Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
권호 표지
DOI QR코드

DOI QR Code

Multi-objective optimization of printed circuit heat exchanger with airfoil fins based on the improved PSO-BP neural network and the NSGA-II algorithm

  • Jiabing Wang (School of Energy and Power Engineering, Huazhong University of Science and Technology) ;
  • Linlang Zeng (School of Energy and Power Engineering, Huazhong University of Science and Technology) ;
  • Kun Yang (School of Energy and Power Engineering, Huazhong University of Science and Technology)
  • Received : 2022.09.17
  • Accepted : 2023.02.19
  • Published : 2023.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

The printed circuit heat exchanger (PCHE) with airfoil fins has the benefits of high compactness, high efficiency and superior heat transfer performance. A novel multi-objective optimization approach is presented to design the airfoil fin PCHE in this paper. Three optimization design variables (the vertical number, the horizontal number and the staggered number) are obtained by means of dimensionless airfoil fin arrangement parameters. And the optimization objective is to maximize the Nusselt number (Nu) and minimize the Fanning friction factor (f). Firstly, in order to investigate the impact of design variables on the thermal-hydraulic performance, a parametric study via the design of experiments is proposed. Subsequently, the relationships between three optimization design variables and two objective functions (Nu and f) are characterized by an improved particle swarm optimization-backpropagation artificial neural network. Finally, a multi-objective optimization is used to construct the Pareto optimal front, in which the non-dominated sorting genetic algorithm II is used. The comprehensive performance is found to be the best when the airfoil fins are completely staggered arrangement. And the best compromise solution based on the TOPSIS method is identified as the optimal solution, which can achieve the requirement of high heat transfer performance and low flow resistance.

Keywords

Acknowledgement

This work was supported by the National Natural Science Foundation of China (No. 51476063).

