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DOE OSTI2023

Thermal Hydraulic Experimental Test Article - Fiscal Year 2023 (Final Report)

The Thermal Hydraulic Experimental Test Article (THETA) is a facility that is used to develop sodium components and instrumentation as well as acquire experimental data for validation of reactor thermal hydraulic and safety analysis codes. The facility simulates nominal conditions as well as protected/unprotected loss of flow accidents in a sodium-cooled fast reactor (SFR). High fidelity distributed temperature profiles of the developed flow field may be acquired with Rayleigh backscatter based optical fiber temperature sensors. The facility was designed in partnership with systems code experts to tailor the experiment to ensure the most relevant and highest quality data for code validation. THETA is comprised of a traditional primary coolant and secondary coolant system. The primary system is submerged in the pool of sodium and consists of a pump, electrically heated core, intermediate heat exchanger, and connected piping and thermal barriers (redan). The secondary system, located outside of the sodium pool, consists of a pump, sodium to air heat exchanger, and connected piping and valves. To date a test matrix has been completed utilizing the primary system of THETA. These tests, along with computational fluid dynamics and systems code models, determined the heat transfer across the core barrel and intermediate heat exchanger outlet was too great to effectively represent scaled thermal hydraulic phenomena of a liquid metal cooled reactor. Therefore, a significant effort was made to remove the primary system from the METL 28” test vessel #4 and clean the residual sodium from the primary system to facilitate upgrades. Thermal insulation was then incorporated in the core barrel and intermediate heat exchanger outlets. The primary system was then replaced, and a series of tests were performed to assess the performance of the thermal insulation. With primary system testing and upgrades complete, the secondary system could then be brought online. The tube side of the shell-and-tube intermediate heat exchanger was installed onto the primary system flange to begin installing the secondary system. The support structure for the secondary system was then erected on the METL mezzanine alongside the THETA primary system to facilitate installation of the secondary system components (sodium-to-air heat exchanger, flowmeter and pump). The piping and expansion tank were welded into the secondary system. Non-destructive examination of the secondary system welds was completed in order to satisfy ASME B31.3 pipe code for class M process fluids. The heating system and insulation were then added to prepare the system to be filled with sodium. The ancillary electrical equipment was installed which included the pump control box, blower VFD, pipe heater control system, etc. The secondary system will be filled, and a test matrix will be completed in early FY2024.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Thermal Hydraulic Experimental Test Article - Status Report FY20 Q2

The Thermal Hydraulic Experimental Test Article (THETA) is a facility that will be used to develop sodium components and instrumentation as well as acquire experimental data for validation of reactor thermal hydraulic and safety analysis codes. The facility will simulate nominal conditions as well as protected/unprotected loss of flow accidents in a sodium-cooled fast reactor (SFR). High fidelity distributed temperature profiles of the developed flow field will be acquired with Rayleigh backscatter based optical fiber temperature sensors. The facility is being designed in partnership with systems code experts to tailor the experiment to ensure the most relevant and highest quality data for code validation. THETA is comprised of a traditional primary and secondary system. The primary system is submerged in the pool of sodium and consists of a pump, electrically heated core, intermediate heat exchanger, and connected piping and thermal barriers (like a redan). The secondary system, located outside of the sodium pool, consists of a pump, sodium to air heat exchanger, and connected piping and valves. Figure 1 illustrates the main components of the primary system. THETA will be installed in the Mechanisms Engineering Test Loop (METL) with the primary system in the 28 inch Test Vessel #4, Figure 2. The design work for the facility has been completed, most primary component have been fabricated, primary components are being assembled in preparation for initial testing, and procurement is continuing with the secondary system components. Since the FY19 THETA status report, The THETA primary system components are at Argonne National Laboratory (ANL) and have been dry assembled. The secondary sodium system for heat rejection from intermediate heat exchanger has all been analyzed according to ASME code. All secondary side piping, fittings and a U-stamped air-to-sodium heat exchanger has been procured.

