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High fidelity transient solver in STREAM based on multigroup coarse-mesh finite difference method

  • Anisur Rahman (Department of Nuclear Engineering, Ulsan National Institute of Science and Technology) ;
  • Hyun Chul Lee (School of Mechanical Engineering, Pusan National University) ;
  • Deokjung Lee (Department of Nuclear Engineering, Ulsan National Institute of Science and Technology)
  • Received : 2022.09.29
  • Accepted : 2023.05.14
  • Published : 2023.09.25

Abstract

This study incorporates a high-fidelity transient analysis solver based on multigroup CMFD in the MOC code STREAM. Transport modeling with heterogeneous geometries of the reactor core increases computational cost in terms of memory and time, whereas the multigroup CMFD reduces the computational cost. The reactor condition does not change at every time step, which is a vital point for the utilization of CMFD. CMFD correction factors are updated from the transport solution whenever the reactor core condition changes, and the simulation continues until the end. The transport solution is adjusted once CMFD achieves the solution. The flux-weighted method is used for rod decusping to update the partially inserted control rod cell material, which maintains the solution's stability. A smaller time-step size is needed to obtain an accurate solution, which increases the computational cost. The adaptive step-size control algorithm is robust for controlling the time step size. This algorithm is based on local errors and has the potential capability to accept or reject the solution. Several numerical problems are selected to analyze the performance and numerical accuracy of parallel computing, rod decusping, and adaptive time step control. Lastly, a typical pressurized LWR was chosen to study the rod-ejection accident.

Keywords

Acknowledgement

This work was partially supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. NRF-2019M2D2A1A03058371) and the project (L20S089000) by Korea Hydro and Nuclear Power Co. Ltd. This work was partially supported by Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government (MOTIE) [RS-2023-00241302]. The authors would like to express their sincere gratitude to Brendan Kochunas, Assistant Professor, Department of Nuclear Engineering and Radiological Sciences, University of Michigan, and Qicang Shen, Post-doctoral Researcher, the University of Michigan, for providing the MPACT results.

