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Effects of grain size and porosity on cladding failure in high-burnup UO 2 : A sensitivity and uncertainty study

Isotopic taggants are being studied to aid in the provenance assessment of nuclear materials. However, these taggants must be selected such that they do not adversely affect fuel performance during normal operation or accident scenarios. Taggants are known to affect the fuel’s grain size and porosity. In the work described in this paper, the BISON fuel performance code was used to assess the potential effects of taggants (i.e., grain size and porosity) on fuel rod behavior and cladding failure during a high-burnup, large-break loss-of-coolant accident. Here, 281 individual fuel rods from the same reactor core were modeled for a sensitivity study, a parametric study, and uncertainty quantification. The cladding failure predictions often exhibited stochastic behavior. After additional study, it was found that the cladding failure model is highly sensitive to residual error inherent to numerical approximation solvers. Some strategies to mitigate this sensitivity are discussed. The study found no relationship between known taggant effects and cladding failure status. However, taggants were found to affect the time and location of failure in certain rods. In conclusion, future work to continue investigating and validating these findings is briefly discussed.

Doped UO 2↗

Computational Investigation of Fuel Dispersal Phenomena during Large-Break Loss of Coolant Accident in Light-Water Reactors

In the event of cladding rupture, which could occur in light water reactor fuel assemblies during a loss-of-coolant accident (LOCA), fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod. This expulsion of fragmented fuel particles, referred as fuel dispersal, is the subject of investigation to evaluate the safety implications of increasing fuel burnup in light water reactors, with a specific focus on fuel fragmentation, relocation, and dispersal. Particle trajectories and the resulting mass distribution of the settled particles within the reactor pressure vessel can pose a long-term cooling challenge for the reactor core. The fuel dispersal phenomenon is significantly influenced by the ejection characteristics of the fuel fragments, as well as the size and shape of the cladding rupture and fuel rod depressurization history during LOCA transients. In this study, the transport of fuel particles within a scaled 5 × 5 lattice of a pressurized water reactor rod bundle geometry is modeled through a two-fluid Eulerian framework that treats the gas and solid phases as interpenetrating continua. The required boundary conditions are evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considers solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum and energy exchange between the gas and solid phases. The simulation results provide the volume fraction of the solids settled on the bottom surface of the fuel bundle, quantifying the deposition within the bundle geometry.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

BISON TRISO Modeling Advancements and Validation to AGR-1 Data

BISON is a finite element-based nuclear fuel performance code. Among its unique characteristics are its ability to model 1D, 2D, and 3D geometries and its applicability to a wide variety of nuclear fuels. For the last eight years, BISON has included a beginning capability to model tri-structural isotropic (TRISO) fuel. Recently, interest in TRISO fuel has grown, and a significant effort has been made to improve BISON’s capabilities in this area. Capability development has occurred for each material present in TRISO fuel particles: the buffer, inner pyrolytic carbon, silicon carbide, and outer pyrolytic carbon layers, as well as the fuel kernel. New elastic, creep, swelling, thermal expansion, thermal conductivity, and fission gas release (FGR) models are available. New models for the graphite matrix are also now available. Another important addition is the ability to perform statistical failure analysis of large samples of fuel particles. This new capability, which continues to grow, enables evaluation of failure due to pressure or crack formation by analyzing many thousands of particles. This enables realistic calculations of fission product release from the many particles in a TRISO-fueled reactor. These capabilities were checked via regression and verification tests. A large number of code benchmarking problems were also run, showing that BISON’s results closely match those of other software tools. Finally, a significant validation effort was completed in which fission product release, measured as part of the AGR-1 capsule experiments, was compared to BISON outputs. BISON outputs compared very well to the experimental data and to PARFUME results. Interest in BISON’s TRISO capabilities is growing, with the U.S. Nuclear Regulatory Commission (NRC) and Westinghouse Electric Company receiving training during the past year. Multiple other entities have expressed interest in or are actively using BISON. Kairos Power, LLC, has a strong partnership with Idaho National Laboratory (INL) regarding the use of BISON for TRISO analysis. While its capabilities still continue to grow, BISON has already become a powerful tool for TRISO analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Microstructural-Level Fuel Performance Modeling of U-Mo Monolithic Fuel

