Validation and Uncertainty Quantification for Wall Boiling Closure Relations in Multiphase-CFD Solver

Abstract

Two-fluid model-based multiphase computational fluid dynamics (MCFD) has been considered one of the most promising tools to investigate a two-phase flow and boiling system for engineering purposes. The MCFD solver requires closure relations to make the conservation equations solvable. The wall boiling closure relations, for example, provide predictions on wall superheat and heat partitioning. The accuracy of these closure relations significantly influences the predictive capability of the solver. In this paper, a study of validation and uncertainty quantification (VUQ) for the wall boiling closure relations in the MCFD solver is performed. The work has three purposes: (1) to identify influential parameters to the quantities of interest (QoIs) of the boiling system through sensitivity analysis (SA), (2) to evaluate the parameter uncertainty through Bayesian inference with the support of multiple data sets, and (3) to quantitatively measure the agreement between solver predictions and data sets. The widely used Kurul-Podowski wall boiling closure relation is studied in this paper. Several statistical methods are used, including the Morris Screening method for global SA, Markov Chain Monte Carlo for inverse Bayesian inference, and confidence interval as the validation metric. The VUQ results indicate that the current empirical correlations-based wall boiling closure relations achieved satisfactory agreement on wall superheat predictions. However, the closure relations also demonstrate intrinsic inconsistency and fail to give consistently accurate predictions for all QoIs over the well-developed nucleate boiling regime.

Keywords:

• Multiphase-CFD
• Bayesian inference
• uncertainty quantification
• global sensitivity analysis
• validation metric

Acknowledgments

This research was partially supported by the Consortium for Advanced Simulation of Light Water Reactors (http://www.casl.gov), an Energy Innovation Hub (http://www.energy.gov/hubs) for Modeling and Simulation of Nuclear Reactors under U.S. Department of Energy contract DE-AC05-00OR22725 and by Nuclear Energy University Program under the grant DE-NE0008530. The authors thank Ralph Smith (North Carolina State University, Department of Mathematics) for his valuable comments on this VUQ work.