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Massively Parallel Bayesian Model Calibration and Uncertainty Quantification with Applications to Nuclear Fuels and Materials

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. Fuel behavior in a nuclear reactor is governed by a complex network of mechanisms interacting with various other physics aspects in the reactor system. Any model developed to represent the fuel behavior will likely be idealized resulting in uncertainties in their predictions compared to the observed data. As such, this report was motivated by the need to identify the sources of uncertainties and quantify and propagate them through the fuel model outputs. Such quantification of uncertainties will establish a level of model trustworthiness, identify approaches to improve the model trustworthiness, and even guide optimal experiment design for maximal information gain. To accomplish the uncertainty quantification for computational models, this report has relied on the Bayesian framework which provides probabilistic treatment of models their inputs and outputs. The current state-of-the-art on performing Bayesian Uncertainty Quantification (UQ) for nuclear engineering models using High Performance Computing (HPC) resources have been reviewed. Implementation of capabilities for massively parallel Bayesian UQ in Multiphysics Object-Oriented Simulation Environment (MOOSE) is discussed. Several verification cases are discussed to verify the accuracy of the quantified uncertainties using the developed computational capabilities in MOOSE. Then, the problem of quantifying the uncertainties in TRI-Structural isOtropic (TRISO) fuel silver release is addressed. For the first time, the uncertainties arising from the TRISO Fission Gas Release (FGR) model due to model inadequacy and experimental noise are quantified. Also, the Bayesian capabilities are applied to the calibration of the MATPRO creep model, a widely used model in several fuel assessment cases. The impact of the prediction uncertainties in the MATPRO model on the fuel cladding behavior as part of the TRIBULATION assessment case (which is an integral effects case) is investigated. This report concludes with a discussion on the future work for the UQ for computational models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Bayesian Analysis of TRISO Fuel: Quantifying Model Inadequacy, Incorporating Lower-Length-Scale Effects, and Developing Parallel Active Learning Capabilities

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel-cycle systems. This program has been providing engineering-scale support for the continued development of BISON, a high-fidelity, high-resolution fuel performance tool. Fuel behavior in nuclear reactors is governed by a complex network of mechanisms that interact with various other physics aspects in the reactor system. Any model developed to represent fuel behavior will likely be idealized, resulting in uncertainties when comparing their predictions against the observed data. In Fiscal Year (FY)-23, we initiated the Uncertainty Quantification (UQ) work by using Bayesian methods to establish a level of model trustworthiness and further improve it, with a particular emphasis on TRI-Structural isOtropic (TRISO) nuclear fuel. This year, we further expanded on that UQ work by investigating an approach to quantifying model inadequacy and accounting for lower-length scale (LLS) effects in TRISO silver (Ag) release modeling. Furthermore, we are implementing parallel active learning capabilities to reduce the computational cost (i.e., required computational resources and elapsed time) of performing UQ. Specifically, we utilized The Kennedy O’Hagan framework for Bayesian uncertainty quantification (KOH) to account for model inadequacy in TRISO Ag release predictions made by BISON. The KOH framework represents an improvement over the standard Bayesian framework used in FY-23. Explicitly accounting for model inadequacy in the Bayesian framework helps establish the level of experimental noise uncertainty in the Advanced Gas Reactor (AGR) data. We compared the inverse UQ results obtained from both the standard Bayesian and KOH frameworks in light of the AGR-2/3/4 data, and also compared the predictive UQ results obtained from these two frameworks in light of the AGR-1 data. Next, we investigated the impact of considering LLS effects in the Ag release simulations. We developed an expanded database of LLS simulated effective diffusivities for Ag, covering a wide range of microstructures and temperatures. Using this database, we developed a framework for incorporating LLS effects into the engineering-scale Ag release UQ. We developed both parametric and non-parametric approaches for bridging the length scales. We then investigated the inverse UQ results in light of the AGR-2/3/4 data and the predictive UQ results in light of the AGR-1 data, and compared the LLS-informed approach and the Arrhenius equation, which does not include microstructure information. Finally, we discussed implementing parallel active learning capabilities in the Multiphysics Object Oriented Simulation Environment (MOOSE)/BISON to reduce the computational cost (i.e., computational resources and elapsed time) of Bayesian UQ. For verification purposes, we first tested these new capabil ities on a species interaction problem. We then demonstrated them on the TRISO Ag release application, showing that parallel active learning capabilities can enhance the accuracy of UQ while also substantially reducing the computational cost in comparison to the reference methods developed in FY-23.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Am-241 Nuclear Safety and Environmental Interactions

