Comparison of spherical harmonics method and discrete ordinates method for radiative transfer in a turbulent jet flame

Wenjun Ge; Chloe David; Michael F. Modest; Ramanan Sankaran; Somesh P. Roy

doi:10.1016/j.jqsrt.2022.108459

Comparison of spherical harmonics method and discrete ordinates method for radiative transfer in a turbulent jet flame

Wenjun Ge, Chloe David, Michael F. Modest, Ramanan Sankaran, Somesh P. Roy

Multiscale Materials

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

In this study, we systematically compared the accuracy and computational cost of two popular solution methods for the radiative transfer equation (RTE): the spherical harmonics method (P_N) and the discrete ordinates method (DOM). We first investigated convergence characteristics of different orders of P_N and DOM in a series of 1D homogeneous configurations with varying optical thicknesses. Both solvers perform better for optically thicker cases. The accuracy of P_N methods increases with its order, N, but the gain in accuracy reduces with the increase in N, i.e., improvement of P₇ over P₅ is less than that of P₃ over P₁. This decreasing trend becomes more prominent as the optical thickness decreases. On the other hand, DOM's accuracy increases almost linearly with the increase in the number of ordinates (or polar angles in this study) in all cases. While comparing the directional profile of radiative intensity, both solvers perform better when the radiative intensity is more isotropic. These solvers were then connected with a full spectrum k-distribution (FSK) spectral model and used to perform radiation-coupled simulations of a turbulent jet flame in an axi-symmetric cylindrical domain. Results obtained from P₁ to P₇ approximations for P_N, and 2 × 4, 4 × 4, 4 × 8, 8 × 8 finite angles for DOM are compared with that from an optically thin model, and a reference solution from line-by-line (LBL) photon Monte Carlo (PMC) method. The choice of radiation solver shows a noticeable impact on the temperature distribution of the flame. The P_N solvers lead to slightly higher radiant fractions and the DOM solvers lead to slightly lower radiant fractions than the PMC benchmark solution. Finally, the computational costs of each of these solvers are also reported and an intermittent evaluation / time blending scheme to improve the computational efficiency of radiation solvers in radiation-coupled simulations are also demonstrated.

Original language	English
Article number	108459
Journal	Journal of Quantitative Spectroscopy and Radiative Transfer
Volume	296
DOIs	https://doi.org/10.1016/j.jqsrt.2022.108459
State	Published - Feb 2023

Funding

This research was supported by National Science Foundation and the Department of Energy through Grant No. NSF1258635 (WG, MFM, SR), and by the National Science Foundation under Grant No. 1756005 (CD, SR). WG and RS acknowledge the support from the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration. Notice: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://www.energy.gov/downloads/doe-public-access-plan ).

Funders	Funder number
National Science Foundation
U.S. Department of Energy	17-SC-20-SC, NSF1258635, 1756005
Office of Science
National Nuclear Security Administration

Keywords

Discrete ordinates method
Radiative transfer
Spherical harmonics method
Turbulent jet flame

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10.1016/j.jqsrt.2022.108459

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title = "Comparison of spherical harmonics method and discrete ordinates method for radiative transfer in a turbulent jet flame",

abstract = "In this study, we systematically compared the accuracy and computational cost of two popular solution methods for the radiative transfer equation (RTE): the spherical harmonics method (PN) and the discrete ordinates method (DOM). We first investigated convergence characteristics of different orders of PN and DOM in a series of 1D homogeneous configurations with varying optical thicknesses. Both solvers perform better for optically thicker cases. The accuracy of PN methods increases with its order, N, but the gain in accuracy reduces with the increase in N, i.e., improvement of P7 over P5 is less than that of P3 over P1. This decreasing trend becomes more prominent as the optical thickness decreases. On the other hand, DOM's accuracy increases almost linearly with the increase in the number of ordinates (or polar angles in this study) in all cases. While comparing the directional profile of radiative intensity, both solvers perform better when the radiative intensity is more isotropic. These solvers were then connected with a full spectrum k-distribution (FSK) spectral model and used to perform radiation-coupled simulations of a turbulent jet flame in an axi-symmetric cylindrical domain. Results obtained from P1 to P7 approximations for PN, and 2 × 4, 4 × 4, 4 × 8, 8 × 8 finite angles for DOM are compared with that from an optically thin model, and a reference solution from line-by-line (LBL) photon Monte Carlo (PMC) method. The choice of radiation solver shows a noticeable impact on the temperature distribution of the flame. The PN solvers lead to slightly higher radiant fractions and the DOM solvers lead to slightly lower radiant fractions than the PMC benchmark solution. Finally, the computational costs of each of these solvers are also reported and an intermittent evaluation / time blending scheme to improve the computational efficiency of radiation solvers in radiation-coupled simulations are also demonstrated.",

