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For code development, Advanced Reactor Technologies - Gas Cooled Reactors Program (ART-GCR) rely on a collaboration with the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, but the cross sections generation and the methodology definition is part of this program area goals. Based on previous studies in FY23, the size of microscopic cross section libraries increases rapidly with the number of tabulations, requiring significant amount of memory and drastically slowing down the Griffin calculations when evaluating cross sections via the multivariate linear interpolation approach. Rising to these challenges, this work investigates constructing Reduced-order Models (ROMs) for the multi-group microscopic cross sections to accelerate the cross section evaluation in Griffin. A database of multigroup cross sections is first collected considering all possible parameters that a designer could change for optimization. Down-selection of the ROM techniques afterward shows Deep Neural Network (DNN) as the best candidate when jointly consider memory efficiency, predictive accuracy, computational cost, scalability, flexibility and ease of implementation of the algorithms in comparison to the multidimensional interpolation. This work develops a specific interface that enables the cross section predictions using pre-trained DNN models into Griffin leveraging the existing ROM capabilities. DNNs have been trained for all isotopes for use in Griffin. Preliminary Griffin testing shows that DNNs exhibit exceptional predictive accuracy and the use of DNNs provides orders of magnitude improvement in memory efficiency compared to conventional interpolation techniques. With such ROM techniques, it holds great promise to further increase the fidelity of the Pebble Bed Reactor (PBR) simulation by increasing the number of tabulations/state variables during cross section evaluation, while maintaining the computational cost affordable in Griffin.

High Temperature Gas Reactor (HTGR) designs incorporate passive safety systems (e.g., the Reactor Cavity Cooling System [RCCS]) that utilize natural principles to manage heat dissipation from the reactor pressure vessel (RPV) during accidents or routine shutdowns. The industry community is experiencing a pressing need for advanced simulation tools that can accurately assess the performance of these types of systems. In the literature, a knowledge gap exists concerning high-fidelity data for the RCCS, and this gap is one of the areas of focus of the present study. This research focuses on a specific RCCS designed for General Atomics' Modular High-Temperature Gas Reactor (GA-MHTGR). Experimental studies on a scaled version (can be seen in Figure 1) of the air-cooled RCCS used in GA-MHTGR were conducted by the University of Wisconsin-Madison (UW-Madison). This work contributes to a broader initiative aimed at establishing a numerical benchmark based on the UW-Madison experiments.

Nuclear energy is increasingly acknowledged as pivotal in the global shift towards cleaner energy solutions. Advanced nuclear technologies, including High Temperature Gas-cooled Reactors (HTGRs), stand out as appealing options among Generation IV reactors due to their high temperature heat output and potential for cogeneration. HTGR designs incorporate passive safety systems, such as the Reactor Cavity Cooling System (RCCS), which utilize natural principles to manage heat dissipation from the reactor pressure vessel (RPV) during accidents or routine shutdowns. Regulatory bodies require thorough validation of safety systems like the RCCS to ensure they meet specified standards. Consequently, there is a pressing need within the industry for advanced simulation tools capable of assessing these systems’ performance accurately. There is a knowladge gap in the literature concerning high-fidelity data for the RCCS, which motivates the focus of this study. This research focuses on a specific RCCS designed for the Modular High-Temperature Gas Reactor developed by General Atomics (GA- MHTGR). Experimental studies on a scaled version of the air-cooled RCCS of GA-MHTGR were conducted by the University of Wisconsin-Madison. This work contributes to a broader initiative aimed at establishing a numerical benchmark based on the UW-Madison experiments. As first step we performed high fidelity simulations of the experimental facility setup, to analyze flow physics in such systems and validate NekRS and the MOOSE heat transfer and radiation modules.