References

  1. M.A. Smith, E.E. Lewis, B.-C. Na, Benchmark on deterministic 2-D MOX fuel assembly transport calculations without spatial homogenization, Prog. Nucl. Energy 45 (2-4) (2004) 107-118, https://doi.org/10.1016/j.pnueene.2004.09.003.
  2. J.E. Hoogenboom, W.R. Martin, B. Petrovic, Monte Carlo performance benchmark for detailed power density calculation in a full-size reactor core, Benchmark specifications (2010) revision 1.2 July 2011, p3.
  3. K.S. Smith, J. Rhodes, CASMO characteristics method for two-dimensional PWR and BWR core calculation, Trans. Am. Nucl. Soc. 83 (2000) 294-296.
  4. S. H, The free lunch is over: a fundamental turn toward concurrency in software, Dr. Dobb's J. 30 (3) (2005).
  5. A. Rineiski, J.Y. Doriath, Time-dependent neutron transport with variational nodal method, Proc. Joint Int. Conf. on Math. Methods and Supercomputing for Nuclear Application (1997) 1661.
  6. J.-Y. Cho, K.-S. Kim, C.C. Lee, H.-G. Joo, W.-S. Yang, T.A. Taiwo, J. Thomas, Transient capability for a MOC-based whole core transport code DeCART, Trans. Am. Nucl. Soc. 92 (2005) 721-722.
  7. P.W. David, S. Tanju, W.S. Yang, J.D. Thomas, J.W. Thomas, Z. Zhong, J.Y. Cho, S.K. Kim, T.H. Chun, H.G. Joo, C.H. Kim, High-fidelity light water reactor analysis with the numerical nuclear reactor, Nucl. Sci. Eng. 155 (3) (2007) 395-408, https://doi.org/10.13182/NSE07-A2672.
  8. A. Zhu, Y. Xu, A. Graham, M.l. Young, T. Downar, L. Cao, Transient methods for pin-resolved whole core transport using the 2D-1D methodology in MPACT, in: M&C, 2015.
  9. B. Wang, Z. Liu, J. Chen, C. Zhao, L. Cao, H. Wu, 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 (2018) 122-135, https://doi.org/10.1016/j.pnucene.2018.05.014.
  10. T.N. Nguyen, Y.S. Jung, T. Downar, C. Lee, Implementation of the transient fixed-source problem in the neutron transport code PROTEUS-MOC, Ann. Nucl. Energy 129 (2019) 199-206, https://doi.org/10.1016/j.anucene.2019.01.005.
  11. N.Z. Cho, G.S. Lee, C.J. Park, Fusion of method of characteristics and nodal method for 3-d whole-core transport calculation, Trans. Am. Nucl. Soc. 86 (2002) 322-324.
  12. S. Choi, D. Lee, Three-dimensional method of characteristics/diamond-difference transport analysis method in STREAM for whole-core neutron transport calculation, Comput. Phys. Commun. 260 (2021), 107332, https://doi.org/10.1016/j.cpc.2020.107332.
  13. S. Choi, W. Kim, J. Choe, W. Lee, H. Kim, B. Ebiwonjumi, E. Jeong, K. Kim, D. Yun, H. Lee, D. Lee, Development of high-fidelity neutron transport code STREAM, Comput. Phys. Commun. 264 (2021), 107915, https://doi.org/10.1016/j.cpc.2021.107915.
  14. S. Choi, W. Kim, D. Lee, Refinements of pin-based pointwise energy slowing-down method for resonance self-shielding calculation-I: theory, Front. Energy Res. 20 (9) (2021), https://doi.org/10.3389/fenrg.2021.765863.
  15. W. Kim, S. Choi, D. Lee, Refinements of pin-based pointwise energy slowing-down method for resonance self-shielding calculation-II: verifications, Front. Energy Res. 15 (9) (2021), https://doi.org/10.3389/fenrg.2021.765865.
  16. S. Choi, K. Smith, H.C. Leec, D. Lee, Impact of inflow transport approximation on light water reactor analysis, J. Comput. Phys. 299 (15) (2015) 352-373, https://doi.org/10.1016/j.jcp.2015.07.005.
  17. A. Rahman, D. Lee, Incorporation of anisotropic scattering into the method of characteristics, Nucl. Eng. Technol. 54 (9) (2022) 3478-3487, https://doi.org/10.1016/j.net.2022.03.041.
  18. A. Vidal-Ferrandiz, R. Fayez, D. Ginestar, G. Verdu, Moving meshes to solve the time-dependent neutron diffusion equation in hexagonal geometry, J. Comput. Appl. Math. 291 (2016) 197-208, https://doi.org/10.1016/j.cam.2015.03.040.
  19. J.H. S, Resolution of the Control Rod Cusping Problem for Nodal Methods, Ph.D. Thesis, Dept. of Nuclear Engineering, Massachusetts Institute of Technology, 1984.
  20. V.F. Boyarinov, P.A. Fomichenko, J. Hou, M. Avramova, K. Ivanov, A. Aures, W. Zwermann, K. Velkov, H.G. Joo, Deterministic Time-dependent Neutron Transport Benchmark without Spatial Homogenization (C5G7-TD) Volume II: Dynamics Phase, OECD Nuclear Energy Agency, 2021.
  21. K. Gustafsson, M. Lundh, G. Derlind, A PI stepsize control for the numerical solution of ordinary differential equations, BIT Numerical Mathematics 28 (2) (1988) 270-287, https://doi.org/10.1007/BF01934091.
  22. A. Carreno, A. Vidal-Ferrandiz, D. Ginestar, G. Verdu, Adaptive time-step control for modal methods to integrate the neutron diffusion equation, Nucl. Eng. Technol. 53 (2) (2021) 399-413, https://doi.org/10.1016/j.net.2020.07.004.
  23. B. Cho, N.Z. Cho, A nonoverlapping local/global iterative method with 2-D/1-D fusion transport kernel and p-CMFD wrapper for transient reactor analysis, Ann. Nucl. Energy 85 (2015) 937-957, https://doi.org/10.1016/j.anucene.2015.07.012.
  24. Q. Shen, Y. Wang, D. Jabaay, B. Kochunas, T. Downar, Transient analysis of C5G7-TD benchmark with MPACT, Ann. Nucl. Energy 125 (2019) 107-120, https://doi.org/10.1016/j.anucene.2018.10.049.
  25. D.J. Diamond, B.P. Bromley, A.L. Aronson, Studies of the Rod Ejection Accident in a PWR, Brookhaven National Laboratory, 2002. W-6382 1/22/02.