Volume 14, no. 3Pages 77 - 91
Application of the Finite Volume Method for Calculating Radiation Heat Transfer in Applied ProblemsK.Yu. Litvintsev, A.V. Sentyabov
A number of numerical models of radiation heat transfer, based on P_1 approximation and finite volume method, were implemented in the in-house CFD code "SigmaFlow'' developed by the Krasnoyarsk group of the Institute of Thermophysics of Russian Academy of Science. The implemented finite volume method allows parallel calculations based on domain decomposition of an unstructured mesh and uses sub-mapped spatially inhomogeneous angular grids. Both conventional in CFD methods for solving linear systems such as BiCGStab, DILU, CG and a marching scheme were considered. A number of applied problems with radiation heat transfer were solved by means of CFD code "SigmaFlow''. They include such problems as the numerical simulation of a gas furnace chamber, a burner and a vacuum electrical furnace.Full text
- radiation heat transfer; finite volume method; numerical simulation.
- 1. Dekteryev A.A., Litvintsev K.Yu., Gavrilov A.A., Kharlamov E.B., Filimonov S.A. The Development of Free Engineering Software Package for Numerical Simulation of Hydrodynamics, Heat Transfer, and Chemical Reaction Processes. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2017, vol. 10, no. 4, pp. 105-112. DOI: 10.14529/mmp170410
2. Jeans J.H. The Equations of Radiative Transfer of Energy. Monthly Notices Royal Astrojwmical Society, 1917, no. 78, pp. 28-36.
3. Eddington A.S. The Internal Constitution of the Stars, New York, Dover Publications, 1959.
4. Raithby G.D., Chui E.H. A Finite-Volume Method for Predicting a Radiant Heat Transfer Enclosures with Participating Media. Journal of Heat Transfer, 1990, no. 11, pp. 415-423.
5. Fiveland W.A. A Discrete Ordinates Method for Predicting Radiative Heat Transfer in Axisymmetric Enclosures. ASME Paper, 1982, no. 82-HT-20, 1982.
6. Litvintsev K.Yu, Dekterev A.A. Comparison of the Finite-Volume and Discrete-Ordinate Methods and Diffusion Approximation for the Radiative Heat Transfer. Heat Transfer Research, 2008, vol. 39, pp. 653-655.
7. Chai J.C., Patankar S.V. Finite-Volume Method for Radiation Heat Transfer, in Advances in Numerical Heat Transfer, New York, Taylor and Francis, 2000.
8. Wray A. Improved Finite-Volume Method for Radiative Hydrodynamics. International Conference on Computational Fluid Dynamics, 2012, article ID: 20120016552.
9. Lygidakis G.N., Nikolos I.K. Improving the Accuracy of a Finite-Volume Method for Computing Radiative Heat Transfer in Three-Dimensional Unstructured Meshes. Proceedings of the 3rd South-East European Conference on Computational Mechanics, Greece, 2013, pp. 599-620.
10. Trovalet L., Jeandel G., Coelho P.J., Asllanaj F. Modified Finite-Volume Method Based on a Cell Vertex Scheme for the Solution of Radiative Transfer Problems in Complex 3D Geometries. Journal of Quantitative Spectroscopy and Radiative Transfer, 2011, no. 112, pp. 2661-2675.
11. Modest M.F. Radiative Heat Transfer, London, New York, Academic Press Books, 2013.
12. Knaus H., Schneider R., Han X., Strohle J., Schnell U., Hein K.R. Comparison of Different Radiative Heat Transfer Models and Their Applicability in Coal-fired Utility Boiler Simulations. Proceedings of 4th International Conference on Technologies and Combustion for a Clean Environment, Lisbon, 1997, pp. 1-8.
13. Howell J.R., Menguc M.P., Siegel R. Thermal Radiation Heat Transfer, New York, CRC Press, 2015.
14. Doyoung B., Changjin L., Seung W.B. Radiative Heat Transfer in Discretely Heated Irregular Geometry with an Absorbing, Emitting, and Anisotropically Scattering Medium Using Combined Monte-Carlo and Finite Volume Method. International Journal of Heat and Mass Transfer, 2004, no. 47, pp. 4195-4203.
