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

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

doi:10.1016/j.jqsrt.2022.108459

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

Journal Article · Wed Dec 07 00:00:00 EST 2022 · Journal of Quantitative Spectroscopy and Radiative Transfer

DOI:https://doi.org/10.1016/j.jqsrt.2022.108459· OSTI ID:1906591

^[1]; David, Chloe ^[2]; Modest, Michael F. ^[3]; ^[1]; Roy, Somesh P. ^[2]

Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Marquette University, Milwaukee, WI (United States)
University of California, Merced, CA (United States)

Here, 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, , but the gain in accuracy reduces with the increase in , 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 x 4, 4 x 4, 4 x 8, 8 x 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.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: Exascale Computing Project; National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1906591

Alternate ID(s):: OSTI ID: 1908857

Journal Information:: Journal of Quantitative Spectroscopy and Radiative Transfer, Journal Name: Journal of Quantitative Spectroscopy and Radiative Transfer Journal Issue: / Vol. 296; ISSN 0022-4073

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (66)

Simplified PN Approximations to the Equations of Radiative Heat Transfer and Applications Larsen, Edward W.; Thömmes, Guido; Klar, Axel Journal of Computational Physics, Vol. 183, Issue 2 https://doi.org/10.1006/jcph.2002.7210	journal	December 2002
High temperature gas radiative property parameters of statistical narrow-band model for H2O, CO2 and CO, and correlated-K model for H2O and CO2 Soufiani, Anouar; Taine, Jean International Journal of Heat and Mass Transfer, Vol. 40, Issue 4 https://doi.org/10.1016/0017-9310(96)00129-9	journal	March 1997
Evaluation of discrete ordinates method for radiative transfer in rectangular furnaces Selçuk, Nevin; Kayakol, Nuray International Journal of Heat and Mass Transfer, Vol. 40, Issue 2 https://doi.org/10.1016/0017-9310(96)00139-1	journal	January 1997
Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous, anisotropically scattering media Mengüç, M. P.; Viskanta, R. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 33, Issue 6 https://doi.org/10.1016/0022-4073(85)90021-4	journal	June 1985
Three-dimensional radiation in absorbing-emitting-scattering media using the discrete-ordinates approximation Truelove, J. S. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 39, Issue 1 https://doi.org/10.1016/0022-4073(88)90016-7	journal	January 1988
Modelling of radiative heat transfer in enclosures with obstacles Coelho, P. J.; GonÇalves, J. M.; Carvalho, M. G. International Journal of Heat and Mass Transfer, Vol. 41, Issue 4-5 https://doi.org/10.1016/S0017-9310(97)00158-0	journal	February 1998
Convective and radiative internal heat transfer augmentation with fiber arrays Martin, A. R.; Saltielb, C.; Chai, J. International Journal of Heat and Mass Transfer, Vol. 41, Issue 22 https://doi.org/10.1016/S0017-9310(98)00066-0	journal	November 1998
Application of composition PDF methods in the investigation of turbulence–radiation interactions Li, Genong; Modest, Michael F. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 73, Issue 2-5 https://doi.org/10.1016/S0022-4073(01)00218-7	journal	April 2002
A model of the cumulative distribution function for wide band radiative properties Marin, O.; Buckius, R. O. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 59, Issue 6 https://doi.org/10.1016/S0022-4073(97)00046-0	journal	June 1998
