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DOE OSTI2016

Analysis of the uncertainties in the physical calculations of water-moderated power reactors of the VVER type by the parameters of models of preparing few-group constants

The article covers the uncertainty analysis of the physical calculations of the VVER reactor core for different meshes of the reference values of the feedback parameters (FBP). Various numbers of nodes of the parametric axes of FBPs and different ranges between them are investigated. The uncertainties of the dynamic calculations are analyzed using RTS RCCA ejection as an example within the framework of the model with the boundary conditions at the core inlet and outlet.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2016

A Case Study in the Application of TSUNAMI-3D - Part 1, Multigroup

The use of the sensitivity and uncertainty tool suite within SCALE, known as the TSUNAMI suite, has grown following its initial introduction more than a decade ago. Proper use of these tools provides a more complete understanding of system responses to perturbations, especially in the area of nuclear cross section uncertainties. Recent advances within TSUNAMI have added generalized perturbation theory to the k{sub eff} sensitivity capability that was included in TSUNAMI originally. The generation of sensitivity data is encouraged in the review process for new critical experiment requests sponsored by the US Department of Energy (DOE) Nuclear Criticality Safety Program (NCSP) to demonstrate that the proposed experiment will satisfy the identified data need. Many individuals participate in this process, but many analysts have not received proper training in the use of the TSUNAMI tools. The adjoint perturbation theory used to calculate sensitivities is not typically included in nuclear engineering curricula, leaving inexperienced engineers particularly at risk for incorrect use of the tools. The first step in the use of the TSUNAMI tools is the generation of a sensitivity data file (SDF), which contains all of the energy-dependent sensitivity data generated for a model. Most often, the SDF is generated from a three-dimensional (3D) model using either the KENO V.a or KENO-VI code within the TSUNAMI-3D sequence. The sensitivity data generated in TSUNAMI-3D must be accurate for correct quantification of system similarity or any other use of the sensitivity data. The sensitivities calculated by TSUNAMI can be affected by many of the input parameters, cross section processing models, and geometry modeling techniques used within the TSUNAMI-3D input. Fortunately, the total sensitivity of the most important nuclides can be confirmed simply by using direct perturbation (DP) calculations. Confirmation of the total sensitivity of these important nuclides provides confidence that the flux and importance function calculated within the TSUNAMI sequence will yield accurate sensitivities for all nuclides, reactions, and energies of interest. This process is essentially identical for the multigroup (MG) methods and the continuous-energy (CE) methods introduced in SCALE 6.2. This paper discusses the use of DP calculations and provides a case study to confirm that accurate sensitivities are generated by TSUNAMI-3D for a particular benchmark experiment. A companion paper provides a similar case study applying the CE TSUNAMI capability to the same critical experiment. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Demonstration of CFD to support the coupled analysis of a reactor pressure vessel subjected to pressurized thermal shock

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Simulation and Analysis on Reactor Pressure Vessel (RPV) subjected to Pressurized Thermal Shock (PTS) under SBLOCA scenario by using Cardinal to support the fracture mechanics analyses

