Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
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Convergence study of traditional 2D/1D coupling method for k-eigenvalue neutron transport problems with Fourier analysis

  • Boran Kong (Institute of Nuclear and New Energy Technology (INET), Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University) ;
  • Kaijie Zhu (Institute of Nuclear and New Energy Technology (INET), Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University) ;
  • Han Zhang (Institute of Nuclear and New Energy Technology (INET), Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University) ;
  • Chen Hao (Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University) ;
  • Jiong Guo (Institute of Nuclear and New Energy Technology (INET), Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University) ;
  • Fu Li (Institute of Nuclear and New Energy Technology (INET), Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University)
  • Received : 2022.07.09
  • Accepted : 2022.12.25
  • Published : 2023.04.25
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Abstract

2D/1D coupling method is an important neutron transport calculation method due to its high accuracy and relatively low computation cost. However, 2D/1D coupling method may diverge especially in small axial mesh size. To analyze the convergence behavior of 2D/1D coupling method, a Fourier analysis for k-eigenvalue neutron transport problems is implemented. The analysis results present the divergence problem of 2D/1D coupling method in small axial mesh size. Several common attempts are made to solve the divergence problem, which are to increase the number of inner iterations of the 2D or 1D calculation, and two times 1D calculations per outer iteration. However, these attempts only could improve the convergence rate but cannot deal with the divergence problem of 2D/1D coupling method thoroughly. Moreover, the choice of axial solvers, such as DGFEM SN and traditional SN, and its effect on the convergence behavior are also discussed. The results show that the choice of axial solver is a key point for the convergence of 2D/1D method. The DGFEM SN based 2D/1D method could converge within a wide range of optical thickness region, which is superior to that of traditional SN method.

