Advertisement

OpenFOAM® pp 93-108 | Cite as

Development of Data-Driven Turbulence Models in OpenFOAM\({^{\textregistered }}\): Application to Liquid Fuel Nuclear Reactors

  • M. Tano-RetamalesEmail author
  • P. Rubiolo
  • O. Doche
Chapter

Abstract

The following chapter presents a new approach for the development of turbulent models, with potential application to the design of liquid fuel nuclear reactors. To begin the chapter, the work being carried out at LPSC (Grenoble) for validating the modeling of molten salt coolants is presented, alongside a Backward-Facing Step (BFS) geometry, which will be studied throughout this work. In the subsequent section, various turbulence models are evaluated in the BFS and their advantages and limitations are analyzed, with the conclusion that some improvements in the turbulence modeling are necessary. Therefore, the next section introduces a methodology for developing a nonlinear closure for turbulence models by means of Symbolic Regression via Genetic Evolutionary Programming (GEATFOAM). Then, this new methodology is implemented for direct numerical simulation data of the BFS, obtaining a new nonlinear closure for the standard k\(\varepsilon \) model. Finally, the new model is compared against classical turbulence models for the BFS, and, then, the extrapolability of this model is analyzed for available experimental data of an axial expansion in a pipe. Encouraging results are obtained in both cases.

