Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
권호 표지
DOI QR코드

DOI QR Code

Investigation on the nonintrusive multi-fidelity reduced-order modeling for PWR rod bundles

  • Kang, Huilun (Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University) ;
  • Tian, Zhaofei (Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University) ;
  • Chen, Guangliang (Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University) ;
  • Li, Lei (Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University) ;
  • Chu, Tianhui (Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University)
  • Received : 2021.06.27
  • Accepted : 2021.10.23
  • Published : 2022.05.25
Download PDF
⟨ Previous Next ⟩

Abstract

Performing high-fidelity computational fluid dynamics (HF-CFD) to predict the flow and heat transfer state of the coolant in the reactor core is expensive, especially in scenarios that require extensive parameter search, such as uncertainty analysis and design optimization. This work investigated the performance of utilizing a multi-fidelity reduced-order model (MF-ROM) in PWR rod bundles simulation. Firstly, basis vectors and basis vector coefficients of high-fidelity and low-fidelity CFD results are extracted separately by the proper orthogonal decomposition (POD) approach. Secondly, a surrogate model is trained to map the relationship between the extracted coefficients from different fidelity results. In the prediction stage, the coefficients of the low-fidelity data under the new operating conditions are extracted by using the obtained POD basis vectors. Then, the trained surrogate model uses the low-fidelity coefficients to regress the high-fidelity coefficients. The predicted high-fidelity data is reconstructed from the product of extracted basis vectors and the regression coefficients. The effectiveness of the MF-ROM is evaluated on a flow and heat transfer problem in PWR fuel rod bundles. Two data-driven algorithms, the Kriging and artificial neural network (ANN), are trained as surrogate models for the MF-ROM to reconstruct the complex flow and heat transfer field downstream of the mixing vanes. The results show good agreements between the data reconstructed with the trained MF-ROM and the high-fidelity CFD simulation result, while the former only requires to taken the computational burden of low-fidelity simulation. The results also show that the performance of the ANN model is slightly better than the Kriging model when using a high number of POD basis vectors for regression. Moreover, the result presented in this paper demonstrates the suitability of the proposed MF-ROM for high-fidelity fixed value initialization to accelerate complex simulation.

Keywords

Acknowledgement

This work was supported by the National Natural Science Foundation of China (Project No. 51909045, China); CNNC's young talents research project (CNNC2019YTEP-HEU01, China)

