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Uncertainty and Sensitivity Analysis of TREAT Transient Test #15

The U.S. Department of Energy (DOE) is preparing for the resumption of transient testing using the Transient Reactor Test Facility (TREAT) located at the Idaho National Laboratory (INL). In order to support the analysis of TREAT operation and experiment planning, the MAMMOTH reactor physics team has recently begun development of uncertainty and sensitivity analysis for the TREAT core simulated via MAMMOTH. MAMMOTH is a high-fidelity three-dimensional transient multi-physics code developed at INL under the DOE-NE Advanced Modeling and Simulation program (NEAMS) [1]. This research is part of the development presenting some initial uncertainty and sensitivity analysis of TREAT Transient Test #15 [2]. In this summary, we employ the Sobol sampling strategy implemented in RAVEN [3] to efficiently perform the sensitivity and uncertainty analysis. The idea is using Sobol functional decomposition with generalized polynomial chaos (gPC) expansions to estimate the responses of interest [4]. The gPC coefficients are then computed via the spectral projection method with sparse grid approach. In addition, this strategy includes evaluation of the second or higher order sensitivity indices, allowing the study of interactions between several input variables. The principal focus of this analysis is to quantify the uncertainties in the total power and maximum fuel temperatures with respect to uncertainties in the initial transient conditions, such as rated power, fuel temperature, graphite fuel density and control rod boron concentration. In addition, both the first order and second order time-dependent sensitivity indices are computed and analyzed. The results show that the interactions between initial control rod boron concentration and the rated power will contribute at most 1% to the total uncertainty of the power peak.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Analysis and Modeling of Lithium Flows in Porous Materials

One of the primary conditions necessary for the success of magnetic fusion reactors is the ability to mitigate damage to the first wall during ELMs and plasma disruptions. A potential solution involves the use of flowing liquid metals such as lithium as a first wall, but ensuring its stability under the extreme environments in the reactor would be imperative. The conditions leading to instabilities on the free surface of flowing liquid lithium (LL) layers on a substrate and in a porous material are investigated using both analytical methods and computational modeling, with consideration for the effects of LL velocity, LL layer thickness, substrate porosity, LL permeability, and hydrogen (H) plasma velocity. Linear stability analysis is used to predict the critical velocity and wavelength-dependence of wave growth, as well as the onset of instability. The modeling of LL flows is performed on a flat substrate and in a porous material for various LL thicknesses, LL and H plasma velocities to analyze the conditions leading to droplet formation and ejection.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Historical perspectives of BEPU research in US

Civilian nuclear energy started in earnest in the 1950s and experienced rapid growth in 1960-80s with increasingly larger reactors. These reactors were initially regulated based on the experience from the smaller reactors, but this could not be applied to the larger power reactors. Therefore, in 1974 the US Nuclear Regulatory Commission set up safety requirements based on defense in depth in 10 CFR 50.46, and set of guidance in 10 CFR 50 presented in Appendix K, for models and simulations of reactor safety analyses, to ensure conservatism in predicted safety parameters. These methods resulted in both conservative safety margins as well as economic and operational penalties. In the late 1970s and early 1980s, a large number of experiential programs provided data that allowed for the creation of best estimate models. These best estimate models showed the conservatism in Appendix K models. In 1988-89, USNRC modified the regulations and allowed the use of best estimate models provided they were coupled to a reliable and defensible measure of uncertainty in the prediction of safety parameters. This change in regulation strongly encouraged global activity for the development of best estimate codes and methods. To aide in this development, the USNRC provided one acceptable approach, the Code Scaling, Acceptability and Uncertainty Evaluation Methodology (CSAU). This approach was later refined in the Evaluation Model Development and Assessment Process (EMDAP).

