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DOE OSTI2021

Predicting structural material degradation in advanced nuclear reactors with ion irradiation

Swelling associated with the formation and growth of cavities is among the most damaging of radiation-induced degradation modes for structural materials in advanced nuclear reactor concepts. Ion irradiation has emerged as the only practical option to rapidly assess swelling in candidate materials. For decades, researchers have tried to simulate the harsh environment in a nuclear reactor in the laboratory at an accelerated rate. Here we present the first case in which swelling in a candidate alloy irradiated ~ 2 years in a nuclear reactor was replicated using dual ion irradiation in ~ 1 day with precise control over damage rate, helium injection rate, and temperature and utilize physical models to predict the effects of radiation in reactors. The capability to predict and replicate the complex processes surrounding cavity nucleation and growth across many decades of radiation dose rate highlights the potential of accelerated radiation damage experiments. More importantly, it demonstrates the capability to predict the swelling evolution and the possibility to predict other features of the irradiated microstructure evolution that control material property degradation required to accelerate the development of new, radiation-tolerant materials.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Summary of Development for Structural Component Modeling in Fiscal Year 2022

This report summarizes efforts performed during Fiscal Year 2022 to develop capabilities for modeling structural component degradation in support of the U.S. Department of Energy's Nuclear Energy Advanced Modeling and Simulation Program. These efforts were centered around development of capabilities for the Grizzly code. Efforts focused both on foundational engineering-scale analysis capabilities for damage and shell formulations and on material-scale tools for accounting for irradiation effects in Grade 91 steel. A major outcome of this effort was the development of a general-purpose tool for nonlocal averaging of material properties, which enabled nonlocal damage models. In addition, the applicability of the shell elements in MOOSE has been expanded to allow modeling a wider range of component geometries and using a wide variety of material models. For irradiation effects on materials, a previously developed cluster dynamics model for light water reactor pressure vessel steels has been adapted for application to Grade 91 alloy. This work builds on prior efforts to build a flexible, capable code for addressing a variety of aging and component performance issues in nuclear power plant structural components.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Lightning Burnthrough to Containment Breach of 55-Gallon TRU Waste Drums

We investigated by arc-plasma heating the feasibility of attributing inherent lightning protection to 55-gallon DOT 7A, Type A, open head carbon steel drums made of 1.5 millimeter painted carbon steel, designed to protect Department of Energy transuranic nuclear waste. The Sandia Lightning Simulator transferred continuing current in 300 ampere (A), 400 A, and 500 A tests to achieve a 350 coulomb charge transfer and simulate cloud-to-ground lightning attachment to test coupons and 9 drums. A tungsten electrode was placed 0.75 inch from the drums. High-speed photography was recorded to observe the exterior containment breach, or "first light," seen on camera when burnthrough opened a hole in the containment. Sheet metal burnthrough occurred between 18 and 71 coulombs in lid and rolling hoop tests, but 12-gauge closure ring tests did not result in burnthrough, which suggests this feature may provide an inherent air terminal protective feature.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

Improvement of mechanistic fuel-cladding chemical interaction modeling in BISON

This report describes work performed during FY2024 under the auspices of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to inform and improve mechanistic models of fuel-cladding chemical interaction (FCCI) in metallic fuel. For fuel-side FCCI, atomistic simulations were performed to determine the diffusivity of iron (Fe) in the $\alpha$ and $\gamma$ phases of uranium (U). A model of liquid penetration of cladding due to melting of the fuel-side FCCI region was updated to account for the finite size of the FCCI region, and the model was validated through comparison with tests performed in the Fuel Behavior Test Apparatus (FBTA). For cladding wastage formation, a reduced-order model was improved by comparison with a multi-scale mechanistic model to better quantify the ROM parameters.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Modeling Flow and Particle Deposition in a Spent Nuclear Fuel Assembly

