Session: Methods for Uncertainty Quantification, Sensitivity Analysis, and Prediction 2

Paper Number: 157800

157800 - A Physics-Based Stochastic Approach for Estimating Model Uncertainty in Reynolds-Averaged Navier-Stokes Simulations 

Abstract: 

While Computational Fluid Dynamics (CFD) codes and capabilities continue to advance across various fields, a significant challenge in their application to nuclear safety analysis lies in the absence of a systematic approach for quantifying the uncertainty in simulation results when experimental data is not available. This issue becomes particularly pronounced in applications involving complex geometries and large thermal-fluid systems, where integral-scale validation data is often scarce. Extrapolating from single experimental geometries and parameter spaces may fail to generalize effectively, leading to inaccurate predictions under different conditions. Meanwhile, data-driven approaches that rely on parameter calibration or hyperparameter tuning risk losing predictive accuracy in the absence of a sufficiently large and diverse training database. Consequently, without a robust uncertainty quantification framework, confidence in simulation results remains limited, creating significant obstacles to regulatory approval and safety assurance.

This research proposes a physics-based stochastic framework for quantifying model uncertainty in Reynolds-Averaged Navier-Stokes (RANS) simulations to address the lack of integral scale validation data. The approach treats turbulence-related uncertainty as a stochastic multiplicative factor applied to the turbulent viscosity, ensuring generality and open-box functionality. As turbulent viscosity takes on unique values in continuous space, the multiplicative factor is modeled as a stochastic field, defined by a marginal distribution and a covariance function.  A physics-guided Gaussian random field is constructed, with its spatial covariance guided by local turbulence characteristics. Realizations of the random field are generated by the Karhunen–Loève expansion, leveraging the eigen-decomposition of the covariance matrix. In this context, the eigenmodes identify uncertain regions where the turbulence may be inaccurately predicted, enabling the Gaussian random field to adaptively perturb the simulation outputs for a given scenario.

 Crucially, unlike parameter calibration or data-driven methods, this physics-based approach effectively explores the solution space, offering general applicability across diverse flow scenarios without the need for hyperparameter tuning. The framework's performance is demonstrated through both steady and unsteady flow cases. Three RANS models, realizable k-ε, nonlinear eddy viscosity k-ε with a cubic stress-strain relation, and Wilcox k-ω model are tested and compared. Using the proposed physics-based approach, model uncertainty is quantified, and each model’s sensitivity to potential errors in turbulence prediction is reported.  Results show that the method generalizes well across a wide variety of turbulent test cases and provides reliable uncertainty bounds. Further, the proposed method identifies deficiencies in regions where model assumptions fail, delivering robust and efficient uncertainty estimation, even in the absence of the experimental data. 

Presenting Author: Yu-Jou Wang Massachusetts Institute of Technology

Presenting Author Biography: Yu-Jou is a postdoctoral associate at MIT. She obtained her Ph.D. in Nuclear Science and Engineering from MIT in 2024, with her doctoral research focused on applying high-fidelity computational models and machine learning algorithms to advance reactor digital twin technology. Before joining MIT, she received a BS and MS degree in Engineering and System Science from the National Tsing-Hua University, Taiwan. Her research expertise includes computational fluid dynamics, multi-physics system modeling, and advanced data analytics. She was awarded the MIT Energy Initiative (MITEI) research fellowship and currently working on understanding the uncertainties in computational fluid dynamics for the applications of Gen-IV reactors.

Authors:

Yu-Jou Wang Massachusetts Institute of Technology
Emilio Baglietto Massachusetts Institute of Technology
Michael Acton Massachusetts Institute of Technology
Ralph Wiser Massachusetts Institute of Technology
Patrick Mcgah TerraPower, LLC
Monica Pham TerraPower, LLC