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Measurement of proton quenching in a plastic scintillator detector

The non-linear energy response of the plastic scintillator EJ-260 is measured with the MicroCHANDLER detector, using neutron beams of energy 5 to 27 MeV at the Triangle Universities Nuclear Laboratory. The first and second order Birks' constants are extracted from the data, and found to be $k_B = (8.70 \pm 0.93)\times 10^{-3}\ {\rm g/cm^2/MeV}$ and $k_C = (1.42 \pm 1.00) \times 10^{-5}\ {\rm (g/cm^2/MeV)^2}$. This result covers a unique energy range that is of direct relevance for fast neutron backgrounds in reactor inverse beta decay detectors. Furthermore, these measurements will improve the energy non-linearity modeling of plastic scintillator detectors. In particular, the updated energy response model will lead to an improvement of fast neutron modeling for detectors based on the CHANDLER reactor neutrino detector technology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Evaluation of available analytical techniques for monitoring the quality of space station potable water

To assure the quality of potable water (PW) on the Space Station (SS) a number of chemical and physical tests must be conducted routinely. After reviewing the requirements for potable water, both direct and indirect analytical methods are evaluated that could make the required tests and improvements compatible with the Space Station operation. A variety of suggestions are made to improve the analytical techniques for SS operation. The most important recommendations are: (1) the silver/silver chloride electrode (SB) method of removing I sub 2/I (-) biocide from the water, since it may interfere with analytical procedures for PW and also its end uses; (2) the orbital reactor (OR) method of carrying out chemistry and electrochemistry in microgravity by using a disk shaped reactor on an orbital table to impart artificial G force to the contents, allowing solution mixing and separation of gases and liquids; and (3) a simple ultra low volume highly sensitive electrochemical/conductivity detector for use with a capillary zone electrophoresis apparatus. It is also recommended, since several different conductivity and resistance measurements are made during the analysis of PW, that the bipolar pulse measuring circuit be used in all these applications for maximum compatibility and redundancy of equipment.

Geer, Richard D.↗

A new database website for nuclear level densities

We introduce a new open-access, web-based database (http://nld.ascsn.net), Current Archive of Nuclear Density of Levels (CANDL), that hosts experimental nuclear level density (NLD) datasets from a variety of techniques and energy ranges. Built using the Dash framework in Python, the database is designed to be interactive and user-friendly, allowing researchers to search, visualize, fit, and export NLD data with minimal effort. This resource includes data extracted from evaporation spectra, Oslo method variants, and other experimental techniques that cover excitation energies beyond the neutron resonance region. The database supports on-the-fly fitting with two widely-used phenomenological models—the Constant Temperature (CT) model and the Back-Shifted Fermi Gas (BSFG) model—selected for their simplicity and computational efficiency. Future versions aim to include additional datasets and model types, as well as easy-to-use interfaces to data science techniques. Here, this platform offers a vital tool for the nuclear physics, astrophysics, medicine, and reactor design communities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Advances in 3D Gel Printing for Enzyme Immobilization

Incorporating enzymes with three-dimensional (3D) printing is an exciting new field of convergence research that holds infinite potential for creating highly customizable components with diverse and efficient biocatalytic properties. Enzymes, nature’s nanoscale protein-based catalysts, perform crucial functions in biological systems and play increasingly important roles in modern chemical processing methods, cascade reactions, and sensor technologies. Immobilizing enzymes on solid carriers facilitates their recovery and reuse, improves stability and longevity, broadens applicability, and reduces overall processing and chemical conversion costs. Three-dimensional printing offers extraordinary flexibility for creating high-resolution complex structures that enable completely new reactor designs with versatile sub-micron functional features in macroscale objects. Immobilizing enzymes on or in 3D printed structures makes it possible to precisely control their spatial location for the optimal catalytic reaction. Combining the rapid advances in these two technologies is leading to completely new levels of control and precision in fabricating immobilized enzyme catalysts. The goal of this review is to promote further research by providing a critical discussion of 3D printed enzyme immobilization methods encompassing both post-printing immobilization and immobilization by physical entrapment during 3D printing. Especially, 3D printed gel matrix techniques offer mild single-step entrapment mechanisms that produce ideal environments for enzymes with high retention of catalytic function and unparalleled fabrication control. Examples from the literature, comparisons of the benefits and challenges of different combinations of the two technologies, novel approaches employed to enhance printed hydrogel physical properties, and an outlook on future directions are included to provide inspiration and insights for pursuing work in this promising field.