CFD (Computational Fluid Dynamic) simulation of aerosol-laden natural convective flow and particle deposition in a spent fuel storage canister with 37 assemblies is currently computationally prohibitive. PWR (Pressurized Water Reactor) assemblies have up to 289 pins or tubes with several spacer grids to align the pins. Spacer grids with mixing vanes induce swirling during operation to increase heat transfer. Each spacer grid contains hundreds of small structures such as retaining clips, channel walls, and openings. The largest canisters store 37 PWR assemblies thus, there are numerous pins, tubes, and spacer grids for which the flow region between and around these structures needs to be determined along with the movement and deposition of aerosol particles. Because of the complicated geometry, modeling the intricate flow even for just one assembly is currently impractical. Nonetheless, we are developing techniques for a practical model to assess the natural aerosol particle deposition process in a canister in the event that a release occurs from one or more fuel pins. In the previous work it was demonstrated that CFD can model the flow through a PWR spacer grid with mixing vanes, including particle deposition, in a reasonable amount of time on a personal computer. In this work, the analysis is extended to include the bypass region between an assembly and the canister basket walls. It is shown that the flow velocity in the bypass region is about three times that of the interstitial region between the pins. The lengths before and after the spacer grid are also extended to determine when the flow becomes fully developed. In addition, the approach of computationally “stitching together” segments of an assembly is demonstrated with the plan to ultimately model a full assembly. The fraction of particles that are deposited in a segment with a spacer grid is determined as a function of particle size and flow velocity.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Methods and Usability Enhancements in Shift for Non-LWR Applications

Several development and analysis tasks were undertaken in FY21 under the Nuclear Energy Advanced Modeling and Simulation program to enhance modeling of non light–water reactors (LWRs) with Shift. Specifically, these efforts targeted enhancements for tristructural isotropic (TRISO) fuel modeling. A new Shift user interface was developed that allows for much better usability and ease of modeling for non-LWR problems and TRISO fuel. Performance studies were conducted using an HTR-10 fuel pebble model by comparing different geometry packages in Shift, KENO-VI, and Serpent. These studies showed that the new geometry package in Shift performs well compared to Serpent for TRISO fuel modeling with consistent tracking options between both packages. The studies also identified the most critical areas of improvement for more efficiently performing Monte Carlo transport on TRISO fuel models with Shift. Tally calculations in Shift were optimized for non-LWR cross section generation and depletion calculations, and areas for further optimization and accuracy improvements were identified. Finally, initial collaboration efforts were formed between Idaho National Laboratory, Argonne National Laboratory, and the Nuclear Regulatory Commission to use Shift for Comprehensive Reactor Analysis Bundle support.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Initial Engineering Framework for Species Tracking in MSRs Involving Fuel Salt and Structures

This report implements a high-fidelity multiphysics modeling framework using the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program tools to track leaching and plating of materials between the fuel salt and structures in Molten Salt Reactors (MSRs). Specifically, this framework is demonstrated in modeling various processes within MSRs including hot and cold leg corrosion, redox potential driven corrosion, colloid precipitation and deposition, and noble metal plating and decay heat modeling. The model integrates neutronics, thermal-hydraulics, depletion, and thermochemistry to simulate the evolving chemical behavior of the fuel salt in interactions with structural materials. Initial findings suggest that hot-cold leg corrosion in MSR systems may become significant if the redox potential of the fuel salt is not sufficiently controlled. Additionally, the impact of noble metal decay heat deposition in large power reactors is explored. The resulting engineering framework for species tracking will be applied in the future toward specific validation work with ongoing experimental efforts focusing on both chloride and fluoride salt loop experiments with in-situ corrosion and redox control instrumentation.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

