Conference Agenda

To evaluate the impact of uncertain input parameters on numerical models, Sensitivity Analysis (SA) is an invaluable tool. It supports the process of quantifying uncertainties in the outputs of numerical simulators used to model and predict physical phenomena. This helps in understanding how these uncertainties influence the model outputs. Among the methods of SA, the one based on estimating HSIC (Hilbert-Schmidt Independence Criterion) indices is particularly interesting. This approach is especially useful when each run of the simulator is CPU-time expensive, as HSIC indices can be well-estimated with fewer than a hundred simulations.
This paper presents the results of a HSIC-based Global SA (GSA), applied to a multi-physics simulator (named CORPUS) modeling a load rejection transient in a Pressurized Water Reactor. Three uncertain input variables were considered: control rod worth, moderator temperature coefficient and fuel conductivity. Two CORPUS outputs, which are time-dependent variables, were selected as quantities of interest: the core power and the axial offset. From a Monte-Carlo sample of one hundred CORPUS simulations, a GSA based on a functional Principal Component Analysis (PCA) combined with the estimation of HSIC indices on the PCA coefficients is performed for each of the two outputs.
The analysis reveals that the most important uncertainty source for the core power is control rod worth, followed by fuel conductivity and then by moderator temperature coefficient. The most important uncertainty source for the axial offset is again control rod worth followed by moderator temperature coefficient, while the impact of fuel conductivity is negligible.

As part of research to ensure pressurized water reactor safety, Thermo-hydraulic (TH) and neutron kinetic tools are deployed to predict scenarios of intense local boiling and radial void fraction within innovative fuel assemblies, which can strongly influence reactor power. Current validation of the TH system tools is limited under these particular conditions (pressure around 70 bar, high void fraction), and given the restricted availability of experimental data in the literature, a comparison with CFD simulations is exploited to support the system scale.

The ultimate goal is to validate the porous 3D module of the system code CATHARE3 (C3) on transverse two-phase flows between parallel sub-channels. The work starts with the validation of a multi-scale post-processing method (from CFD tool neptune_cfd to C3) on a single channel experimental test case from the PSBT benchmark. It is then extended to a two sub-channels geometry from “Rowe and Angle” 1967 experiment, which focuses on two-phase cross-flows.

The multi-scale post-processing method has proven to be a valuable tool for comparing results between the different codes’ scales. Numerical results from C3 and neptune_cfd are in good agreement with experimental data from PSBT experiment. However, results from Rowe and Angle's experiment show that the C3 turbulence model overestimates turbulent viscosity, resulting in inaccurate two-phase cross-flow predictions. Alternative models are tested to improve C3 code prediction.

Propagating uncertainties in nuclear thermal-hydraulics simulations is challenged by the anal-
yses in complex domains under extreme operating conditions and multi-physics. The compu-
tational cost becomes particularly high for liquid metal cooled reactors, for which the similar
thermal conductivity of fluids and solid parts require a Conjugate Heat Transfer (CHT) ap-
proach.
In the present work, we applied a methodology based on surrogate modeling and data of
multiple fidelities to propagate these uncertainties to the maximum cladding temperature. The
correlation between the data collected for fluid and solid regions is exploited to retrieve uncer-
tainty estimates for the cladding temperature with a limited number of CHT simulations. The
computed probability distributions show the impact of deformation on the excess temperature
and highlight the different response to deformed bulk, edge and corner pins.

Accurate estimation of mesh related numerical errors and the associated uncertainties is critical in computational fluid dynamics (CFD) simulations to ensure the credibility of the results. Traditional Richardson extrapolation-based approaches often exhibit limitations when applied to turbulent flow regimes. In real-world CFD applications, factors such as turbulence models, complex geometries, and algorithm limiters can result in nonlinear responses during numerical convergence studies, leading to unphysically large uncertainty bounds. Notably, these uncertainties stem from the error estimation approach itself, rather than the CFD solver, and hinder the consistent application of CFD to complex reactor simulations. In this work, we present a robust stochastic framework for estimating mesh related uncertainty in unsteady turbulent flow simulations. The framework starts with quantifying the potential numerical errors in local turbulence characteristics using the least-squares method; the errors are then propagated into the system through the physics-based stochastic field modeling. The framework removes the deficiencies of the conventional approaches and properly accounts for the intricate interactions between numerical and model error. The impact of numerical uncertainties on turbulence predictions and, consequently, on the overall flow field predictions of unsteady flow can be well described by propagating the local turbulence characteristics. To demonstrate the efficacy of the proposed approach, an unsteady mixed-convection problem is presented. The results show that, compared to the conventional approach, the proposed framework is robust in estimating potential numerical error. Moreover, the framework can identify the error caused by poor spatial/temporal resolutions and alert the user to the quality of the numerical model.

This study explores the capabilities of the Generalized Turbulent Flame Closure approach, recently presented by Karanam and Verma, for scalable Deflagration-to-Detonation Transition (DDT) modeling in hydrogen-air mixtures. The TFC-DDT approach introduces key simplifications that enable DDT simulations on underresolved meshes, which could make it suitable for large-scale applications, including those relevant for nuclear safety. This work offers re-implementation of the TFC-DDT model within the nuclear-focused open-source combustion framework flameFoam to conduct its independent validation.

The validation focuses on the model’s ability to capture flame acceleration, detonation onset, and shock behavior under varying conditions, while also examining grid resolution requirements and sensitivity to numerical parameters. This investigation aims to further understand the TFC-DDT model's potential for large-scale detonation applications in safety and industrial contexts, contributing to the advancement of simplified, computationally efficient DDT modeling techniques.

Given the lack of validated systems level open source codes for coupled natural circulation, a model for coupled natural circulation in the Compact Integral Effects Test (CIET) was built using the Open Source Thermo-hydraulic Uniphase Solver for Advection and Convection in Salt Flows (TUAS). This model was validated using experimental data of natural circulation mass flowrate within CIET at various prevailing boundary conditions. The resulting CIET model built in TUAS agreed well with the experimental data as the discrepancy between the TUAS model and experimental data was comparable to the discrepancy between the SAM model and experimental data. Moreover, the TUAS model of CIET was able to run in real-time on a personal computer due to simplifications such as the Boussinesq approximation and the fact that it was built using the Rust programming language which has execution speed comparable to Fortran and C++. These results show that TUAS is potentially useful for systems level code analysis, digital twin applications as well as real-time reactor simulators. Its open source license also contributes to repeatability of results and the potential to expand it to many applications. This could greatly contribute to the molten salt thermal hydraulics community as an additional tool for systems level reactor analysis.