References

  1. G. Chen, Z. Zhang, Z. Tian, X. Dong, Y. Wang, CFD simulation for the optimal design and utilization of experiment to research the flow process in PWR, Ann. Nucl. Energy 94 (2016) 1-9. https://doi.org/10.1016/j.anucene.2016.02.007
  2. G. Chen, Z. Zhang, Z. Tian, L. Li, X. Dong, H. Ju, Design of a CFD scheme using multiple RANS models for PWR, Ann. Nucl. Energy 102 (2017) 349-358. https://doi.org/10.1016/j.anucene.2016.12.030
  3. M. Conner, Y. Hassan, E. Dominguez-Ontiveros, Hydraulic benchmark data for PWR mixing vane grid, Nucl. Eng. Des. 264 (2013) 97-102. https://doi.org/10.1016/j.nucengdes.2012.12.001
  4. S. Chang, K. Sang, Moon, D. Bok, T. Kim, P. Won, W.-P. Baek, Y. Choi, Phenomenological investigations on the turbulent flow structures in a rod bundle array with mixing devices, Nuclear Engineering and Design - NUCL ENG DES (2008) 238.
  5. S. Bhattacharjee, G. Ricciardi, S. Viazzo, Comparative study of the contribution of various PWR spacer grid components to hydrodynamic and wall pressure characteristics, Nucl. Eng. Des. 317 (2017) 22-43. https://doi.org/10.1016/j.nucengdes.2017.03.011
  6. B. Liu, S. He, C. Moulinec, J. Uribe, Sub-channel CFD for nuclear fuel bundles, Nucl. Eng. Des. 355 (2019) 110318. https://doi.org/10.1016/j.nucengdes.2019.110318
  7. M. Wang, Y. Wang, X.I. Tian, S.Z. Qiu, G. Su, Recent progress of CFD applications in PWR thermal hydraulics study and future directions, Ann. Nucl. Energy 150 (2021) 107836. https://doi.org/10.1016/j.anucene.2020.107836
  8. B.-W. Yang, B. Han, A. Liu, S. Wang, Recent challenges in subchannel thermalhydraulics-CFD modeling, subchannel analysis, CHF experiments, and CHF prediction, Nucl. Eng. Des. 354 (2019) 110236. https://doi.org/10.1016/j.nucengdes.2019.110236
  9. G. Fernandez, C. Park, N. Kim, R. Haftka, Review of multi-fidelity models, arXiv preprint arXiv:1609.07196 (2016). https://www.researchgate.net/publication/315486356_Review_of_multi-fidelity_models/citations.
  10. M. Zarei, On a reduced order modeling of the nuclear reactor dynamics, Appl. Math. Comput. (2020) 393. https://doi.org/10.1016/S0096-3003(02)00856-1
  11. Y. Sun, J. Yang, Y.-H. Wang, Z. Li, Y. Ma, A POD reduced-order model for resolving the neutron transport problems of nuclear reactor, Ann. Nucl. Energy 149 (2020) 107799. https://doi.org/10.1016/j.anucene.2020.107799
  12. S. Lorenzi, A. Cammi, L. Luzzi, G. Rozza, POD-Galerkin method for finite volume approximation of Navier-Stokes and RANS equations, Comput. Methods Appl. Mech. Eng. (2016) 311.
  13. L. Vergari, A. Cammi, S. Lorenzi, Reduced order modeling approach for parametrized thermal-hydraulics problems: inclusion of the energy equation in the POD-FV-ROM method, Prog. Nucl. Energy 118 (2020) 103071. https://doi.org/10.1016/j.pnucene.2019.103071
  14. D. Alonso, A. Velazquez, J. Vega, Robust reduced order modeling of heat transfer in a back step flow, Int. J. Heat Mass Tran. 52 (2009) 1149-1157. https://doi.org/10.1016/j.ijheatmasstransfer.2008.09.011
  15. R. Chen, J. Xu, S. Zhang, C.-H. Chen, L.H. Lee, An Effective Learning Procedure for Multi-Fidelity Simulation Optimization with Ordinal Transformation, 2015.
  16. A. Forrester, A. Sobester, A. Keane, Engineering Design via Surrogate Modelling, A Practical Guide, 2008.
  17. E. Minisci, M. Vasile, Robust design of a reentry unmanned space vehicle by multifidelity evolution control, AIAA J. 51 (2013) 1284-1295. https://doi.org/10.2514/1.J051573
  18. M. Fossati, W. Habashi, Multiparameter analysis of aero-icing problems using proper orthogonal decomposition and multidimensional interpolation, AIAA J. 51 (2013) 946-960. https://doi.org/10.2514/1.J051877
  19. F. Alsayyari, M. Tiberga, Z. Perko, D. Lathouwers, J. Kloosterman, A nonintrusive adaptive reduced order modeling approach for a molten salt reactor system, Ann. Nucl. Energy 141 (2020).
  20. X. Wang, J. Kou, W. Zhang, Multi-fidelity surrogate reduced-order modeling of steady flow estimation, Int. J. Numer. Methods Fluid. (2020) 92. https://doi.org/10.1002/fld.3977
  21. M.J. Mifsud, D. MacManus, S. Shaw, A Variable-Fidelity Aerodynamic Model Using Proper Orthogonal Decomposition, 2016.
  22. B. Noack, From snapshots to modal expansions - bridging low residuals and pure frequencies, J. Fluid Mech. 802 (2016) 1-4. https://doi.org/10.1017/jfm.2016.416
  23. Z. Karoutas, C.Y. Gu, B. Scholin, 3-D flow analyses for design of nuclear fuel spacer, Proceedings of the Seventh International Meeting on Nuclear Reactor Thermal-Hydraulics (1995) 3153-3174.
  24. F. Wiltschko, W. Qu, J. Xiong, Validation of RANS models and Large Eddy simulation for predicting crossflow induced by mixing vanes in rod bundle, Nuclear Engineering and Technology 53 (2021) 3625-3634. https://doi.org/10.1016/j.net.2021.05.034
  25. C.C. Liu, Y.-M. Ferng, C.K. Shih, CFD evaluation of turbulence models for flow simulation of the fuel rod bundle with a spacer assembly, Appl. Therm. Eng. 40 (2012) 389-396. https://doi.org/10.1016/j.applthermaleng.2012.02.027
  26. M. Holloway, D. Beasley, M. Conner, Investigation of swirling flow in rod bundle subchannels using computational fluid dynamics, international conference on nuclear engineering, Proceedings, ICONE (2006) 2006.
  27. L. Xiaochang, Y. Gao, Methods of simulating large-scale rod bundle and application to a 17 × 17 fuel assembly with mixing vane spacer grid, Nucl. Eng. Des. 267 (2014) 10-22. https://doi.org/10.1016/j.nucengdes.2013.11.064
  28. M.D. McKay, R.J. Beckkman, W. Conover, Comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics 21 (2000) 266-294.
  29. ANSYS Inc, ANSYS Fluent Customization Manual. USA, 2016.
  30. A. Ayodeji, Z. Wang, W. Wang, W. Qin, C. Yang, S. Xu, X. Liu, Causal augmented ConvNet: a temporal memory dilated convolution model for long-sequence time series prediction, ISA Trans. (2021).
  31. G. Chen, J. Wang, Z. Zhang, Z. Tian, L. Li, H. Kang, Y. Jin, Distributed-parallel CFD computation for all fuel assemblies in PWR core, Ann. Nucl. Energy 141 (2020) 107340. https://doi.org/10.1016/j.anucene.2020.107340