3D printing↗

Investigation B: Laminar confined coaxial entrance flow with heat generation

The results of a parametric study on the entrance flow region in a gas core nuclear reactor are presented. The physical system is modeled as laminar confined, coaxial flow with heat generation in the inner fluid. The governing equations include the boundary layer approximations and the assumptions of only radial radiative transport of energy represented as an energy diffusion term. The Von Mises transformation and a zeta transformation are used to transform the equations into nonlinear nonhomogeneous convective-diffusion equations. A unique combination of forward and backward difference equations which yields accurate results at moderate computational times, is used in the numerical method. Results show that the rapidly accelerating, heat generating inner stream actually shrinks in radius as it expands axially.

Bobba, G. K. M.↗

AN OVERVIEW OF REDUCED ORDER MODELING TECHNIQUES FOR SAFETY APPLICATIONS

The RISMC project is developing new advanced simulation-based tools to perform Computational Risk Analysis (CRA) for the existing fleet of U.S. nuclear power plants (NPPs). These tools numerically model not only the thermal-hydraulic behavior of the reactors primary and secondary systems, but also external event temporal evolution and component/system ageing. Thus, this is not only a multi-physics problem being addressed, but also a multi-scale problem (both spatial, µm-mm-m, and temporal, seconds-hours-years). As part of the RISMC CRA approach, a large amount of computationally-expensive simulation runs may be required. An important aspect is that even though computational power is growing, the overall computational cost of a RISMC analysis using brute-force methods may be not viable for certain cases. A solution that is being evaluated to assist the computational issue is the use of reduced order modeling techniques. During the FY2015, we investigated and applied reduced order modeling techniques to decrease the RISMC analysis computational cost by decreasing the number of simulation runs; for this analysis improvement we used surrogate models instead of the actual simulation codes. This article focuses on the use of reduced order modeling techniques that can be applied to RISMC analyses in order to generate, analyze, and visualize data. In particular, we focus on surrogate models that approximate the simulation results but in a much faster time (microseconds instead of hours/days).

97 MATHEMATICS AND COMPUTING↗

Use of the Manuela 3D/Radiation Scanning Tool at Nuclear Facilities - 20437

Licensees, facility operators and decommissioning contractors have a need for comprehensive, accurate and precise radiological and topographical data to plan and execute safe and efficient Decontamination and Decommissioning (D and D) projects. Traditional approaches rely greatly upon labor and administratively intensive data collection methods that require considerable time and effort to glean the relevant data to plan and perform work in a radiological work area. Orano Decommissioning Services has developed and utilized at French nuclear facilities a lightweight portable scanning instrument called MANUELA (Mobile Apparatus for Nuclear Expertise Localization Assistance). Recently Orano conducted demonstrations at two United States nuclear facilities using MANUELA that may prove useful in areas of the fuel cycle including: - ALARA (As Low As Reasonably Achievable) planning during facility operations; - Scoping and site characterization during the D and D planning phase; - Remedial action support during active decommissioning work; - Radiation and modeling planning for plant modifications; - Support Final Status Survey and demonstration of 'end state' compliance for license termination. MANUELA is currently being evaluated for use during decommissioning of nuclear facilities and could aide in demonstrating compliance with end state criteria after decommissioning. Of particular interest are decommissioning projects planned for various sites across the United States. Most of these sites present unique challenges and opportunities to safely and efficiently decommission in a regulatory compliant manner. The two demonstration site's current conditions of relatively low radiation levels inside containment proved to be ideal platforms to deploy the MANUELA instrument for evaluation of the complex geometries typically found in a nuclear facility. The MANUELA instrument was able to precisely identify local hot spots of the reactor system's primary equipment and was able to simultaneously overlay the dose information onto the scanned 3D images. Using data like this, a licensee would be able to make informed technical and personnel decisions on methods to remediate, shield or properly dispose of the radioactive source term. MANUELA can be used throughout the decommissioning process to validate progress and continue to refine the work activities to optimize the efforts of the crew which reduces downtime waiting for survey results, whereas traditional survey methodology relies on a physical survey to be performed and the data transcribed onto survey maps that are only two dimensional. The traditional format tends to be inaccurate and difficult to interpret the precise location(s) of hot spots or generalized dose rates. The resultant scan also allows the user to know the exact extent of the survey versus transposing information onto a map with only a portion of the map area scanned. MANUELA also compiles all of the relevant survey data into a downloadable table format which includes the measurement identification number, time stamp, point space location on the XYZ plane, and the dose rate value. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