Keywords

References

  1. J.Y. Cho, H.G. Joo, K.S. Kim, S.Q. Zee, Three-dimensional heterogeneous whole core transport calculation employing planar MOC solutions, Trans. Am. Nucl. Soc. 87 (2002) 234-236. 
  2. N.Z. Cho, G.S. Lee, C.J. Park, Refinement of the 2D/1D fusion method for 3D whole core transport calculation, Trans. Am. Nucl. Soc. 87 (2002) 417-420. 
  3. H.G. Joo, J.Y. Cho, K.S. Kim, C.C. Lee, S.Q. Zee, Methods and Performance of a Three-Dimensional Whole Core Transport Code DeCART. Proc. PHYSPR, American Nuclear Society, CD-ROM, 2004, 2004, Chicago, April 25-29, 2004. 
  4. G.S. Lee, N.Z. Cho, 2D/1D fusion method solutions of the three-dimensional transport OECD benchmark problems C5G7 MOX, Prog. Nucl. Energy 48 (2006) 410-423.  https://doi.org/10.1016/j.pnucene.2006.01.010
  5. J.Y. Cho, K.S. Kim, C.C. Lee, et al., Axial SPN and radial MOC coupled whole core transport calculation, J. Nucl. Sci. Technol. (Tokyo, Jpn.) 44 (2007) 1156-1171.  https://doi.org/10.1080/18811248.2007.9711359
  6. Y. Jung, H.G. Joo, Decoupled Planar MOC Solution for Dynamic Group Constant Generation in Direct Three-Dimensional Core Calculations. Proc. M&C, vol. 44, Saratoga Springs, NY. USA., 2009. May 3-7. 
  7. Q. Shen, Y. Wang, D. Jabaay, et al., Transient analysis of C5G7-TD benchmark with MPACT, Ann. Nucl. Energy 125 (2018) 107-120. MAR.).  https://doi.org/10.1016/j.anucene.2018.10.049
  8. B. Wang, Z. Liu, J. Chen, et al., A modified predictor-corrector quasi-static method in NECP-X for reactor transient analysis based on the 2D/1D transport method, Prog. Nucl. Energy 108 (Sep) (2018) 122-135.  https://doi.org/10.1016/j.pnucene.2018.05.014
  9. J. Ma, C. Hao, L. Liu, et al., Perturbation theory-based whole-core eigenvalue sensitivity and uncertainty (SU) analysis via a 2D/1D transport code, Sci. Technol.Nucl. Install. 2020 (2020) 13. Article ID 9428580. 
  10. B.W. Kelly, E.W. Larsen, 2D/1D Approximations to the 3D Neutron Transport Equation I: Theory. Proc. M&C, 2013, Sun Valley, ID, USA, 2013. May 5-9. 
  11. M. Jarrett, B. Kochunas, et al., Progress in Characterizing 2D/1D Accuracy in MPACT. Proc. M&C, 2017. Jeju, Korea. April 16-20. 
  12. S.G. Hong, K.S. Kim, J.S. Song, Fourier convergence analysis of the rebalance methods for discrete ordinates transport equations in eigenvalue problems, Nucl. Sci. Eng. 164 (1) (2010) 33-52.  https://doi.org/10.13182/NSE09-18
  13. A. Zhu, M. Jarret, Y. Xu, B. Kochunas, E. Larsen, T. Downar, An optimally diffusive coarse mesh finite difference method to accelerate neutron transport calculations, Ann. Nucl. Energy 95 (2016) 116-124.  https://doi.org/10.1016/j.anucene.2016.05.004
  14. B.W. Kelly, E.W. Larsen, A consistent 2D/1D approximation to the 3D neutron transport equation, Nucl. Eng. Des. 295 (2015) 598-614.  https://doi.org/10.1016/j.nucengdes.2015.07.026
  15. K.P. Keady, E.W. Larsen, Stability of SN k-eigenvalue iterations using CMFD acceleration, in: Proc. Int. Conf. On Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method, American Nuclear society, Nashville, Tennessee, USA, 2015. April 19-23. 
  16. Y. Chan, S. Xiao, Convergence study of variants of CMFD acceleration schemes for fixed source neutron transport problems in 2D cartesian geometry with Fourier analysis, Ann. Nucl. Energy 134 (2019) 273-283.  https://doi.org/10.1016/j.anucene.2019.06.021
  17. Y. Chan, S. Xiao, Convergence study of CMFD and lpCMFD acceleration schemes for k-eigenvalue neutron transport problems in 2D cartesian geometry with Fourier analysis, Ann. Nucl. Energy 133 (2019) 327-337.  https://doi.org/10.1016/j.anucene.2019.05.035
  18. L. Jain, Prabhakaran, et al., Convergence study of CMFD based acceleration schemes for multi-group transport calculations with fission source using Fourier analysis, Ann. Nucl. Energy 160 (2021) (2021), 108314. 
  19. L. Jain, Karthikeyan, et al., Comparative studies of iterative methods for solving the optimally diffusive coarse mesh finite difference accelerated transport equation, Ann. Nucl. Energy 157 (2021) (2021), 108211. 
  20. B. Kong, K. Zhu, H. Zhang, C. Hao, J. Guo, F. Li, A discontinuous Galerkin finite element method based axial SN for the 2D/1D transport method, Prog. Nucl. Energy 152 (2022), 104391. October. 
  21. X. Zhou, Z. Liu, L. Cao, H. Wu, Convergence analysis for the CMFD accelerated 2D/1D neutron transport method based on Fourier analysis, Nucl. Sci. Eng. 17 (2022), 108982. 
  22. Y. Chan, S. Xiao, A linear prolongation CMFD acceleration for two-dimensional discrete ordinate k-eigenvalue neutron transport calculation with pinresolved mesh using discontinuous Galerkin finite element method, Ann. Nucl. Energy 154 (2021), 108103. 
  23. D. Wang, S. Xiao, A linear prolongation approach to stabilizing CMFD, Nucl. Sci. Eng. 190 (1) (2018) 45-55.  https://doi.org/10.1080/00295639.2017.1417347
  24. D. Wang, S. Xiao, Stabilizing CMFD with Linear Prolongation, PHYSOR, Cancun, Mexico, 2018. April 22-26. 
  25. K. Paul, E. Nicholas, et al., OpenMC: a state-of-the-art Monte Carlo code for research and development, Ann. Nucl. Eng. 82 (2015) 90-97.  https://doi.org/10.1016/j.anucene.2014.07.048
  26. J.J. Klingensmith, Y.Y. Azmy, J.C. Gehin, et al., Tort solutions to the three-dimensional MOX benchmark, 3D extension C5G7MOX, Prog. Nucl. Energy 48 (5) (2006) 445-455.  https://doi.org/10.1016/j.pnucene.2006.01.011
  27. M.A. Smith, et al., Benchmark on Deterministic Transport Calculations without Homogenization, Nuclear energy agency organization for economic cooperation and development (NEA-OECD), 2003. 
  28. B. Kong, K. Zhu, et al., Convergence study of DGFEM SN based 2D/1D coupling method for solving neutron transport k-eigenvalue problems with Fourier analysis, Ann. Nucl. Energy 177 (2022), 109327. 
  29. Hyun Chul Lee, et al., Fourier convergence analysis of two-dimensional/one-dimensional coupling methods for the three-dimensional neutron diffusion eigenvalue problems, Nucl. Sci. Eng.J. Am. Nucl. Soc. 156 (1) (2014) 74-85. https://doi.org/10.13182/NSE06-32