NASA’s supply of radioisotopes for Radioisotope Heat Units (RHU) and Radioisotope Thermoelectric Generator (RTG) power sources is facing a crisis due to shortages of Pu-238 for future missions. Am-241 is a possible replacement for Pu-238 since its stockpile from the nuclear weapons program has remained relatively intact. The purpose of this project was to assess the safety of Am-241 and the risks associated with it as compared with PU-238. The project has resulted in a journal article, F. De-La-Torre-Aguilar, N. White, M. Prelas, R. V. Tompson, and S. K. Loyalka "Space nuclear power system accidents: Doses from Pu-238 and Am- 241 inhalation," Progress in Nuclear Energy vol.100C (2017), pp.171-182, which showed that the radiation dosage resulting from Am-241 inhalation are about 1/2.5 of the dosage resulting from Pu-238 inhalation per KW of Pu-238 power. Considerable progress was also made on the Direct Simulation Monte Carlo Method (DSMC) for simulation of aerosol evolution during accidents resulting in three publications: 1.I. Saldivar, F. De-La-Torre-Aguilar, M. Boraas, and S. K. Loyalka “Benchmark problems in aerosol evolution: Comparison of some exact and DSMC results” in Annals of Nuclear Energy vol.117 (2018), pp.213-222. 2. I. Saldivar and S. K. Loyalka, “Evolution of Aerosols Coupled to Environments: Verification of Direct Simulation Monte Carlo (DSMC)”, Nuclear Technology 204 (2018), pp.172-183. 3. M. Boraas and S. K. Loyalka, “Mesh Free Simulation of Spatially Inhomogeneous aerosols in Arbitrary Geometries” Nuclear Science and Engineering (2018). Further, we have computations on Am-241/Pu-238 vapor and aerosol interactions, and found that the vapor condensation rate is relatively insensitive to the mass effects, confirming some previous results. We have also completed computations of charge effects on evolution of different species aerosols and a manuscript is in preparation. Additionally, we have compared atmospheric dispersion and deposition of Pu-238 and Am-241 using the HYSPLIT code. We have also used a real lung model and the CFD program FLUENT to compute PuO2 and AmO2 deposition to explore improvements upon the ICPR-66 model. We have found that the deposition efficiencies of PuO2 and AmO2 are similar. These results (four manuscripts) will be submitted for publication in the post project period. We have made progress using framework of Mars 2020 mission nuclear risk assessment model to integrate all results, but our progress has been limited as the improved consequence modeling itself has been quite involved and challenging. We will integrate and complete the more extensive risk modeling computations and publish the results in the post-project period. In addition to the above, the project has resulted in research training of four PhD students

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Tsunami evacuation mathematical model for the city of Padang