The structural components that comprise nuclear reactors and their supporting structures are subjected to harsh operating environments that can challenge their integrity, especially after exposure for extended durations or under accident condition. As one of the most significant components of a Reactor, the Reactor Pressure Vessel (RPV) is exposed to an aggressive environment during the operation time (e.g. more than 40 years). Ageing degradation mechanisms (e.g. thermos-fatigue) could grow initial defects up to a critical size, increasing the susceptibility to failure in the RPV. The conventional methods are mostly based on simple crack and structure geometries. Very limited studies consider the real conditions of the RPV subjected to a thermal shock due to a Loss of Coolant Accident (LOCA). During a LOCA event, the most severe conditions take place when the emergency core cooling (ECC) water is injected inside the cold legs filled initially with hotter water and/or steam. The rapid cooling of the down-comer and the internal RPV surface followed probably by re-pressurization of the RPV causes large temperature gradients and variation of pressure which induces thermal-mechanical stresses. In order to develop the model for integrity assessment of a reactor pressure vessel (RPV) subjected to pressurized thermal shock (PTS), a multi-physics simulation, which includes the thermo-hydraulic, thermo-mechanical and fracture mechanics analyses is necessary. The multi-physics simulations are performed using Cardinal, a wrapping of the GPU-oriented spectral element Computational Fluid Dynamics (CFD) code NekRS and other multi-physics sub-modules within the MOOSE framework. Cardinal now fully supports MOOSE stochastic perturbations of NekRS models with varying boundary conditions, initial conditions, material properties, and any other quantity which is defined by a kernel (such as coefficients in a momentum source model). The implementation is designed in a flexible manner so that scalar values are sent from MOOSE into a user scratch space in NekRS, which can then be applied for any purpose within the NekRS case files (both on the host and device). When modeling PTS, several factors can impact the results significantly. In this report, the impacts of the geometry of the model, Reynolds number and buoyancy effect are investigated. Two geometry, i.e., a simplified model and a realistic RPV model, with both laminar and turbulent flow condition are adopted for the PTS simulation with and without buoyancy effect. The purpose of the investigation is to understand the impact of these factors on the prediction of temperature history of RPV. The accurate prediction on the temperature evolution, which will be exported to Grizzly code for further analyses on the progression of aging mechanisms and their effects on the integrity of RPV structures, is very crucial. Based on the understanding of these factors, a more sophisticated model is built to analysis the PTS under SBLOCA scenario. A literature survey is conducted to pick the SBLOCA scenario for the multi-physics simulation. The analysis helps to explain the form and the transformation of the cold plum when the ECC is activated under SBLOCA. This model can be can be applied to study the PTS effect for different RPV configurations. The results can help to assess structural component degradation for advanced reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

Model Calibration vs. Physics-guided Coverage Mapping: Case Study - Pressure Drop Calculations

This work deals with a fundamental question in model validation: given a body of available experiments and an envisaged domain of nuclear reactor operating conditions (referred to as the reactor application), how can one develop a quantitative approach that measures the portion of the prior uncertainties of the reactor application that is covered by the available experiments? Coverage here means that the uncertainties of the reactor application are originating from and behaving in exactly the same way as those observed at the experimental conditions. This approach is valuable as it provides a scientifically defendable criterion by which experimentally measured biases can be credibly extrapolated (i.e., mapped) to biases for the reactor applications. This work focuses on the application of a new methodology, referred to as physics-guided coverage mapping (PCM), to the estimation of hydraulic pressure losses in reactor pipes. PCM provides a generic, calibration-free approach to the mapping of experimental biases by relying on high fidelity physics simulation and information theoretic measure how much of the application domain is covered by the experiments. The idea is to employ the physics models to establish a joint probability distribution that relates the application and the available body of experiments. An information-theoretic measure, referred to as the mutual information, is used to calculate a quantitative metric that measures the inter-dependence between the application and the experiment. A virtual experiment is employed to demonstrate the application of PCM, wherein the pressure drop is calculated for both the experiment and the application using two different flow conditions, i.e., laminar and turbulent, and the experimental values are simulated. All parameters introducing uncertainties, such as geometry, friction factor formulas and their associated parameters are also incorporated. The results obtained with PCM are compared to a conventional calibration-based approach. This work show that the proposed approach can circumvent a number of challenges that face calibration-based methods, such as nonlinearity, ill-posedness and error compensation in high dimensional models with many parameters. This work focus primarily in this summary on parameter uncertainties and how they can be treated using PCM. In a separate summary, discuss performance of PCM under the presence of modeling uncertainties. This simple study has shown that calibration techniques for very simple situations cannot correctly scale the measurements from the experimental to the application domain. It is our view that is occurs primarily due the phenomenon of error compensation where on artificially changes the value of selected parameters to account for all sources of uncertainties. The situation gets more complicated when one calibrates multiple parameters where now the problem could potentially have an infinite number of ways by which the errors can be compensated. (authors)

42 ENGINEERING↗

DOE OSTI2020

Hydrodynamic Characterization of a Shallow Rectangular Spouted Bed Using Bed Pressure Signals and Image Processing Methods

To support the design of spouted bed reactors, experiments are performed in a rectangular spouted bed to measure the peak pressure drop (Δ P max ) and the internal and external spouting velocities ( U is and U es ). Four particle types spanning under Geldart D and B are used. U is and U es are measured from bed pressure drop and expansion ratio profiles, respectively, with the U es / U is ratio of each particle type obtained. Additionally, correlations predicting the Δ P max of Geldart D and B particles are developed by reviewing published correlations and investigating the nozzle effect. Good prediction is achieved with a slope of 0.997 and an adjusted R 2 of 0.998 in a 95% confidence interval. U es is predicted through correlations developed by adding effects of d p / D i and H 0 in the Mathur–Gishler equation. The calculated U es agrees well with the experimental data, achieving a slope of 0.998 and an adjusted R 2 of 0.998 in a 95% confidence interval.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Electrodialysis: An effective methodology to purify the leachate of spent Li-ion batteries

