Thermal mixing and stratification in large pools and enclosures play a critical role in the safety and performance of pool-type nuclear reactors, particularly during transient scenarios involving significant temperature differences between incoming and bulk coolant. Accurate modeling of these phenomena is essential for predicting system behavior and supporting passive safety features such as natural circulation. This paper presents a new 1D model for thermal mixing and stratification, developed and implemented in the SAM code. The model represents a large pool as 1D coolant jet channels and zero-dimensional bulk pool volumes, enabling the simulation of a wide range of flow configurations, including hot and cold jet interactions, stratified layers, and the influence of complex geometries such as ceilings, free surfaces, and internal obstacles. Heat exchange between jet and pool regions is governed by closure relations calibrated against 3D computational fluid dynamics (CFD) simulations. The model improves upon earlier approaches by incorporating time-dependent jet characteristics and capturing the associated delay effects more accurately. Code-to-code comparisons and validation against experimental data from the Thermal Stratification Test Facility demonstrate the model's accuracy and flexibility. This work offers two key contributions: (1) an efficient and robust method for simulating thermal mixing and stratification at the system level, eliminating the need for external coupling between system analysis codes and CFD, and (2) a significant enhancement of SAM's capabilities to analyze thermal stratification phenomena in advanced reactor systems.

Real-time supervisory control of advanced reactors requires accurate forecasting of plant-wide thermal-hydraulic states, including locations where physical sensors are unavailable. Meeting this need calls for surrogate models that combine predictive fidelity, millisecond-scale inference, and robustness to partial observability. In this work, we present a physics-informed message-passing Graph Neural Network coupled with a Neural Ordinary Differential Equation (GNN-ODE) to addresses all three requirements simultaneously. We represent the whole system as a directed sensor graph whose edges encode hydraulic connectivity through flow/heat transfer-aware message passing, and we advance the latent dynamics in continuous time via a controlled Neural ODE. A topology-guided missing-node initializer reconstructs uninstrumented states at rollout start; prediction then proceeds fully autoregressively. The GNN-ODE surrogate achieves satisfactory results for the system dynamics prediction. On held-out simulation transients, the surrogate achieves an average MAE of 0.91 K at 60 s and 2.18 K at 300 s for uninstrumented nodes, with R^2 up to 0.995 for missing-node state reconstruction. Inference runs at approximately 105 times faster than simulated time on a single GPU, enabling 64-member ensemble rollouts for uncertainty quantification. To assess sim-to-real transfer, we adapt the pretrained surrogate to experimental facility data using layerwise discriminative fine-tuning with only 30 training sequences. The learned flow-dependent heat-transfer scaling recovers a Reynolds-number exponent consistent with established correlations, indicating constitutive learning beyond trajectory fitting. The model tracks a steep power change transient and produces accurate trajectories at uninstrumented locations.

In recent years, there has been renewed interest in Molten Salt Reactors (MSRs) for their potential advantages compared to reactors that rely on solid fuel. In response to such interest, many methods and codes have been developed to capture the unique features of MSRs. Among them, the System Analysis Module (SAM) is a modern system analysis tool that provides fast-running, modest-fidelity, whole-plant transient analysis capabilities, essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. For liquid-fuel MSRs, the complex physics and chemistry involved in MSR operation—such as reactor kinetics, fluid flow, heat transfer, and salt composition dynamics—pose significant challenges for system-level modeling. Specific modeling capabilities are needed for system-level transient simulation. This paper presents recent advancements in SAM capability enhancements for system-level modeling of MSRs, focusing on improved simulation fidelity, computational efficiency, and multi-physics integration. Key enhancements include the development of species transport, Delayed Neutron Precursor (DNP) drift, modified Point Kinetics Equations (PKE), decay heat modeling, key fission product behavior, salt corrosion, and thermal-hydraulic coupling, as well as code robustness and performance enhancements for MSR applications. The code enhancement allows for better predictive accuracy in safety analysis, transient behavior, and operational optimization, thus supporting the design and licensing of next-generation MSRs. Results from case studies are presented to demonstrate the benefits of these enhancements in accurately capturing key reactor transient behaviors.

