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On the transient models of the VITAS code: applications to the C5G7-TD pin-resolved benchmark problem

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Abstract

This article describes the transient models of the neutronics code VITAS that are used for solving time-dependent, pin-resolved neutron transport equations. VITAS uses the stiffness confinement method (SCM) for temporal discretization to transform the transient equation into the corresponding transient eigenvalue problem (TEVP). To solve the pin-resolved TEVP, VITAS uses a heterogeneous variational nodal method (VNM). The spatial flux is approximated at each Cartesian node using finite elements in the \(x{-}y\) plane and orthogonal polynomials along the z-axis. Angular discretization utilizes the even-parity integral approach at the nodes and spherical harmonic expansions at the interfaces. To further lower the computational cost, a predictor–corrector quasi-static SCM (PCQ-SCM) was developed. Within the VNM framework, computational models for the adjoint neutron flux and kinetic parameters are presented. The direct-SCM and PCQ-SCM were implemented in VITAS and verified using the two-dimensional (2D) and three-dimensional (3D) exercises on the OECD/NEA C5G7-TD benchmark. In the 2D and 3D problems, the discrepancy between the direct-SCM solver’s results and those reported by MPACT and PANDAS-MOC was under 0.97% and 1.57%, respectively. In addition, numerical studies comparing the PCQ-SCM solver to the direct-SCM solver demonstrated that the PCQ-SCM enabled substantially larger time steps, thereby reducing the computational cost 100-fold, without compromising numerical accuracy.

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References

  1. G. Zhong, K. Xu, Y. Lu et al., Study on application of DAG-OPENMC in fusion neutronics analysis. Nucl. Tech. 45(5), 050602 (2022). https://doi.org/10.11889/j.0253-3219.2022.hjs.45.050602 (in Chinese)

    Article  Google Scholar 

  2. Z. Zeng, S. Chen, Y. Zhang et al., Neutronics experiments of dual functional lithium-lead blanket based on D-T fusion neutron source. Nucl. Tech. 45(4), 040601 (2022). https://doi.org/10.11889/j.0253-3219.2022.hjs.45.040601

    Article  Google Scholar 

  3. X. Du, Y. Wang, Y. Zheng et al., The steady-state neutronic analysis and transient simulation of ADANES reactor design based on deterministic method. Nucl. Tech. 45(10), 100601 (2022). https://doi.org/10.11889/j.0253-3219.2022.hjs.45.100601

    Article  Google Scholar 

  4. Q. Shen, Y. Wang, D. Jabaay et al., Transient analysis of C5G7-TD benchmark with MPACT. Ann. Nucl. Energy 125, 107–120 (2019). https://doi.org/10.1016/j.anucene.2018.10.049

    Article  Google Scholar 

  5. A. Hsieh, G. Zhang, W.S. Yang, Consistent transport transient solvers of the high-fidelity transport code PROTEUS-MOC. Nucl. Sci. Eng. 194(7), 508–540 (2020). https://doi.org/10.1080/00295639.2020.1746619

    Article  ADS  Google Scholar 

  6. S. Tao, Y. Xu, Neutron transport analysis of C5G7-TD benchmark with PANDAS-MOC. Ann. Nucl. Energy 169, 108966 (2022). https://doi.org/10.1016/j.anucene.2022.108966

    Article  Google Scholar 

  7. 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, 122–135 (2018). https://doi.org/10.1016/j.pnucene.2018.05.014

    Article  Google Scholar 

  8. Z. Shen, Q. Sun, D. He et al., Comparison and verification of NECP-X and OpenMC using high-fidelity BEAVRS benchmark models. Nucl. Tech. 45(01), 010602 (2022). https://doi.org/10.11889/j.0253-3219.2022.hjs.45.010602. ((in Chinese))

