Application of data-driven model reduction techniques in reactor neutron field calculations
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High-order harmonic techniques can be used to recreate neutron flux distributions in reactor cores using the neutron diffusion equation. However, traditional source iteration and source correction iteration techniques have sluggish convergence rates and protracted calculation periods. The correctness of the implicitly restarted Arnoldi method (IRAM) in resolving the eigenvalue problems of the one-dimensional and two-dimensional neutron diffusion equations was confirmed by computing the benchmark problems SLAB_1D_1G and two-dimensional steady-state TWIGL using IRAM. By integrating Galerkin projection with Proper Orthogonal Decomposition (POD) techniques, a POD-Galerkin reduced-order model was developed and the IRAM model was used as the fullorder model. For 14 macroscopic cross-section values, the TWIGL benchmark problem was perturbed within a 20% range. We extracted 100 sample points using the Latin hypercube sampling method, and 70% of the samples were used as the testing set to assess the performance of the reduced-order model The remaining 30% were utilized as the training set to develop the reduced-order model, which was employed to rebuild the TWIGL benchmark problem. The reduced-order model demonstrates good flexibility and can efficiently and accurately forecast the effective multiplication factor and neutron flux distribution in the core. The reduced-order model predicts keff and neutron flux distribution with a high degree of agreement compared to the full-order model. Additionally, the reduced-order model’s computation time is only 10.18% of that required by the full-order model.The neutron flux distribution of the steady-state TWIGL benchmark was recreated using the reducedorder model. The obtained results indicate that the reduced-order model can accurately predict the keff and neutron flux distribution of the steady-state TWIGL benchmark.Overall, the proposed technique not only has the potential to accurately project neutron flux distributions in transient settings, but is also relevant for reconstructing neutron flux distributions in steady-state conditions; thus, its applicability is bound to increase in the future.
Abstract
High-order harmonic techniques can be used to recreate neutron flux distributions in reactor cores using the neutron diffusion equation. However, traditional source iteration and source correction iteration techniques have sluggish convergence rates and protracted calculation periods. The correctness of the implicitly restarted Arnoldi method (IRAM) in resolving the eigenvalue problems of the one-dimensional and two-dimensional neutron diffusion equations was confirmed by computing the benchmark problems SLAB_1D_1G and two-dimensional steady-state TWIGL using IRAM. By integrating Galerkin projection with Proper Orthogonal Decomposition (POD) techniques, a POD-Galerkin reduced-order model was developed and the IRAM model was used as the fullorder model. For 14 macroscopic cross-section values, the TWIGL benchmark problem was perturbed within a 20% range. We extracted 100 sample points using the Latin hypercube sampling method, and 70% of the samples were used as the testing set to assess the performance of the reduced-order model The remaining 30% were utilized as the training set to develop the reduced-order model, which was employed to rebuild the TWIGL benchmark problem. The reduced-order model demonstrates good flexibility and can efficiently and accurately forecast the effective multiplication factor and neutron flux distribution in the core. The reduced-order model predicts keff and neutron flux distribution with a high degree of agreement compared to the full-order model. Additionally, the reduced-order model’s computation time is only 10.18% of that required by the full-order model.The neutron flux distribution of the steady-state TWIGL benchmark was recreated using the reducedorder model. The obtained results indicate that the reduced-order model can accurately predict the keff and neutron flux distribution of the steady-state TWIGL benchmark.Overall, the proposed technique not only has the potential to accurately project neutron flux distributions in transient settings, but is also relevant for reconstructing neutron flux distributions in steady-state conditions; thus, its applicability is bound to increase in the future.
