Uncertainty Quantification for Multiphase Computational Fluid Dynamics Closure Relations with a Physics-Informed Bayesian Approach

References

• N. SAMKHANIANI and M. R. ANSARI, “Numerical Simulation of Bubble Condensation Using CF-VOF,” Prog. Nucl. Energy, 89, 120 (2016); 10.1016/j.pnucene.2016.02.004.
   Web of Science ®Google Scholar
• X. ZHANG, J. WANG, and D. WAN, “An Improved Multi-Scale Two Phase Method for Bubbly Flows,” Int. J. Multiph. Flow, 133, 103460 (2020); 10.1016/j.ijmultiphaseflow.2020.103460.
   Web of Science ®Google Scholar
• L. BUREŠ and Y. SATO, “Direct Numerical Simulation of Evaporation and Condensation with the Geometric VOF Method and a Sharp-Interface Phase-Change Model,” Int. J. Heat Mass Transf., 173, 121233 (2021); 10.1016/j.ijheatmasstransfer.2021.121233.
   Web of Science ®Google Scholar
• N. SAINI and I. A. BOLOTNOV, “Interface Capturing Simulations of Droplet Interaction with Spacer Grids Under DFFB Conditions,” Nucl. Eng. Des., 364, 110685 (2020); 10.1016/j.nucengdes.2020.110685.
   Web of Science ®Google Scholar
• J. FANG and I. A. BOLOTNOV, “Bubble Tracking Simulations of Turbulent Two-Phase Flows,” Proc. ASME 2016 Fluids Engineering Division Summer Meeting, Washington, D.C., July 10–14, 2016, ASME (2016).
   Google Scholar
• M. GRIEBEL and M. KLITZ, “CLSVOF As a Fast and Mass-Conserving Extension of the Level-Set Method for the Simulation of Two-Phase Flow Problems,” Numer. Heat Transfer Part B, 71, 1, 1 (2017); 10.1080/10407790.2016.1244400.
   Web of Science ®Google Scholar
• S. SAHA, J. KHAN, and T. FAROUK, “Numerical Study of Evaporation Assisted Hybrid Cooling for Thermal Powerplant Application,” Appl. Therm. Eng., 166, 114677 (2020); 10.1016/j.applthermaleng.2019.114677.
   Web of Science ®Google Scholar
• J. FANG et al., “Direct Numerical Simulation of Reactor Two-Phase Flows Enabled by High-Performance Computing,” Nucl. Eng. Des., 330, 409 (2018); 10.1016/j.nucengdes.2018.02.024.
   Web of Science ®Google Scholar
• M. ISHII and T. HIBIKI, Thermo-Fluid Dynamics of Two-Phase Flow, Springer (2011).
   Google Scholar
• Y. LIU, X. SUN, and N. T. DINH, “Validation and Uncertainty Quantification of Multiphase-CFD Solvers: A Data-Driven Bayesian Framework Supported by High-Resolution Experiments,” Nucl. Eng. Des., 354, 110200 (2019); 10.1016/j.nucengdes.2019.110200.
   Web of Science ®Google Scholar
• M. C. KENNEDY and A. O’HAGAN, “Bayesian Calibration of Computer Models,” J. Royal Stat. Soc: Series B, 63, 3, 425 (2001); 10.1111/1467-9868.00294.
   Web of Science ®Google Scholar
• X. WU et al., “Inverse Uncertainty Quantification Using the Modular Bayesian Approach Based on Gaussian Process, Part 1: Theory,” Nucl. Eng. Des., 335, 339 (2018); 10.1016/j.nucengdes.2018.06.004.
   Web of Science ®Google Scholar
• Z. XIE, F. ALSAFADI, and X. WU, “Towards Improving the Predictive Capability of Computer Simulations by Integrating Inverse Uncertainty Quantification and Quantitative Validation with Bayesian Hypothesis Testing,” Nucl. Eng. Des., 383, 111423 (2021); 10.1016/j.nucengdes.2021.111423.