42 ENGINEERING↗
DOE OSTI2022

ARDP Natrium Neutronic Methodology: Argonne Neutronic Assessment of ABR-1000

The Natrium Sodium-cooled Fast Reactor (SFR) concept developed by TerraPower, LLC was selected as one of the advanced reactor designs for demonstration under the Advanced Reactor Demonstration Program Natrium Demo project. In collaboration with TerraPower, the Argonne National Laboratory (ANL) team provide independent reviews of the neutronic methodology being used for the Natrium design. As part of this activity, both the TerraPower and ANL teams agreed to perform independent neutronics analyses of the ABR-1000 reactor problem as a demonstration on the usage of the neutronics methodologies. Comparison of the results from TerraPower and ANL would expose any methodological differences in the modeling approaches. This report describes and presents the Argonne analysis work on the ABR-1000, and will be provided to TerraPower, along with data files, to complete the comparison study. The comparison will cover the methodology to evaluate the reactivity coefficients for a safety analysis, the shutdown margin, and the reconstructed pin power distribution. The methods and models used to calculate the kinetic parameters and the reactivity coefficients (density, Doppler, axial/radial expansion, etc.) are described in detail with recommendations of specific method options and modelling techniques. The control system reactivity worth and the excess reactivity due to temperature defect are calculated for the shutdown margin analysis. The method to evaluate the excess reactivity is discussed in detail. The pin power reconstruction methodology used in SE2ANL, SE2RCT, and DASSH are discussed in this report. The pin power distribution evaluated by different methods are compared and discussed in the report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Sodium Chemistry Assessment and Initiation of Sodium Exposure Experiment on A709 Commercial Heats and LPBF 316H SS

This report documents sodium chemistry characterization and the initiation of forced‑convection sodium exposure experiments for two structural materials for sodium‑cooled fast reactors (SFRs): Alloy 709 (solution‑annealed and with an additional 775 °C/10 h precipitation treatment) and laser powder bed fusion (LPBF) 316H stainless steel tensile specimens printed with an as‑built surface condition. The sodium exposure experiment was conducted in a forced‑convection sodium loop with two vessels operated at 550 °C and 600 °C, and a cold trap maintained at <130 °C. Carbon activity in sodium was quantified using a nickel‑foil equilibration method. Initial post‑exposure evaluation after ~1,000 h indicates negligible thickness change for Alloy 709 and a small but measurable mass decrease. To isolate thermal effects from sodium effects, parallel thermal‑aging experiments were performed on Alloy 709 at 550 °C and 600 °C. Baseline tensile tests at room temperature, 550 °C, and 600 °C show expected reduction in strength with increasing temperature and serration tensile curves at elevated temperatures, consistent with dynamic strain aging. After 3,000 h thermal aging, Alloy 709 exhibits modest strengthening and reduced ductility at 550 °C. Together, these results establish the loop chemistry conditions and provide the initial corrosion and mechanical property results for ongoing long‑duration sodium exposure of Alloy 709 and LPBF 316H stainless steel.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Multiscale Thermal-hydraulic analysis of the MARVEL micro-reactor using coupled MOOSE Subchannel (SCM) and SAM

MARVEL is a natural-convection-cooled sodium-potassium microreactor that is anticipated to generate 85 kilowatts of thermal energy. It will operate within Idaho National Laboratory’s Transient Reactor Test Facility and is being developed by the DOE Microreactor Program. MARVEL will be used to test microreactor applications, evaluate systems for remote monitoring, and develop autonomous control technologies. A thermal-hydraulic computational model of this facility is a valuable tool to study important transients and calculate the safety limits of the micro-reactor design. For this purpose, the authors have chosen to use a multiscale coupled simulation: SCM for modeling the reactor core and SAM for the reactor’s primary cooling system. SCM is MOOSE physics module for subchannel analysis, which was designed to model single-phase flows through liquid-metal cooled, wire-wrapped fuel pin sub-assemblies, ordered in a triangular lattice. The SCM code was modified to be able to model MARVEL’s unique geometry. SAM is a systems analysis module based on the MOOSE framework. It aims to provide fast-running, whole-plant transient analyses capability with improved-fidelity for various advanced reactor types. The coupling between the two SCM and SAM for MARVEL modeling is done implementing a domain over-lapping approach. The resulting coupled simulation can model transients such as reactor startup/shutdown and provide an intermediate fidelity picture of the temperature field and other variables, in the core. Results for the steady-state simulations are presented in the article as well as flow blockage transient.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Multiscale Thermal-hydraulic analysis of the MARVEL microreactor using a coupled SAM and SCM simulation. (PPTX)