    Article  Google Scholar 

  9. Y. Wang, S. Schunert, J. Ortensi et al., Rattlesnake: a MOOSE-based multiphysics multischeme radiation transport application. Nucl. Technol. 207(7), 1047–1072 (2021). https://doi.org/10.1080/00295450.2020.1843348

    Article  ADS  Google Scholar 

  10. T. Zhang, Z. Li, Variational nodal methods for neutron transport: 40 years in review. Nucl. Eng. Technol. 54(9), 3181–3204 (2022). https://doi.org/10.1016/j.net.2022.04.012

    Article  Google Scholar 

  11. T. Zhang, Y. Wang, E.E. Lewis et al., A three-dimensional variational nodal method for pin-resolved neutron transport analysis of pressurized water reactors. Nucl. Sci. Eng. 188(2), 160–174 (2017). https://doi.org/10.1080/00295639.2017.1350002

    Article  ADS  Google Scholar 

  12. T. Zhang, E.E. Lewis, M.A. Smith et al., A variational nodal approach to 2D/1D pin resolved neutron transport for pressurized water reactors. Nucl. Sci. Eng. 186(2), 120–133 (2017). https://doi.org/10.1080/00295639.2016.1273023

    Article  ADS  Google Scholar 

  13. M.A. Smith, E.E. Lewis, E.R. Shemon, DIF3D-VARIANT 11.0: a decade of updates. https://doi.org/10.2172/1127298 (2017)

  14. Y. Wang, H. Wu, Y. Li, Comparison of two three-dimensional heterogeneous variational nodal methods for PWR control rod cusping effect and pin-by-pin calculation. Prog. Nucl. Energy 101, 370–380 (2017). https://doi.org/10.1016/j.pnucene.2017.06.002

    Article  Google Scholar 

  15. T. Zhang, W. Xiao, H. Yin et al., VITAS: a multi-purpose simulation code for the solution of neutron transport problems based on variational nodal methods. Ann. Nucl. Energy 178, 109335 (2022). https://doi.org/10.1016/j.anucene.2022.109335

    Article  Google Scholar 

  16. F. He, X. Cai, W. Guo et al., The transient analysis of molten salt reactor reactivity insertion based on RELAP5/FLUENT coupled program. Nucl. Tech. 44(3), 030601 (2021). https://doi.org/10.11889/j.0253-3219.2021.hjs.44.030601. (in Chinese)

    Article  Google Scholar 

  17. S. Dulla, E.H. Mund, P. Ravetto, The quasi-static method revisited. Prog. Nucl. Energy 50(8), 908–920 (2008). https://doi.org/10.1016/j.pnucene.2008.04.009

    Article  Google Scholar 

  18. D. Caron, S. Dulla, P. Ravetto, New aspects in the implementation of the quasi-static method for the solution of neutron diffusion problems in the framework of a nodal method. Ann. Nucl. Energy 87, 34–48 (2016). https://doi.org/10.1016/j.anucene.2015.02.035

    Article  Google Scholar 

  19. Y.-A. Chao, A. Attard, A resolution of the stiffness problem of reactor kinetics. Nucl. Sci. Eng. 90(1), 40–46 (1985). https://doi.org/10.13182/NSE85-A17429

    Article  ADS  Google Scholar 

  20. S. Aoki, T. Suemura, J. Ogawa et al., The verification of 3 dimensional nodal kinetics code ANCK using transient benchmark problems. J. Nucl. Sci. Technol. 44(6), 862–868 (2007). https://doi.org/10.1080/18811248.2007.9711323

    Article  Google Scholar 

  21. B.W. Park, H.G. Joo, Improved stiffness confinement method within the coarse mesh finite difference framework for efficient spatial kinetics calculation. Ann. Nucl. Energy 76, 200–208 (2015). https://doi.org/10.1016/j.anucene.2014.09.029

    Article  Google Scholar 

  22. C. Tang, Application of stiffness confinement method in transient transport calculation. J. Nucl. Eng. Radiat. Sci. (2019). https://doi.org/10.1115/1.4044749