Tsunami is a series of wave trains which travels with high speed on the sea surface. This traveling wave is caused by the displacement of a large volume of water after the occurrence of an underwater earthquake or volcano eruptions. The speed of tsunami decreases when it reaches the sea shore along with the increase of its amplitudes. Two large tsunamis had occurred in the last decades in Indonesia with huge casualties and large damages. Indonesian Tsunami Early Warning System has been installed along the west coast of Sumatra. This early warning system will give about 10-15 minutes to evacuate people from high risk regions to the safe areas. Here in this paper, a mathematical model for Tsunami evacuation is presented with the city of Padang as a study case. In the model, the safe areas are chosen from the existing and selected high rise buildings, low risk region with relatively high altitude and (proposed to be built) a flyover ring road. Each gathering points are located in the radius of approximately 1 km from the ring road. The model is formulated as an optimization problem with the total normalized evacuation time as the objective function. The constraints consist of maximum allowable evacuation time in each route, maximum capacity of each safe area, and the number of people to be evacuated. The optimization problem is solved numerically using linear programming method with Matlab. Numerical results are shown for various evacuation scenarios for the city of Padang.

54 ENVIRONMENTAL SCIENCES↗

Investigating Application of LiDAR for Nuclear Power Plants

Many evaluation, assessment, and modeling tasks at nuclear power plants require spatial in-formation; this often requires physical visits to locations within the facility because the 2D or 3D schematics and current models do not contain enough detail or do not capture as-built and real-world conditions. These visits require extensive manual labor for not only the requesting party, but also support groups, such as security. Light Detection and Ranging (LiDAR) mapping is trying to solve that problem by providing very detailed 3D models for low costs. However, the use of these models can be very limited because either component reference information is missing and too costly to add or there is no way to extract specific spatial data needed for other tools. This report outlines two main efforts. First, to reduce the effort of “Tagging” data in large 3D models, a general Application Programming Interface (API) was developed to import a variety of existing plant database information into a 3D-visualization engine. Filters allow the user to have only zone-specific items listed; then, they can simply click and assign the information to a specific spot or component in the 3D model. The second part of the work is the development of an interface for importing pieces from the3D-LiDAR model into other systems needed for modeling and simulation, outlined around fire modeling. This interface allows for the retrieval of item location and boundaries, enabling the auto generation of models for varying tools.

3D Modelling↗

Phase-field modeling for restructuring in the dark zone of high burnup UO 2

This report summarizes the mesoscale modeling work performed in fiscal year 2024 under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to capture the microstructural evolution and restructuring observed in the dark regions of high burnup UO 2 nuclear fuel. This is the first attempt to realistically simulate the restructuring behavior observed in different region of a high burnup fuel. We employ a grand-potential based phase-field model to concurrently evaluate the formation of subgrains and growth of fission bubbles within the fuel. A energy-based subgrain formation criteria is introduced to simulate the restructuring process. Effect of different initial conditions and different modeling parameters are studies systematically to capture how each of these parameters influence the characteristics of the restructured fuel. It is observed that the subgrain formation begins around existing fission gas bubbles and then proceeds towards triple junctions, grain boundaries and grain interiors. It is demonstrated that restructuring is influenced by a combination of initial dislocation densities, subgrain formation rate, and temperature. Rate of restructuring increases with increase in fuel temperature. A restructuring bias is observed within the microstructure due to variation in defect accumulation among different grains. Furthermore, bubble sizes and distribution does not have a significant effect on rate of restructuring. The predicted microstructures resembles the characteristics of the restructured regions as observed in experiments. Finally, a correlation is presented that demonstrates the evolution of the restructuring volume fraction as a function of local effective burnup. This work provides a first of its kind restructuring model for darkzone that can be used by BISON for performance prediction of high burnup UO 2 fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Multi-Physics Coupled Seismic Safety Analysis of Molten-Salt Reactors