The electrification of transportation and the transition of society towards low or net-zero carbon emissions has led to a skyrocketing global demand for Li-ion batteries. After a service life of three to ten years, Li-ion batteries have less than 80 % of their initial capacities and draw near to the end of their lives for practical utilization. Due to potential supply chain shortages and the value embodied in Li-ion batteries, it is imperative to recycle them, to recover the materials, and to improve the circularity and the sustinability of the industry. How to cost-effectively purify spent batteries while reducing time, energy, and waste emissions is a challenge faced by Li-ion battery recyclers. The first electrochemical membrane reactor reported in our group hasa high selectivity towards lower Cu 2+ , Al 3+ and Fe 3+ ions (<5 ppm) and retains >95% of the Ni 2+ , Co 2+ and Mn 2+ ions in the leachate. An advanced electrochemical membrane reactor was developed in this study. Further, not only does the new reactor have the same selectivity as the original reactor, but other advantages including a faster leachate processing rate (up to 10X faster). The advanced reactor can also directly generate acid at the anode side; eliminating the reactor restoration step. The prominent advantages that this electrodialysis technology has over chemical-precipitation methods include: (1) ion recovery efficiencies do not diminish after removing the impurities, Ni 2+ , Co 2+ and Mn 2+ , even at a higher initial Ni 2+ ion concentrations; in comparison, chemical precipitation has Ni 2+ , Co 2+ and Mn 2+ ion recovery efficiencies reduced significantly when the initial Ni 2+ , Co 2+ and Mn 2+ ion concentrations increase. (2) electrodialysis does not change the concentrations of Ni 2+ , Co 2+ and Mn 2+ ions significantly, but chemical precipitation could reduce Ni 2+ and Co 2+ ions to less than half of their initial values. Through electro-dialyzing the leachate, the H 2 evolution reaction mechanism was found to switch from the Volmer-acid Heyrovsky mechanism to the Volmer-alkaline Heyrovsky mechanism at a pH of around 3.7.

25 ENERGY STORAGE↗

DOE OSTI2019

CTF Code Verification and Solution Verification

The CTF code is part of the suite of codes developed with DOE funding under the CASL Program to bring the benefits of high-performance computing to issues of importance to the US nuclear power industry. This document primarily focuses on code and solution verification test problems that have been developed to ensure that CTF converges to the correct answer for the intended application. Convergence behavior and numerical errors are quantified for each of the tests. The observed convergence behavior in all available tests is consistent with expectations for the numerical methods employed by CTF, providing evidence that there are no significant code bugs or algorithm deficiencies in the code. The suite of code verification and solution verification tests are mapped to core capabilities of CTF. Gaps were identified in the code verification test suite and they are being addressed. Two new code verification problems were developed to address gaps that were identified.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2019

Impacts of Fast-Spectrum Molten Salt Reactor Characteristics on Fuel Cycle Performance

The System Analysis and Integration Campaign nuclear fuel cycle evaluation and screening study was conducted to outline the potential benefits and challenges of nuclear fuel cycle options. The study identified continuous recycle in fast critical reactors as a common characteristic shared among some of the most promising future nuclear fuel cycles. This study was technology agnostic to focus on the underpinning physics that drives fuel cycle outcomes. This process used an analysis example to generate a physics-based understanding of the fuel cycle, and it yielded performance metrics over ranges rather than comparing absolute numbers. While no fast-spectrum molten salt reactor (MSR) has ever been built, several concepts exist using different fuels and carrier salts, many of which target high-burnup objectives, such as lightwater reactor nuclear waste consumption. Putting the resulting fuel cycle impacts of these reactor choices (e.g., fuel and neutron spectrum) into perspective is informative for our current understanding of a given fuel cycle’s performance, and it also demonstrates the applicability of MSRs to different fuel cycles. It has been established that in a fuel cycle transition, performance of a given fast-spectrum MSR depends in part on the initial fuel loading requirements and processing methods.