As the physics that governs the microstructural evolution of nuclear fuel span various time and spatial scales, to fully understand the fuel behavior inevitably involves atomic to mesoscale resolution that can be difficult to determine experimentally. Microstructural-level modeling and simulations can be used to develop physics-based materials models that can provide physical understanding to inform fabrication process control, as well as a valuable feedback mechanism between post-irradiation examination (PIE) results and fabrication parameters. In accordance with the program schedule, the primary goals of the microstructure modeling effort are to: 1. Address critical microstructural questions and provide practical guidance to the fabricator via the fuel product specification; 2. Provide mechanistic inputs for the existing fuel performance code to improve its descriptive and predictive capability at the macroscopic scale. In fiscal year (FY)-21, the work scope consisted of six main facets: (1) the effect of carbides on fuel performance; (2) gas diffusivity in different phases; (3) integration of microstructural fuel performance modeling; (4) property degradation; (5) irradiation creep; and (6) historical analysis of microstructure data. Brief summaries of each are included below.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Evaluation of ceria as a surrogate material for UO 2 in experiments on fuel cracking driven by resistive heating

A variety of normal operation and accident scenarios can generate thermal stresses large enough to cause cracking in light-water reactor (LWR) fuel pellets. Cracking of fuel pellets can lead to reduced heat removal, larger centerline temperatures, and localized stress in cladding all of which impact fuel performance. Furthermore, pellet cracking also contributes to a temperature reduction in the pellet since the pellet fragments tend to move towards the heat sink (cladding), and the heat flow remains predominantly radial despite the presence of cracks. It is important to understand the temperature profile on the pellet before and after cracking to improve cracking models in fuel performance codes However, in-reactor observation and measurement of cracking is very challenging owing to the harsh environment and design of fuel rods. Recently, an experimental pellet cracking test stand was developed for separate effects testing of normal operations and accident temperature conditions, using thermal imaging to capture the pellet surface temperature for evaluation of thermal stresses and optical imaging to capture the evolution of cracking in real time. Cracking experiments were initially performed using ceria (CeO 2 ) as a surrogate fuel material, which is useful for developing and demonstrating the experimental approaches but is also valuable in its own right for cracking model development and validation. A combination of induction and resistance heating was used for volumetric heat generation in the pellet creating a thermal gradient. The material properties of CeO 2 and UO 2 are reviewed and compared for use in model development. Simulations of the experiment were performed to evaluate the behavior of the surrogate (CeO 2 ) fuel in BISON. The measured temperature profiles from BISON models match reasonably well with the observed experiments for the ceria pellets before cracking. The findings from this work will help improve confidence in fracture models used for fuel pellets under similar in-reactor conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Assessment of BISON capabilities for component-level prediction of tritium transport in fusion and fission applications

Here we assessed the hydrogen migration and redistribution model implemented in the BISON fuel performance code for component-level tritium transport applications in fusion and fission example scenarios. We developed BISON models of an ITER heat exchanger, light water reactor fuel cladding, and a fluoride salt cooled high temperature reactor heat exchanger. Reasonable agreement between reported values in reference studies and BISON predictions demonstrated the ability of the BISON models to predict tritium transport behavior through steel materials. Next, sensitivity and uncertainty analysis was used to understand key parameter sensitivities within the BISON model for evaluation of tritium migration and redistribution. . The sensitivity analysis showed that the diffusivity activation energy was the most important parameter and that the heat of transport was the least important parameter for tritium migration in steels. Overall, the capabilities of the BISON code for component level modeling of tritium transport are promising.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