keywords = "Discrete ordinates method, Radiative transfer, Spherical harmonics method, Turbulent jet flame",

author = "Wenjun Ge and Chloe David and Modest, {Michael F.} and Ramanan Sankaran and Roy, {Somesh P.}",

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AU - Ge, Wenjun

AU - David, Chloe

AU - Modest, Michael F.

AU - Sankaran, Ramanan

AU - Roy, Somesh P.

PY - 2023/2

Y1 - 2023/2

N2 - In this study, we systematically compared the accuracy and computational cost of two popular solution methods for the radiative transfer equation (RTE): the spherical harmonics method (PN) and the discrete ordinates method (DOM). We first investigated convergence characteristics of different orders of PN and DOM in a series of 1D homogeneous configurations with varying optical thicknesses. Both solvers perform better for optically thicker cases. The accuracy of PN methods increases with its order, N, but the gain in accuracy reduces with the increase in N, i.e., improvement of P7 over P5 is less than that of P3 over P1. This decreasing trend becomes more prominent as the optical thickness decreases. On the other hand, DOM's accuracy increases almost linearly with the increase in the number of ordinates (or polar angles in this study) in all cases. While comparing the directional profile of radiative intensity, both solvers perform better when the radiative intensity is more isotropic. These solvers were then connected with a full spectrum k-distribution (FSK) spectral model and used to perform radiation-coupled simulations of a turbulent jet flame in an axi-symmetric cylindrical domain. Results obtained from P1 to P7 approximations for PN, and 2 × 4, 4 × 4, 4 × 8, 8 × 8 finite angles for DOM are compared with that from an optically thin model, and a reference solution from line-by-line (LBL) photon Monte Carlo (PMC) method. The choice of radiation solver shows a noticeable impact on the temperature distribution of the flame. The PN solvers lead to slightly higher radiant fractions and the DOM solvers lead to slightly lower radiant fractions than the PMC benchmark solution. Finally, the computational costs of each of these solvers are also reported and an intermittent evaluation / time blending scheme to improve the computational efficiency of radiation solvers in radiation-coupled simulations are also demonstrated.

AB - In this study, we systematically compared the accuracy and computational cost of two popular solution methods for the radiative transfer equation (RTE): the spherical harmonics method (PN) and the discrete ordinates method (DOM). We first investigated convergence characteristics of different orders of PN and DOM in a series of 1D homogeneous configurations with varying optical thicknesses. Both solvers perform better for optically thicker cases. The accuracy of PN methods increases with its order, N, but the gain in accuracy reduces with the increase in N, i.e., improvement of P7 over P5 is less than that of P3 over P1. This decreasing trend becomes more prominent as the optical thickness decreases. On the other hand, DOM's accuracy increases almost linearly with the increase in the number of ordinates (or polar angles in this study) in all cases. While comparing the directional profile of radiative intensity, both solvers perform better when the radiative intensity is more isotropic. These solvers were then connected with a full spectrum k-distribution (FSK) spectral model and used to perform radiation-coupled simulations of a turbulent jet flame in an axi-symmetric cylindrical domain. Results obtained from P1 to P7 approximations for PN, and 2 × 4, 4 × 4, 4 × 8, 8 × 8 finite angles for DOM are compared with that from an optically thin model, and a reference solution from line-by-line (LBL) photon Monte Carlo (PMC) method. The choice of radiation solver shows a noticeable impact on the temperature distribution of the flame. The PN solvers lead to slightly higher radiant fractions and the DOM solvers lead to slightly lower radiant fractions than the PMC benchmark solution. Finally, the computational costs of each of these solvers are also reported and an intermittent evaluation / time blending scheme to improve the computational efficiency of radiation solvers in radiation-coupled simulations are also demonstrated.

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KW - Radiative transfer

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M1 - 108459

ER -

Comparison of spherical harmonics method and discrete ordinates method for radiative transfer in a turbulent jet flame

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