This is .pptx document presenting a summary of the paper of the same name that has been submitted and accepted to NURETH-21: MARVEL is a natural-convection-cooled sodium-potassium microreactor that is anticipated to generate 85 kilowatts of thermal energy. It will operate within Idaho National Laboratory Transient Reactor Test Facility and is being developed by the DOE Microreactor Program. MARVEL will be used to test microreactor applications, evaluate systems for remote monitoring, and develop autonomous control technologies. A thermal-hydraulic computational model of this facility is a valuable tool to study important transients and calculate the safety limits of the micro-reactor design. For this purpose, the authors have chosen to use a multiscale coupled simulation: SCM for modeling the reactor core and SAM for the reactor's primary cooling system. SCM is MOOSE physics module for subchannel analysis, which was designed to model single-phase flows through liquid-metal cooled, wire-wrapped fuel pin sub-assemblies, ordered in a triangular lattice. The SCM code was modified to be able to model MARVEL?s unique geometry. SAM is a systems analysis module based on the MOOSE framework. It aims to provide fast-running, whole-plant transient analyses capability with improved-fidelity for various advanced reactor types. The coupling between the two SCM and SAM for MARVEL modeling is done implementing a domain over-lapping approach. The resulting coupled simulation can model transients such as reactor startup/shutdown and provide an intermediate fidelity picture of the temperature field and other variables, in the core. Results for the steady-state simulations are presented in the article as well as flow blockage transient.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
DOE OSTI2021

Machine Learning Assisted Safety Modeling and Analysis of Advanced Reactors

With the advances in computational power and numerical methods, analysts can now rely on first-principle simulations to predict ultra-fine details in a variety of applications. Advances in machine learning (ML) have produced algorithms that can now learn high-level abstractions via hierarchical models. This project aims to leverage advances in ML techniques and the available high-resolution simulation data to develop a novel modeling and simulation (M\&S) methodology for reactor safety analysis. While application-agnostic ML techniques are available, complex physics constraints need to be incorporated into ML techniques to build ML-based closures for computationally efficient predictive simulations. This project intends to develop a physics-guided data-driven multi-scale methodology for M\&S of advanced reactors. The project focuses on thermal fluid (T/F) phenomena, which play major roles in advanced reactor safety. Specifically, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor (SFR). The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data with Reynolds-averaged Navier-Stokes (RANS) turbulence model to ensure accuracy. Three different neural networks are developed and tested for loss-of-flow transients in the hot pool of SFR, i.e. the densely connected convolutional neural network (DCNN), long-short-term-memory network based on proper orthogonal decomposition (POD-LSTM), and the DCNN informed by LSTM (DCNN-LSTM). The performances of these three neural networks are evaluated based on baseline models. The DCNN-LSTM model has been chosen for further hyperparameter optimization. Furthermore, based on a simplified two-dimensional case, uncertainty quantification (UQ) of the developed ML-based closure are investigated with three methods, i.e. Monte Carlo dropout, deep ensemble, and Bayesian neural network. The developed ML-based turbulent viscosity closure relation based on deep ensemble is then integrated into the system analysis module SAM and serves as a term in the conservation equations. Such a SAM-ML based procedure guarantees that the obtained results are consistent with the physical constraints of the thermal-fluid system. The SAM-ML simulation on the same loss-of-flow transient showed comparable accuracy with the CFD simulation but with a much coarser mesh setup. Last but not least, the ML-based closure improvement with the support of higher-fidelity data from large eddy simulation (LES) is discussed. As a first step towards this direction, a baseline LES simulation is performed to obtain comparable data with RANS results. Based on the early results, future investigation on further improving the ML-based closure is discussed. We believe the developed approach that combines scientific machine learning with nuclear system analysis code can benefit the advanced reactor community as more accurate safety analyses will better characterize reactor safety margins and reduce licensing efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

An Efficient 1-D Thermal Stratification Model for Pool-Type Sodium-Cooled Fast Reactors

