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Overview of graphite model development. Discuss graphite in motel salt, potential degradation mechanisms, stress due to volumetric heating, and the role of different parameters. Also wear modeling, modeling salt infiltration into graphite, oxidation modeling, and the existing graphite models.
Nuclear-grade graphites are extensively utilized in the core designs of various advanced nuclear reactors. Within the reactor environment, graphite is subjected to prolonged exposure to extreme conditions, including high temperatures, radiation, and potentially molten salt and oxygen. Such exposure can induce several degradation mechanisms in graphite, such as nonuniform volumetric strains caused by irradiation and thermal expansion, leading to stresses that may compromise the performance of graphite components. Assessing component integrity, forecasting component performance over the reactor's lifespan, and developing design standards necessitate robust tools for predicting fracture initiation and propagation in graphite structural components within nuclear reactors. This code enables the Bayesian calibration of properties for nuclear-grade graphites. Using a hierarchical Bayesian approach, multiple experimental data sources are combined to develop Gaussian process models for the properties. Using the Kennedy O'Hagan framework, the uncertainties due inadequacies in the model and the inherent spread in the experimental data are quantified.
Graphite under high temperatures and irradiation is central to advanced reactors. We develop a Bayesian calibration framework for graphite property models that explicitly represents model-data mismatch via a Gaussian-process discrepancy. The approach propagates uncertainty from parameters, experimental noise, and model form, with a hierarchical variance structure to capture group and cross-group noise. Using two predictive models across five grades (IG-110, NBG-18, PCEA, NBG-17, 2114) and four properties-irradiation-induced dimension change, creep, Young’s modulus change ratio, and coefficient of thermal expansion change ratio-we obtain average predictive-error reductions of 54%, 65%, 17%, and 17% when discrepancy is included. We illustrate engineering impact with a multiphysics model of a very-high-temperature reactor prismatic reflector brick, analyzing stresses under high fluence and temperature. Accounting for model discrepancy markedly improves predictive accuracy and provides a robust basis for reliable graphite component design in advanced reactors.
Nuclear-grade structural graphite is extensively utilized in the core designs of various advanced nuclear reactors. In the reactor environment, graphite is subjected to prolonged exposure to extreme conditions, including high temperatures, radiation, and potentially molten salt and oxygen. Such exposure can induce several degradation mechanisms in graphite, including nonuniform volumetric strains caused by irradiation and thermal expansion, leading to stresses that may compromise the performance of graphite components. Assessing component integrity requires accurate models of graphite's thermomechanical response. This report documents the Bayesian calibration of thermomechanical properties for nuclear-grade graphite and their application to graphite component modeling and simulation using the Grizzly code. As part of this work, uncertainty-quantified models were developed for the elastic modulus, coefficient of thermal expansion, irradiation-induced dimensional change, and irradiation-induced creep for graphite grades IG-110, NBG-18, NBG-17, PCEA, and 2114. Using a hierarchical Bayesian approach, multiple experimental data sources were combined to develop Gaussian process models for the properties. Using the Kennedy O'Hagan framework, the uncertainties due to inadequacies in the model and the inherent spread in the experimental data were quantified for three different models. These uncertainty-quantified models, with a model-form correction, were subsequently applied to a coupled-physics simulation of representative graphite components, revealing that the uncertainties have a large impact on the components' deformation.