Pool-type Molten Salt Reactors (MSRs) are a promising advanced nuclear reactor concept relying on passive physical behavior to provide increased safety characteristics. The high heat capacity, high boiling point, unpressurized liquid salt contains the nuclear fuel and as it passes through the vessel achieves criticality and produces nuclear power. The salt then carries away the heat produced along with the delayed neutron precursors towards heat exchangers and primary pumps before entering the core. This forms a highly coupled multiphysics problem between neutronics and fluid flow, which makes modeling these reactors challenging. The safety/licensing case heavily relies on modeling and simulation to prove their safety, and significant effort has been expanded by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to develop the appropriate simulation tools. Their safety/licensing will require a thorough analysis of their behavior during earthquake-based transients. Earthquakes are a transient condition commonly experienced in many regions, and are safely survived by dozens of reactors every year. Nonetheless, significant conservatisms were introduced with limited predictive modeling and simulation available. The first-of-a-kind capability developed by this research will allow for engineers to analyze ranges of design-basis and beyond-design basis accident scenarios to assess the integrity of the reactor vessel and surrounding system, possibly allowing for limiting the costly conservatisms in the design. This projects uses MASTODON, Griffin, and Pronghorn in the NEAMS ecosystem to model the coupled multiphysics problem posed by an earthquake in a molten salt reactor. It marches through a number of number of coupling schemes, from uncoupled simulations to tightly two-way coupled simulations. The appropriate level of coupling for these simulations will then be determined based on the accuracy in the quantities of interest (QoI) and computational effort involved in each scheme. The QoIs chosen for this paper include the mass flow rate across the heat exchanger (for Pronghorn simulations), power output of the reactor (for Griffin simulations), and the maximum Von Mises stress (for MASTODON simulations). This summary paper reports on the current progress of this project, with 2D tightly coupled multiphysics results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Adding a MOAB Geometry Interface to SHARP Structural Mechanics

The authors briefly summarize the development of, and test experience with, an initial data interface between the structural mechanics code Diablo and the SHARP reactor simulation system data hub MOAB. That interface has been exercised both to write MOAB databases from Diablo, and then also to use such a database to read in part of a simulation definition for a subsequent Diablo execution. All enhancements are integrated into the central Diablo source repository. The SHARP software system for advanced simulation of nuclear reactors and power plant systems is sponsored by DOE's Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SHARP has been architected as a federation of single-physics simulation tools to permit flexibility in programming languages and leveraging of past and on-going investments. Solution of multi-physics problems will be coordinated by, and data passed through, a central 'hub'. SHARP's hub implementation is utilizing MOAB: a Mesh-Oriented datABase. This same data hub approach is also intended to enable multi-resolution simulations, e.g, lower-dimension plant-scale simulations can be informed by high-fidelity 3D models of particular critical components.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Multiscale modeling for high burnup structure formation and associated pulverization

This report summarizes the lower length scale modeling work performed in the fiscal year 2023 under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to capture the microstrutural evolution and associated pulverization criteria in the high burnup regions. This year, the resolution mechanisms within the cluster dynamics code has been updated and it influence on the bubble growth in HBS regions at the mesoscale is studied. To improve the accuracy of phase-field models of fission gas bubble growth, a new Helmholtz free energy for high-density Xe gas is derived from a virial equation of state. Two previously used strategies for representing net vacancy production in phase-field models of fission gas bubble growth are compared with each other and with analytical models of bubble growth. The vacancy source only model is found to be more convenient to parameterize realistically compared with the vacancy source+sink model. Furthermore, the phase-field-fracture simulation have been performed using MD- informed failure stress values and realistic HBS structure obtained from the phase-field simulations. We also present the uncertainty bands on prediction of the critical stress to account for the effect of the lower length scale variabilities on the failure criteria at the mesoscale. It is observed that pulverization may occur in partially restructured regions with restructuring fraction as low as 17%. In light of this, an update to the BISON’s pulverization criteria is recommended.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Nuclide Release Pathways in and Around a Trench Repository for Radioactive Waste - 16014