High Quality, Low Cost Bulk Gallium Nitride Substrates Grown by the Electrochemical Solution Growth Method

The objective of this project was to develop the Electrochemical Solution Growth (ESG) method conceived / patented at Sandia National Laboratory into a commercially viable bulk gallium nitride (GaN) growth process that can be scaled to low cost, high quality, and large area GaN wafer substrate manufacturing. The goal was to advance the ESG growth technology by demonstrating rotating seed growth at the lab scale and then transitioning process to prototype commercial system, while validating the GaN material and electronic / optical device quality. The desired outcome of the project is a prototype commercial process for US-based manufacturing of high quality, large area, and lower cost GaN substrates that can drive widespread deployment of energy efficient GaN-based power electronic and optical devices. In year 1 of the project (Sept 2012 – Dec 2013) the overall objective was to demonstrate crystalline GaN growth > 100um on a GaN seed crystal. The development plan included tasks to demonstrate and implement a method for purifying reagent grade salts, develop the reactor 1 process for rotating seed Electrochemical Solution Growth (ESG) of GaN, grow and characterize ESG GaN films, develop a fluid flow and reaction chemistry model for GaN film growth, and design / build an improved growth reactor capable of scaling to 50mm seed diameter. The first year’s project objectives were met in some task areas including salt purification, film characterization, modeling, and reactor 2 design / fabrication. However, the key project objective of the growth of a crystalline GaN film on the seed template was not achieved. Amorphous film growth on the order of a few tenths of a micron has been detected with a film composition including Ga and N, plus several other impurities originating from the process solution and hardware. The presence of these impurities, particularly the oxygen, has inhibited the demonstration of crystalline GaN film growth on the seed template. However, the presence of both Ga and N at the growth surface indicates that the reactor hardware physics is all functioning properly; achieving film growth is a matter of controlling the chemistry at the interface. The impurities originating from the hardware are expected to be straightforward to eliminate. Activities were defined for an extension of budget period 1 to eliminate the undesired impurities originating from the reactor hardware and interfering with crystalline GaN film growth. The budget period 1 extension was negotiated during the 1st half of 2014. The budget period 1 extension spanned approximately from August 2014 to August 2015. The project objective for this extension period was to demonstrate at least 0.5um crystalline GaN film on a GaN seed in the lab scale reactor. The focus of the budget 1 extension period from August 2014 to August 2015 was to eliminate oxygen contamination interference with GaN film growth. The team procured the highest purity lowest oxygen salt for testing. Low oxygen crucible materials such as silicon carbide were installed and evaluated in the laboratory reactor. Growth experiments were performed with high purity salt, high purity hardware, and optimized oxide removal from the seed surface. Experiments were characterized with methods including UV inspection, profilometry, x-ray diffraction (XRD) to determine crystalline structure, optical and scanning electron microscopy, photoluminescence, x-ray photon spectroscopy (XPS), transmission electron microscopy (TEM), and secondary ion mass spectroscopy (SIMS). Despite successfully integrating the low oxygen materials in the laboratory reactor, the goal of depositing 0.5um of crystalline GaN on the MOCVD GaN seed was not met. Very thin (ca. 10nm) cubic phase GaN deposition was observed on the hexagonal MOCVD GaN seeds. But there was a competing etching reaction which was also observed and thought to be related to the presence of metallic lithium, a byproduct of the LiCl-KCl salt used as the process medium. The etching reaction could potentially be addressed by alternate salts not containing lithium, but would necessitate starting all over on the reactor and process design. Further, controlling the reaction of Ga and N in the bulk salt to favor deposition on the seed has proved to be very difficult and unlikely to be solved within the scope of this project in a manner consistent with the original objective for wafer or crystal scale thickness for GaN deposition on a GaN seed. Upon completion of the budget 1 extension period in August 2015 the project partners and DOE agreed to stop work on the project.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Support for Reactor Operators in Case of Cyber-Security Threats (NEUP Final Report)