Molten-salt reactors (MSRs) represent a promising next-generation reactor design, with graphite serving as a moderator and/or reflector in several designs. However, due to limited experimental data and operational experience, a technical understanding of the structural integrity of graphite in molten salt environments remains incomplete. This report presents a modeling-based evaluation of graphite degradation in MSR environments, focusing on the effects of salt infiltration in fuel salt-based designs and surface wear in pebble bed reactor designs. The objective of this study is to enhance understanding of the structural integrity challenges posed by these degradation mechanisms and to provide a framework for assessing graphite behavior in MSRs. The first part of the report investigates the phenomenon of molten salt infiltration into graphite. This infiltration occurs when molten salt permeates the interconnected pore structure of the graphite moderator, driven by factors such as pressure differentials and the physical properties of both the salt and graphite. The infiltration process is influenced by characteristics of the pore structure, viscosity of the molten salt, and the interfacial energies between the graphite, salt, and the atmosphere within the graphite pore. Utilizing a coupled multiphysics modeling approach with Grizzly software, the study evaluates the stress induced by internal heat sources due to infiltration, which can lead to structural concerns. This evaluation is crucial for understanding how infiltration affects the mechanical integrity of graphite components in MSRs. The study considers the Molten-Salt Reactor Experiment (MSRE) graphite stringer geometry due to the availability of relevant data. Through detailed finite element analysis, the study examines stress distributions at varying infiltration percentages, revealing that stress levels increase with higher amounts of infiltration. Rare-event simulations, using the parallel subset simulation (PSS) framework, further quantify the failure probabilities under input uncertainties, with a user-specified failure metric. The PSS framework also identifies critical input parameters that significantly affect the stress values, including infiltration amount, thermal conductivity, and power density. Additionally, considering realistic reactor scenarios, the analysis was performed to account for the combined effects of radiation and infiltration, and modeling strategies on how to analyze new reactor designs or new graphite grades are discussed. The second part of the report focuses on wear mechanisms in pebble bed-based MSRs. As graphite fuel pebbles interact with the graphite reflector block, wear can result in material loss and the formation of surface defects, which may act as stress concentrators. A similar multiphysics modeling framework is employed to assess the impact of wear on the structural integrity of graphite components. This study considers a generic fluoride-cooled high-temperature reactor (gFHR) design due to the availability of comprehensive data. Worst-case scenario dimensions of the reflector blocks were analyzed under thermal and radiation conditions. Subsequently, wear in the form of idealized pits and grooves is modeled on the inner surface of the graphite block, with the maximum stress from previous simulations. The simulations show that groove-type defects are more detrimental than pits, leading to higher stress concentrations. Considering worst-case simulation scenarios and experimental wear rates, it was determined that the formation of a surface defect critical enough to affect the stress may not be possible in a gFHR design. Overall, the findings of this research contribute to the development of robust modeling tools for predicting graphite behavior under various operational conditions in MSRs.
Molten salt reactors (MSRs) often employ graphite as a moderator and reflector. An important challenge for deploying graphite in these reactors is that, due to limited experimental data, our understanding of graphite’s structural integrity in molten salt environments remains incomplete. Here, this study addresses heat generation from fuel-bearing salt that has infiltrated open pores in the graphite, driven primarily by pressure differentials. This is one of multiple identified physical and chemical mechanisms through which molten salt could potentially degrade graphite. Thermally driven stresses are quantified using the Molten-Salt Reactor Experiment (MSRE) graphite moderator elements as a case study. Finite element simulations predict stress distributions at varying infiltration levels, indicating that thermal stresses increase with higher infiltration. Rare-event simulations using the parallel subset simulation framework identify the combinations and corresponding ranges of input parameters that lead to stresses above a specified threshold. In particular, combinations involving high infiltration amounts, high power density, and low thermal conductivity tend to induce the highest stresses. Under the inputs and assumptions considered in this work, the magnitudes of the thermally driven stresses are quite low, with a very low likelihood of causing failure due to exceeding the graphite’s tensile strength. Additionally, rare-event simulations were performed for two more scenarios: a scaled-up moderator geometry and a localized hotspot in the original geometry. Both cases resulted in increased susceptibility to failure, though not to a detrimental extent. Furthermore, the combined effects of irradiation and infiltration-induced thermal stresses were evaluated. The results showed that thermal stresses from infiltration were negligible compared to those caused by irradiation. The findings of such a study are inherently component-specific, but the methodology presented here could be used for similar assessments of salt-infiltration effects in other graphite components.