Investigating thermal stratification in the upper plenum of a sodium fast reactor (SFR) is presently a technology gap in SFR safety analysis. Understanding thermal stratification will promote safe operation of the SFR before its commercial deployment. Stratified layers of liquid sodium with a large vertical temperature gradient could be established in the upper plenum of an SFR during a down-power or a loss-of-flow transient. These stratified layers are unstable and could result in uncertainties for the core safety of an SFR. In order to predict the occurrence of the thermal stratification efficiently, we developed a one-dimensional (1-D) transport model to estimate the temperature profile of the ambient fluid in the upper plenum. This model demands much less computational effort than computational fluid dynamics (CFD) codes and provides calculations with higher fidelity than historical system-level codes. Two flow conditions were considered separately in the current study depending on if in-vessel components are presented in the upper plenum. For the condition where in-vessel components, specifically the upper internal structure, are presented, we assumed that the impinging sodium was evenly dispersed in the ambient fluid within the distance between the bottom of the in-vessel component and the jet inlet surface. For the condition where no in-vessel components are presented, we assumed that the impinging sodium was evenly dispersed in the ambient fluid within the jet length, which was determined through data-driven trainings. The newly developed 1-D model showed similar performance with the CFD model in both cases. However, due to the assumption of flat profiles of the impinging jet axial dispersion rate, nonnegligible discrepancies between the 1-D prediction and the measured data were observed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Single Primary Heat Extraction and Removal Emulator (SPHERE) Long Duration Testing

For the development of heat-pipe cooled microreactors, it is crucial to thoroughly understand the characteristics and functioning of heat pipes across a wide spectrum of operating conditions. Passive heat removal and its long-term performance stability are critical factors in this context. Enhanced experimental data is vital for evaluating the operational lifespan of alkali metal heat pipes. Idaho National Laboratory (INL) has successfully conducted an extended duration test on a high-performance sodium-filled heat pipe, closely monitoring the axial temperature profile, power supplied by the heaters, and heat removed by a gas-gap calorimeter. The results from this testing provide valuable data that are instrumental in supporting heat pipe validation efforts. Specifically, this data aids in the development and validation of Sockeye, the Multiphysics Object-Oriented Simulation Environment (MOOSE) tool under the US-DOE NEAMS program designed for heat pipe modeling. By comparing experimental results with Sockeye’s predictions, the tool's accuracy and reliability can be assessed and improved, thereby enhancing its capability to simulate heat pipe operations under various conditions.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Gripper Test Assembly Status of Fabrication and Assembly Report – FY2023

The Gripper Test Assembly (GrTA) is an experimental test article designed for use at the Mechanisms Engineering Test Loop (METL) at Argonne National Laboratory (ANL). The GrTA will test mechanical components intended for use in compact in-vessel fuel handling machines (FHM) for sodium cooled fast reactors (SFR). The GrTA will test radial and thrust ball bearings, radial and thrust roller bearings, ball screws and nuts, spline shafts and ball nuts, radial spur gears, and universal joints submerged in liquid sodium at high temperatures (250°C-650°C). These components will be tested in a prototypic, full-scale gripper head and under prototypic SFR fuel handling loads. The design of the GrTA was completed in FY2022 and has progressed into fabrication and initial assembly. All custom manufactured components have been fabricated and delivered to ANL following inspection. All custom gears have been fabricated and delivered to ANL. Bearings, ball screws, and spline shafts have been purchased to allow for initial assembly in air, and sodium compatible versions have either been purchased or are in design at appropriate manufacturers. The drive motor systems that operate the various functions of the GrTA have been purchased and delivered to ANL. Instrumentation and control hardware has been purchased and delivered to ANL as well. All sodium facing components of the GrTA have been assembled and show proper fit. The three main functions of the GrTA are to raise or lower a gripper head under prototypic fuel handling loads, rotate the gripper head while carrying a fuel handling load, and extend or retract gripper jaws that lock a fuel assembly to the gripper head. All three functions have been demonstrated in air, while under no load. The GrTA project will move forward next fiscal year by completing the initial assembly, incorporating the drive system and I&C, and preparing the assembly for introduction to sodium.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Transmission electron microscopy study of a high burnup U-10Zr metallic fuel