Increasing use of digital technology in nuclear power plants (NPPs) poses cyber-security as a crucial threat to public safety and to continuous energy production. Cyber-security risks are comprised of complex known and unknown interactions between various entities, system vulnerabilities, network protocols, human users and malicious attacks. There is little understanding or research geared towards plant operators’ response under cyber-security threats and operational procedures to cope with such threats. This is particularly critical when a cyber-security event masquerades as a safety incident or an evolving accident. Instead of leading operators to the remediation of the accident, the masked cyber event may lead them to circumvent the safety mechanisms of the plant. Given these challenges, the objective of this project is to develop a tool to characterize abnormal NPP events as “cyber” or “safety” incidents, and to further develop this tool as a real-time operator aid to assist in response to the incident. This NEUP Final Report summarizes the research efforts towards the above goals and the results in the following three aspects. First, a methodology for classifying abnormal NPP events as cyber-attacks or safety incidents was developed. This provides the basis for responding to potential cyber-attacks. In this methodology, the causal relationships between various variables (i.e., physical variables, network variables, and control variables) for a nuclear system under consideration are modeled using dynamic Bayesian networks. Based on observations of certain variables (i.e., the evidence), inference is performed to identify the state of hidden variables, which helps indicate the occurrence of cyber-attacks or safety incidents. The proposed methodology was applied to the full scope NPP simulator system at The Ohio State University as a case study. The result shows that the proposed methodology is capable of distinguishing between cyber-attacks and safety incidents. Second, a game-theoretic approach for responding to cyber-attacks on nuclear power plants was developed. This is the second major goal of the project, and the method is used to recommend optimal responses to reactor operators in the case of cyber-attacks. We consider two cases in this research. In the first case, the interaction between the defender (i.e., the reactor operator) and the attacker is modeled as a two-player, nonzero-sum, Markov game with an infinite time horizon. In the second case, we consider a semi-Markov game between the defender and the attacker within a finite time horizon. The model in the second case enables us to consider the time sensitive response of the defender. In each case, the method for deriving the Nash equilibrium is developed. The Nash Equilibrium of the game provides the valid prediction of both players’ actions because no single player can benefit from unilaterally deviating from the equilibrium policy if the other player adheres to his/hers, hence it provides the best response of the defender to cyber-attacks. The proposed method in each case is demonstrated through a simplified benchmark digital feedwater control system. Third, a prototype display is developed to integrate the above information. The prototype display depicts the communication information to the operator and incorporates the cyber-security tool developed by the team into the interface. It consists of the regular display in current control rooms, as well as a panel used to indicate the occurrence of cyber-attacks or safety events and a panel used to guide the operator’s response to detected cyber-attacks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Sensitivity and Uncertainty Analysis of Plutonium and Cesium Isotopes in Modeling of BR3 Reactor Spent Fuel

Nuclear forensics has a broad task to characterize recovered nuclear or radiological material and interpret the results of investigation. One approach to isotopic characterization of nuclear material obtained from a reactor is to chemically separate and perform isotopic measurements on the sample and verify the results with modeling of the sample history, for example, operation of a nuclear reactor. The major actinide plutonium and fission product cesium are commonly measured signatures of the fuel history in a reactor core. This study investigates the uncertainty of the plutonium and cesium isotope ratios of a fuel rod discharged from a research pressurized water reactor when the location of the sample is not known a priori. A sensitivity analysis showed overpredicted values for the 240 Pu/ 239 Pu ratio toward the axial center of the rod and revealed a lower probability of the rod of interest (ROI) being on the periphery of the assembly. The uncertainty analysis found the relative errors due to only the rod position and boron concentration to be 17% to 36% and 7% to 15% for the 240 Pu/ 239 Pu and 137 Cs/ 135 Cs ratios, respectively. Lastly, this study provides a method for uncertainty quantification of isotope concentrations due to the location of the ROI. Similar analyses can be performed to verify future chemical and isotopic analyses.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A Case Study in the Application of TSUNAMI-3D - Part 2, Continuous Energy