   Web of Science ®Google Scholar
• K. ZENG et al., “Uncertainty Quantification and Propagation of Multiphysics Simulation of the Pressurized Water Reactor Core,” Nucl. Technol., 205, 12, 1618 (2019); 10.1080/00295450.2019.1580533.
   Web of Science ®Google Scholar
• J. ZHANG et al., “Development of a Pragmatic Approach to Model Input Uncertainty Quantification for BEPU Applications,” Nucl. Technol., 205, 1–2, 140 (2019); 10.1080/00295450.2018.1516055.
   Web of Science ®Google Scholar
• X. WU et al., “Evaluation of Public Dose from FHR Tritium Release with Consideration of Meteorological Uncertainties,” Sci. Total Environ., 709, 136085 (2020); 10.1016/j.scitotenv.2019.136085.
   PubMed Web of Science ®Google Scholar
• Y. LIU et al., “Uncertainty Analysis of PIV Measurements in Bubbly Flows Considering Sampling and Bubble Effects with Ray Optics Modeling,” Nucl. Eng. Des., 364, 110677 (2020); 10.1016/j.nucengdes.2020.110677.
   Web of Science ®Google Scholar
• Y. LIU and N. DINH, “Validation and Uncertainty Quantification for Wall Boiling Closure Relations in Multiphase-CFD Solver,” Nucl. Sci. Eng., 193, 1–2, 81 (2019); 10.1080/00295639.2018.1512790.
   Web of Science ®Google Scholar
• C. LU, Z. WU, and X. WU, “Enhancing the One-Dimensional SFR Thermal Stratification Model via Advanced Inverse Uncertainty Quantification Methods,” Nucl. Technol., 207, 5, 692 (2021); 10.1080/00295450.2020.1805259.
   Web of Science ®Google Scholar
• R. COCCI et al., “Extension of the CIRCE Methodology to Improve the Inverse Uncertainty Quantification of Several Combined Thermal-Hydraulic Models,” Nucl. Eng. Des., 398, 111974 (2022); 10.1016/j.nucengdes.2022.111974.
   Web of Science ®Google Scholar
• H. ZHOU, V. SEKER, and T. DOWNAR, “Enhanced Lasso Regularization-Based Self-Adaptive Feature Selection Algorithm for the High-Dimensional Uncertainty Quantification of TREAT Transient Test Modeling,” Nucl. Technol., 206, 6, 839 (2020); 10.1080/00295450.2020.1746620.
   Web of Science ®Google Scholar
• X. WU et al., “A Comprehensive Survey of Inverse Uncertainty Quantification of Physical Model Parameters in Nuclear System Thermal–Hydraulics Codes,” Nucl. Eng. Des., 384, 111460 (2021); 10.1016/j.nucengdes.2021.111460.
   Web of Science ®Google Scholar
• X. WU, T. KOZLOWSKI, and H. MEIDANI, “Kriging-Based Inverse Uncertainty Quantification of Nuclear Fuel Performance Code BISON Fission Gas Release Model Using Time Series Measurement Data,” Reliab. Eng. Syst. Saf., 169, 422 (2018); 10.1016/j.ress.2017.09.029.
   Web of Science ®Google Scholar
• X. WU et al., “Inverse Uncertainty Quantification Using the Modular Bayesian Approach Based on Gaussian Process, Part 2: Application to TRACE,” Nucl. Eng. Des., 335, 417 (2018); 10.1016/j.nucengdes.2018.06.003.
   Web of Science ®Google Scholar
• M. I. RADAIDEH, K. BOROWIEC, and T. KOZLOWSKI, “Integrated Framework for Model Assessment and Advanced Uncertainty Quantification of Nuclear Computer Codes Under Bayesian Statistics,” Reliab. Eng. Syst. Saf., 189, 357 (2019).