To support the development of U-10 wt.% Zr (U-10Zr) metallic fuel for Gen IV sodium-cooled fast reactors, we analysed a solid, Na-bonded, U-10Zr (by weight percent) fuel cross section that was irradiated to a burnup of ~ 12.4 % at.% at the Fast Flux Test Facility (FFTF). Advanced characterization techniques, including site specific sample preparation by focused ion beam (FIB) and phase/chemical determination by transmission electron microscopy (TEM), were used to reveal the constituent redistribution of Zr, characterize the fuel phases and the secondary phases (such as solid fission products) present at the end of life. It is shown that the fuel pin cross section is divided into three major concentric zones: a Zr-rich central region, a Zr-lean intermediate region, and a Zr intermediate peripherical region. The phase characterization revealed that the irradiation environment enhanced the development and stabilization of phases not predicted by the standard equilibrium U-Zr phase diagrams. Comparing the current results with the ones from previous studies, it is reaffirmed that the irradiation temperature and the time spent in the reactor, rather than the fuel burnup, are the two factors that most influence the formation of redistribution zones and their extension along the fuel cross section. Various solid fission products precipitated inside the fission gas pores, such as lanthanides, ZrRu, BaTe, CsI, and Ba and Sr oxides. Here, this study provides unprecedented nanoscale understandings in the U-10Zr fuel system that may benefit fuel performance modelling and advanced fuel development.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

SAM User's Guide

The System Analysis Module (SAM) is a modern system analysis tool being developed at Argonne National Laboratory for advanced non-LWR safety analysis. It aims to provide fast-running, whole-plant transient analyses capability with improved-fidelity for Sodium-cooled Fast Reactors (SFR), Lead-cooled Fast Reactors (LFR), and Molten Salt Reactors (MSR) or Fluoride-cooled High-temperature Reactors (FHR). SAM takes advantage of advances in physical modeling, numerical methods, and software engineering to enhance its user experience and usability. It utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage the modern advanced software environments and numerical methods. This document provides a user’s guide, which will help users understand the input description and core capabilities of the SAM code. A brief overview of the code is presented, as well as how to obtain and run it. The input syntax for various parts of the code is provided. Additionally, a number of example problems, starting with simple unit component problems to problems with increasing complexity, are provided. Because the code is still under active development, this SAM User’s Guide will evolve with periodic updates.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

EVALUATION OF PRESSURE DROP CORRELATIONS FOR THE WIRE-WRAPPED ROD BUNDLES

The accurate prediction of pressure drop in the fuel rod bundle is of importance for the design and thermal-hydraulic analysis of nuclear reactor system. Due to very complex geometry of wire-wrapped fuel rod bundle geometry for the Sodium Fast Reactor (SFR), a simple method using hydraulic (equivalent) diameter is not sufficient to predict the pressure drop of rod bundle accurately. For several decades, many experimental works have been performed to develop an accurate correlation for wire-wrapped fuel bundle friction factor. In these works, the friction factor correlation of wire-wrapped fuel bundle has been developed as a function of Reynolds number of the flow and the design parameters such as fuel pin diameter, wire diameter, rod pitch, and wire lead length. The Cheng and Todreas correlations are well-known and used in many subchannel analysis code, such as CADET, TRIO-U, MATRA-LMW, SE2-ANL, etc. Novendstern model, Rehme model, Baxi and Dalle Donne model are also well-known and widely referred. Computational Fluid Dynamics is another typical approach to predict the pressure drop of wire-wrapped fuel rod bundle, but it requires the model validation because the accuracy of pressure drop prediction by the CFD simulation depends on what turbulence model is employed. The present work aims at evaluating the existing pressure drop correlations for the wire-wrapped fuel rod bundle and evaluating the pressure drop of 217-pin rod bundle by the CFD analysis.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2020

Thermal Hydraulic Experimental Test Article (FY2020 Status Report)