The use of the sensitivity and uncertainty tool suite within SCALE, which is known as the TSUNAMI suite, has grown following its initial introduction more than a decade ago. Proper use of this tool 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 sensitivities can also be used to quantify the similarity of two systems. As an example, calculated sensitivities can be combined with cross section uncertainties to determine the similarity index ck. 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 analysts participate in this process, but many 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 multigroup (MG) and continuous-energy (CE) methods introduced in SCALE 6.2. This paper discusses the use of direct perturbation calculations and provides a case study in the use of DP calculations to confirm accurate sensitivities generated by the CE CLUTCH methods in TSUNAMI-3D for a particular benchmark experiment. A companion paper provides a similar case study applying the MG TSUNAMI capability to the same critical experiment. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Radiochemical Methodology Applied To Determination of gamma-Emitting Radionuclides In Waste Samples From IEA-R1 Reactor - 17265

The Brazilian reactor IEA-R1 has been in operation since 1957. It is an open pool-type nuclear research reactor, operating at 2 to 5 MW that uses water as coolant, moderator and biological shield. Polypropylene filter cartridges are part of the water treatment system of the reactor and become radioactive as they remove suspended solid material from the cooling water during the operation of the reactor. Annually, the replacement of the filters from the reactor's water treatment system generates about 36 units. The development of a method for the characterization of the radionuclides present in the filters is required for routine operation in the Radioactive Waste Management Facility (RWMF) in order to determine the radioisotopic inventory of the waste packages. Wastes from nuclear reactors contain transuranic elements, activation and fission products, only few of them emitting gamma radiation measurable by simple gamma scanning methods. The method of the Scaling Factors (SF) uses empirically determined proportions between the concentrations of Difficult to Measure (DTM) radionuclides and that of easily measurable gamma emitters called Key Nuclide (KN), to calculate DTM concentrations. The objective of this study is to describe a method of the dissolution of the filter cartridges for determination of gamma emitting radionuclides. To determine the activity of a sample by means of of gamma spectrometry, it is necessary previous knowledge of the efficiency curve for a given geometry, which can be obtained by calibrating the efficiency and energy of the detector. The need to dissolve the filter cartridges has arisen given the difficulty in obtaining a standard source with the same filter geometry. Therefore, for this work, the calibration curve was constructed using a mixed gamma-ray standard with known activities, same geometry, density, physical state and chemical composition of the source to be analyzed. A sample with background count (BG) was prepared and analyzed under the same conditions as the samples and the result was subtracted from the results obtained for each filter sample. After many tests, it was possible to establish a method for the dissolution of filter cartridges for the determination of gamma-emitting radionuclides. A mixed gamma-ray standard was produced in liquid form, containing the following radionuclides: {sup 241}Am, {sup 137}Cs and {sup 60}Co, which have photo-peaks at the following energies: 59.54, 661.66 and 1332.49 keV, respectively. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Application of the SHARP Toolkit to Sodium-Cooled Fast Reactor Challenge Problems

The Simulation-based High-efficiency Advanced Reactor Prototyping (SHARP) toolkit is under development by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) Campaign of the U.S. Department of Energy, Office of Nuclear Energy. To better understand and exploit the benefits of advanced modeling simulations, the NEAMS Campaign initiated the “Sodium-Cooled Fast Reactor (SFR) Challenge Problems” task, which include the assessment of hot channel factors (HCFs) and the demonstration of zooming capability using the SHARP toolkit. If both challenge problems are resolved through advanced modeling and simulation using the SHARP toolkit, the economic competitiveness of a SFR can be significantly improved. The efforts in the first year of this project focused on the development of computational models, meshes, and coupling procedures for multi-physics calculations using the neutronics (PROTEUS) and thermal-hydraulic (Nek5000) components of the SHARP toolkit, as well as demonstration of the HCF calculation capability for the 100 MWe Advanced Fast Reactor (AFR-100) design. Testing the feasibility of the SHARP zooming capability is planned in FY 2018. The HCFs developed for the earlier SFRs (FFTF, CRBR, and EBR-II) were reviewed, and a subset of these were identified as potential candidates for reduction or elimination through high-fidelity simulations. A one-way offline coupling method was used to evaluate the HCFs where the neutronics solver PROTEUS computes the power profile based on an assumed temperature, and the computational fluid dynamics solver Nek5000 evaluates the peak temperatures using the neutronics power profile. If the initial temperature profile used in the neutronics calculation is reasonably accurate, the one-way offline method is valid because the neutronics power profile has weak dependence on small temperature variation. In order to get more precise results, the proper temperature profile for initial neutronics calculations was obtained from the STAR-CCM+ calculations. The HCFs of the peak temperatures at cladding outer surface, cladding inner wall surface, and fuel centerline induced by cladding manufacturing tolerance and uncertainties on the cladding, coolant, and fuel properties were evaluated for the AFR-100. Some assessment on the effect of wire wrap configuration and size of the bundle shows that it is practical to use the 7-pin bare rod bundle to calculate the HCFs. The resulting HCFs obtained from the high-fidelity SHARP calculations are generally smaller than those developed for the earlier SFRs because the most uncertainties involved in the modeling and simulations were disappeared. For completeness, additional investigations are planned in FY 2018, which will use random sampling techniques.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Basic Research Needs for Inverse Methods for Complex Systems under Uncertainty