   Web of Science ®Google Scholar
• Y. LIU et al., “Uncertainty Quantification for Multiphase-CFD Simulations of Bubbly Flows: A Machine Learning-Based Bayesian Approach Supported by High-Resolution Experiments,” Reliab. Eng. Syst. Saf., 212, 107636 (2021); 10.1016/j.ress.2021.107636.
   Web of Science ®Google Scholar
• Y. LIU et al., “Uncertainty Quantification of Two-Phase Flow and Boiling Heat Transfer Simulations Through a Data-Driven Modular Bayesian Approach,” Int. J. Heat Mass Transf., 138, 1096 (2019); 10.1016/j.ijheatmasstransfer.2019.04.075.
   Web of Science ®Google Scholar
• 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); 10.1016/j.jcp.2015.11.012.
   Web of Science ®Google Scholar
• H. XIAO et al., “Quantifying and Reducing Model-Form Uncertainties in Reynolds-Averaged Navier–Stokes Simulations: A Data-Driven, Physics-Informed Bayesian Approach,” J. Comput. Phys., 324, 115 (2016); 10.1016/j.jcp.2016.07.038.
   Web of Science ®Google Scholar
• R. C. SMITH, Uncertainty Quantification: Theory, Implementation, and Applications, SIAM, Philadelphia, Pennsylvania (2014).
   Google Scholar
• Y. LIU et al., “Data-Driven Modeling of Coarse Mesh Turbulence for Reactor Transient Analysis Using Convolutional Recurrent Neural Networks,” Nucl. Eng. Des., 390, 111716 (2022); 10.1016/j.nucengdes.2022.111716.
   Web of Science ®Google Scholar
• M. A. IGLESIAS, K. J. LAW, and A. M. STUART, “Ensemble Kalman Methods for Inverse Problems,” Inverse Prob., 29, 4, 045001 (2013); 10.1088/0266-5611/29/4/045001.
   Web of Science ®Google Scholar
• P. SIEMENS, “Simcenter STAR-CCM+ User Guide V13. 04,” Siemens PLM (2018).
   Google Scholar
• T. HIBIKI, M. ISHII, and Z. XIAO, “Axial Interfacial Area Transport of Vertical Bubbly Flows,” Int. J. Heat Mass Transf., 44, 10, 1869 (2001); 10.1016/S0017-9310(00)00232-5.
   Web of Science ®Google Scholar
• A. A. TROSHKO and Y. A. HASSAN, “A Two-Equation Turbulence Model of Turbulent Bubbly Flows,” Int. J. Multiph. Flow, 27, 11, 1965 (2001); 10.1016/S0301-9322(01)00043-X.
   Web of Science ®Google Scholar
• M. ISHII and N. ZUBER, “Drag Coefficient and Relative Velocity in Bubbly, Droplet or Particulate Flows,” AIChE J., 25, 5, 843 (1979); 10.1002/aic.690250513.
   Web of Science ®Google Scholar
• A. TOMIYAMA, “Struggle with Computational Bubble Dynamics,” Multiph. Sci. Technol., 10, 4, 369 (1998).
   Google Scholar
• Q. LIU et al., “Experimental Study of Post-CHF Heat Transfer in a Vertical Tubular Test Section,” Int. J. Heat Mass Transf., 120697 (2020).
   Google Scholar
• J. WU, C. MICHELÉN-STRÖFER, and H. XIAO, “Physics-Informed Covariance Kernel for Model-Form Uncertainty Quantification with Application to Turbulent Flows,” Comput. Fluids, 193, 104292 (2019); 10.1016/j.compfluid.2019.104292.
   Web of Science ®Google Scholar
• Y. LIU et al., “Data-Driven Modeling for Boiling Heat Transfer: Using Deep Neural Networks and High-Fidelity Simulation Results,” Appl. Therm. Eng., 144, 305 (2018); 10.1016/j.applthermaleng.2018.08.041.
   Web of Science ®Google Scholar
• 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).
   Web of Science ®Google Scholar