This study presents a comprehensive benchmarking and verification effort of several thermal-hydraulic and multiphysics capabilities for high-temperature gas-cooled reactor (HTGR) applications. The first part of this effort focuses on the running-in verification of Griffin's multiphysics capabilities, specifically for simulating the evolution of Pebble Bed reactor cores from startup to equilibrium. In the absence of validation data, code-to-code comparisons are conducted with Kugelpy, showing good agreement for key quantities like maximum power density and fresh core k-eigenvalue predictions. However, discrepancies in equilibrium core predictions suggest potential issues with cross sections, underscoring the need for further refinement and evaluation. The HTTF system analysis code benchmark involves RELAP5-3D, SAM, and GAMMA+ to assess their predictive capabilities for HTTF behavior under both normal operation and pressurized conduction cooldown (PCC) transient conditions. While there is good agreement in predicting major parameters such as coolant temperature, solid temperature, and flow distribution, discrepancies in transient behavior highlight differences in modeling approaches, nodalizations, and heat transfer models. The HTTF lower plenum CFD benchmark employs nekRS to simulate flow mixing phenomena, successfully capturing relevant flow physics and demonstrating mesh independence in complex geometries. Preliminary results suggest a relatively uniform temperature field but significant unsteadiness in the flow, requiring time-averaging analyses. The GPBR200 system analysis code benchmark uses SAM's core channel and porous media models, incorporating an RCCS loop for decay heat removal. During steady-state and transient conditions, including protected de-pressurized and pressurized loss of forced cooling (DLOFC and PLOFC), both models show good agreement in predicting temperature profiles and key parameters. Notably, while the core channel model underpredicts convective heat transfer effects, both models maintain temperatures well below the TRISO fuel safety limit. These benchmarking efforts collectively enhance the predictive capabilities of the tools used in HTGR design and safety analysis, guiding developments to improve their accuracy and applicability.

Pebble-bed reactors are an important class of advanced reactors under consideration for various applications where their fuel would give a significant advantage in siting and high-quality heat production. However, the disposal of their fuel is not as thoroughly studied as other fuel forms. In this study, pebble fuel is analysed in a well known spent fuel canister design to characterize the behavior of this fuel form over a long time scale. The results indicate that after approximately 100 years, decay heat is significantly reduced and the maximum temperature in the canister equalizes with the external temperature. The simulation goes on to an end time of a million years, demonstrating the capability of dealing with long time scales efficiently. We conclude that the canister temperatures seem manageable even with very aggressive loading times and while there are several improvements to be implemented in the future, MOOSE is technically capable of simulating the required scenarios.

Griffin, a MOOSE (Multiphysics Object-Oriented Simulation Environment) based application targeting transient modelling of advanced reactors, has been used recently to model pebble-bed reactors (PBRs). The modelling effort has focused thus far on modelling the equilibrium core. A new capability to simulate the running-in phase of PBR operation has been added to Griffin. This work demonstrates the newcapability with a sample multiphysics running-in simulation. The basic features of the new running-in capability were documented previously; however, the sample simulation results presented there did not include multiphysics; the fuel temperatures were assumed to be constant. In this work, Griffin computes power densities in the core at each timestep of the running-in simulation and passes these to Pronghorn which models fluid flow and heat transfer to calculate temperatures that are passed back to Griffin and accounted for with temperature dependent cross-sections.

Pebble-bed reactors are an important class of advanced reactors under consideration for various applications where their fuel would give a significant advantage in siting and high-quality heat production. However, the disposal of their fuel is not as thoroughly studied as other fuel forms. This article provides an example of evaluating advanced reactor spent nuclear fuel in MOOSE. In this study, pebble fuel is analyzed in a well-known spent fuel canister design to characterize the behavior of this fuel form over a long time scale. The results indicate that after approximately 100 years, decay heat is significantly reduced and the maximum temperature in the canister equalizes with the external temperature. The simulation goes on to an end time of one million years, demonstrating the capability of efficiently dealing with long time scales efficiently. We conclude that the canister temperatures seem manageable even with very aggressive loading times and while there are several improvements to be implemented in the future, MOOSE is currently capable of simulating the required scenarios.