BISON-FIPD integration enhanced low-burnup SFR metallic fuel swelling model evaluation framework

Experiments indicated that metallic fuel in sodium-cooled fast reactors (SFRs) rapidly swells radially and axially at low burnup. Despite that, prior studies have been focused on describing high burnup axial fuel elongation. With recent conventional and non-conventional metallic fuel concepts being considered for license applications, understanding multidimensional fuel swelling at a wide range of burnup levels is important to fuel analysis and qualification activities. Here, we report the development and demonstration efforts of a low-burnup SFR metallic fuel swelling model evaluation framework using the BISON advanced fuel performance code. The framework leverages the Integral Fast Reactor (IFR) program X423 experiment data through the ongoing integration project to enable standardized and automated use of legacy metallic fuel irradiation data maintained in the SFR fuel irradiation and physics database (FIPD) for BISON metallic fuel model verification and validation. In conclusion, the performance of the framework was demonstrated using the two representative metallic fuel swelling model sets implemented in BISON, with a series of insights about future advanced swelling model development.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

3-D reconstruction and microstructural characterization of neutron-irradiated U-10Zr fuel using FIB-SEM serial sectioning

Herein, focused ion beam-scanning electron microscopy serial sectioning was applied to characterize the three-dimensional (3-D) porosity and phase regions of a neutron-irradiated U-10 wt% Zr fuel. The specimen was removed from an intermediate radial region of a fuel pin irradiated to 5.7 at.% burn-up. Backscattered electron imaging and energy-dispersive spectroscopy were performed on each serial section, allowing for the characterization of microstructural morphology and composition. Porosity size followed a lognormal distribution, ranging from 1.46 × 10 –4 to 25.58 µm 3 with a total porosity volume fraction of 13.02%. Distinctive microstructural regions were identified by composition and porosity: (1) a Zr-rich region with an average composition of 28.4 wt% Zr and a local porosity fraction of 6.88%, and (2) a U-rich region with an average composition of 97.0 wt% U and a local porosity fraction of 14.11%; subdivided into U-rich—high porosity (16.68%) and U-rich—low porosity (8.04%) regions. The detailed 3-D compositional and porosity regions can improve nuclear fuel performance codes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Probing Microstructure-induced Swelling & Thermal Property Changes in Ion-Irradiated Oxide Fuels using Laser-generated Surface Acoustic Waves

Radiation of fuel rods with neutrons during a fission reaction in a nuclear reactor is known to affect the material microstructure of the fuel as a result of fission fragment damage, and lead to the formation of atomic-level defects such as voids, dislocation loops, and lattice swelling from fission-gas release. A consequence of the radiation-induced damage in nuclear fuels is the drastic alteration of material properties, in particular, the reduction of the thermal conductivity – a key parameter that governs the transport of thermal energy released from fissile fuel atoms to the surrounding coolant. Swelling can induce high stresses and ultimate failure of the cladding. A fundamental understanding of the role of radiation-induced damage on the thermal transport and mechanical properties of nuclear fuels is therefore critical for efficient, reliable and safe operation of a nuclear power plant. As opposed to conventional post-irradiation examination techniques that are often time-consuming and require significant sample preparation, laser-based characterization methods have emerged as promising non-contact, non-destructive tools to measure the evolution of microstructure-induced material property changes. Moreover, laser methods offer the promise of in-situ characterization while the material is being irradiated. This project aims to develop an improved understanding of the impact of radiation-induced changes to material microstructure on the thermal and elastic properties of nuclear materials. A laser ultrasonic technique, known as the transient grating (TG) spectroscopy method, is used to simultaneously measure thermal diffusivity and elastic properties in unirradiated and ion-irradiated oxide nuclear fuel samples. The results will complement on-going investigations on electron- and phonon-mediated thermal transport in nuclear materials and will provide foundational work for incorporating the influence of defects in fuel performance codes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Dynamic System Scaling Application to Accelerated Nuclear Fuel Testing