A new radiation solution method for incorporation in general combustion prediction procedures Lockwood, F. C.; Shah, N. G. Symposium (International) on Combustion, Vol. 18, Issue 1 https://doi.org/10.1016/S0082-0784(81)80144-0	journal	January 1981
Effects of turbulence on species mass fractions in methane/air jet flames Barlow, R. S.; Frank, J. H. Symposium (International) on Combustion, Vol. 27, Issue 1 https://doi.org/10.1016/S0082-0784(98)80510-9	journal	January 1998
Assessment of narrow-band and full spectrum gas radiation methods in a real industrial glass furnace configuration Galtier, M.; Woelffel, W.; André, F. Applied Thermal Engineering, Vol. 216 https://doi.org/10.1016/j.applthermaleng.2022.119020	journal	November 2022
Effects of radiation model on the modeling of a laminar coflow methane/air diffusion flame Liu, Fengshan; Guo, Hongsheng; Smallwood, Gregory J. Combustion and Flame, Vol. 138, Issue 1-2 https://doi.org/10.1016/j.combustflame.2004.04.007	journal	July 2004
Extinction of counterflow diffusion flames with radiative heat loss and nonunity Lewis numbers Wang, H. Y.; Chen, W. H.; Law, C. K. Combustion and Flame, Vol. 148, Issue 3 https://doi.org/10.1016/j.combustflame.2006.10.005	journal	February 2007
The interaction between soot and NO formation in a laminar axisymmetric coflow ethylene/air diffusion flame Guo, Hongsheng; Smallwood, Gregory J. Combustion and Flame, Vol. 149, Issue 1-2 https://doi.org/10.1016/j.combustflame.2006.11.006	journal	April 2007
Determination of laminar flame speeds using stagnation and spherically expanding flames: Molecular transport and radiation effects Jayachandran, Jagannath; Zhao, Runhua; Egolfopoulos, Fokion N. Combustion and Flame, Vol. 161, Issue 9 https://doi.org/10.1016/j.combustflame.2014.03.009	journal	September 2014
Comparison of accuracy and computational expense of radiation models in simulation of non-premixed turbulent jet flames Pal, Gopalendu; Gupta, Ankur; Modest, Michael F. Combustion and Flame, Vol. 162, Issue 6 https://doi.org/10.1016/j.combustflame.2015.02.017	journal	June 2015
Impact of radiation models in CFD simulations of steam cracking furnaces Habibi, A.; Merci, B.; Heynderickx, G. J. Computers & Chemical Engineering, Vol. 31, Issue 11 https://doi.org/10.1016/j.compchemeng.2006.11.009	journal	November 2007
Investigation of the role of turbulent fluctuations on the time-averaged radiative emission in large-scale, turbulent pool fires Fraga, G. C.; Coelho, P. J.; Petry, A. P. Fire Safety Journal, Vol. 112 https://doi.org/10.1016/j.firesaf.2019.102945	journal	March 2020
The impact of radiative heat transfer in combustion processes and its modeling – with a focus on turbulent flames Liu, Fengshan; Consalvi, Jean-Louis; Coelho, Pedro J. Fuel, Vol. 281 https://doi.org/10.1016/j.fuel.2020.118555	journal	December 2020
Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium Mishra, Subhash C.; Chugh, Pranshu; Kumar, Pranav International Journal of Heat and Mass Transfer, Vol. 49, Issue 11-12 https://doi.org/10.1016/j.ijheatmasstransfer.2005.10.043	journal	June 2006
Full-scale 3D-modelling of the radiative heat transfer in rotary kilns with a present bed material Gunnarsson, Adrian; Andersson, Klas; Adams, Bradley R. International Journal of Heat and Mass Transfer, Vol. 147 https://doi.org/10.1016/j.ijheatmasstransfer.2019.118924	journal	February 2020
Semi-implicit time integration for thermal radiative transfer McClarren, Ryan G.; Evans, Thomas M.; Lowrie, Robert B. Journal of Computational Physics, Vol. 227, Issue 16 https://doi.org/10.1016/j.jcp.2008.04.029	journal	August 2008
Robust and accurate filtered spherical harmonics expansions for radiative transfer McClarren, Ryan G.; Hauck, Cory D. Journal of Computational Physics, Vol. 229, Issue 16 https://doi.org/10.1016/j.jcp.2010.03.043	journal	August 2010