CONNECT Neutronics Initial Report

This report represents the first status update from the Creation of Next-generation Nuclear Energy Computational Technology (CONNECT) effort within the Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program and is intended to satisfy the reporting requirements of the following milestones: • M3MS-24OR0101321: Assess needs, requirements and opportunities for high-fidelity neutronics and transport as used in DOE-NE program. • M3MS-24AN0101301: Generate a community report on the needs, requirements, and opportunities for high-fidelity neutronics and transport as used in DOE-NE programs and industry. • M3MS-24OR0202433: Implement and assess numerical strategies leveraging Monte Carlo neutron transport on GPUs for production analysis. In particular, Sections 1, 2, and 3 detail the assessment of the current state of practice and the landscape of the broader advanced computing world to meet the objectives of M3MS-24OR0101321 and M3MS-24AN0101301, while Sections 4 and 5 describe new work during FY24 to extend current GPU Monte Carlo capabilities in areas relevant to active NEAMS development to satisfy M3MS-24OR0202433. Section 6 offers some thoughts about the potential future impact of Monte Carlo neutronics on NEAMS and the nuclear industry.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Demonstration and Verification of Thermo-Mechanical Bowing in a Limited Free-Bow SFR Concept Using MOOSE

Core bowing due to thermal gradients and irradiation induced swelling and creep introduces significant reactivity feedback effects in liquid metal-cooled fast spectrum reactors. During startup, normal operations, and transient events, differential thermal and flux gradients cause expansion, creep, and swelling, which results in bowing in preferential directions depending on local material properties and load-pad and restraint-ring design. The bowing phenomenon produces negative reactivity during accident conditions provided the restraint system has been properly designed to optimally guide the deformation outwards in the active core region. Under the Department of Energy Nuclear Energy Advanced Modeling and Simulation program, a Multiphysics Object Oriented Simulation Environment (MOOSE)-based multiphysics approach to model core bowing is being developed. The present work expands on previous modeling of simpler International Atomic Energy Agency (IAEA) verification problems with these tools by modeling IAEA Verification Problem 4, which involves a symmetric sector of a reactor core with ducted assemblies undergoing differential thermal expansion due to thermal gradients bowing outward with duct-to-duct contact. This model is available on the National Reactor Innovation Center Virtual Test Bed repository. This example was verified against benchmark participant results, which includes bowing deformation evaluation and duct-to-duct interactions at load pads with mechanical contact.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Application of Machine Learning Algorithms to Identify Problematic Nuclear Data

In this work we aim to show that Machine learning algorithms are promising tools for the identification of nuclear data that contribute to increased errors in transport simulations. We demonstrate this through an application of a machine learning algorithm (Random Forest) to the Whisper/MCNP6 criticality validation library to identify nuclear data that are associated with an increase of the bias (simulated - experimental $k_{eff}$) in the calculations. Specifically, the $k_{eff}$ sensitivity profiles (w.r.t. nuclear data) of 233 U solution benchmarks are used to predict the bias and Shapley Additive Explanations (SHAP) are used to explain how the sensitivities are related to the predicted bias. The SHAP values can be interpreted as sensitivity coefficients of the machine learning model to the $k_{eff}$ sensitivities which are used to make predictions of bias. Using the SHAP values we can identify specific subsets of nuclear data which have the highest probability of influencing bias. We demonstrate the utility of this method by showing how SHAP values were used to identify an inconsistency in the 19 F inelastic scattering nuclear data. The methodology presented here is not limited to transport problems and can be applied to other simulations if there are experimental measurements to compare against, simulations of those experimental measurements, and the ability to calculate sensitivities of the model output with respect to the data inputs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Infrastructure improvements in the National Reactor Innovation Center Virtual Test Bed

The National Reactor Innovation Center’s (NRIC) mission is to support deployment of novel reactor concepts. This is achieved by providing physical and virtual spaces for building and testing various components, systems, and complete pilot plants. The Virtual Test Bed (VTB) represents the virtual counterpart to the physical test bed. The VTB is being developed in collaboration with the Department of Energy’s (DOE) Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. The mission of the VTB is to accelerate the deployment and licensing of advanced reactors by leveraging state-of-the-art modeling and simulation (M&S) tools developed by the DOE NEAMS program. This is accomplished via three primary means: (1) openly hosting simulations that showcase analysis capabilities, (2) continuously testing the models hosted against code updates to avoid deprecation, and (3) filling key M&S gaps that are relevant for the physical NRIC test beds. The VTB repository consists of two sub-entities: • A documentation website detailing the models: https://mooseframework.inl.gov/virtual_test_bed • A GitHub repository that hosts the corresponding files: https://github.com/idaholab/virtual_test_bed. This paper presents the infrastructure added to the VTB in the last two fiscal years. Additional information about the VTB can be found in various publications [1, 2, 3, 4, 5, 6, 7, 8].