The development of nuclear fuel and materials requires a continuous effort to investigate the acute and prolonged effects of irradiation, thermal-material stress, chemical change, or other conceivable damage mechanics acquired during normal operation or accident scenarios throughout its lifetime. As in-core fuel property measurement techniques advance to support in the real-time, non-invasive, and enhanced accuracy realm, it is the future of fuel development to pursue to higher degrees of control, predictability of integral test behavior via separate effects test (SET), and shorter test time intervals. The fuel development life cycle from initial concept to commercial licensing is approximated to be 20 years and current literature suggests by optimizing fuel performance codes with SETs, the process could possibly be compressed to 5 to 10 years. Recently, a research group in the Idaho National Laboratory (INL) is testing reduced scale fuel rods and increased power density to accelerate evolution of fuel phenomena in metallic fuels. In support of nuclear fuel rod development, compressing fuel test process, and accelerating fuel phenomena, it was the purpose of this study to investigate nuclear fuel performance phenomena via literature review and effectively scale the initial conditions, boundary conditions, and geometric properties to describe the time-dependent response including to fuel burnup, thermal and mechanical stress, transmutations and inter-diffusion, and other relevant observed phenomena. The study was based on BISON simulations of historic EBR-II metallic fuel experiments and Dynamical System Scaling (DSS) method are utilized to assess effects of scaling activity including fuel phenomena acceleration and calculations of time-dependent distortions. The research successfully scaled metallic fuel phenomena, accelerated fuel testing, and assessed the distortions for each scaled case derived.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Evaluation of the Effect of Burnup Acceleration on UO 2 Microstructure Evolution

Accelerated fuel qualification (AFQ) is a methodology by which new nuclear fuels are developed in an accelerated time frame compared with historical fuel qualification approaches. AFQ generally relies on high-fidelity physics-based modeling and simulation tools to adequately describe fuel performance as well as on revolutionary methods to accelerate burnup accumulation and collect relevant data more quickly. This report summarizes the use of advanced fuel modeling and simulation tools to evaluate microstructures from commercially irradiated fuel and microstructures from proposed MiniFuel irradiations, in which burnup accumulation is accelerated while prototypic temperature conditions are maintained. In this milestone, we used the mesoscale fuel performance code MARMOT to model the evolution of irradiated UO 2 microstructures and their potential restructuring at high burnup. The simulation conditions were informed by BISON models of both commercially irradiated fuel and MiniFuel. A first set of simulations investigated the recrystallization behavior of fully dense microstructures and showed full recrystallization at burnups as low as 52 MWd/kgU at 950°C. However, these simulations did not account for the presence of fission gas bubbles (predicted by BISON). Therefore, a second set of simulations including fission gas bubbles was performed and indicated that at the lowest temperature considered (650°C), the porous UO 2 microstructures have the highest total Gibbs free energies and are likely to recrystallize earlier than higher temperature cases (800 and 950°C), which agrees with high-burnup fuel characterization data. The results also showed that at lower temperature (650°C), the total free energies of the PWR fuel and MiniFuel microstructures are not significantly different. However, at the highest temperature (950°C), MiniFuel microstructures have a lower free energy than that of the PWR fuel microstructure. The competing effects between the temperature-dependent grain nucleation rate and the reduction of the free energy of the microstructure at higher temperature as a result of diffusion indicated that restructuring may occur at even higher temperatures than those considered in this study. In addition to the microstructure evolution modeling efforts, the burnup gradient across a single fuel specimen was also considered. This evaluation was for the VXF-15 position of the High Flux Isotope Reactor (HFIR) using the code suite HFIRCON, which was developed to automate the workflow for evaluating targets and fuel as they are irradiated in HFIR. The burnup gradient evaluation showed a dependence on both the axial and radial locations within the specimen, with a maximum difference of 1.7 between the inner and outermost radial layers. This relationship was further supported by considering the fission product speciation with respect to location within the specimen, which showed a higher concentration of 239 Pu, 240 Pu, and 241 Pu on the outer radial locations of the specimen than the center. The findings of the burnup and speciation evaluation show that some amount of self-shielding is occurring in the specimen when irradiated in the high-flux environment of HFIR; however, this impact is more pronounced for natural uranium when compared to 6% enrichment due to the higher ratio of 238 U in the specimen. Further analyses are required to understand the sensitivity of this gradient to spatial mesh and enrichment of the specimen.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Updating and Refining BISON TRISO Assessment

