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Research Articles

Data-Driven RANS Turbulence Closures for Forced Convection Flow in Reactor Downcomer Geometry

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Pages 1167-1184 | Received 04 Oct 2022, Accepted 19 Feb 2023, Published online: 15 Mar 2023

References

  • B. E. LAUNDER and D. B. SPALDING, “The Numerical Computation of Turbulent Flows,” Comput. Methods Appl. Mech. Eng., 3, 2, 269 (1974); https://doi.org/10.1016/0045-7825(74)90029-2.
  • S. THANGAM, R. ABID, and C. G. SPEZIALE, “Application of a New k-tau Model to Near Wall Turbulent Flows,” AIAA J., 30, 2, 552 (1992); https://doi.org/10.2514/3.10952.
  • H. XIAO and P. CINNELLA, “Quantification of Model Uncertainty in RANS Simulations: A Review,” Prog. Aerosp. Sci., 108, 1, 1 (2019); https://doi.org/10.1016/j.paerosci.2018.10.001.
  • A. S. ISKHAKOV et al., “A Perspective on Data-Driven Coarse Grid Modeling for System Level Thermal Hydraulics,” Nucl. Sci. Eng., 197, 2527 (2023); https://doi.org/10.1080/00295639.2022.2107864.
  • S. BRUNTON, J. PROCTOR, and N. KUTZ, “Discovering Governing Equations from Data by Sparse Identification of Nonlinear Dynamical Systems,” Proc. Natl. Acad. Sci. U.S.A, 113, 15, 3932 (2016); https://doi.org/10.1073/pnas.15173841.
  • N. KOVACHKI et al., “On Universal Approximation and Error Bounds for Fourier Neural Operators,” Journal of Machine Learning Research, 22, 1 (2021); https://www.jmlr.org/papers/volume22/21-0806/21-0806.pdf.
  • L. LU et al., “Learning Nonlinear Operators via DeepONet Based on the Universal Approximation Theorem of Operators,” Nat. Mach. Intell., 3, 3, 218 (2021); https://doi.org/10.1038/s42256-021-00302-5.
  • E. J. PARISH and K. DURAISAMY, “A Paradigm for Data-Driven Predictive Modeling Using Field Inversion and Machine Learning,” J. Comput. Phys., 305, 758 (2016); https://doi.org/10.1016/j.jcp.2015.11.012.
  • K. DURAISAMY, “Perspectives on Machine Learning-Augmented Reynolds-Averaged and Large Eddy Simulation Models of Turbulence,” Phys. Rev. Fluids, 6, 050504 (2021); https://doi.org/10.1103/PhysRevFluids.6.050504.
  • R. D. SANDBERG and Y. ZHAO, “Machine-Learning for Turbulence and Heat-Flux Model Development: A Review of Challenges Associated with Distinct Physical Phenomena and Progress to Date,” Int. J. Heat Fluid Flow, 95, 108983 (2022); https://doi.org/10.1016/j.ijheatfluidflow.2022.108983.
  • I. A. BOLOTNOV et al., “Challenge Problem 1: Benchmark Specifications for the Direct Numerical Simulation of Canonical Flows,” ANL/NSE-21/11, Argonne National Laboratory (2021); https://doi.org/10.2172/1873405.
  • K. DURAISAMY, G. IACCARINO, and H. XIAO, “Turbulence Modeling in the Age of Data,” Annu. Rev. Fluid Mech., 51, 1, 357 (2019); https://doi.org/10.1146/annurev-fluid-010518-040547.
  • J. LING et al., “Development of Machine Learning Models for Turbulent Wall Pressure Fluctuations,” presented at the 55th AIAA Aerospace Sci. Mtg., paper 0755 (2017); https://doi.org/10.2514/6.2017-0755.
  • J. LING, A. KURZAWSKI, and J. TEMPLETON, “Reynolds Averaged Turbulence Modelling Using Deep Neural Networks with Embedded Invariance,” J. Fluid Mech., 807, 155 (2016); https://doi.org/10.1017/jfm.2016.615.
  • X. XU, A. S. H. OOI, and R. D. SANDBERG, “Reynolds-Averaged Stress and Scalar-Flux Closures via Symbolic Regression for Vertical Natural Convection,” Int. J. Heat Fluid Flow, 96, 108981 (2022); https://doi.org/10.1016/j.ijheatfluidflow.2022.108981.
  • Y. LIU et al., “SAM-ML: Integrating Data-Driven Closure with Nuclear System Code SAM for Improved Modeling Capability,” Nucl. Eng. Des., 400, 112059 (2022); https://doi.org/10.1016/j.nucengdes.2022.112059.
  • M. FIORE et al., “Physics-Constrained Machine Learning for Thermal Turbulence Modelling at Low Prandtl Numbers,” Int. J. Heat Mass Transf., 194, 122998 (2022); https://doi.org/10.1016/j.ijheatmasstransfer.2022.122998.
  • P. M. MILANI, J. LING, and J. K. EATON, “Turbulent Scalar Flux in Inclined Jets in Crossflow: Counter Gradient Transport and Deep Learning Modelling,” J. Fluid Mech., 906, A27 (2021); https://doi.org/10.1017/jfm.2020.820.