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Compare predictions of transient fission gas release by empirical and mechanistic models to experiments in high burnup UO 2 fuel

Understanding and predicting fuel performance at high burnup require improving our understanding of transient fission gas release. High-burnup operations enable new mechanisms of fission gas release, which affect fuel performance. The Nuclear Regulatory Commission has recently published its interpretation of existing fuel fragmentation, relocation, and dispersal data in a research information letter. There, transient fission gas release was identified as one of the main factors that contributes to fuel fragmentation, relocation, and dispersal, and therefore limits fuel extension to high burnup. However, transient fission gas release is a complex phenomenon that cannot be fully described by simple empirical descriptions. This report summarizes the development of a mechanistic model for high-burnup transient fission gas release in the fuel performance code BISON. This research was supported by the Nuclear Energy Advanced Modeling and Simulation program during fiscal year 2023 to improve our understanding of high-burnup transient fission gas release and ability to predict it as a function of operation history. To support the development of a mechanistic transient fission gas release model, the existing Simple Integrated Fission Gas Release and Swelling (Sifgrs) model in BISON has been completely refactored to make it more modular and extensible. This effort supports the model's application to high-burnup conditions, its extension to other fuel forms, and the continuous improvement of its current features. Once refactoring was completed, models for high-burnup structure formation, fission gas transfer from non-restructured fuel to high-burnup structure, high-burnup structure intragranular and intergranular fission gas behavior, high-burnup structure bubble evolution, fuel pulverization, and the resulting transient fission gas release were tested and implemented in the Simple Integrated Fission Gas Release and Swelling (Sifgrs) model or tightly coupled to it. The new mechanistic model was then compared to an empirical model developed in parallel by a Nuclear Energy University Program project using a Studsvik high-burnup loss-of-coolant-accident assessment case. Finally, the report details the preliminary BISON results for a benchmark activity organized by the Nuclear Energy Agency to evaluate fuel performance codes' predictive capabilities for burst fission gas release. This work represents an important step toward a mechanistic understanding of fission gas release in high-burnup conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Reactivity Coefficient Measurements to Aid in Reducing Compensating Errors in Plutonium Nuclear Data

Compensating errors between several nuclear data observables in a nuclear data library can adversely impact application simulations. The primary goal of the EUCLID project (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) is to reduce compensating errors between fast (0.1–5 MeV) 239Pu nuclear data for prompt fission neutron spectra (PFNS), average prompt fission neutron multiplicities, and neutron induced fission, capture, elastic, and inelastic cross sections. This work will focus on the design and execution of void reactivity coefficient measurements in the EUCLID experiment, performed on the Planet vertical lift critical assembly machine at the National Criticality Experiments Research Center (NCERC). Two different base configurations were designed and measured, one with high neutron leakage, and one with low neutron leakage. Both were primarily made up of plutonium metal (Zero Power Physics Reactor plates) without interstitial moderators and reflected by half-inch aluminum. Design optimization showed that void reactivity coefficient measurements in three locations per configuration was most impactful to reduce nuclear data uncertainties due to the varying impacts from elastic and inelastic scattering, as well as fission and capture. The locations for measurements were chosen based on preliminary studies which balanced measurement uncertainty and measurement practicality. The measurements were also selected to have sensitivities maximally complementary to previous arrangements. Comparisons across nuclear data libraries highlight the potential impact.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