The Thermal Hydraulic Experimental Test Article (THETA) is a facility that will be used to develop sodium components and instrumentation as well as acquire experimental data for validation of reactor thermal hydraulic and safety analysis codes. The facility will simulate nominal conditions as well as protected/unprotected loss of flow accidents in a sodium-cooled fast reactor (SFR). High fidelity distributed temperature profiles of the developed flow field will be acquired with Rayleigh backscatter based optical fiber temperature sensors. The facility is being designed in partnership with systems code experts to tailor the experiment to ensure the most relevant and highest quality data for code validation. THETA is comprised of a traditional primary and secondary system. The primary system is submerged in the pool of sodium and consists of a pump, electrically heated core, intermediate heat exchanger, and connected piping and thermal barriers (redan). The secondary system, located outside of the sodium pool, consists of a pump, sodium to air heat exchanger, and connected piping and valves. Figure 1 illustrates the main components of the primary system. THETA will be installed in the Mechanisms Engineering Test Loop (METL) with the primary system in the 28 inch Test Vessel #4, Figure 2. The design work for the facility has been completed. Since the FY19 THETA status report, the THETA primary system components have been assembled and tested using de-ionized water. Some results of this testing at select Richardson and Reynolds numbers are included herein. The custom THETA sodium flowmeter (permanent magnet submersible sodium flowmeter) has been built and calibrated using sodium in an auxiliary facility against a NIST traceable vortex shedder type flowmeter. The permanent magnet flowmeter showed excellent performance, following the theoretical equation for measured voltage quite well, with an error < 3.5% at flow rates ranging from 3-24 GPM at temperatures up to 400 °C. The secondary sodium system for heat rejection from intermediate heat exchanger has been analyzed according to ASME code. All secondary side piping, fittings and a U-stamped air-to-sodium heat exchanger have been procured.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Design of Microwave Resonant Cavity Transducer. Development of sensor performance model of microwave cavity flow meter for advanced reactor high temperature fluids

High-temperature fluid reactors, such as molten salt cooled reactors (MSCR) and sodium fast reactors (SFR), are a promising advanced reactor option. Measurement of high-temperature fluid process variables, in particular the flow inside the pressure vessel, is a challenging task because of harsh environment, which includes high radiation, high temperature, and contact with highly corrosive coolant fluid. We are investigating a microwave cavity-based transducer for high-temperature fluid flow sensing. This sensor is a hollow metallic cylindrical cavity, which can be fabricated from stainless steel, and as such is expected to be resilient to radiation, high temperature and corrosive environment of MSCR and SFR. The principle of sensing consists of making one wall of the cylindrical cavity flexible enough so that dynamic pressure, which is proportional to fluid velocity, will cause membrane deflection. A cavity is characterized by its resonant frequencies. Membrane deflection causes cavity volume change, which leads to a shift in the resonant frequency. Feasibility of the flow sensor is evaluated with signal sensitivity using COMSOL computer simulations. A right cylinder geometry stainless steel cavity with dimeter of 0.8in was investigated. We choose membrane thickness of 10mil, so that corrosion anticipated to proceed at the rate of 1mil/year in liquid sodium would affect no more than 10% of the membrane. Using the properties of liquid sodium fluid, and stainless-steel material property values at 500oC, we calculate frequency shift for a range of values of fluid velocity from 0.5m/s to 2m/s. Results of computer simulations indicate measurable sensitivity to flow for this cavity design. Following these simulations, we have developed a preliminary design for fabrication of a transducer operating in microwave K-band for proof-of-principle tests.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Uncertainty estimation of bifurcated solutions in the Rayleigh–Bénard problem for advanced nuclear reactors applications