15. Dombrovsky L.A., Dembele S., Wen J.X., Sikic I. Two-Step Method for Radiative Transfer Calculations in a Developing Pool Fire at the Initial Stage of its Suppression by a Water Spray. International Journal of Heat and Mass Transfer, 2018, no. 127, pp. 717-726.
16. Gordon I.E., Rothman L.S., Hill С., Kochanov R.V. et al. The HITRAN2016 Molecular Spectroscopic Database. Journal of Quantitative Spectroscopy and Radiative Transfer, 2017, no. 203, pp. 3-69.
17. Yujia Sun, Xiaobing Zhang. Contributions of Gray Gases in SLW for Non-Gray Radiation Heat Transfer and Corresponding Accuracies of FVM and P_1 Method. International Journal of Heat and Mass Transfer, 2018, no. 121, pp. 819-831. DOI: 10.1016/j.ijheatmasstransfer.2018.01.045
18. Dombrovsky L.A. Evaluation of the Error of the P_1 Approximation in Calculations of Thermal Radiation Transfer in Optically Inhomogeneous Media. High Temperature, 1997, vol. 35, no. 4, pp. 676-679.
19. Viskanta R. Radiative Transfer in Combustion Systems: Fundamentals and Applications, New York, Begell House, 2005.
20. Litvintsev K.Yu., Dekterev A.A., Neobyavlyashy P.A. Modeling of Radiative Heat Transfer in a Burner Device for Anode Gases Reburning. Thermal Processes in Engineering, 2013, vol. 5, no. 8, pp. 354-360. (in Russian)
21. Smith T.F., Shenand Z.F., Friedman J.N. Evaluation of Coefficients for the Weighted Sum of Gray Gases Model. Journal of Heat Transfer, 1982, no. 104, pp. 602-608.
22. Yu M.J., Baek S.W., Park J.H. An Extension of the Weighted Sum of Gray Gases Non-Gray Gas Radiation Model to a Two Phase Mixture of Non-Gray Gas with Particles. International Journal of Heat and Mass Transfer, 2000, no. 43, pp. 1699-1713.
23. Litvintsev K.Yu., Finnikov K.A., Kharlamov E.B. Features of a Mathematical Model of Heat Transfer in a Vacuum Resistance Furnace. Journal of Physics: Conference Series, 2017, no. 891, article ID: 012108. DOI: 10.1088/1742-6596/891/1/012108
24. Litvintsev K.Yu., Finnikov K.A. Development of a Specialized Mathematical Model of Heat Transfer in a Vacuum Electric Furnace. Journal of Physics: Conference Series, 2018, no. 1128, article ID: 12088. DOI: 10.1088/1742-6596/1128/1/012088
25. Guedri K., Naceur B.M., Rachid M., Rachid S. Formulation and Testing of the FTn Finite Volume Method for Radiation in 3-D Complex Inhomogeneous Participating Media. Journal of Quantitative Spectroscopy and Radiative Transfer, 2006, no. 98, pp. 425-445.
26. Guedri K., AL-Ghamdi A. Radiative Heat Transfer in Complex Enclosures Using NVD Differencing Schemes of the FTn Finite Volume Method. Heat Transfer Research, 2017, vol. 48, no. 15, pp. 1379-1398.
27. Kim S.H., Huh K.Y. A New Angular Discretization Scheme of the Finite Volume Method for 3-D Radiative Heat Transfer in Absorbing, Emitting and Anisotropically Scattering Media. International Journal of Heat and Mass Transfer, 2000, no. 43, pp. 1233-1242.
28. Barrett R., Berry M.W., Chan T.F., Demmel J.W. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, Philadelphia, SIAM, 1994.
29. VanderVorst H.A. Bi-CGSTAB: a Fast and Smoothly Converging Variant of Bi-CG for Solution of Non-Symmetric Linear Systems. SIAM Journal on Scientific Computing, 1992, no. 2, pp. 631-644.
30. Charest M.R.J., Groth C.P.T., Gulder O.L. Solution of the Equation of Radiative Transfer Using a Newton-Krylov Approach and Adaptive Mesh Refinement. Journal of Computational Physics, 2012, no. 231, pp. 3023-3040.