    Article  Google Scholar 

  23. W. Xiao, Q. Sun, X. Liu et al., Application of stiffness confinement method within variational nodal method for solving time-dependent neutron transport equation. Comput. Phys. Commun. 279, 108450 (2022). https://doi.org/10.1016/j.cpc.2022.108450

    Article  MathSciNet  Google Scholar 

  24. E.E. Lewis, W.F. Miller, Computational Methods of Neutron Transport (Wiley, New York, 1993)

    MATH  Google Scholar 

  25. K.O. Ott, D.A. Meneley, Accuracy of the quasistatic treatment of spatial reactor kinetics. Nucl. Sci. Eng. 36(3), 402–411 (1969). https://doi.org/10.13182/NSE36-402

    Article  ADS  Google Scholar 

  26. M. Kheradmand Saadi, A. Abbaspour, Effective point kinetic parameters calculation in Tehran research reactor using deterministic and probabilistic methods. Nucl. Sci. Technol. 28(12), 171 (2017). https://doi.org/10.1007/s41365-017-0323-7

    Article  Google Scholar 

  27. K.F. Laurin-Kovitz, E.E. Lewis, Variational nodal transport perturbation theory. Nucl. Sci. Eng. 123(3), 369–380 (1996). https://doi.org/10.13182/NSE96-A24200

    Article  ADS  Google Scholar 

  28. A. Zhu, Y. Xu, T. Downar, A multilevel quasi-static kinetics method for pin-resolved transport transient reactor analysis. Nucl. Sci. Eng. 182(4), 435–451 (2016). https://doi.org/10.13182/NSE15-39

    Article  ADS  Google Scholar 

  29. F. Alcaro, S. Dulla, P. Ravetto, Implementation of the quasi-static method for neutron transport, in International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M &C 2011), Rio de Janeiro, RJ, Brazil, May 8–12 (2011)

  30. W.M. Stacey, Nuclear Reactor Physics, 2nd edn. (Wiley-VCH, Weinheim, 2007), pp.603–604

    Book  Google Scholar 

  31. J. Hou, K. Ivanov, V. Boyarinov et al., C5G7-TD benchmark for time-dependent heterogeneous neutron transport calculations, in International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M &C 2011), Jeju, Korea (2017)

  32. J. Hou, K.N. Ivanov, V.F. Boyarinov et al., OECD/NEA benchmark for time-dependent neutron transport calculations without spatial homogenization. Nucl. Eng. Des. 317, 177–189 (2017). https://doi.org/10.1016/j.nucengdes.2017.02.008

    Article  Google Scholar 

  33. C. Hao, J. Ma, X. Zhou et al., Development, verification and application of the uncertainty analysis platform CUSA. Ocean Eng. 261, 112160 (2022). https://doi.org/10.1016/j.oceaneng.2022.112160

    Article  Google Scholar 

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Acknowledgements

We would like to thank Professor Yun-Lin Xu of Purdue University for providing the detailed C5G7-TD benchmark results data of the PANDAS-MOC.

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Authors and Affiliations

  1. School of Nuclear Science and Engineering, Shanghai Jiao Tong University, Shanghai, 2002040, China

    Wei Xiao, Han Yin, Xiao-Jing Liu, Hui He & Teng-Fei Zhang

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  1. Wei Xiao
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  2. Han Yin
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  3. Xiao-Jing Liu
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Wei Xiao. The first draft of the manuscript was written by Wei Xiao, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Teng-Fei Zhang.

Additional information

This research was supported by the National Natural Science Foundation of China (Nos. 12175138, U20B2011) and the Young Talent Project of the China National Nuclear Corporation.

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Xiao, W., Yin, H., Liu, XJ. et al. On the transient models of the VITAS code: applications to the C5G7-TD pin-resolved benchmark problem. NUCL SCI TECH 34, 20 (2023). https://doi.org/10.1007/s41365-023-01170-x

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