References

  1. B.W. Brook, A. Alonso, D.A. Meneley, J. Misak, T. Blees, J.B. van Erp, Why nuclear energy is sustainable and has to be part of the energy mix, Sustain.Mater. Technol 1-2 (2014) 8-16.
  2. D.O.E. US, A technology roadmap for generation IV nuclear energy systems, in: Nuclear Energy Research Advisory Committee and the Generation IV International Forum, 2002, pp. 48-52.
  3. N. Bartel, M. Chen, V.P. Utgikar, X. Sun, I.H. Kim, R. Christensen, P. Sabharwall, Comparative analysis of compact heat exchangers for application as the intermediate heat exchanger for advanced nuclear reactors, Ann. Nucl. Energy 81 (2015) 143-149. https://doi.org/10.1016/j.anucene.2015.03.029
  4. X. Li, R. Le Pierres, S.J. Dewson, Heat exchangers for the next generation of nuclear reactors, in: International Congress on Advances in Nuclear Power Plants (ICAPP) 2006 , Reno, Nevada, USA, June 4-8, 2006.
  5. S.K. Mylavarapu, X. Sun, R.N. Christensen, R.R. Unocic, R.E. Glosup, M.W. Patterson, Fabrication and design aspects of high-temperature compact diffusion bonded heat exchangers, Nucl. Eng. Des. 249 (2012) 49-56. https://doi.org/10.1016/j.nucengdes.2011.08.043
  6. L. Chai, S.A. Tassou, A review of printed circuit heat exchangers for helium and supercritical CO2 Brayton cycles, Therm. Sci. Eng. Prog. 18 (2020), 100543.
  7. T. Ma, F. Xin, L. Li, X.Y. Xu, Y.T. Chen, Q.W. Wang, Effect of fin-endwall fillet on thermal hydraulic performance of airfoil printed circuit heat exchanger, Appl. Therm. Eng. 89 (2015) 1087-1095. https://doi.org/10.1016/j.applthermaleng.2015.04.022
  8. S.H. Yoon, H.C. No, G.B. Kang, Assessment of straight, zigzag, S-shape, and airfoil PCHEs for intermediate heat exchangers of HTGRs and SFRs, Nucl. Eng. Des. 270 (2014) 334-343. https://doi.org/10.1016/j.nucengdes.2014.01.006
  9. G. Liao, Z. Li, F. Zhang, L. Liu, E. Jiaqiang, A review on the thermal-hydraulic performance and optimization of compact heat exchangers, Energies 14 (19) (2021) 6056.
  10. T. Ishizuka, Thermal-hydraulic characteristics of a printed circuit heat exchanger in a supercritical CO_2 loop, in: Proceedings of the 11th International Topical Meeting on Nuclear Reactor Thermal-Hydraulics, NURETH-11, 2005, pp. 218-232.
  11. S.M. Lee, K.Y. Kim, Comparative study on performance of a zigzag printed circuit heat exchanger with various channel shapes and configurations, Heat Mass Tran. 49 (2013) 1021-1028.
  12. S.M. Lee, K.Y. Kim, A parametric study of the thermal-hydraulic performance of a zigzag printed circuit heat exchanger, Heat Tran. Eng. 35 (2014) 1192-1200. https://doi.org/10.1080/01457632.2013.870004
  13. T.L. Ngo, Y. Kato, K. Nikitin, N. Tsuzuki, New printed circuit heat exchanger with S-shaped fins for hot water supplier, Exp. Therm. Fluid Sci. 30 (2006) 811-819. https://doi.org/10.1016/j.expthermflusci.2006.03.010
  14. T.L. Ngo, Y. Kato, K. Nikitin, T. Ishizuka, Heat transfer and pressure drop correlations of microchannel heat exchangers with S-shaped and zigzag fins for carbon dioxide cycles, Exp. Therm. Fluid Sci. 32 (2007) 560-570. https://doi.org/10.1016/j.expthermflusci.2007.06.006
  15. D.E. Kim, M.H. Kim, J.E. Cha, S.O. Kim, Numerical investigation on thermal-hydraulic performance of new printed circuit heat exchanger model, Nucl. Eng. Des. 238 (2008) 3269-3276. https://doi.org/10.1016/j.nucengdes.2008.08.002
  16. X. Xu, T. Ma, L. Li, M. Zeng, Y. Chen, Y. Huang, Q. Wang, Optimization of fin arrangement and channel configuration in an airfoil fin PCHE for supercritical CO2 cycle, Appl. Therm. Eng. 70 (2014) 867-875. https://doi.org/10.1016/j.applthermaleng.2014.05.040
  17. W.X. Chu, X.H. Li, T. Ma, Y.T. Chen, Q.W. Wang, Study on hydraulic and thermal performance of printed circuit heat transfer surface with distributed airfoil fins, Appl. Therm. Eng. 114 (2017) 1309-1318. https://doi.org/10.1016/j.applthermaleng.2016.11.187
  18. F. Chen, L. Zhang, X. Huai, J. Li, H. Zhang, Z. Liu, Comprehensive performance comparison of airfoil fin PCHEs with NACA 00XX series airfoil, Nucl. Eng. Des. 315 (2017) 42-50. https://doi.org/10.1016/j.nucengdes.2017.02.014