References

  1. 1.
    Lund, Henrik, et al. “4th Generation District Heating (4GDH): Integrating smart thermal grids into future sustainable energy systems.” Energy 68 (2014): 1–11.CrossRefGoogle Scholar
  2. 2.
    Heuer, D., Merle-Lucotte, E., Allibert, M., Brovchenko, M., Ghetta, V., and Rubiolo, P. (2014). Towards the thorium fuel cycle with molten salt fast reactors. Annals of Nuclear Energy, 64, 421–429.CrossRefGoogle Scholar
  3. 3.
    Raffel, Markus, Christian E. Willert, Steven Wereley, and Jrgen Kompenhans. Particle image velocimetry: a practical guide. Springer, 2013.Google Scholar
  4. 4.
    Moser, Robert D., John Kim, and Nagi N. Mansour. “Direct numerical simulation of turbulent channel flow up to Re= 590.” Phys. Fluids 11, no. 4 (1999): 943–945.zbMATHCrossRefGoogle Scholar
  5. 5.
    Pope, Stephen B. “Turbulent flows.” (2001): 2020.CrossRefGoogle Scholar
  6. 6.
    Germano, M. “Turbulence: the filtering approach.” Journal of Fluid Mechanics 238 (1992): 325–336.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Rubiolo, P. R., et al. “Overview of the Salt at WAll Thermal ExcHanges (SWATH) Experiment.” 2016 International Topical Meeting on High Temperature Reactor Technology (HTR2016). 2016.Google Scholar
  8. 8.
    Thangam, S., Speziale, C. G. (1991). Turbulent separated flow past a backward-facing step: a critical evaluation of two-equation turbulence models INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA.(No. ICASE-91-23).Google Scholar
  9. 9.
    Kopera M., Kerr R., Blackburn H. and Barkley D. (2014). Direct numerical simulation of turbulent flow over a backward-facing step. Approved to appear in the Journal of Fluid Mechanics.Google Scholar
  10. 10.
    Le, H., Moin, P., Kim, J. (1997). Direct numerical simulation of turbulent flow over a backward-facing step. Journal of fluid mechanics, 330(1), 349–374.zbMATHCrossRefGoogle Scholar
  11. 11.
    LIM, H., et al. Chaos, transport and mesh convergence for fluid mixing. Acta Mathematicae Applicatae Sinica (English Series), 2008, vol. 24, no 3, p. 355–368.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
  13. 13.
    Kwon, Y. S., N. Hutchins, and J. P. Monty. “On the use of the Reynolds decomposition in the intermittent region of turbulent boundary layers.” Journal of Fluid Mechanics 794 (2016): 5–16.MathSciNetCrossRefGoogle Scholar
  14. 14.
    Launder, B. E., and B. I. Sharma. “Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc.” Letters in heat and mass transfer 1, no. 2 (1974): 131–137.CrossRefGoogle Scholar
  15. 15.
    Van Driest, Edward R. “On turbulent flow near a wall.” Journal of the Aeronautical Sciences (2012).Google Scholar
  16. 16.
    Chen, Y-S., and S-W. Kim. “Computation of turbulent flows using an extended k-epsilon turbulence closure model.” (1987).Google Scholar
  17. 17.
    Wilcox, David C. “Formulation of the kw turbulence model revisited.” AIAA journal 46, no. 11 (2008): 2823–2838.CrossRefGoogle Scholar
  18. 18.
    Schfer, F., M. Breuer, and F. Durst. “The dynamics of the transitional flow over a backward-facing step.” Journal of Fluid Mechanics 623 (2009): 85–119.zbMATHCrossRefGoogle Scholar
  19. 19.
    Craft, T. J., B. E. Launder, and K. Suga. “Development and application of a cubic eddy-viscosity model of turbulence.” International Journal of Heat and Fluid Flow 17, no. 2 (1996): 108–115.CrossRefGoogle Scholar
  20. 20.
    Speziale, Charles G., Sutanu Sarkar, and Thomas B. Gatski. “Modelling the pressurestrain correlation of turbulence: an invariant dynamical systems approach.” Journal of Fluid Mechanics 227 (1991): 245–272.zbMATHCrossRefGoogle Scholar
  21. 21.
    Lu, Hao, and Fernando Port-Agel. “A modulated gradient model for scalar transport in large-eddy simulation of the atmospheric boundary layer.” Physics of Fluids (1994-present) 25, no. 1 (2013): 015110.CrossRefGoogle Scholar
  22. 22.
    Ghaisas, Niranjan S., and Steven H. Frankel. “Dynamic gradient models for the sub-grid scale stress tensor and scalar flux vector in large eddy simulation.” Journal of Turbulence 17, no. 1 (2016): 30–50.MathSciNetCrossRefGoogle Scholar
  23. 23.
    Billard, Lynne, and Edwin Diday. “Symbolic regression analysis.” Classification, Clustering, and Data Analysis. Springer Berlin Heidelberg, 2002. 281–288.zbMATHCrossRefGoogle Scholar
  24. 24.
    Keijzer, Maarten. “Scaled symbolic regression.” Genetic Programming and Evolvable Machines 5.3 (2004): 259–269.CrossRefGoogle Scholar
  25. 25.
    Smits, Guido, and Mark Kotanchek. “Pareto-front exploitation in symbolic regression.” Genetic programming theory and practice II (2005): 283–299.Google Scholar
  26. 26.
    Vladislavleva, Ekaterina J., Guido F. Smits, and Dick Den Hertog. “Order of nonlinearity as a complexity measure for models generated by symbolic regression via pareto genetic programming.” IEEE Transactions on Evolutionary Computation 13.2 (2009): 333–349.CrossRefGoogle Scholar
  27. 27.
    Yu, Tina, Rick Riolo, and Bill Worzel, eds. Genetic programming theory and practice III. Vol. 9. Springer Science and Business Media, 2006.Google Scholar
  28. 28.
    Deb, Kalyanmoy, Amrit Pratap, Sameer Agarwal, and T. A. M. T. Meyarivan. “A fast and elitist multiobjective genetic algorithm: NSGA-II.” IEEE transactions on evolutionary computation 6, no. 2 (2002): 182–197.CrossRefGoogle Scholar
  29. 29.
    Cantwell, Brian J. “On the behavior of velocity gradient tensor invariants in direct numerical simulations of turbulence. Physics of Fluids A: Fluid Dynamics 5.8 (1993): 2008–2013.zbMATHCrossRefGoogle Scholar
  30. 30.
    Takahashi, Hiro, Anna Takahashi, Satoshi Naito, and Hitoshi Onouchi. “BAIUCAS: a novel BLAST-based algorithm for the identification of upstream open reading frames with conserved amino acid sequences and its application to the Arabidopsis thaliana genome.” Bioinformatics 28, no. 17 (2012): 2231–2241.CrossRefGoogle Scholar
  31. 31.
    Forsgren, Anders, Philip E. Gill, and Elizabeth Wong. “Active-set methods for convex quadratic programming.” arXiv preprint ArXiv:1503.08349 (2015).
  32. 32.
    Gen, Mitsuo, and Runwei Cheng. Genetic algorithms and engineering optimization. Vol. 7. John Wiley and Sons, 2000.Google Scholar
  33. 33.
    Khezzar, L., J. H. Whitelaw, and M. Yianneskis. “An experimental study of round sudden-expansion flows.” In 5th Symposium on Turbulent Shear Flows, vol. 1, p. 5. 1985.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University Grenoble Alpes, CNRS, Grenoble INP, LPSCGrenobleFrance
  2. 2.University Grenoble Alpes, CNRS, Grenoble INP, SIMAPGrenobleFrance

Personalised recommendations