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Temperature sensitivity of the equilibrium neutronics and accident analysis of the HTR-10

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.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS

Computational Modeling of Molten Salt Infiltration and Oxidation in Nuclear Graphite

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.

Computational Modeling of Molten Salt Infiltration

Dynamic Modeling and Characterization of Nuclear-grade Graphite

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.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Modeling and Testing of the Viscoelastic Properties of a Graphite Nanoplatelet/Epoxy Composite

In order to facilitate the interpretation of experimental data, a micromechanical modeling procedure is developed to predict the viscoelastic properties of a graphite nanoplatelet/epoxy composite as a function of volume fraction and nanoplatelet diameter. The predicted storage and loss moduli for the composite are compared to measured values from the same material using three test methods; Dynamical Mechanical Analysis, nanoindentation, and quasi-static tensile tests. In most cases, the model and experiments indicate that for increasing volume fractions of nanoplatelets, both the storage and loss moduli increase. Also, the results indicate that for nanoplatelet sizes above 15 microns, nanoindentation is capable of measuring properties of individual constituents of a composite system. Comparison of the predicted values to the measured data helps illustrate the relative similarities and differences between the bulk and local measurement techniques.

Odegard, Gregory M.

Comparative Analysis via CFD Simulation on the Impact of Graphite Anode Morphologies on the Discharge of a Lithium-Ion Battery

The morphology of electrode materials plays a crucial role in determining the performance of lithium-ion batteries. Traditional computational models often simplify graphite flakes as uniformly sized spheres, which limits their predictive accuracy. In this study, we present a computational workflow that overcomes these limitations by incorporating a more realistic representation of graphite morphologies. This workflow is designed to be flexible and reproducible, enabling efficient evaluation of electrochemical performance across diverse material structures. By exploring different graphite morphologies, our approach accelerates the optimization of material preparation techniques and processing conditions. Our findings reveal that incorporating greater morphological complexity leads to significant deviations from classical model predictions. Instead, our refined model offers a more accurate representation of battery discharge behavior, closely aligning with experimental data. This improvement underscores the importance of detailed morphological descriptions in advancing battery design and performance assessments. To promote accessibility and reproducibility, we provide the developed code for seamless integration with the COMSOL API, allowing researchers to implement and adapt it easily. This computational framework serves as a valuable tool for investigating the impact of graphite morphology on battery performance, bridging the gap between theoretical modeling and experimental validation to enhance lithium-ion battery technology.

25 ENERGY STORAGE

Quantifying the Temperature Dependence of the Multi-Species, Multi-Reaction Model. Part 1: Parameterization for a Meso-Carbon Micro-Bead Graphite

In this work, the temperature impact on the Multi-Species, Multi-Reaction (MSMR) model is studied. This is accomplished by acquiring data from slow rate lithiation and delithiation of a meso-carbon micro-bead (MCMB) graphite. The MSMR model is used to simulate linear-sweep voltammetry data of a porous electrode composed of graphite, and because the electrode is close to a state of dynamic equilibrium, the peaks in the differential voltage spectroscopy plot can be analyzed. Through this analysis, the temperature impact on the total fraction of available host sites in a particular MSMR gallery (X j ), the impact on the reference potential (U° j ), and the impact on the parameter detailing the deviation from Nernstian behavior ( ω j ) can be found. This is the first time the temperature dependence of the MSMR parameters have been experimentally analyzed. In Part 2, the impact of the temperature dependence of the MSMR parameters on the entropy coefficient of an intercalation material will be studied.