Several advanced reactor concepts consider tristructural isotropic (TRISO) fuel in their designs. To support the advanced reactor industry, the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program within the U.S. Department of Energy (DOE) is developing modeling and simulation capabilities within the BISON fuel performance code. Assessment of these capabilities against available experi- mental data, such as the Advanced Gas Reactor (AGR) program, is essential in instilling confidence in the code predictions. Associated uncertainties in model inadequacy, experimental measurements, and manufacturing are also of importance. This report discusses the updating and standardization of the existing assessment suite in BISON for TRISO fuel performance analysis. The cases considered the AGR-1, AGR-2, and AGR-3/4 experimental programs. The report also includes a preliminary investigation into the sources of model inadequacy associated with silver (Ag) release fractions using the AGR-2 Compact 2-1-2 as a case study. The results indicate that uncertainties in the operating temperatures supplied to the model and the form of those temperature conditions (spatially averaged versus spatially resolved) both affect Ag release predictions. This suggests that previously observed model inadequacy can be attributed to both physical models and the operating conditions supplied to them. These findings will be leveraged to guide development of assessment cases for additional experiments and refinement of physical models for behaviors that potentially influence Ag release, such as palladium penetration.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Sensitivity of UO 2 fuel performance to microstructural evolutions driven by dilute additives

Use of dilute additives to nuclear fuel is being considered to increase the security of commercial fuel management through traceability of fabricated fuel elements. Taggants, as additives are denoted when included for traceability purposes, may also improve fuel performance, as demonstrated in Cr-containing uranium dioxide as described in the literature, and they may also improve fuel safety. In fact, studies have shown that some additives affect fuel material properties such as grain size and density after sintering. Given the possible range of elements that could be used as additives, the impact of such fuel property variations on the fuel’s thermomechanical behavior becomes relevant. These effects can be evaluated through a sensitivity study of standard fuel models to analyze changes in these properties using a fuel performance code. In this work, the BISON code is being used to investigate these effects through a 2D axisymmetric model of smeared UO 2 fuel pellets and ZIRLO® cladding under realistic pressurized water reactor core irradiation conditions. Here, randomly sampled densities and grain sizes within specified ranges are used as input parameters in the simulations, and several fuel model-related outputs are evaluated. The thermomechanical response of the cladding is also addressed in this study. The simultaneous variation of both input parameters offers a more comprehensive path to identify key sensitivities. Outputs explored include temperature, fission gas release, creep, and radial stress. Results show that although most of these outputs are sensitive to grain size to a certain extent, density mainly affects fuel temperature and elastic strain. Furthermore, sensitivities can vary depending on the radial position within the fuel pellet.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Modeling fission product diffusion in TRISO fuel particles with BISON