An effective model for a safety assessment of a conceptual trench repository system, in which low-and intermediate level radioactive waste (LILW) is disposed of has been developed. The repository system is assumed to be located in the surface area of a mountain hill near the seashore. An easy-to-use computer program based on this model, developed as a GoldSim template, has been extended based on the previous one in consideration of the rather possible complex pathways in and around the trench for its performance assessment, which is able to evaluate a nuclide release from the repository and farther transport into the geosphere and biosphere under various normal, disruptive natural, and manmade events, and scenarios that can occur after a failure of waste drums with associated uncertainty. To demonstrate the nuclide release and transport behavior through these various possible pathways in the near- and far-fields of the repository system under certain scenarios, some illustrative evaluations and a simple sensitivity investigation with C-14 for the concrete barriers of the trench were made. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Grizzly Development for Light Water Reactor and Advanced Reactor Applications in Fiscal Year 2021

This report summarizes work performed during Fiscal Year (FY) 2021 at Idaho National Laboratory (INL) for the U.S. Department of Energy’s Nuclear Engineering Advanced Modeling and Simulation (NEAMS) program for the Structural Materials and Chemistry Technical Area in the work package entitled “MS-21IN050106 - Structural Materials - INL.” This effort mainly focused on development and application of capabilities for engineering-scale analysis of nuclear reactor structural components in the Grizzly and BlackBear codes. These efforts include performance improvements and application of models for high-temperature component response, cluster dynamics modeling of precipitation in light water reactor pressure vessel steel, engineering-scale capability development in the areas of concrete simulation and reactor pressure vessel analysis, and preparation for and conducting an independent assessment of the adherence of these codes to software quality standards.

36 MATERIALS SCIENCE↗

Assessment of the CTF subchannel code for modeling a large-break loss-of-coolant accident reflood transient

With increased industry interest in extending reactor operating cycles, the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program has been investigating the behavior of high-burnup fuel during design basis accidents such as the large-break loss-of-coolant accident (LBLOCA) with consideration for risk of fuel fragmentation, relocation, and dispersal (FFRD). As part of that activity, the NEAMS subchannel thermal/ hydraulics (T/H) code, CTF, is being used for modeling of LBLOCA and to determine the impact of subchannel resolution on results. Although CTF includes a wide range of models for LBLOCA conditions, the code has not been used for this application while maintained at Oak Ridge National Laboratory (ORNL) until now. Therefore, here, in this work, a preliminary assessment of several of these models was performed using openly available reflood experimental data from the Flooding Experiments in Blocked Arrays (FEBA) tests. One coarse mesh and one fine mesh model were set up in CTF for high and low flooding rate tests performed in the unblocked FEBA facility. A coarse TRACE model was set up to be as consistent as possible with the coarse CTF model to allow for code-to-code benchmarking. The assessment shows a tendency of the codes to over-predict peak cladding temperature (PCT) near the top of the bundle and to quench early. Advanced spacer grid models were shown to improve upper bundle predictions in CTF. The resolved CTF model over-predicted PCT by a larger degree in the center channels in the low-flooding rate test, and it is believed that the radiative heat transfer model, which was not used in this study, may be needed to correct this over-prediction. Finally, this work demonstrates the importance of the droplet model in determining quench time and vapor temperature and PCT prediction, which necessitates a more in-depth validation of these models in the future.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Integrated Simulation of Weld Residual Stress Evolution and Crack Propagation Using XFEM

Nuclear power plant components operate in environments that promote multiple degradation mecha- nisms, several of which involve crack initiation and growth. An ongoing effort in the U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program is developing a general capability within the Multiphysics Object Oriented Simulation Environment (MOOSE) framework for simulating three-dimensional crack growth under a range of driving conditions, including fatigue, stress corrosion cracking (SCC), brittle fracture, and stress-relaxation cracking. This report demonstrates an end-to-end workflow that uses this capability to model weld-residual-stress-driven SCC in the J-groove weld of a pressurized-water reactor control rod drive mechanism penetration in the vessel head. The workflow consists of a thermomechanical welding simulation with temperature-dependent plasticity, followed by cooldown to ambient conditions, and a restart of the simulation using the MOOSE extended finite element method (XFEM) module to propagate a three-dimensional crack through the residual stress field. New welding capabilities were developed to properly initialize newly activated elements in the weld region, and robustness improvements were made to the mesh-based algorithm for defining cutting planes in the 3D XFEM algorithm, allowing it to handle complex crack fronts and stress fields. Together these advances allowed the simulated SCC crack to grow from an initial elliptical flaw in the weld, across the weld, through the tube wall, and almost to the triple point (where the weld, tube, and reactor pressure vessel head intersect) over roughly 36 years of simulated service. These results demonstrate a workflow that can be extended to fully three-dimensional welding simulations and more complex crack interaction problems.