This work summarizes a feasibility study on testing numerical algorithms that are suitable and efficient for advanced system analysis code development under the mutli-physics framework, MOOSE. The key to the test bed is the implementation of the high-order, one-dimensional, staggered-grid (SG) finite volume method (FVM) and its direct interaction with the linear/nonlinear solver, PETSc. The test bed utilized a more flexible code structure to enable the FVM implementation and direct interaction with the solver package, instead of using the natively supported finite element method (FEM) by the framework.Using a suite of selected test problems with different problem sizes and levels of complexity, the implemented SG FVM demonstrated superior performance improvement against a direct FEM implementation through MOOSE. On two computer systems, the speedup was observed to be significant, with at least an order of magnitude solving time reduction. For a complex reactor model, transient simulation was performed using the newly developed FEM code, the results of which agreed very well with the reference results from the FVM code. Overall, this study demonstrated a successful feasibility study on the proposed numerical algorithms and software structure to support advanced system analysis tool development.

Liquid metals such as lithium and lead-lithium eutectics are leading candidates for use as breeder and coolant materials in fusion blankets, where they enable both tritium breeding and efficient heat removal. In the presence of strong magnetic fields, magnetohydrodynamic (MHD) effects significantly influence flow distribution, pressure drop, and heat transfer, posing major challenges for blanket design and performance assessment. While high-fidelity computational fluid dynamics (CFD) tools exist for MHD analysis, there remains a lack of modern system-level analysis codes that integrate MHD effects with thermal-hydraulic and systems modeling. This paper presents recent developments at Argonne National Laboratory to address this gap through the implementation of MHD modeling capabilities in the System Analysis Module (SAM), a modern system analysis code built on the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. A reduced-order MHD modeling approach applicable to high Hartmann number and high interaction parameter flows is adopted, enabling efficient system-level simulations relevant to fusion liquid metal blankets. In parallel, MHD capabilities are being implemented in the high-performance CFD code NekRS to provide high-fidelity simulations for verification and model development. Analytical verification, code-to-code comparisons, and validation against historical experimental data from the Argonne Liquid Metal Experiment (ALEX) facility are presented for both square and round duct configurations under applied magnetic fields. The results demonstrate good agreement between SAM and NekRS predictions with analytical solutions in uniform magnetic fields; good agreement between SAM predictions with legacy MHD codes, and experimental measurements in varying magnetic fields. Ongoing and future work includes extension to insulating duct configurations, further NekRS development, and application to conceptual fusion blanket designs and ITER test blanket modules.

A SAM system-level model of a generic stable salt reactor has been developed to investigate thermal-hydraulic behavior and safety performance under steady and transient conditions. The model integrates information generated from a reactor physics analysis using PROTEUS and PERSENT, and a computation fluid dynamics (CFD) analysis using STAR-CCM+. A loose, iterative coupling scheme between PROTEUS and SAM is implemented to calculate the equilibrium power and temperature distributions in the steady-state critical core condition. The converged steady-state model is then used in PERSENT to calculate the four reactivity feedback temperature coefficients (Doppler, fuel density, coolant density, and core radial expansion) and kinetic parameters that are needed in SAM to model the temperature feedback effects in transient simulations. Within the fully enclosed liquid fuel pins, natural convection is the dominant heat transfer mechanism. The STAR-CCM+ model of the fuel pin considers conjugate heat transfer from the liquid fuel salt to the pin cladding and external reactor coolant. The CFD results of the axial and radial temperature profiles are used to empirically determine an effective fuel salt thermal conductivity in the SAM fuel pin model so that the temperatures predicted by the SAM model match as closely as possible the CFD results. In the central region of the fuel pin, the effective thermal conductivity is as high as similar to 60 times the physical fuel salt thermal conductivity. The whole-plant SAM model is then used to simulate an unprotected station blackout transient. The results of this simulation showed that the large negative fuel axial expansion reactivity feedback reduces fission power to similar to 2.4% nominal power. The core is cooled by natural circulation, which removes heat in the core to the emergency heat removal system, and ultimately, to the ambient. However, peak fuel salt and cladding temperatures can potentially reach as high as 1500 K, albeit briefly, if the shutdown mechanism fails to operate.

