jun 14, 2016) (11 pages) Paper No: HT-15-1393; doi: 10.1115/1.4033699 History: Received June 03, 2015; Revised May 20, 2016

The discrete ordinates method is a popular and versatile technique for solving the radiative transport equation, a major drawback of which is the presence of ray effects. Mitigation of ray effects can yield significantly more accurate results and enhanced numerical stability for combined mode codes. When ray effects are present, the solution is seen to be highly dependent upon the relative orientation of the geometry and the global reference frame. This is an undesirable property. A novel ray effect mitigation technique of averaging the computed solution for various reference frame orientations is proposed.

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Figures

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Fig. 1

Angle-integrated intensity predictions for four different random rotations of the PN–TN quadrature in a square X–Y geometry with N = 2 (one ordinate per octant). The medium is purely absorbing with an optical side length of unity.

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Fig. 2

Exact heat flux along top wall [10], approximate rotationally invariant solution found using 10,000 random rotations, and two realizations of the LQ4 quadrature (three ordinates per octant) after averaging the solutions from 30 different random rotations

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Fig. 3

Relative error in the average LQN-3D heat flux prediction as an increasing number of rotations (Ns) is considered

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Fig. 4

Standard deviation of the relative error in the average LQN-3D heat flux prediction as a function of the number of rotations (Ns) is considered

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Fig. 5

Relative error in the average PNTN-3D heat flux prediction as an increasing number of rotations (Ns) is considered

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Fig. 6

Standard deviation of the relative error in the average PNTN-3D heat flux prediction as a function of the number of rotations (Ns) is considered

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Fig. 7

Relative error in the average PNTN-z heat flux prediction as an increasing number of rotations (Ns) is considered

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Fig. 8

Standard deviation of the relative error in the average PNTN-z heat flux prediction as a function of the number of rotations (Ns) is considered

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Fig. 9

Relative error in the average AR heat flux prediction as an increasing number of rotations (Ns) is considered

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Fig. 10

Standard deviation of the relative error in the average AR heat flux prediction as a function of the number of rotations (Ns) is considered

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Fig. 11

Relative error in the average heat flux prediction as a function of the number of ordinates per octant. Symbols denote data for LQN-3D (x), PNTN-3D (○), PNTNz (□), and AR (*) quadratures, while the lines represent linear fits to that data.

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Fig. 12

Standard deviation of the mean of the samples as a function of the number of ordinates per octant. Symbols denote data for LQN-3D (x), PNTN-3D (○), PNTNz (□), and AR (*) quadratures, while the lines represent linear fits to that data.

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Fig. 13

The computational expense involved in the solution of a single sample as a function of the number of ordinate directions is considered

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