  19. C.Y. Zhu, Y. Guo, H.Q. Yang, B. Ding, X.Y. Duan, Investigation of the flow and heat transfer characteristics of helium gas in printed circuit heat exchangers with asymmetrical airfoil fins, Appl. Therm. Eng. 186 (2021), 116478.
  20. S. Soleimani, S. Eckels, Multi-objective optimization of 3D micro-fins using NSGA-II, Int. J. Heat Mass Tran. 197 (2022), 123315.
  21. K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Trans. Evol. Comput. 6 (2002) 182-197. https://doi.org/10.1109/4235.996017
  22. J. Moore, Application of Particle Swarm to Multiobjective Optimization, Technical Report, 1999.
  23. S. Mirjalili, P. Jangir, S. Saremi, Multi-objective ant lion optimizer: a multiobjective optimization algorithm for solving engineering problems, Appl. Intell. 46 (2017) 79-95. https://doi.org/10.1007/s10489-016-0825-8
  24. S. Mirjalili, Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems, Neural Comput. Appl. 27 (2016) 1053-1073.
  25. Z. Cheng, Z. Wang, X. Sun, T. Fu, Multi-objective optimization of self-excited oscillation heat exchange tube based on multiple concepts, Appl. Therm. Eng. 197 (2021), 117414.
  26. H. Xu, C. Duan, H. Ding, W. Li, Y. Zhang, G. Hong, H. Gong, The optimization for the straight-channel PCHE size for supercritical CO2 Brayton cycle, Nucl. Eng. Technol. 53 (6) (2021) 1786-1795. https://doi.org/10.1016/j.net.2020.12.002
  27. S.M. Lee, K.Y. Kim, Optimization of zigzag flow channels of a printed circuit heat exchanger for nuclear power plant application, J. Nucl. Sci. Technol. 49 (2012) 343-351. https://doi.org/10.1080/00223131.2012.660012
  28. S.M. Lee, K.Y. Kim, Multi-objective optimization of arc-shaped ribs in the channels of a printed circuit heat exchanger, Int. J. Therm. Sci. 94 (2015) 1-8. https://doi.org/10.1016/j.ijthermalsci.2015.02.006
  29. S.M. Lee, K.Y. Kim, S.W. Kim, Multi-objective optimization of a double-faced type printed circuit heat exchanger, Appl. Therm. Eng. 60 (2013) 44-50. https://doi.org/10.1016/j.applthermaleng.2013.06.039
  30. Z.H. Rao, T.C. Xue, K.X. Huang, S.M. Liao, Multi-objective optimization of supercritical carbon dioxide recompression Brayton cycle considering printed circuit recuperator design, Energy Convers. Manag. 201 (2019), 112094.
  31. N.D. Lagaros, M. Papadrakakis, Learning improvement of neural networks used in structural optimization, Adv. Eng. Software 35 (2004) 9-25. https://doi.org/10.1016/S0965-9978(03)00112-1
  32. K. Ermis, ANN modeling of compact heat exchangers, Int. J. Energy Res. 32 (2008) 581-594. https://doi.org/10.1002/er.1380
  33. A. Ridluan, M. Manic, A. Tokuhiro, EBaLM-THP-A neural network thermohydraulic prediction model of advanced nuclear system components, Nucl. Eng. Des. 239 (2009) 308-319. https://doi.org/10.1016/j.nucengdes.2008.10.027
  34. A. Pacheco-Vega, M. Sen, K. Yang, R.L. McClain, Neural network analysis of fin-tube refrigerating heat exchanger with limited experimental data, Int. J. Heat Mass Tran. 44 (2001) 763-770. https://doi.org/10.1016/S0017-9310(00)00139-3
  35. R.J. Schalkoff, Artificial Neural Networks, McGraw-Hill Higher Education, 1997.
  36. T. Ma, M.J. Li, J.L. Xu, F. Cao, Thermodynamic analysis and performance prediction on dynamic response characteristic of PCHE in 1000 MW S-CO2 coal fired power plant, Energy 175 (2019) 123-138. https://doi.org/10.1016/j.energy.2019.03.082
  37. F. Jin, D. Chen, L. Hu, Y. Huang, S. Bu, Optimization of zigzag parameters in printed circuit heat exchanger for supercritical CO2 Brayton cycle based on multi-objective genetic algorithm, Energy Convers. Manag. 270 (2022), 116243.
  38. Y. Lee, S.H. Oh, M.W. Kim, The effect of initial weights on premature saturation in back-propagation learning, in: IJCNN-91-Seattle International Joint Conference on Neural Networks, vol. 1, IEEE, 1991, pp. 765-770.
  39. J.R. Zhang, J. Zhang, T.M. Lok, M.R. Lyu, A hybrid particle swarm optimization-back-propagation algorithm for feedforward neural network training, Appl. Math. Comput. 185 (2007) 1026-1037.