The SAM code is under development as a modern system-level modeling and simulation tool for advanced non-light water reactor safety analyses, with recent efforts to add capabilities to evaluate radiological source term risks in these novel reactor concepts. By leveraging the established system-level multiphysics thermal-hydraulic models in SAM, a framework for tightly coupled species transport modeling has been integrated into the code for engineering-scale source term evaluation.This species transport framework was first applied to the simulation of tritium, which is a well-known source term in conventional light water reactors. Tritium poses a unique risk in salt-cooled reactors, especially those with lithium-bearing salts such as the fluoride salt-cooled high-temperature reactor (FHR) concept, as tritium is generated in the salt coolant in significant quantities due to neutron interactions. A compounding factor is the increased mobility of tritium at high temperatures, which is able to permeate through metals while also potentially being retained in graphite pebbles and structures.Engineering-scale models for the tritium transport pathways in a FHR have been developed using the new species transport framework in SAM. The capabilities are assessed through analytical verification problems and validated with data from a graphite retention experiment. The system-level model is demonstrated by performing an initial estimate of baseline tritium generation and flows in a generic reference SAM FHR model, setting a foundation for future studies of source term transient analysis with the potential for further multiscale and multiphysics integration.

With the increased interest in the design and deployment of advanced reactor systems, a desire for simulation tools supporting system analyses of reactor operation and safety is rising. Molten salt reactors (MSRs), one of the advanced reactor systems, utilize liquid-fused salt fuel as both coolant and fuel. During operation, MSRs generate insoluble fission products, including noble metals and gases. The buildup of these species in the fuel salt presents safety concerns, as they may deposit on surfaces of critical components and produce excessive decay heat, causing the failure of system components. The timely removal of these noble metals and gases would ensure the safe operation of the reactor system. The dynamic nature of salt fuel systems, involving the generation, decay, deposition, and extraction of noble metals and gases, calls for robust species transport models to facilitate system analysis and monitoring and the design of efficient species removal components. This paper concentrates on the development of a computational framework for species transport consisting of multiphase transport model formulation, mass transfer between phases, numerical implementation in the MOOSE environment, verification through the method of manufacture solutions, and validation against experimental data from the Molten Salt Reactor Experiment. Integrating this framework into the System Analysis Module (SAM) code further enhances SAM's capabilities for advanced reactor analysis in the future.

Deep neural networks (DNNs) are increasingly important to scientific computing and engineering system simulations. Accurate uncertainty quantification (UQ) for DNNs is critical in safety-sensitive engineering domains. Traditional Deep Ensemble (DE) methods, while easy to implement, frequently suffer from poorly calibrated uncertainty estimates and limited predictive accuracy due to reliance on fixed architectures with varied weight initializations. To address these issues, we introduce a workflow that combines Bayesian Optimization (BO) and DE. The workflow is modular, scalable, and integrates parallel BO initialized with Sobol sequences to individually optimize the hyperparameters of each ensemble member. This method enhances ensemble diversity, improves predictive accuracy, and provides reliable uncertainty estimates.We evaluate the proposed BODE approach in a sodium fast reactor thermal stratification modeling case study, where we used a densely connected convolutional neural network to predict turbulent viscosity during the reactor transient with consideration of data noise. We benchmark its performance against several optimization approaches, including baseline deep ensemble, evolutionary algorithm-optimized ensemble, ensemble formed via random search combined with greedy selection, and a BO ensemble using random initialization. Our results demonstrate superior performance of the developed BODE approach. In noise-free scenarios, BODE notably reduces incorrect aleatoric uncertainty and significantly enhances predictive accuracy. Under conditions of 5% and 10% Gaussian noise, BODE adaptively quantifies uncertainty proportional to data noise, achieving up to an 80% reduction in root mean square error compared to baseline methods and producing well-calibrated prediction intervals.