참고문헌 (24)
- Zhongsheng Xie, "Nuclear Reactor Physics Analysis" (1994), Atomic Energy Press
- Yaolin. Jiang, "Model Reduction Methods", pp.1~7 (2010), Science Press
- Y. Huang, "Implicitly Restarted Arnoldi Method and its application to the solution of higher order harmonics", Chinese Journal of Nuclear Science and Engineering, 28(2), pp.102~106 (2008)[DOI]
- C. Wang, "Harmonic expansion method for online monitoring of PWR core power distribution", Nucl. Power Eng. S, 2, pp.97~101 (2010)
- J. Xie, "Harmonic calculation analysis of one-dimensional flat reactor λ and instantaneous α eigenvalue problems based on implicitly restarted Arnoldi method", Journal of University of South China(Science and Technology), 30(3), pp.9~13 (2016)[DOI]
- K. PearsonLIII, "On lines and planes of closest fit to systems of points in spaceLondon", Edinburgh Dublin Phil. Mag. J. Sci, 2(11), pp.559~572 (1901)[DOI]
- H. Hotelling, "Analysis of a complex of statistical variables into principal components", J. Educ. Psychol, 24(6), pp.417~ (1933)[DOI]
- L. Sirovich, "Turbulence and the dynamics of coherent structures, Parts I, II and III", Quart. Appl. Math, pp.561~590 (1987)[DOI]
- A. G. Buchan, "A POD reduced-order model for eigenvalue problems with application to reactor physics", Int. J. Numer. Methods Eng, 95(12), pp.1011~1032 (2013)[DOI]
- A. G. Buchan, "A POD reduced-order model for eigenvalue problems with application to reactor physics", Int. J. Numer. Methods Eng, 95(12), pp.1011~1032 (2013)[DOI]
- Y. Sun, "A POD reduced-order model for resolving the neutron transport problems of nuclear reactor", Ann. Nucl. Energy, 149, pp.107799~ (2020)[DOI]
- Yaolin, "Model order reduction based on galerkin kpod for partial differential equations with variable coefficients", Journal on Numerica Methods and Computer Applications, 42(3), pp.226~ (2021)[DOI]
- Mingjun Wang, "Recent progress of CFD applications in PWR thermal hydraulics study and future directions", Ann. Nucl. Energy, 150, pp.107836~ (2021)[DOI]
- Shaopeng He, "A deep-learning reduced-order model for thermal hydraulic characteristics rapid estimation of steam generators", Int. J. Heat Mass Tran, 198, pp.123424~ (2022)[DOI]
- Zhengyang Dong, "The development of nuclear reactor three-dimensional neutronic thermal–hydraulic coupling code, CorTAF-2.0", Nucl. Eng. Des, 415, pp.112689~ (2023)[DOI]
- L. Vergari, "Reduced order modeling for coupled thermalhydraulics and reactor physics problems", Prog. Nucl. Energy, 140, pp.103899~ (2021)[DOI]
- D. C. Sorensen, "Implicit application of polynomial filters in a k-step Arnoldi method", SIAM J. Matrix Anal. Appl, 13(1), pp.357~385 (1992)[DOI]
- Y. Sun, "A POD reduced-order model for resolving the neutron transport problems of nuclear reactor", Ann. Nucl. Energy, 149, pp.107799~ (2020)[DOI]
- Y. Feng, "POD-Based Dimensionality Reduction Algorithm for Numerical Simulation of Heat Transfer and Fluid Flow", pp.2017
- R. Elzohery, "Modeling neutronic transients with Galerkin projection onto a greedy-sampled, POD subspace", Ann. Nucl. Energy, 162, pp.108487~ (2021)[DOI]
- J. Ge, "Steady and transient solutions of neutronics problems based on finite volume method(FVM)with a CFD code", Prog. Nucl. Energy, 85, pp.366~374 (2015)[DOI]
- M. D. McKay, "A Comparison of three methods for selecting values of input variables in the analysis of output from a computer code", Technometrics, 21(2), pp.239~245 (1979)[DOI]
- Xinyuan Liang, "Uncertainty analysis of neutron diffusion eigenvalue problem based on reduced-order model", Atomic Energy Sci. Technol, pp.1~8 (2023)[DOI]
- "The Impact of Nuclear Data Uncertainty on the Integral Quantities of the ADS System Keff and the Development of WIMS82" (2004)[URL]