Multiphysics models of nuclear reactors frequently comprise nonlinear systems of equations. The nonlinear nature of these models could lead to solution bifurcations, where a small change in a certain parameter, e.g., the thermophysical properties of the coolant, can lead to a sudden change in the system’s behavior. At the point in parameter space where this happens, called a critical point, the Jacobian matrix of the model’s nonlinear operator becomes singular potentially permitting multiple solutions to coexist. In this paper, we perform uncertainty estimation (UE) in a parameter range that includes bifurcated solutions within the context of Rayleigh–Bénard problem. We perform this analysis assuming uncertain temperature difference, and tilt angle for the iterative solution algorithm with a unit Prandtl number (Pr = 1). Also, we perform this analysis under uncertain thermophysical properties for both FLiBe molten salt and liquid sodium as working fluid. We deploy two approaches to compute statistical moments for the resulting distributions of selected flow-field variables. The first approach is the blind computation of the mean and the standard deviation without any consideration of solution bifurcation, while the second approach utilizes k-means clustering to cluster each branch’s solutions together and compute separate statistical moments for each branch. The statistical distributions are obtained by perturbing the selected parameters about nominal values that correspond to a solution on one of the valid branches, and that solution is used as initial guess for the iterative solution algorithm. We found that perturbation of any parameter when its nominal value is close to its critical point always leads to branch jumping, i.e., the iterations converge to a solution on a branch different from the branch of the initial guess. This produces a statistical ensemble comprised of fundamentally different solutions leading to wrong mean values and uncertainty estimates, whereas clustering provides an efficient way to deal with this type of computation. This work is important for developing Gen IV nuclear systems because many of these systems rely on natural convection for cooling especially in accident conditions.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Monte Carlo Dropout Uncertainty Quantification of Long Short-Term Memory Autoencoder Anomaly Detection in a Liquid Sodium Cold Trap

Advanced high-temperature fluid reactors, such as sodium-cooled fast reactors (SFRs) and molten salt–cooled reactors (MSCRs), require coolant purification systems to prevent fluid contamination and local freezing that can lead to plugging. Liquid sodium purification can be achieved with a cold trap, where the sodium temperature is reduced to a near-freezing point to precipitate out impurities. Automation of monitoring of the cold trap performance with machine learning algorithms can aid in early detection of incipient anomalies. An efficient approach to loss-of-coolant–type anomaly detection in a cold trap monitored with more than two dozen thermal-hydraulic sensors consists of a long short-term memory (LSTM) autoencoder. This work develops the uncertainty quantification of the LSTM autoencoder performance for cold trap anomaly detection using the Monte Carlo (MC) dropout method. The MC dropout methodology creates a distribution of sister distributions that all slightly differ from each other because of random neurons being turned off for testing. The variances of the sister network distributions are used to make an uncertainty interval. Our analysis shows that the uncertainty in the autoencoder performance is largest near the peak of the anomaly signal. Using the MC dropout method, we investigate the uncertainty in the anomaly detection with missing sensor inputs. This capability allows the reactor operator to evaluate resilience of the anomaly detection system and to make informed decisions about continuity of operation in the event of sensor failure.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Probabilistic Analysis of Long-Term Degradation of Microwave Cavity Flow Sensor

We are investigating a microwave resonant cavity transducer for flow sensing in the vessel of a high temperature fluid advanced reactor (AR), such as a molten salt cooled reactor (MSCR) or a sodium fast reactor (SFR). This transducer is a hollow metallic cylindrical cavity, with the flat wall of the cylinder flexible enough to undergo microscopic deflection due to dynamic fluid pressure. Membrane deflection leads to a shift in the resonant frequency, which can be detected with a spectrum analyzer. We have performed a proof-of-concept experiment of flow sensing with the transducer in liquid sodium at 340°C in impinging liquid jet geometry. The transducer remained in liquid sodium for 70 days. After removal, no structural damage was observed, and the expected transducer response was verified in a water test. Because long-term (multi-year) experimental tests of transducer resilience to harsh environment are not practical, we have developed a probabilistic model of creep to estimate transducer resilience to the harsh environment. The probabilistic model considers diffusion creep under the condition of high temperature and low stress, where the stress and temperature are allowed to be random variables with Gaussian distributions. Using the probabilistic model, we estimate inelastic membrane deflections due to creep for several temperature ranges. We conclude that for temperatures less than 650°C, creep has negligible long-term effect on the transducer performance. Since a yellowish residue was observed on the transducer surface after 70 days of immersion in liquid sodium, we have investigated possible evidence of corrosion. Chromium depletion is a typical indicator of the corrosion process in stainless steel. Scraping off a residue from the transducer and performing scanning electron microscopy (SEM) with energy dispersive analysis (EDS) did not find any chromium in the residue. Approximately 60% of the residue consisted of copper, which can be attributed to contamination of sodium due to powder residue from machining of copper and brass components of the transducer.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