Assembly of full-spectrum k-distributions from a narrow-band database; effects of mixing gases, gases and nongray absorbing particles, and mixtures with nongray scatterers in nongray enclosures Modest, Michael F.; Riazzi, Robert J. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 90, Issue 2 https://doi.org/10.1016/j.jqsrt.2004.03.007	journal	January 2005
Elliptic PDE formulation of general, three-dimensional high-order -approximations for radiative transfer Yang, Jun; Modest, Michael F. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 104, Issue 2 https://doi.org/10.1016/j.jqsrt.2006.07.017	journal	March 2007
Elliptic PDE formulation and boundary conditions of the spherical harmonics method of arbitrary order for general three-dimensional geometries Modest, Michael F.; Yang, Jun Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 109, Issue 9 https://doi.org/10.1016/j.jqsrt.2007.12.018	journal	June 2008
HITEMP, the high-temperature molecular spectroscopic database Rothman, L. S.; Gordon, I. E.; Barber, R. J. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 111, Issue 15 https://doi.org/10.1016/j.jqsrt.2010.05.001	journal	October 2010
The HITRAN2012 molecular spectroscopic database Rothman, L. S.; Gordon, I. E.; Babikov, Y. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 130, p. 4-50 https://doi.org/10.1016/j.jqsrt.2013.07.002	journal	November 2013
Improved full-spectrum k-distribution implementation for inhomogeneous media using a narrow-band database Cai, Jian; Modest, Michael F. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 141 https://doi.org/10.1016/j.jqsrt.2014.02.028	journal	July 2014
Two-dimensional axisymmetric formulation of high order spherical harmonics methods for radiative heat transfer Ge, Wenjun; Modest, Michael F.; Marquez, Ricardo Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 156 https://doi.org/10.1016/j.jqsrt.2015.01.013	journal	May 2015
A full-spectrum k-distribution look-up table for radiative transfer in nonhomogeneous gaseous media Wang, Chaojun; Ge, Wenjun; Modest, Michael F. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 168 https://doi.org/10.1016/j.jqsrt.2015.08.017	journal	January 2016
Development of high-order P models for radiative heat transfer in special geometries and boundary conditions Ge, Wenjun; Modest, Michael F.; Roy, Somesh P. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 172 https://doi.org/10.1016/j.jqsrt.2015.09.001	journal	March 2016
A comparison of specularly reflective boundary conditions and rotationally invariant formulations for Discrete Ordinate Methods in axisymmetric geometries Cai, Jian; Roy, Somesh; Modest, Michael F. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 182 https://doi.org/10.1016/j.jqsrt.2016.05.005	journal	October 2016
Evaluation of three different radiative transfer equation solvers for combined conduction and radiation heat transfer Sun, Yujia; Zhang, Xiaobing; Howell, John R. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 184 https://doi.org/10.1016/j.jqsrt.2016.07.024	journal	November 2016
The rank correlated FSK model for prediction of gas radiation in non-uniform media, and its relationship to the rank correlated SLW model Solovjov, Vladimir P.; Webb, Brent W.; Andre, Frederic Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 214 https://doi.org/10.1016/j.jqsrt.2018.04.026	journal	July 2018
Challenges for radiative transfer 1: Towards the effective solution of conjugate heat transfer problems Howell, John R.; Mengüç, M. Pinar Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 221 https://doi.org/10.1016/j.jqsrt.2018.10.016	journal	December 2018