Paul, Abigail (ORCID:0000000172892069)

16-38 micron spectroscopy of NGC 7027

Medium-resolution spectroscopy of the planetary nebula NGC 7027 over the wavelength range from 16 to 38 microns is reported which was performed from NASA's Kuiper Airborne Observatory. It is found that within the errors, the spectrum is smooth and has the shape of a dilute 130-K blackbody but falls below that curve at the longer wavelengths. The absence of two theoretically predicted features in the 16-40-micron band, a forbidden fine-structure line of O IV at 25.91 microns and a broad emission feature in the 22-35-micron region due to carbonate materials, is discussed; a lower limit of 25,000 per cu cm is placed on the electron density in the ionized region. A simple model involving small graphite grains at a temperature around 90 K is proposed to explain the observed featureless continuum. This model is shown to require a dust mass of about 0.025 solar mass and a gas mass of approximately 1 solar mass, which imply that most of this mass would be associated with the molecular cloud surrounding the ionized region.

Mccarthy, J. F.

When and Where Lithium Plating Occurs, Its Correlation with Microstructure Heterogeneity, and the Mechanisms That Initiate and Self-Regulate Electrochemical Heterogeneity (A02-0444)

A microstructure scale electrochemical LIB model was used to investigate lithium plating onset, material non-uniform utilization, and in-plane heterogeneities for an NMC-graphite full cell. Model predicts active material particle surface roughness and size distribution (respectively, non-uniform curvature within and between particles) initiate in-plane heterogeneity, and that particle size heterogeneity at the separator interface controls the lithium plating preferential deposition ("Where"). These in-plane heterogeneities are then exacerbated by through-plane heterogeneities induced at fast charge as electrolyte depletion occurs and concentrates intercalation reaction near the anode-separator interface. Also, magnitude and occurrence of lithium plating is controlled by effective, or macroscale, microstructure parameters ("When"). As local states of charge start to diverge between nearby active material regions, overpotential differences induced by OCP difference kick in and contribute to reduce these SOC local heterogeneities. However, for staged materials such as graphite, with OCP profile alternating between plateaus and varying regions, this balancing mechanism is, respectively, inactive and active. This leads to a dynamic, non-monotonic, in-plane heterogeneity time evolution for state of charge and Faraday current density, for which their respective in-plane heterogeneity magnitude alternates. Such behavior has been modeled both for the whole electrode at the microstructure scale and at the particle scale. In-plane heterogeneities are usually considered to be detrimental, as they result in material non-uniform utilization (i.e., under and over stressed regions) and earlier degradations. However, this work provides a more granular approach as it discriminates between a harmful in-plane heterogeneity (non-uniform curvature) that triggers SOC in-plane heterogeneity, and a beneficial in-plane heterogeneity (Faraday current density) that contributes to reduce SOC in-plane heterogeneity. This work comprehensively explains the mechanisms that initiate, exacerbate, and regulate heterogeneity at the microstructure scale, while providing some design suggestions to reduce both in-plane and through-plane heterogeneities, as summarized in the graphical abstract.

ADVANCED PROPULSION SYSTEMS

Understanding the Reaction of Nuclear Graphite with Molecular Oxygen

A thorough understanding of oxidation is important when considering the health and integrity of graphite components in graphite reactors. For the next generation of graphite reactors, HTGRs specifically, an unlikely air ingress has been deemed significant enough to have made its way into the licensing applications of many international licensing bodies. While a substantial body of literature exists on nuclear graphite oxidation in the presence of molecular oxygen and significant efforts have been made to characterize oxidation kinetics of various grades, the value of existing information is somewhat limited. Often, multiple competing processes, including reaction kinetics, mass transfer, and microstructural evolution, are lumped together into a single rate expression that limits the ability to translate this information to different conditions. This article reviews the reaction of graphite with molecular oxygen in terms of the reaction kinetics, gas transport, and microstructural evolution of graphite. It also presents the foundations of a model for the graphite-molecular oxygen reaction system that is kinetically independent of graphite grade, and is capable of describing both the bulk and local oxidation rates under a wide range of conditions applicable to air-ingress.