High-Burnup LOCA Burst Susceptibility BISON Analysis in PWRs and BWRs

Accurately assessing high-burnup fuel behavior during loss-of-coolant accidents (LOCAs) is essential for understanding fuel fragmentation, relocation, and dispersal (FFRD) risks across the US light-water reactor fleet. This work updates previous Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program multiphysics LOCA analyses for a pressurized water reactor (PWR) and a boiling water reactor (BWR) by incorporating recent model and material property advancements in the BISON fuel performance code, including a high-burnup structure (HBS) model, revised cladding burst criteria, and updated thermal–mechanical correlations. This update was needed to support ongoing industry initiatives and upcoming regulatory changes. Full-core, rod-resolved operating histories generated using Virtual Environment for Reactor Analysis (VERA) and system-level LOCA conditions obtained from TRACE were applied to statistically representative rod samples in BISON to evaluate burst behavior and FFRD susceptibility. These calculations used two cladding burst correlations and three fuel pulverization models so that the predictions of these models could be compared. The updated PWR simulations show markedly improved numerical stability as the number of crashed simulations decreased by 95% compared to the previous study, and hence higher confidence in results. The updated PWR simulations predicted cladding bursts exclusively among once-burned, high-power rods, with two different cladding burst models identifying the same burst-susceptible population. Resulting FFRD susceptibility estimates are significantly reduced compared with earlier studies, driven by cooler predicted fuel and plenum temperatures, lower hoop strains, and reduced fission gas release in the updated models. In contrast, none of the BWR rods were predicted to burst under either burst criterion, reaffirming minimal BWR FFRD susceptibility even with updated HBS and material models. Comparisons between the PWR and BWR end-of-cycle predictions are made. Comparison with prior work highlights significant shifts in PWR fuel performance metrics and confirmation of earlier BWR conclusions. Overall, the updated results underscore the importance of having high-resolution detailed modeling capability and continuously integrating evolving material models and physics into high-resolution multiphysics simulations. The unified assessment presented here strengthens confidence in predicting high-burnup LOCA behavior by improving agreement between different cladding burst correlations. These results also provide an improved foundation for future BISON model development, FFRD susceptibility calculations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

The ARENA Test Bed – A Versatile Resource for I&C Development and Validation

The Accelerated and Real-time Experimental Nodal Assessment (ARENA) Test Bed at the Pacific Northwest National Laboratory (PNNL) is a versatile resource for development and validation of instrumentation and control (I&C) technologies. This capability was created to facilitate in-situ testing of nuclear electrical cables in various simulated operational environments. Using cable trays, a control box, and selected test components, low voltage cables can be staged to experience local adverse environments such as elevated temperature and water immersion. Cable condition can be continuously monitored over time to track the effect of local stresses using nondestructive assessment tools. A heads-up display (ARENA TV) plots key data in real-time for users. The ARENA Test Bed has recently been used to evaluate the potential for spread spectrum time domain reflectometry (SSTDR) to monitor thermal aging of a portion of live cable powering a three-phase motor. The arrangement provided the opportunity to directly compare the performance of the novel online SSTDR method with offline results from the more standard frequency domain reflectometry (FDR) method. The ability of SSTDR and FDR to identify the presence of water in immersed shielded and unshielded cables and to detect ground faults was also assessed. A digital twin is being developed to track and predict FDR signals from a thermally aging conceptual cable region to compare with measured signals from the ARENA physical counterpart. The test bed concept addresses an important need in nuclear I&C monitoring tool development. New tools and techniques can be developed in the test bed and validated versus known methods and physical measurements. Digital twins and machine learning engines can be populated with measured data in a controlled environment that would not be readily available in the actual nuclear power plant. Proposed monitoring strategies can be confirmed for effectiveness through objective evaluation. It is anticipated that the PNNL ARENA Test Bed will be a valuable resource in advancing nuclear plant instrumentation.