Inverse problems, which aim to infer unknown properties of a system using experimental and observational data, are central to addressing many of the U.S. Department of Energy’s (DOE) most critical scientific and engineering challenges. Accurate, computationally efficient, and data-efficient solutions to inverse problems are essential for advancing DOE mission-critical science drivers, including analyzing data from large-scale experimental facilities, optimizing fusion reactor performance, accelerating materials discovery, enhancing geophysical imaging, improving wildfire predictions, and enabling autonomous systems and digital twins. However, these problems are becoming increasingly complex, often involving nonlinear, highdimensional, and interconnected systems and models that span multiple physics and scales, while relying on data with varying quantity, quality, and information content. Compounding these challenges is the uncertainty inherent in DOE-relevant systems, where errors in inputs, noise in data, incompleteness of data, and discrepancies between models and reality constrain the accuracy and precision of solutions. At the same time, the convergence of recent scientific computing trends—scientific machine learning, artificial intelligence, and computing advances such as exascale computing—is creating unprecedented opportunities for tackling these challenges. The cross-cutting nature of inverse problems, combined with their growing complexity and rapidly evolving data and algorithmic demands, strongly motivates the formulation of a prioritized research agenda to maximize their capabilities and impact. In response to this need, DOE’s Advanced Scientific Computing Research (ASCR) program in the Office of Science convened the Workshop on Basic Research Needs for Inverse Problems for Complex Systems Under Uncertainty in June 2025. This workshop brought together experts across disciplines to identify grand challenges and major opportunities in the field. Through collaborative discussions, the workshop defined transformative research directions aimed at addressing the mathematical, statistical, and computational challenges posed by inverse problems under uncertainty. As a result of these efforts, four priority research directions (PRDs) were identified to guide future research and development in this area. These PRDs, summarized below, represent a roadmap for advancing the foundational science and mathematics of inverse problems, enabling robust, scalable, and uncertainty-aware solutions that are critical for DOE applications.

97 MATHEMATICS AND COMPUTING↗

Extension of Clad Damage Propagation Model for Fission Gas Dispersal and Two-Phase Flow Effects in MOOSE SubChannel Module

This report presents an extension of the Clad Damage Propagation (CDAP) model implemented in the MOOSE SubChannel Module (SCM) to capture post-failure fission-gas dispersal and two-phase flow effects in sodium-cooled fast reactor assemblies. The extended model tracks discharged gas axially and radially, computes channel-averaged flow quality and void fraction using a Lockhart–Martinelli framework, evaluates two-phase frictional pressure-drop multipliers, determines inlet mass-flow degradation under fixed core pressures, and applies an intensified-void-based heat-transfer degradation to affected fuel pins. Radial plume expansion is parameterized using mineral-oil jet experiments mapped to sodium conditions via Reynolds–Weber similarity. Implementation details are documented, along with the new methods and user inputs needed to control plume mapping and two-phase behavior. Demonstration simulations for 19- and 37-pin bundles show that breach size and inlet velocity strongly influence propagation potential: small breaches (≤0.5 mm) produce limited degradation while larger breaches (~1 mm) can drive oscillatory temperature spikes and enhanced failure propagation, especially at higher velocities. These results demonstrate that the extended CDAP model provides a more complete framework for quantifying cladding damage propagation and evaluating propagation potential in transient scenarios. The approach remains computationally efficient, consistent with subchannel-level analysis, yet incorporates sufficient physics to bridge localized post-failure effects with bundle- and assembly-scale degradation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