  • J. LING, R. JONES, and J. TEMPLETON, “Machine Learning Strategies for Systems with Invariance Properties,” J. Comput. Phys., 318, 22 (2016); https://doi.org/10.1016/j.jcp.2016.05.003.
  • N. GENEVA and N. ZABARAS, “Quantifying Model Form Uncertainty in Reynolds-Averaged Turbulence Models with Bayesian Deep Neural Networks,” J. Comput. Phys., 383, 125 (2019); https://doi.org/10.1016/j.jcp.2019.01.021.
  • H. D. AKOLEKAR et al., “Development and Use of Machine-Learnt Algebraic Reynolds Stress Models for Enhanced Prediction of Wake Mixing in Low-Pressure Turbines,” J. Turbomach., 141, 4, 041010 (2019); https://doi.org/10.1115/1.4041753.
  • P. M. MILANI, J. LING, and J. K. EATON, “On the Generality of Tensor Basis Neural Networks for Turbulent Scalar Flux Modeling,” Int. Commun. Heat Mass Transfer, 128, 105626 (2021); https://doi.org/10.1016/j.icheatmasstransfer.2021.105626.
  • X. XU et al., “Towards Robust and Accurate Reynolds-Averaged Closures for Natural Convection via Multi-Objective CFD-Driven Machine Learning,” Int. J. Heat Mass Transfer, 187, 122557 (2022); https://doi.org/10.1016/j.ijheatmasstransfer.2022.122557.
  • C.-K. TAI et al., “Direct Numerical Simulation of Low and Unitary Prandtl Number Fluids in Reactor Downcomer Geometry,” Nucl. Technol. , 210, 1097 (2024); https://doi.org/10.1080/00295450.2023.2213286.
  • T. NGUYEN et al., “Direct Numerical Simulation of High Prandtl Number Fluid Flow in the Downcomer of an Advanced Reactor,”, arXiv:2203.14157 (2022); https://arxiv.org/abs/2203.14157.
  • P. FISCHER et al., “NekRS, a GPU-Accelerated Spectral Element Navier-Stokes Solver,” arXiv:2104.05829 (2021); https://arxiv.org/abs/2104.05829.
  • T. NGUYEN et al., “Toward Improved Correlations for Mixed Convection in the Downcomer of Molten Salt Reactors,” Nucl. Technol., (submitted for publication) (2023).
  • S. DONG, E. KARNIADAKIS, and C. CHRYSSOSTOMIDIS, “A Robust and Accurate Outflow Boundary Condition for Incompressible Flow Simulations on Severely- Truncated Unbounded Domains,” J. Comput. Phys., 261, 83, 83 (2014); https://doi.org/10.1016/j.jcp.2013.12.042.
  • S. B. POPE, Turbulent Flows, Cambridge University Press (2000); https://doi.org/10.1017/CBO9780511840531.
  • S. B. POPE, “A More General Effective-Viscosity Hypothesis,” J. Fluid Mech., 72, 2, 331 (1975); https://doi.org/10.1017/S0022112075003382.
  • Q.-S. ZHENG, “Theory of Representations for Tensor Functions—A Unified Invariant Approach to Constitutive Equations,” Appl. Mech. Rev., 47, 11, 545 (1994); https://doi.org/10.1115/1.3111066.
  • T.-H. SHIH and J. L. LUMLEY, “Remarks on Turbulent Constitutive Relations,” Math. Comput. Modell., 18, 2, 9 (1993); https://doi.org/10.1016/0895-7177(93)90002-G.
  • S. MANSERVISI and F. MENGHINI, “A CFD Four Parameter Heat Transfer Turbulence Model for Engineering Applications in Heavy Liquid Metals,” Int. J. Heat Mass Transfer, 69, 312 (2014); https://doi.org/10.1016/j.ijheatmasstransfer.2013.10.017.
  • J. WEATHERITT et al., “Data-Driven Scalar-Flux Model Development with Application to Jet in Cross Flow,” Int. J. Heat Mass Transfer, 147, 118931 (2020); https://doi.org/10.1016/j.ijheatmasstransfer.2019.118931.
  • G. E. KARNIADAKIS et al., “Physics-Informed Machine Learning,” Nat. Rev. Phys., 3, 422 (2021); https://doi.org/10.1038/s42254-021-00314-5.
  • C.-K. TAI et al., “Towards Data-Driven Turbulence Modeling of Mixed Convection in Advanced Reactors Using DNS Data,” presented at the 19th Int. Topl. Mtg. on Nuclear Reactor Thermal Hydraulics (NURETH-19), paper 36432, Brussels, Belgium (2022).
  • A. J. BANKO and J. K. EATON, “Estimating Performance Bounds of Machine-Learning Reynolds-Stress Models via Optimal Tensor Basis Expansions,” Center for Turbulence Research Annual Research Briefs (2020); http://web.stanford.edu/group/ctr/ResBriefs/2020/19_Banko.pdf.
  • A. PASZKE et al., “PyTorch: An Imperative Style, High-Performance Deep Learning Library,” arXiv:1912.01703v1 (2019); https://arxiv.org/abs/1912.01703v1.

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