Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
권호 표지
DOI QR코드

DOI QR Code

Application of POD reduced-order algorithm on data-driven modeling of rod bundle

  • 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) ;
  • Wang, Tianyu (Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University)
  • Received : 2021.04.26
  • Accepted : 2021.07.09
  • Published : 2022.01.25
Download PDF
⟨ Previous Next ⟩

Abstract

As a valid numerical method to obtain a high-resolution result of a flow field, computational fluid dynamics (CFD) have been widely used to study coolant flow and heat transfer characteristics in fuel rod bundles. However, the time-consuming, iterative calculation of Navier-Stokes equations makes CFD unsuitable for the scenarios that require efficient simulation such as sensitivity analysis and uncertainty quantification. To solve this problem, a reduced-order model (ROM) based on proper orthogonal decomposition (POD) and machine learning (ML) is proposed to simulate the flow field efficiently. Firstly, a validated CFD model to output the flow field data set of the rod bundle is established. Secondly, based on the POD method, the modes and corresponding coefficients of the flow field were extracted. Then, an deep feed-forward neural network, due to its efficiency in approximating arbitrary functions and its ability to handle high-dimensional and strong nonlinear problems, is selected to build a model that maps the non-linear relationship between the mode coefficients and the boundary conditions. A trained surrogate model for modes coefficients prediction is obtained after a certain number of training iterations. Finally, the flow field is reconstructed by combining the product of the POD basis and coefficients. Based on the test dataset, an evaluation of the ROM is carried out. The evaluation results show that the proposed POD-ROM accurately describe the flow status of the fluid field in rod bundles with high resolution in only a few milliseconds.