  40. J. Hu, X. Zeng, A hybrid PSO-BP algorithm and its application, in: 2010 Sixth International Conference on Natural Computation, vol. 5, IEEE, 2010, pp. 2520-2523.
  41. J. Ren, S. Yang, An improved PSO-BP network model, in: 2010 Third International Symposium on Information Science and Engineering, IEEE, 2010, pp. 426-429.
  42. Y.J. Lai, T.Y. Liu, C.L. Hwang, TOPSIS for MODM, Eur. J. Oper. Res. 76 (1994) 486-500. https://doi.org/10.1016/0377-2217(94)90282-8
  43. C. Wang, R. Ballinger, P. Stahle, E. Demetri, M. Koronowski, Design of a power conversion system for an indirect cycle, helium cooled pebble bed reactor system, in: Proceedings of the First International Topical Meeting on High Temperature Reactors Technology (HTR-2002), Petten, Netherlands, April 22-24, 2002.
  44. F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J. 32 (1994) 1598-1605. https://doi.org/10.2514/3.12149
  45. X. Cui, J. Guo, X. Huai, K. Cheng, H. Zhang, M. Xiang, Numerical study on novel airfoil fins for printed circuit heat exchanger using supercritical CO2, Int. J. Heat Mass Tran. 121 (2018) 354-366. https://doi.org/10.1016/j.ijheatmasstransfer.2018.01.015
  46. S.D. Marshall, B. Li, R. Arayanarakool, P. Seng Lee, L. Balasubramaniam, P.C. Chen, Heat exchanger improvement via curved microfluidic channels: impacts of cross-sectional geometry and dean vortex strength, J. Heat Tran. 140 (2018), 011801.
  47. S.R. Pidaparti, M.H. Anderson, D. Ranjan, Experimental investigation of thermal-hydraulic performance of discontinuous fin printed circuit heat exchangers for supercritical CO2 power cycles, Exp. Therm. Fluid Sci. 106 (2019) 119-129. https://doi.org/10.1016/j.expthermflusci.2019.04.025
  48. B. Durakovic, Design of experiments application, concepts, examples: state of the art, Period. Eng. Nat. Sci. 5 (2017) 421-439.
  49. D.E. Rumelhart, G.E. Hinton, R.J. Williams, Learning representations by back-propagating errors, nature 323 (1986) 533-536. https://doi.org/10.1038/323533a0
  50. I.A. Basheer, M. Hajmeer, Artificial neural networks: fundamentals, computing, design, and application, J. Microbiol. Methods 43 (2000) 3-31. https://doi.org/10.1016/S0167-7012(00)00201-3
  51. J. Li, J.H. Cheng, J.Y. Shi, F. Huang, Brief introduction of back propagation (BP) neural network algorithm and its improvement, in: Advances in Computer Science and Information Engineering, Springer, 2012, pp. 553-558.
  52. B. Karlik, A.V. Olgac, Performance analysis of various activation functions in generalized MLP architectures of neural networks, Int. J. Artif. Intell. Expet. Syst. 1 (2011) 111-122.
  53. A. Ranganathan, The levenberg-marquardt algorithm, Tutoral on LM algorithm 11 (2004) 101-110.
  54. D. Chicco, M.J. Warrens, G. Jurman, The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation, PeerJ. Comput. Sci. 7 (2021) e623.
  55. J. Kennedy, R. Eberhart, Particle swarm optimization, in: Proceedings of ICNN'95-International Conference on Neural Networks, vol. 4, IEEE, 1995, pp. 1942-1948.
  56. R.C. Eberhart, Y. Shi, Comparing inertia weights and constriction factors in particle swarm optimization, in: Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No. 00TH8512), IEEE, 2000, pp. 84-88.
  57. K. Hareesh, K.V. Nalina Pramod, N.K. Linu Husain, K.B. Binoy, R. Dipin Kumar, N.K. Sreejith, Influence of process parameters of wire EDM on surface finish of Ti6Al4V, Mater. Today Proc. 47 (2021) 5017-5023. https://doi.org/10.1016/j.matpr.2021.04.590
  58. F. Calignano, D. Manfredi, E. Ambrosio, L. Iuliano, P. Fino, Influence of process parameters on surface roughness of aluminum parts produced by DMLS, Int. J. Adv. Manuf. Technol. 67 (2013) 2743-2751. https://doi.org/10.1007/s00170-012-4688-9
  59. D. Xu, Z. Hui, Y. Liu, G. Chen, Morphing control of a new bionic morphing UAV with deep reinforcement learning, Aero. Sci. Technol. 92 (2019) 232-243. https://doi.org/10.1016/j.ast.2019.05.058