The NEAMS Multiphysics Applications team continues to assess code usability and functionality for microreactor design and safety analyses, while demonstrating that NEAMS tools capture both steady-state and transient behavior across distinct microreactor concepts. In FY2025, the team advanced full-core, high-fidelity, multiphysics models that solve more complex problems and strengthen verification/validation for several microreactor systems: heat-pipe microreactor (HPMR), gas-cooled microreactor (GCMR), and the KRUSTY experiment. These models employ the MOOSE MultiApp/Transfers architecture with Griffin for neutronics, BISON for heat conduction/thermomechanics, Sockeye for heat pipes, SAM/THM for coolant channels and loops, and SWIFT for hydride behavior, with meshes generated via the MOOSE Reactor Module. The graphite models available in the Grizzly code were also investigated for future analyses. For the HPMR, a Na-HPMR variant was constructed to align with recently validated heat-pipe experiments and Sockeye’s LCVF capability, enabling mechanistic heat-pipe transients and startup modeling. The Na-HPMR will serve as the primary model for HPMR investigations in upcoming tasks. The load-following and single heat-pipe failure scenarios (Griffin/BISON/Sockeye), which were previously modeled for the K-HPMR, were replicated for the Na-HPMR, showing strong negative temperature feedback and highly localized thermal effects, respectively, while the startup case captured vapor-front progression and heat-removal activation. Solid mechanics was added to the previously built K-HPMR full-core model in BISON, showing minimal impact on steady-state reactivity yet enabling stress-field predictions that prepare the path for full-core TRISO performance analyses. For the GCMR, automated steady-state and four transient scenarios were executed using Griffin/BISON/SAM/SWIFT. Results confirm robust inherent safety: power collapses promptly in loss-of-cooling events, the inlet-temperature drop settles to a new equilibrium, and a single-channel blockage yields only a ~30 K local fuel-temperature rise with <0.4% power decrease. SWIFT-predicted hydrogen redistribution affects reactivity during both steady-state and transient conditions, underscoring its importance. A Brayton-cycle balance of plant (BOP) model in SAM/THM demonstrated stable startup behavior, and xenon-driven reactivity during load following was analyzed. To improve TRISO-compact temperature fidelity, a fast multiscale Heat Source Decomposition (HSD) treatment was implemented. Against heterogeneous benchmarks, HSD reduces underprediction of kernel temperatures and lowers predicted peak powers in reactivity-insertion transients compared to previous homogenized models. KRUSTY warm-critical validation progressed from FY2024 baselines: the 15Ȼ insertion shows excellent agreement in peak power (~2% high) and temperature trends, and the 30Ȼ case was automated via a feedback controller that maintained power near 3 kW for ~150 s with close agreement to data. The successful modeling of the warm critical tests has laid a strong foundation for simulating more complex nuclear system tests in the years ahead. Throughout FY2025, developer feedback was provided (e.g., MOOSE batch mesh generation, distributed pre-split meshes, Griffin sweeper on displaced meshes), several new models were contributed to the Virtual Test Bed, and an OECD-NEA WPRS multiphysics benchmark based on the HPMR was initiated to enable broader cross-comparison and best-practice development with the nuclear community at large.
Introduction of ART Graphite R&D to include oxidation activities, oxidation resistant graphite, model development, ASME component failure, ASME code development (design rules), ceramic composites, AGC update, molten salt intrusion, split-disk studies, wear testing, and concluding remarks.
The importance of graphite-hydrogen chemical reactions to fusion, fission, and hydrogen storage applications, combined with the rapidly evolving knowledge on the underlying mechanisms, has led to the development of multiple models to describe hydrogen transport in graphite. Significant differences exist among these models, resulting from discrepancies in the modeling assumptions, intended degree of fidelity, and conditions of applicability. This paper attempts at reconciling these apparent differences by providing a comprehensive description of the constitutive equations governing hydrogen transport in graphite at high-temperature, identifying outstanding gaps in knowledge, illustrating how these different models approach them, and proposing alternative analytical formulations grounded on experimental results from hydrogen-graphite studies. Governing equations, closing relations, and simplifying assumptions are discussed for hydrogen transport at the inter-granular and intra-granular level, accompanied by compiled experimental data and illustrated energy diagrams associated to the proposed transport mechanisms. Analytical formulations are provided to reproduce competing hypotheses on the mechanisms, supporting the development of a range of computational models that can enable resolution of outstanding knowledge gaps through comparative testing against experimental data.
The SAM code is under development and supported by DOE-NE’s Nuclear Energy Advanced Modeling and Simulation program as a modern system-level modeling and simulation tool for advanced non-light water reactor safety analyses. These advanced reactor concepts incorporate novel and improved approaches to achieve safety and economic feasibility. This report summarizes recent efforts and progress in addressing the code capability gaps in SAM for the modeling of the air-ingress phenomenon in High-Temperature Gas-Cooled Reactors (HTGRs). The capability enhancements implemented to the code include: a multi-component flow model to capture the air-helium mixture during air ingress, a 0-D graphite oxidation model to capture the reaction of graphite with oxygen in the air, and an isentropic critical flow model to more accurately predict the de-pressurization of the reactor system due to a small break in the primary loop. Verification cases and demonstrations are provided to showcase these capabilities in SAM. Existing gaps in the code’s capability are also identified.