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. K. Rehme, The structure of turbulence in rod bundles and the implications on natural mixing between the subchannels, Int. J. Heat Mass Tran. 35 (2) (Feb. 1992) 567-581, https://doi.org/10.1016/0017-9310(92)90291-Y.
  2. D.S. Rowe, B.M. Johnson, J.G. Knudsen, Implications concerning rod bundle crossflow mixing based on measurements of turbulent flow structure, Int. J. Heat Mass Tran. 17 (3) (Mar. 1974) 407-419, https://doi.org/10.1016/0017-9310(74)90012-X.
  3. C.M. Lee, Y.D. Choi, Comparison of thermo-hydraulic performances of large scale vortex flow (LSVF) and small scale vortex flow (SSVF) mixing vanes in 17 × 17 nuclear rod bundle, Nucl. Eng. Des. 237 (24) (Dec. 2007) 2322-2331, https://doi.org/10.1016/J.NUCENGDES.2007.04.011.
  4. W. Qu, J. Xiong, S. Chen, Z. Qiu, J. Deng, X. Cheng, PIV measurement of turbulent flow downstream of mixing vane spacer grid in 5×5 rod bundle, Ann. Nucl. Energy 132 (Oct. 2019) 277-287, https://doi.org/10.1016/J.ANUCENE.2019.04.016.
  5. H. Wang, D. Lu, Y. Liu, "PIV measurement and CFD analysis of the turbulent flow in a 3 × 3 rod bundle, Ann. Nucl. Energy 140 (Jun. 2020), https://doi.org/10.1016/J.ANUCENE.2019.107135, 107135.
  6. S.Y. Han, J.S. Seo, M.S. Park, Y.D. Choi, Measurements of the flow characteristics of the lateral flow in the 6 × 6 rod bundles with Tandem Arrangement Vanes, Nucl. Eng. Des. 239 (12) (Dec. 2009) 2728-2736, https://doi.org/10.1016/J.NUCENGDES.2009.09.026.
  7. A.C. Trupp, R.S. Azad, The structure of turbulent flow in triangular array rod bundles, Nucl. Eng. Des. 32 (1) (Apr. 1975) 47-84, https://doi.org/10.1016/0029-5493(75)90090-4.
  8. J. Xiong, R. Cheng, C. Lu, X. Chai, X. Liu, X. Cheng, CFD simulation of swirling flow induced by twist vanes in a rod bundle, Nucl. Eng. Des. 338 (Nov. 2018) 52-62, https://doi.org/10.1016/J.NUCENGDES.2018.08.003.
  9. Y. Wang, et al., CFD simulation of flow and heat transfer characteristics in a 5×5 fuel rod bundles with spacer grids of advanced PWR, Nucl. Eng. Technol. (Dec. 2019), https://doi.org/10.1016/J.NET.2019.12.012.
  10. J. Zang, X. Yan, Y. Li, X. Zeng, Y. Huang, "The flow resistance experiments of supercritical pressure water in 2 × 2 rod bundle, Int. J. Heat Mass Tran. 147 (Feb. 2020), https://doi.org/10.1016/J.IJHEATMASSTRANSFER.2019.118873, 118873.
  11. Y. Wang, Y.M. Ferng, L.X. Sun, CFD assist in design of spacer-grid with mixingvane for a rod bundle, Appl. Therm. Eng. 149 (Feb. 2019) 565-577, https://doi.org/10.1016/J.APPLTHERMALENG.2018.12.090.
  12. X.-Z. Cui, K.-Y. Kim, Three-dimensional analysis of turbulent heat transfer and flow through mixing vane in A subchannel of nuclear reactor, J. Nucl. Sci. Technol. 40 (10) (Oct. 2003) 719-724, https://doi.org/10.1080/18811248.2003.9715412.
  13. W. K, T.-H. Chun, C.-H. Shin, D.-S. Oh, Numerical computation of heat transfer enhancement of a PWR rod bundle with mixing vane spacers, Nucl. Technol. 161 (1) (Jan. 2008) 69-79, https://doi.org/10.13182/NT08-A3914.
  14. M.A. Navarro, A.A.C. Santos, Evaluation of a numeric procedure for flow simulation of a 5 × 5 PWR rod bundle with a mixing vane spacer, Prog. Nucl. Energy 53 (8) (Nov. 2011) 1190-1196, https://doi.org/10.1016/J.PNUCENE.2011.08.002.
  15. 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 (Apr. 2017) 349-358, https://doi.org/10.1016/J.ANUCENE.2016.12.030.
  16. X. Li, 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 (Feb. 2014) 10-22, https://doi.org/10.1016/J.NUCENGDES.2013.11.064.
  17. T. Cong, G. Su, S. Qiu, W. Tian, Applications of ANNs in flow and heat transfer problems in nuclear engineering: a review work, Prog. Nucl. Energy 62 (Jan. 2013) 54-71, https://doi.org/10.1016/J.PNUCENE.2012.09.003.
  18. J. Zhang, et al., Prediction of flow boiling heat transfer coefficient in horizontal channels varying from conventional to small-diameter scales by genetic neural network, Nucl. Eng. Technol. 51 (8) (Dec. 2019) 1897-1904, https://doi.org/10.1016/J.NET.2019.06.009.
  19. N. Amanifard, N. Nariman-Zadeh, M. Borji, A. Khalkhali, A. Habibdoust, Modelling and Pareto optimization of heat transfer and flow coefficients in microchannels using GMDH type neural networks and genetic algorithms, Energy Convers. Manag. 49 (2) (Feb. 2008) 311-325, https://doi.org/10.1016/J.ENCONMAN.2007.06.002.