Modeling the run-in of a pebble-bed reactor (PBR) can be challenging as a result of changes in the power, fuel type, and temperatures that occur throughout the run-in period. Previous work utilized high-fidelity neutronics simulations or lower-fidelity coupled neutronics/thermal-hydraulics models to capture the general characteristics of the run-in process. Here, the present work employs high-fidelity neutronics simulations (using Serpent) coupled with thermal-hydraulics simulations (using Griffin–Pronghorn) to capture the thermal feedback present during the run-in and approach to equilibrium for a PBR. Incorporating thermal feedback enables important distinctions to be made about conditions occurring inside the core, as the power distribution, discharge burnup, and isotopic compositions are all affected by the temperature distribution.

This research provides a valuable tool that streamlines the optimization process while significantly increasing its accuracy. This study creates a robust framework for reactor design optimization by incorporating comprehensive modeling using the Comprehensive Reactor Analysis Bundle, or BlueCRAB, within the Multiphysics Object-Oriented Simulation Environment (MOOSE). BlueCRAB is the United States Nuclear Regulatory Commission's code suite for non-light water reactor analysis and includes the Griffin, Pronghorn, and Bison applications. This not only improves the efficiency of the optimization process but also enhances the reliability of the results. Such a tool is essential for advancing the state-of-the-art in pebble-bed reactor technology and is critical for achieving the goals of Generation IV reactors, which aim for safe, sustainable, and economically viable nuclear energy solutions. This work presents and applies this workflow on pebble-bed reactors while considering both normal and off-normal conditions. A representative gas-cooled pebble-bed reactor at equilibrium core conditions serves as the nominal design specification for normal operation and is based on previous research. The depressurized loss-of-forced-cooling accident is deployed for off-normal conditions in this work. After defining design-related parameters and quantities of interest regarding reactor safety and performance, this multiphysics model is sampled using the MOOSE stochastic tools module. The result is a comprehensive dataset of configurations, enabling sensitivity analysis and the generation of surrogate models. Subsequently, the dataset and surrogate models are employed in two optimization studies aimed at maximizing fuel utilization and economic profit while adhering to safety and operational constraints. Performing the optimization process with fuel utilization as the metric leads to an improvement of approximately 10%, compared to engineering-judgment-based nominal conditions. The optimization on economic profit leads to an estimated increase of ~300 million USD over the lifetime of the reactor.

While typical validation and verification approaches focus on identifying the associations between data elements using statistical and machine learning methods, the novel methods in this paper focus instead on identifying causal relationships between data elements. Statistical and machine-learning-based approaches are strictly data-driven, meaning that they provide quantitative comparison measures between data sets without explicitly considering the hypotheses behind them. This can lead to the erroneous conclusion that, if two data sets are close enough, the models that generated them are similar. In addition, when experimental and simulated data differ to an extent that fails to meet the acceptance criteria, calibration techniques are used to tweak simulation model parameters to reduce the gap between the two types of data. This produces the false expectation that a simulation model will match reality. The methods presented in this paper move away from these strictly data-driven methods for validation and calibration toward more robust, model-driven methods based on causal inference. Causal inference aims to identify the possible mechanisms that might have generated data. Thus, this analysis targets the prediction of the effects when one (or more) of the identified mechanisms are altered. There are many approaches to identify, quantify, and illustrate causal relationships. For the scope of this paper, directed graphs are employed as causal models. If the directed graph lacks cycles, it is known as a directed acyclic graph. A node in such a graph represents an observed data element while a directed edge connecting two nodes represents a causal relationship between two variables. The developed causal methods are designed to extract causal models from simulation models and experimental data. Causal models capture the causal relationships between data elements (e.g., simulated and experimental data). In this context, validation and verification are performed by comparing causal models. The proposed approach does not only inform system analysts on how a simulation model matches real-world data, but also identifies elements of the simulation model that should be revised when discrepancies between simulation and experimental data are observed. Through these causal methods, analysts can identify the portion of the model equation(s) that are behind an edge connecting two variables. Hence, once the structural differences between causal models have been determined, model calibration can occur by changing only those model parameters that impact the identified causal relationships.