Diffusion of fission products in intact TRISO particles depends on particle geometry, fission product source rates, time, temperature, and temperature-dependent diffusion coefficients. Simulating this diffusion process requires models for source rates and diffusion coefficients, plus computation of the temperature field if not prescribed. In addition, simulation quality depends on discretization of the geometry, appropriate time stepping, and the accuracy of the solution method. In this paper, we explore the simulation of fission product diffusion in TRISO fuel particles using the finite element method via the fuel performance code Bison. Recent material model development has occurred in Bison for each material present in tri-structural isotropic (TRISO) fuel particles: the buffer, inner pyrolytic carbon, silicon carbide, and outer pyrolytic carbon layers, as well as the fuel kernel. Also, new mesh generation and fission product release fraction capabilities have been added. Diffusion capabilities are shown to converge to the correct solution via formal verification tests. A large number of code benchmarking problems are also given, with good results, showing that Bison’s computed release fractions closely match those of other software tools. Finally, a significant validation effort is detailed in which fission product release, measured as part of the AGR-1 capsule experiments, is compared to Bison outputs. Bison outputs compare very well to the experimental data and to PARFUME results.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Thermochemically-informed mass transport model for interdiffusion of U and Zr in irradiated U-Pu-Zr fuel with fission products

A new formulation for redistribution of constituents in metallic U-Pu-Zr nuclear fuel is presented that can incorporate the contributions from fission products. The formulation is based on the thermodynamic driving forces derived from the generalized chemical potential that includes effects of composition and temperature. As a result, the redistribution model can readily account for the composition changes due to the generation of fission products while using only a limited set of transport coefficients. The thermodynamic model for the metallic fuel and thermochemistry solver Thermochimica were coupled with the nuclear fuel performance code BISON to implement the redistribution model. The simulations reproduce an experimentally observed Zr-depletion zone in the mid-radius region of an irradiated fuel slug. The generation of fission products during burnup is shown to have a stabilizing effect on the fuel chemistry, slowing the rate of U-Zr interdiffusion and reducing the size of the Zr-depleted zone. Here, the overall objective of the work is to advance predictive capabilities of fission product behaviour in U-Zr metallic fuel in the context of fuel performance and safety.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Estimation of Fission Product Transport Parameters for Cesium in the AGR-3/4 TRISO Fuel Experiment

A one-dimensional (1D) finite-element model of fission product transport in the AGR-3/4 experiment has been developed using the Multiphysics Object Oriented Simulation Environment (MOOSE) framework and implemented in the fuel performance code, BISON. The model resolves capsule-specific geometries, materials, and temperature histories and simulates radial migration of fission products from the fuel compact through the inner ring, outer ring, and into the sink ring. Model parameters governing diffusion and sorption were estimated for key fission products – cesium (Cs), and europium (Eu) – by simultaneously fitting modeled isotopic concentration profiles and total ring inventories to a post-irradiation experimental measurement. These data include gamma scanning, liquid scintillation for Sr-90, radial deconsolidation leach-burn-leach analysis, tomographic reconstructions, and destructive physical sampling. A mortar-based interfacial sorption framework was implemented to enforce physically consistent mass transfer and flux conservation across gas gaps. Two classes of parameter sets were derived: a least-squares best-fit, and a safety-oriented conservative-fit, what applies strong penalties for underprediction of sink inventories. Across all twelve capsules, the model successfully reproduces the dominant radial transport trends for Cs, Sr, with decreasing concentrations from the compact outward through successive rings. Cs behavior is captured most consistently, while strontium predictions reveal systematic trade-offs between compact accuracy and conservative sink-ring bounding. The results demonstrate that sink ring weighted calibration provides conservative, safety relevant bounds on low temperature fission product transport, but at the cost of underpredicting compact inventories for Sr isotopes. These discrepancies highlight the need for additional physics, including fast-slow diffusion model, incorporating trapping mechanism in the transport behavior. Overall, this work establishes a robust, capsule-specific modeling framework for AGR-3/4 fission product transport and provides a defensible basis for parameter selection in source-term and fuel performance analyses for high temperature gas-cooled reactors.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Modeling and design of a separate effects irradiation test targeting fission gas release from Cr-doped UO 2