  20. D. Ma, T. Zhou, J. Chen, S. Qi, M. Ali Shahzad, Z. Xiao, Supercritical water heat transfer coefficient prediction analysis based on BP neural network, Nucl. Eng. Des. 320 (Aug. 2017) 400-408, https://doi.org/10.1016/J.NUCENGDES.2017.06.013.
  21. P.L.S. Serra, P.H.F. Masotti, M.S. Rocha, D.A. de Andrade, W.M. Torres, R.N. de Mesquita, Two-phase flow void fraction estimation based on bubble image segmentation using Randomized Hough Transform with Neural Network (RHTN), Prog. Nucl. Energy 118 (Jan. 2020), https://doi.org/10.1016/J.PNUCENE.2019.103133, 103133.
  22. H.M. Park, J.H. Lee, K.D. Kim, Wall temperature prediction at critical heat flux using a machine learning model, Ann. Nucl. Energy 141 (Jun. 2020), https://doi.org/10.1016/J.ANUCENE.2020.107334, 107334.
  23. N. Vaziri, A. Hojabri, A. Erfani, M. Monsefi, B. Nilforooshan, Critical heat flux prediction by using radial basis function and multilayer perceptron neural networks: a comparison study, Nucl. Eng. Des. 237 (4) (Feb. 2007) 377-385, https://doi.org/10.1016/J.NUCENGDES.2006.05.005.
  24. J. Li, T. Zhou, Z. Ju, Q. Huo, Z. Xiao, Sensitivity analysis of CHF parameters under flow instability by using a neural network method, Ann. Nucl. Energy 71 (Sep. 2014) 211-216, https://doi.org/10.1016/J.ANUCENE.2014.03.040.
  25. B.T. Jiang, J.S. Ren, P. Hu, F.Y. Zhao, Prediction of critical heat flux for water flow in vertical round tubes using support vector regression model, Prog. Nucl. Energy 68 (Sep. 2013) 210-222, https://doi.org/10.1016/J.PNUCENE.2013.07.004.
  26. Y. Mi, M. Ishii, L.H. Tsoukalas, Flow regime identification methodology with neural networks and two-phase flow models, Nucl. Eng. Des. 204 (1-3) (Feb. 2001) 87-100, https://doi.org/10.1016/S0029-5493(00)00325-3.
  27. R.N. de Mesquita, et al., Classification of natural circulation two-phase flow image patterns based on self-organizing maps of full frame DCT coefficients, Nucl. Eng. Des. 335 (Aug. 2018) 161-171, https://doi.org/10.1016/J.NUCENGDES.2018.05.019.
  28. J. Huang, H. Liu, W. Cai, Online in situ prediction of 3-D flame evolution from its history 2-D projections via deep learning, J. Fluid Mech. 875 (Sep. 2019), https://doi.org/10.1017/jfm.2019.545.R2.
  29. L. Sun, H. Gao, S. Pan, J.-X. Wang, Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data, Comput. Methods Appl. Mech. Eng. 361 (Apr. 2020), https://doi.org/10.1016/J.CMA.2019.112732, 112732.
  30. T. Aaron, O.T. Schmidt, C. Tim, Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis, J. Fluid Mech. 847 (2017) 821-867, https://doi.org/10.1017/jfm.2018.283.
  31. Z. Luo, J. Du, Z. Xie, Y. Guo, A reduced stabilized mixed finite element formulation based on proper orthogonal decomposition for the nonstationary Navier-Stokes equations, Int. J. Numer. Methods Eng. 88 (1) (2011) 31-46, https://doi.org/10.1002/nme.3161.
  32. Xu Wang, Jiaqing Kou, Weiwei Zhang, Multi-fidelity surrogate reduced-order modeling of steady flow estimation, Int. J. Numer. Methods Fluid. (2020), https://doi.org/10.1002/fld.4850, 2020.
  33. L. Sirovich, Turbulence and the dynamics of coherent structures. I - coherent structures. II - symmetries and transformations. III - dynamics and scaling, Q. Appl. Math. 45 (3) (1987), https://doi.org/10.1090/qam/910463.
  34. Z. Karoutas, C. Gu, B. Sholin, 3-D flow analyses for design of nuclear fuel spacer, in: Proceedings of the 7th International Meeting on Nuclear Reactor Thermal-Hydraulics, NURETH-7), New York, USA, 1995, pp. 3153-3174.
  35. 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 (Aug. 2016) 1-9, https://doi.org/10.1016/J.ANUCENE.2016.02.007.
  36. G. Chen, Z. Zhang, Z. Tian, Optimal meshing methods and schemes for the simulation of assembly, Trans. Am. Nucl. Soc. 111 (2014) 1572-1575.
  37. 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 (Jul. 2012) 389-396, https://doi.org/10.1016/J.APPLTHERMALENG.2012.02.027.
  38. M.V. Holloway, D.E. Beasley, M.E. Conner, "Investigation of swirling flow in rod bundle subchannels using computational fluid dynamics," in International Conference on Nuclear Engineering, Proceedings, ICONE (2006), https://doi.org/10.1115/ICONE14-89068.
  39. M.D. McKay, R.J. Beckman, W.J. Conover, Comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics 21 (1979) 239-245, https://doi.org/10.1080/00401706.1979.10489755.
  40. D. Balduzzi, M. Frean, L. Leary, J.P. Lewis, K.W.D. Ma, B. McWilliams, "The shattered gradients problem: if resnets are the answer, then what is the question?," in 34th International Conference on Machine Learning, ICML 1 (2017) 536-549, 2017.