The thermo-mechanical response of an ATJ graphite sample to controlled runaway electron (RE) dissipation, realized in DIII-D, is modelled with a novel work-flow that features the RE orbit code KORC, the Monte Carlo particle transport code Geant4 and the finite element multiphysics software COMSOL. KORC provides the RE striking positions and momenta, Geant4 calculates the volumetric energy deposition and COMSOL simulates the thermoelastic response. Brittle failure is predicted according to the maximum normal stress criterion, which is suitable for ATJ graphite owing to its linear elastic behavior up to fracture and its isotropic mechanical properties. Measurements of the conducted energy, damage topology, explosion timing and blown-off material volume, impose a number of empirical constraints that suffice to distinguish between different RE impact scenarios and to identify RE parameters which provide the best match to the observations.
Flat bands and nontrivial topological physics are two important topics of condensed matter physics. With a unique stacking configuration analogous to the Su–Schrieffer–Heeger model, rhombohedral graphite (RG) is a potential candidate for realizing both flat bands and nontrivial topological physics. Here, in this study, we report experimental evidence of topological flat bands (TFBs) on the surface of bulk RG, which are topologically protected by bulk helical Dirac nodal lines via the bulk-boundary correspondence. Moreover, upon in situ electron doping, the surface TFBs show a splitting with exotic doping evolution, with an order-of-magnitude increase in the bandwidth of the lower split band, and pinning of the upper band near the Fermi level. These experimental observations together with Hartree–Fock calculations suggest that correlation effects are important in this system. Our results demonstrate RG as a platform for investigating the rich interplay between nontrivial band topology, correlation effects, and interaction-driven symmetry-broken states.
Immobilized cobalt phthalocyanine (CoPc) is a highly promising architecture for the six-proton, six-electron reduction of CO 2 to methanol. This electroreduction process relies on proton-coupled electron transfer (PCET) reactions that can occur by sequential or concerted mechanisms. Immobilization on a conductive support such as carbon nanotubes or graphitic flakes can fundamentally alter the PCET mechanisms. We use density functional theory (DFT) calculations of CoPc adsorbed on an explicit graphitic surface model to investigate intermediates in the electroreduction of CO 2 to methanol. Our calculations show that the alignment of the CoPc and graphitic electronic states influences the reductive chemistry. These calculations also distinguish between charging the graphitic surface and reducing the CoPc and adsorbed intermediates as electrons are added to the system. This analysis allows us to identify the chemical transformations that are likely to be concerted PCET, defined for these systems as the mechanism in which protonation of a CO 2 reduction intermediate is accompanied by electron abstraction from the graphitic surface to the adsorbate without thermodynamically stable intermediates. Furthermore, this work establishes a mechanistic pathway for methanol production that is consistent with experimental observations and provides fundamental insight into how immobilization of the CoPc impacts its CO 2 reduction chemistry.
This presentation covers motivations and DNCSH, individual particle measurements, infinite lattice study, application study, and conclusions.
Pebble-Bed High-Temperature Gas-cooled Reactors (PB-HTGR) are moderated by the graphite in the fuel pebbles and the graphite reflector surrounding the pebble-bed. Because graphite is by far the most abundant material in PB-HTGRs and the primary moderator, accurate modeling of the graphite material, including density, impurities, and temperatures, is crucial for accurate computational modeling and simulation of these reactors. While main characteristics of the graphite components are often known, the local temperature is less well known and often averaged over all components. Here, this work studies the impact of considering accurate temperature profiles in the graphite material on the generation of a small PB-HTGR model at the state of equilibrium operation and on short-term accident progression. The fuel compositions for the PB-HTGR were determined using a jump-in equilibrium modeling method, the Axial Radial Zone Equilibrium Modeling (AR-ZEM) method. In contrast to previous work, the AR-ZEM method was used considering thermal-hydraulic feedback from the MELCOR code to determine temperatures of the fuel pebbles and the surrounding graphite reflector. The consideration of an axial and radial temperature profile in the core and reflector, as opposed to uniform material temperatures, had an impact of almost 1,300 pcm on the equilibrium core eigenvalue and caused significant differences in the discharged plutonium fuel inventory with up to 4.9% and 11.0% for Pu-239 and Pu-242, respectively. To assess the impact on short-term accident progression, two Anticipated Transient Without SCRAM (ATWS) events, a Pressurized Loss of Forced Coolant (PLOFC) and a Control Rod Withdrawal (CRW) with loss of flow, were simulated with MELCOR. The use of temperature profiles in the equilibrium core models did not reveal a significant impact on the temperature, power, or reactivity responses during the transients. In conclusion, a need for consideration of accurate temperature profiles, in particular for the graphite reflector, was found for the generation of equilibrium PB-HTGRs core models using jump-in methods, but detailed temperature profiles may not be necessary when performing conservative transient analysis.