Betzler, Benjamin↗

DOE OSTI2018

Inductive System for Reliable Magnesium Level Detection in a Titanium Reduction Reactor

The determination of the Magnesium level in a Titanium reduction retort by inductive methods is often hampered by the formation of Titanium sponge rings which disturb the propagation of electromagnetic signals between excitation and receiver coils. We present a new method for the reliable identification of the Magnesium level which explicitly takes into account the presence of sponge rings with unknown geometry and conductivity. The inverse problem is solved by a look-up-table method, based on the solution of the inductive forward problems for several tens of thousands parameter combinations.

36 MATERIALS SCIENCE↗

DOE OSTI2017

A practical globalization of one-shot optimization for optimal design of tokamak divertors

In past studies, nested optimization methods were successfully applied to design of the magnetic divertor configuration in nuclear fusion reactors. In this paper, so-called one-shot optimization methods are pursued. Due to convergence issues, a globalization strategy for the one-shot solver is sought. Whereas Griewank introduced a globalization strategy using a doubly augmented Lagrangian function that includes primal and adjoint residuals, its practical usability is limited by the necessity of second order derivatives and expensive line search iterations. In this paper, a practical alternative is offered that avoids these drawbacks by using a regular augmented Lagrangian merit function that penalizes only state residuals. Additionally, robust rank-two Hessian estimation is achieved by adaptation of Powell's damped BFGS update rule. The application of the novel one-shot approach to magnetic divertor design is considered in detail. For this purpose, the approach is adapted to be complementary with practical in parts adjoint sensitivities. Using the globalization strategy, stable convergence of the one-shot approach is achieved.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

In this paper, three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MG Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. Finally, this solver set is a strong choice for very large and challenging problems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Determination of Molecular Structure and Dynamics of Molten Salts by Advanced Neutron and X-ray Scattering Measurements and Computer Modeling

The design and development of fully functional Molten-Salt Reactors (MSR) require detailed knowledge of the molten salt properties in order to understand and predict the salt’s behavior. Fundamental properties of interest include molecular structure, speciation, and dynamics (such as diffusion coefficients) of salt components and dissolved corrosion and fission products. Computer modeling is necessary to predict changes in physical and chemical properties due to irradiation, burning of dissolved fuel, and corrosion. The modeling requires experimental data, and advanced neutron and x-ray scattering and spectroscopy provide the most reliable and direct determination of the structure (Pair-Distribution Functions, PDF), and dynamics of ions in the melt. This project dealt with both fluoride and chloride salts. The PDFs have been measured by a combination of neutron and x-ray diffraction. We utilized the techniques of isotope substitutions, a very powerful tool available for neutron-scattering, to extract the details of the liquid structure. Although similar measurements have been done before, modern advanced neutron and x-ray-scattering techniques allow collecting the data at much higher resolution and in a wider range of temperatures. Importantly, we were among the first to study fluoride salts by neutron scattering. The importance of impurities and their effects on salt properties have become apparent recently and so new methods of salt purification were developed. We took advantage of these developments to produce reliable data, which have been used for computer simulations of both clean salts and those with added fission and corrosion products most relevant for MSRs. Ab initio molecular dynamics simulations have been performed to understand the multi-component liquid solution, in particular solubility of impurities and thermodynamic interactions in relation to the ionic-cluster structure of the fluid. We applied machine learning to regress from the simulation and experimental data in order to develop a fast-acting model that can handle molten salt with an arbitrary (≥ 10) number of chemical elements and be able to predict chemical potential as a function of composition and temperature. This project resulted in a number of experimental and computer-simulation publications, a patent application, and numerous conference presentations (American Physical Society, American Chemical Society, and The Electrochemical Society among others). Multiple students and postdocs participated and collaborated on aspects of this project. This project seeded new collaborations between MIT and other institutions, such as the University of Massachusetts Lowell, the University of Illinois Urbana-Champaign, the University of California Berkeley, and Oak Ridge and Los Alamos National Labs. As such, this project has had a broad and lasting impact beyond its original scientific scope.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Foundational Science to Accelerate Nuclear Energy Innovation [Brochure]