nuclear electrical cables, ARENA Test Bed, conditi↗

DOE OSTI2026

2026 Annual Molten Salt Reactor Campaign Review

This report documents the 2026 Annual Molten Salt Reactor (MSR) Campaign Review held in Albuquerque, New Mexico, from April 21–24, 2026. The review was organized by Dr. Patricia Paviet, National Technical Director of the Advanced Reactor Technology (ART) MSR program for the U.S. Department of Energy Office of Nuclear Energy (DOE-NE), and included participation from principal investigators, federal managers, developers, regulators, and members of the broader MSR community. The 2026 review expanded beyond the ART-MSR campaign to include related DOE-NE programs supporting molten salt reactor advancement, including the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, the Advanced Materials and Manufacturing Technologies (AMMT) program, Advanced Reactor Safeguards and Security (ARSS), Material Protection, Accounting and Control Technologies (MPACT), and relevant advanced fuels activities. Three days were dedicated to technical presentations and panel discussions covering thermal properties, off-gas management, modeling and simulation, safety and licensing, safeguards and security, materials and corrosion, and irradiation activities. A fourth day was dedicated to technical tours of Sandia National Laboratories and Kairos Power facilities. Attendance was strong and comparable to the prior annual review, with approximately 75 in-person participants per day, 75–80 virtual attendees per day, and approximately 30 participants in the tour day. The review fostered significant technical exchange across national laboratories, universities, industry, regulators, and international participants. This report summarizes the review structure, technical themes, participation, tours, feedback, and conclusions relevant to future planning for the MSR campaign.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

The Stability of SiO{sub 2} Fe{sub 3}O{sub 4} Nanoparticles for Uranium Extraction in Acidic Media - 20189

This comprehensive study has shown that the proposed strategy of SiO{sub 2} coating of Fe{sub 3}O{sub 4} nanoparticles (NPs) for the use of uranium (U) extraction in acidic media was successful. The breakdown of Fe{sub 3}O{sub 4} in acidic media has proven to be a challenge when applying to a nuclear waste removal scenario, leading to the dissolution of Fe{sub 3}O{sub 4} and preventing uptake of U ions in the waste. To overcome this a SiO{sub 2} passivating layer was grafted to the Fe{sub 3}O{sub 4} NPs, to which an acid stability test was conducted between pH 3 and pH 4. It has been shown via Transmission Electron Microscopy (TEM) and zeta potential measurements that the uncoated Fe{sub 3}O{sub 4} NPs exhibit rapid coagulation when exposed to acidic conditions, moving from a stable zeta potential of -44 mV to an unstable zeta potential of +6 mV. SiO{sub 2} coated Fe{sub 3}O{sub 4} on the other hand can remain stable for several hours and continue to be stable beyond that. Throughout acid exposure the zeta potential of these NPs remained at ∼ -38 mV, showing great stability. As a functionality is needed on the surface of the NPs for separation and extraction, the phosphate complex used was also tested for its acid stability. It was determined that with a constant zeta potential of ∼ -20 mV, the phosphate functionality was able to remain stable in the acidic conditions simulating the environment of certain nuclear wastes. Overall SiO{sub 2} coated (PO)x-Fe{sub 3}O{sub 4} NPs show great promise for application in separation and removal of U in acid media. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2025

Griffin Capability Improvements in Support of Ex-core Deep-Penetration Problems

Advanced reactor designs, especially portable reactors that are designed to be located closer to humans and operate autonomously, require the ability to accurately compute the ex-core neutron and gamma flux solutions in terms of shielding design optimization to reduce dose rates at the vessel boundary and detector signal prediction to drive the reactor control system. The Nuclear Energy Advanced Modeling and Simulation program has prioritized improvements to the Griffin discrete ordinates (SN) solver for deep-penetration problems in fiscal year 2025. Significant advancements have been made to the Griffin methodologies for solving ex-core deep-penetration problems for steady-state, fixed-source and transient calculations. This work presents the methodology improvements as well as a comprehensive demonstration with a Transient Test Reactor model and measurements.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