42 - ENGINEERING↗

Energy savings and life cycle cost analysis of advanced double skin facade system applied to old apartments in South Korea

South Korea is one of the most densely populated countries in the world, and the population density in urban areas is much higher among others. Apartments are the most common form of residential buildings due to their high population density. More than 60% of domestic residential buildings are apartments, with more than 10 million households. The high population density is a problem that has long plagued South Korea because more than 45% of apartments are old apartments that are more than 20 years old. Old apartment buildings have low thermal performance that results in lots of energy consumption. Balconies, which worked as a thermal buffer, are also being removed by residents to expand indoor space. According to the green remodeling project supported by the Korean government, the typical retrofitting method is replacing external windows with the high-efficiency window in old apartments in South Korea. Here, this paper proposes a retrofitting method using an extended double-skin façade (DSF) system that replaces exterior windows and acts as a thermal buffer. The simulation model is developed with the EnergyPlus simulation program to conduct energy performance analyses. The simulation model has been calibrated using actual experimental data collected between October 1, 2019, and January 15, 2020. Results show that the cooling, heating, and lighting energy can be reduced up to 44.1% by fully utilizing electric energy generated by solar PV panels integrated with the DSF system. The payback period is about 15 years based on the energy price provided by the utility company. Although the payback period is long, it has great potential of energy savings and CO 2 emission reductions. The DSF system should be considered as a way of renovation, considering other factors such as increased real estate values and energy cost increases in the future.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

SIPMaP: A Tool for Modeling Irregular Parallel Computations in the Super Instruction Architecture

Performance modeling is becoming an increasingly important part of the parallel application development process, particularly for expensive computations that will be run on very high-end systems where resources are scarce. We describe a performance modeling tool SIPMaP (Super Instruction Processor Modeling and Prediction) developed for the Super-Instruction Architecture (SIA). The SIA is designed for applications where the dominant data structures are large multi-dimensional arrays and it comprises a DSL, the Super-Instruction Assembly Language (SIAL) that supports expressing algorithms in terms of blocks (tiles), and its runtime system Super Instruction Processor (SIP) that manages distribution and disk storage of the arrays. SIPMaP generates performance models from the SIAL source code. In comparison with many applications where useful performance models have been developed and reported, these programs are irregular and have other difficult to model characteristics such as extensive overlapping of communication and computation.

Computer Science↗

A Decomposition Approach for Solving Seasonal Transmission Switching

Economic transmission switching has been proposed as a new control paradigm to improve the economics of electric power systems. In practice, the transmission switching operation itself is a disruptive action to the system. Frequently switching lines into or out of service can create undesirable effects on the security and reliability of power systems and may require new investments in the automation and control systems. In this paper, we formulate an economic seasonal transmission switching model where transmission switching occurs once at the beginning of a time period (season) and then the transmission topology remains unchanged during that period. The proposed seasonal transmission switching model is a large-scale mixed integer programming problem. The objective of the optimization model is to minimize the total energy generation cost over the season subject to loads and N-1 reliability requirements. We develop a novel decomposition method that decomposes the seasonal problem into one-hour problems which are then solved efficiently. We demonstrate our model and the decomposition approach on the 14-bus, 39-bus, and 118-bus power systems and show potential cost savings in each case.

Decomposition↗