J. Kane, Joshua

Statistical Models of Fracture Relevant to Nuclear-Grade Graphite: Review and Recommendations

The nuclear-grade (low-impurity) graphite needed for the fuel element and moderator material for next-generation (Gen IV) reactors displays large scatter in strength and a nonlinear stress-strain response from damage accumulation. This response can be characterized as quasi-brittle. In this expanded review, relevant statistical failure models for various brittle and quasi-brittle material systems are discussed with regard to strength distribution, size effect, multiaxial strength, and damage accumulation. This includes descriptions of the Weibull, Batdorf, and Burchell models as well as models that describe the strength response of composite materials, which involves distributed damage. Results from lattice simulations are included for a physics-based description of material breakdown. Consideration is given to the predicted transition between brittle and quasi-brittle damage behavior versus the density of damage (level of disorder) within the material system. The literature indicates that weakest-link-based failure modeling approaches appear to be reasonably robust in that they can be applied to materials that display distributed damage, provided that the level of disorder in the material is not too large. The Weibull distribution is argued to be the most appropriate statistical distribution to model the stochastic-strength response of graphite.

Nemeth, Noel N.

Modeling Intermolecular Interactions in Nanotubes, Fullerenes and Graphite using a New Long-Range Potential

The cohesive energy and compressibility of strands of a single-wall nanotube rope has been computed using a new long-range potential energy function derived from accurate ab initio quantum chemistry calculations of the benzene dimer and calibrated for energetic and mechanical properties of graphite (at pressures up to 12 GPa). We also use this potential to calculate a variety of properties of carbon nanotubes (both single- and multi-wall) and fullerenes. Extensive comparisons are made with previously published potentials.

Jaffe, Richard

Modeling Initial Stage of Ablation Material Pyrolysis: Graphitic Precursor Formation and Interfacial Effects

Reactive molecular dynamics simulations are used to study initial stage of pyrolysis of ablation materials and their composites with carbon nanotubes and carbon fibers. The products formed during pyrolysis are characterized and water is found as the primary product in all cases. The water formation mechanisms are analyzed and the value of the activation energy for water formation is estimated. A detailed study on graphitic precursor formation reveals the presence of two temperature zones. In the lower temperature zone (less than 2000 K) polymerization occurs resulting in formation of large, stable graphitic precursors, and in the high temperature zone (greater than 2000 K) polymer scission results in formation of short polymer chains/molecules. Simulations performed in the high temperature zone on the phenolic resin composites (with carbon nanotubes and carbon fibers) shows that the presence of interfaces had no substantial effect on the chain scission rate or the activation energy value for water formation.

Desai, Tapan G.

Electron and proton absorption calculations for a graphite/epoxy composite model

The Bethe-Bloch stopping power relations for inelastic collisions were used to determine the absorption of electron and proton energy in cured neat epoxy resin and the absorption of electron energy in a graphite/epoxy composite. Absorption of electron energy due to bremsstrahlung was determined. Electron energies from 0.2 to 4.0 MeV and proton energies from 0.3 to 1.75 MeV were used. Monoenergetic electron energy absorption profiles for models of pure graphite, cured neat epoxy resin, and graphite/epoxy composites are reported. A relation is determined for depth of uniform energy absorption in a composite as a function of fiber volume fraction and initial electron energy. Monoenergetic proton energy absorption profiles are reported for the neat resin model. A relation for total proton penetration in the epoxy resin as a function of initial proton energy is determined. Electron energy absorption in the composite due to bremsstrahlung is reported. Electron and proton energy absorption profiles in cured neat epoxy resin are reported for environments approximating geosynchronous earth orbit.

Long, E. R., Jr.

Comparison of Graphite Fabric Reinforced PMR-15 and Avimid N Composites After Long Term Isothermal Aging at Various Temperatures