A quasi-Monte Carlo solver for thermal radiation in participating media Farmer, Joseph; Roy, Somesh Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 242 https://doi.org/10.1016/j.jqsrt.2019.106753	journal	February 2020
Comparison and refinement of the various full-spectrum k-distribution and spectral line weighted-sum-of-gray-gases models for nonhomogeneous media Wang, Chaojun; Modest, Michael F.; Ren, Tao Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 271 https://doi.org/10.1016/j.jqsrt.2021.107695	journal	September 2021
Numerical simulation of the interaction between turbulence and radiation in reactive flows Coelho, P. J. Progress in Energy and Combustion Science, Vol. 33, Issue 4 https://doi.org/10.1016/j.pecs.2006.11.002	journal	August 2007
Recent advances in the measurement of strongly radiating, turbulent reacting flows Nathan, G. J.; Kalt, P. A. M.; Alwahabi, Z. T. Progress in Energy and Combustion Science, Vol. 38, Issue 1 https://doi.org/10.1016/j.pecs.2011.04.001	journal	February 2012
Thermal stability of radiating fluids: The Bénard problem Arpaci, Vedat S. Physics of Fluids, Vol. 16, Issue 5 https://doi.org/10.1063/1.1694391	journal	January 1973
Further Development of the Elliptic PDE Formulation of theP_NApproximation and its Marshak Boundary Conditions Modest, Michael F. Numerical Heat Transfer, Part B: Fundamentals, Vol. 62, Issue 2-3 https://doi.org/10.1080/10407790.2012.702645	journal	August 2012
Radiative heat Transfer in Axisymmetric Geometries Using an Unstructured Finite-Volume Method Murthy, J. Y.; Mathur, S. R. Numerical Heat Transfer, Part B: Fundamentals, Vol. 33, Issue 4 https://doi.org/10.1080/10407799808915040	journal	June 1998
Discussion of the Finite-Volume Method for Radiation, and its Application Using 3d Unstructured Meshes Raithby, G. D. Numerical Heat Transfer, Part B: Fundamentals, Vol. 35, Issue 4 https://doi.org/10.1080/104077999275802	journal	June 1999
Assessment of the Finite-Volume Method and the Discrete Ordinate Method for Radiative heat Transfer in a Three-Dimensional Rectangular Enclosure No authors listed Numerical Heat Transfer, Part B: Fundamentals, Vol. 35, Issue 1 https://doi.org/10.1080/104077999276027	journal	February 1999
The Equations of Radiative Transfer of Energy Jeans, J. H. Monthly Notices of the Royal Astronomical Society, Vol. 78, Issue 1 https://doi.org/10.1093/mnras/78.1.28	journal	November 1917
Note on the Spherical Harmonic Method As Applied to the Milne Problem for a Sphere Marshak, R. E. Physical Review, Vol. 71, Issue 7 https://doi.org/10.1103/PhysRev.71.443	journal	April 1947
The Full-Spectrum Correlated-k Distribution for Thermal Radiation From Molecular Gas-Particulate Mixtures Modest, Michael F.; Zhang, Hongmei Journal of Heat Transfer, Vol. 124, Issue 1 https://doi.org/10.1115/1.1418697	journal	June 2001
A Finite-Volume Method for Predicting a Radiant Heat Transfer in Enclosures With Participating Media Raithby, G. D.; Chui, E. H. Journal of Heat Transfer, Vol. 112, Issue 2 https://doi.org/10.1115/1.2910394	journal	May 1990
Two-Dimensional Radiation in Absorbing-Emitting Media Using the P-N Approximation Ratzel, A. C.; Howell, J. R. Journal of Heat Transfer, Vol. 105, Issue 2 https://doi.org/10.1115/1.3245583	journal	May 1983
Radiative Transfer in Axisymmetric, Finite Cylindrical Enclosures Mengu¨c¸, M. P.; Viskanta, R. Journal of Heat Transfer, Vol. 108, Issue 2 https://doi.org/10.1115/1.3246915	journal	May 1986
Radiative Transfer in Anisotropically Scattering Media: Allowance for Fresnel Reflection at the Boundaries Hottel, H. C.; Sarofim, A. F.; Evans, L. B. Journal of Heat Transfer, Vol. 90, Issue 1 https://doi.org/10.1115/1.3597460	journal	February 1968