The foundational science gaps inhibiting the advancement of nuclear energy technologies are identified and tackled in five priority research opportunities. These opportunities pave the way to accelerate the development and ultimately the adoption of new nuclear energy systems. They include the fundamental aspects of ion-electron interactions; novel properties of next-generation coolants and solvents; interfacial dynamics, not only in solids, but in other aspects of nuclear reactors; novel operando and in-situ monitoring and sensing; and artificial intelligence to accelerate condensed phases discovery. Building on the foundation established by previous BES workshops, these opportunities encompass recent advances in fundamental knowledge and focus on the experimental and computational methods needed to resolve major technical challenges for nuclear energy technologies. Through developing fundamental scientific insight as well as pushing the frontiers of modeling complex systems and probing the operation of materials and chemical systems in extreme environments, research motivated by the priorities identified here will further develop the promise, potential, and utilization of nuclear energy for a clean energy future. The PROs are as follows: (1) Master complex electronic structures to tailor thermochemical reactivity, transport, and microstructural evolution; (2) Interrogate and direct the physics and chemistry underpinning next-generation coolants and solvents; (3) Elucidate and control the underlying physics and chemistry of interfaces in complex nuclear environments; (4) Bridge multi-fidelity multi-resolution experiments, computational modeling, and data science to control dynamic behavior; and (5) Harness artificial intelligence to design inherently resilient condensed phases.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

A Cybersecurity Event Simulation Tool and Platform

Digital Instrumentation and Control Systems (ICSs) have replaced analog control systems in nuclear power plants raising cybersecurity concerns. To study and understand the cybersecurity risks of nuclear power plants both high fidelity models of the plant physics and controllers must be created, and a framework to test and evaluate cyber security events must be established. A testing and evaluation framework of cybersecurity events consists of a method of interfering with control systems, a simulation of the plant network, and a network packet capture and recording tool. Sandia National Labs (SNL) in collaboration with the University of New Mexico’s Institute for Space and Nuclear Power Studies (UNM-ISNPS) is developing such a cybersecurity testing framework.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Feasibility Study on Implementing a Staggered-Grid Finite Volume Method for System Analysis Code Development Under the MOOSE Framework

Here, this work summarizes a feasibility study on testing numerical algorithms that are suitable and efficient for advanced system analysis code development under the mutli-physics framework, MOOSE. The key to the test bed is the implementation of high-order one-dimensional staggered-grid finite volume method (SG-FVM), and its direct interaction with the linear/nonlinear solver, PETSc. The test bed utilized a more flexible code structure to enable the finite volume method implementation and direct interacting with the solver package, instead of using the natively supported finite element method by the framework. Using a suite of selected test problems with different problem sizes and levels of complexity, the implemented SG-FVM demonstrated superior performance improvement against a direct finite element method implementation through MOOSE. On two computer systems, the speedup was observed to be significant, with at least one order of magnitude of solving time reduction. For a complex reactor model, transient simulation was performed using the newly developed finite volume method code, the results of which agree very well with the reference results from the finite element method code. Overall, this study demonstrates a successful feasibility study on the proposed numerical algorithms and software structure to support advanced system analysis tool development.

MOOSE↗

DOE OSTI2019

A Code to Code Benchmark for HTGR Fuel Element Depletion

The current lack of well-qualified experimental measurements for spent HGTR fuel elements limits the validation of advanced doubly heterogeneous depletion methods. Because of this shortage of data, a benchmark was developed as the first, simplest phase in a planned series of increasingly complex set of code-to-code benchmarks. The intent of this benchmark was to encourage submission of a wide range of computational results for depletion calculations in a set of basic fuel cell models. Comparison of results using independent methods and data should provide insight into potential limitations in various modeling approximations. The benchmark seeks to provide the simplest possible models, in order to minimize the effect of competing and potentially offsetting phenomena that might mask weaknesses in given methods. Twenty-one sets of results were submitted by twelve participants internationally. Various approaches were used for the treatment of microscopic grains dispersed in fuel elements in the second and third parts of the benchmark, including explicit treatment of grains distributed within a regular lattice, a randomized distribution of explicit grains, reactivity-equivalent physical transformation and a two-pass homogenization with disadvantage factors. The broad agreement appears to validate each of the double heterogeneity treatments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2019

Solution of the Feynman Equation for Time Evolving Fission Chains

The partial differential equation proposed by Feynman describing the time evolution of a fission chain in metal is solved by a method also proposed by Feynman. The partial differential equation is reduced to a transcendental algebraic equation. The solution involves roots of a 7th order polynomial. Both the roots and the transcendental equation are then solved numerically. Two populations are computed from the probability generating function, the internal number of neutrons in time, and the accumulated number of leaked neutrons in time. This same equation also describes a limit of a thermal reactor, where induced fission is totally driven by neutrons that have thermalized and are diffusing in a moderator.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