Extensive effort is currently being expended to demonstrate the feasibility of using high-performance, polymer-matrix composites as engine structural materials over the expected operating lifetime of the aircraft, which can extend from 18,000 to 30,000 hr. The goal is to develop light-weight, high-strength, and high-modulus materials for use in higher temperature sections of advanced 21 st century aircraft propulsion systems. To accomplish this goal, it is necessary to pursue the development of thermal and mechanical durability models for graphite-fiber-reinforced, polymer-matrix composites. Numerous investigations have been reported regarding the thermo-oxidative stability (TOS) of the polyimide PMR-15 (1-5). A significant amount of this work has been directed at edge and geometry effects, reinforcement fiber influences, and empirical modeling of high-temperature weight loss behavior. It is yet to be determined if the information obtained from the PMR-15 composite tests is applicable to other polyimide-matrix composites. The condensation-curing polymer Avimid N is another advanced composite material often considered for structural applications at high temperatures. Avimid N has better thermo-oxidative stability than PMR-15 (6), but the latter is more easily processed. The most comprehensive study of the thermo-oxidative stability of Avimid N neat resin and composites at 371 (infinity)C is found in Salin and Seferis (7). The purposes of the work described herein were to compare the thermal aging behavior of these two matrix polymers and to determine the reasons for and the consequences of the difference in thermal durability. These results might be of some use in improving future polymer development through the incorporation of the desirable characteristics of both polyimides.

Bowles, Kenneth J.

Durability/life of fiber composites in hygrothermomechanical environments

Statistical analysis and multiple regression were used to determine and quantify the significant hygrothermomechanical variables which infuence the tensile durability/life (cycle loading, fatigue) of boron-fiber/epoxy-matrix (B/E) and high-modulus-fiber/epoxy-matrix (HMS/E) composites. The use of the multiple regression analysis reduced the variables from fifteen, assumed initially, to six or less with a probability of greater than 0.999. The reduced variables were used to derive predictive models for compression an intralaminar shear durability/life of B/E and HMS/E composites assuming isoparametric fatigue behavior. The predictive models were subsequently generalized to predict the durability/life of graphite-fiber-r generalized model is of simple form, predicts conservative values compared with measured data and should be adequate for use in preliminary designs.

Chamis, C. C.

Design and testing of high-performance mini-channel graphite heat exchangers in thermoelectric energy recovery systems

Recent national energy usage studies by Lawrence Livermore National Laboratory in 2015 [1] show that there is approximately 59 Quads (1015 Btu’s) of waste thermal energy throughout various industrial, residential, power generation, and transportation sectors of the U.S. economy. Thermoelectric energy recovery is one important technology for recovering this waste thermal energy in high-temperature industrial, transportation and military energy systems. Thermoelectric generator (TEG) systems in these applications require high performance hot-side and cold-side heat exchangers to provide the critical temperature differential and transfer the required thermal energy. High performance hot-side heat exchangers in these systems are often metal-based due to requirements for high-temperature operation, strength at temperature, corrosion resistance, and chemical stability. However, the generally selected metal-based hot-side heat exchangers (i.e., Inconels, Stainless Steels) suffer from low thermal conductivity, high thermal expansion, and high density, which degrades their thermal performance, leads to high thermal-expansion-driven stresses, and creates relatively high mass/high volume (i.e., low power density) TEG systems that are then difficult to fabricate and integrate into viable energy recovery systems. This paper describes the design and testing of a new, high-temperature minichannel graphite heat exchanger designed for operation up to 500C that is a critical element of a high-power-density TEG power system for aircraft energy recovery. This high-performance graphite heat exchanger represents a new state-of-the-art standard in high-temperature heat exchangers for TEG systems, which provides higher thermal transport, less thermal expansion at operation, lower system level stresses on TE components, and a lighter weight TEG system. This new heat exchanger creates a new design paradigm in TEG system design for terrestrial energy recovery and potential NASA technology infusion into terrestrial energy system applications. This paper will present and discuss the key heat transfer, pressure drop, pumping power analyses and design tradeoffs that created this unique design. Heat transfer and pressure drop modeling was performed with both empirical models based on known heat transfer and friction factor correlations and COMSOL thermal/fluid dynamic modeling of the graphite heat exchanger structure. We will also discuss resulting thermal transport and heat fluxes predicted at the TEG interface level. Heat exchanger performance testing was performed under simulated operating conditions and correlation with test data at the anticipated operating temperature conditions will be presented and discussed.

Shevade, Abhijit