Fission gas release (FGR) from nuclear fuel during operation can diminish heat transfer properties across the pellet-cladding gap and increase the fuel rod internal pressure, thereby posing a concern to fuel reliability and safety during an accident. Enlarging the fuel grain size, which has been shown to improve fission gas retention, can be achieved by doping the fuel feedstock prior to sintering. In this work, the BISON fuel performance code was used to predict FGR from undoped and chromia-doped UO 2 (referred to as Cr-doped UO 2 ) fuel specimens with different grain sizes and across various temperatures. The BISON models identified the irradiation conditions for which FGR is most significant, and a separate effects irradiation experiment in the High Flux Isotope Reactor (HFIR) was then developed targeting those conditions. Further, the experiment leveraged the MiniFuel irradiation capability at Oak Ridge National Laboratory and consisted of 12 fuel specimens of varying grain size and Cr content. A coupling scheme between BISON FGR results and the ANSYS finite element thermal model used for experiment design was formulated to predict cumulative FGR from each fuel specimen based on expected irradiation temperature histories. The fuel samples were fabricated and characterized as a part of this work, and the fuel compositions modeled in BISON were representative of the specimens used in the experiment. This combined modeling and experimental effort aims to study the effect of fuel grain size and Cr content on FGR and to provide simulated BISON FGR results that can be used for future model validation activities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Calibration of the Diffusivity Predictions of Centipede Using Approximate Bayesian Computation and Applications in Nyx (Engineering Scale) and Xolotl-MARMOT (Meso-Scale) Simulations

Fission gas evolution and release in UO 2 nuclear fuel are important fuel performance metrics and occur in several distinct stages: 1) nucleation, growth and resolution of intra-granular bubbles, 2) diffusion to grain boundaries and 3) nucleation and growth of bubbles at grain boundaries, which eventually form a connected network (percolation) enabling release of gas from grain boundaries through connections to triple junctions, grain edges or free surfaces. The NE-SciDAC project is developing several computational tools to model this problem, which are connected in a hierarchical multi-scale framework. The information transfer in the multi-scale framework is a critical step that, in addition to best-estimates, should include uncertainty quantification. Despite taking a first-principles multi-scale approach, there is a need to perform parameter calibration to ensure consistency with available experimental data. In the present study, uncertainty quantification (UQ) and parameter calibration is demonstrated for one of the lower length scale codes in the multi-scale framework (Centipede) and then the results, including instances of the propagated uncertainties, are used in other codes within the framework, specifically Nyx and Xolotl-MARMOT. We calibrated the model parameters in Centipede, a computer code used to predict diffusivities of uranium (U) and xenon (Xe) in the context of the simulation of fission gas in uranium oxide (UO 2 ) nuclear fuel. The Centipede code depends on 183 parameters, all of which are subject to uncertainty. The three data sets used in our calibration effort are taken from the literature. This data is available as a set of measurements, including measurement errors. Our goal is to calibrate a statistical model that predicts both the value of the measurement and the uncertainty associated with the measurement. We perform a Bayesian calibration of the model parameters using a dedicated approximate Bayesian computation (ABC) likelihood function. To avoid excessive computational costs, we replace the expensive Centipede simulation code by a higher-order surrogate model, constructed using only the 9 most important parameters. These important parameters are identified by a preliminary global sensitivity analysis (GSA) study. Among the important parameters are T0 (the temperature at which UO 2 is perfectly stoichiometric) and Hf_pO2 (the temperature dependence of the oxygen (O) partial pressure) that should be considered as operating conditions to be estimated along with the other parameters. We consider two different cases: one where we define one set of these operating conditions for all data sets, and one where we define distinct operating condition parameters for each data set. The Xe diffusivities predicted by the latter case show distinct features that could not be observed in the former. Next, we use the diffusivity predictions by Centipede as input to Nyx, a reduced order fuel performance code focused on gas behavior alone, in order to estimate quantities associated with inter-granular bubble formation at conditions specified by the experiments. Finally, the diffusivities obtained from the calibrated Centipede runs were used in coupled Xolotl-MARMOT simulations of intra- and inter-granular gas evolution. The results are compared to simulations using the baseline diffusivities from Turnbull et al.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