Solution of the Radiative Transfer Equation in Three-Dimensional Participating Media Using a Hybrid Discrete Ordinates: Spherical Harmonics Method Sankar, Maathangi; Mazumder, Sandip Journal of Heat Transfer, Vol. 134, Issue 11 https://doi.org/10.1115/1.4007129	journal	September 2012
A Hybrid Wavenumber Selection Scheme for Line-By-Line Photon Monte Carlo Simulations in High-Temperature Gases Ren, Tao; Modest, Michael F. Journal of Heat Transfer, Vol. 135, Issue 8 https://doi.org/10.1115/1.4024385	journal	July 2013
Implementation of High-Order Spherical Harmonics Methods for Radiative Heat Transfer on openfoam Ge, Wenjun; Marquez, Ricardo; Modest, Michael F. Journal of Heat Transfer, Vol. 137, Issue 5 https://doi.org/10.1115/1.4029546	journal	May 2015
Line-by-Line Random-Number Database for Monte Carlo Simulations of Radiation in Combustion System Ren, Tao; Modest, Michael F. Journal of Heat Transfer, Vol. 141, Issue 2 https://doi.org/10.1115/1.4041803	journal	November 2018
Use of Discrete-Ordinates Methods for Solution of Photon Transport Problems Lathrop, K. D. Nuclear Science and Engineering, Vol. 24, Issue 4 https://doi.org/10.13182/NSE66-A16408	journal	April 1966
A comparison of approximate models for radiation in gas turbines Frank, M.; Seaid, M.; Klar, A. Progress in Computational Fluid Dynamics, An International Journal, Vol. 4, Issue 3/4/5 https://doi.org/10.1504/PCFD.2004.004087	journal	January 2004
Analysis of Discrete Ordinates Method with Even Parity Formulation Liu, J.; Shang, H. M.; Chen, Y. S. Journal of Thermophysics and Heat Transfer, Vol. 11, Issue 2 https://doi.org/10.2514/2.6230	journal	April 1997
Finite Volume Method for Radiative Heat Transfer Using Unstructured Meshes Murthy, J. Y.; Mathur, S. R. Journal of Thermophysics and Heat Transfer, Vol. 12, Issue 3 https://doi.org/10.2514/2.6363	journal	July 1998
Prediction of radiative transfer in cylindrical enclosures with the finite volume method Chui, E. H.; Raithby, G. D.; Hughes, P. M. J. Journal of Thermophysics and Heat Transfer, Vol. 6, Issue 4 https://doi.org/10.2514/3.11540	journal	October 1992
Three-dimensional spectral radiative heat transfer solutions by the discrete-ordinates method Fiveland, W. A.; Jamaluddin, A. S. Journal of Thermophysics and Heat Transfer, Vol. 5, Issue 3 https://doi.org/10.2514/3.268	journal	July 1991
Dynamics of a radiating gas with application to flow over a wavy wall. Cheng, Ping AIAA Journal, Vol. 4, Issue 2 https://doi.org/10.2514/3.3424	journal	February 1966
Comparison of discrete ordinates formulations for radiative heat transfer in multidimensional geometries Fiveland, W. A.; Jessee, J. P. Journal of Thermophysics and Heat Transfer, Vol. 9, Issue 1 https://doi.org/10.2514/3.627	journal	January 1995
Finite volume radiative heat transfer procedure for irregular geometries Chai, John C.; Parthasarathy, Girija; Lee, HaeOk S. Journal of Thermophysics and Heat Transfer, Vol. 9, Issue 3 https://doi.org/10.2514/3.682	journal	July 1995

Similar Records

Comparison of Radiation Models for a Turbulent Piloted Methane/Air Jet Flame: A Frozen-Field Study

Conference · Tue Jun 01 00:00:00 EDT 2021 · OSTI ID:1807265

Acceleration schemes for the discrete ordinates method

Conference · Sat Dec 30 23:00:00 EST 1995 · OSTI ID:455357

Assessment of the finite-volume method and the discrete ordinate method for radiative heat transfer in a three-dimensional rectangular enclosure

Journal Article · Thu Dec 31 23:00:00 EST 1998 · Numerical Heat Transfer. Part B, Fundamentals · OSTI ID:328379

Related Subjects

42 ENGINEERING
discrete ordinates method
radiative transfer
spherical harmonics method
turbulent jet flame

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

Citation Formats

References (66)

Similar Records

Related Subjects