Graphite is utilized as a moderator and reflector in advanced nuclear reactor designs due to its high thermal conductivity, neutron moderation properties, and resistance to radiation damage. However, its longterm performance and reliability are challenged by degradation mechanisms such as molten salt infiltration in molten salt reactors (MSRs) and oxidation in gas-cooled reactors (GCRs). These mechanisms can compromise the structural integrity and operational lifetime of graphite components, necessitating a more detailed assessment of their physical behavior. This report focuses on the development of computational models for molten salt infiltration and oxidation of graphite to aid the design and performance analysis of graphite components. For molten salt infiltration, a computational framework is developed that couples incompressible Navier-Stokes and phase-field model to simulate the penetration of molten salt into graphite?s interconnected pore structure. Initial model verification is performed using two-phase flows in two dimensions, demonstrating the models ability to capture fundamental physical behavior and agree with analytical solution. This framework is then applied to a realistic IG110 nuclear graphite , where a computed tomography extracted pore geometry is used to analyse the infiltration behavior of FLiNaK molten salt. This model provides insights into how the microstructure and other relevant parameters influence the transport pathways of molten salt into graphite, potentially offering a means to rapidly evaluate a graphite grade?s resistance to infiltration. For oxidation, the report details pore-scale mass and heat transport models, describing the diffusion of gases, reaction kinetics, and thermal effects. Additionally, this report highlights inconsistencies in the existing volume-averaged macroscopic model, particularly in upscaling of reaction kinetics and flux terms, and surface to volume transformations. These inconsistencies suggest that current formulations may not accurately capture the experimentally observed graphite oxidation process, highlighting the need for improved model development. This work advances the development of physics-based computational models for graphite degradation, contributing to improved predictive models for next-generation nuclear reactor designs. Future efforts will focus on refining the infiltration model to address non-physical behaviors and enhance its robustness. Additionally, for oxidation, further studies will employ the principles of volume averaging to rigorously derive the upscaled equations, potentially in collaboration with subject matter experts.
Idaho National Labs serves as the spearhead for many innovative energy solutions to the world's energy crisis. One such solution is the INL's Microreactor which is designed to deploy to extreme/remote environments where other sources of power are either unavailable or unreliable. In order to best design these energy solutions for their operational environments, it is crucial to understand how the design, components, and materials will respond to the environmental conditions. One key material in these innovative designs is a nuclear-grade graphite known as PCEA. This study examines the behavior of PCEA graphite under dynamic loading, similar to that which may occur in extreme environments. The objective is to characterize the dynamic behavior and produce an accurate, reliable constitutive model suitable for use in simulation tools such as INL's MOOSE. Graphite specimens were tested using a Split Hopkinson Pressure Bar (SHPB) to administer the dynamic compressive load. The SHPB was charged at various pressures to produce a range of strain rates on the material in compression. Data was acquired via strain gauges on the SHPB setup, from which stress, strain, and time data were collected. Analysis revealed the stress-strain behavior of the material as well as insights into the material behavior's relationship to strain rate. Further work must continue to characterize the various other dynamic behaviors of the material which will combine to create a substantially trustworthy constitutive model for this grade of nuclear-grade graphite. Ultimately, this will allow for realistic simulation of the material in reactor designs, allowing for prediction of design weaknesses and leading to improved designs for increased resilience, security, and reliability.
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