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At least 1,423 records · Page 79

Reverse Osmosis Simulation Data

This dataset consists of computational fluid dynamics (CFD) output for various spacer configurations in a feed-water channel in reverse osmosis (RO) applications. Feed-water channels transport brine solution to the RO membrane surfaces. The spacers embedded in the channels help improve membrane performance by disrupting the concentration boundary layer growth on membrane surfaces. Refer to the "Related Work" resource below for more details. This dataset considers a feed-water channel of length 150mm. The inlet brine velocity and concentration are fixed at 0.1m/s and 100kg/m3 respectively. The diameter of the cylindrical spacers is fixed as 0.3mm and six varying inter-spacer distances of 0.75mm, 1mm, 1.5mm, 2mm, 2.5mm, and 3mm are simulated. The dataset comprising the steady, spatial fields of solute concentration, velocity, and density near each spacer is placed in the folder corresponding to the spacer configuration considered. We run two sets of CFD simulations and include the outputs from both sets for each configuration: (1) with a coarser mesh, producing low-resolution (LR) data of spatial resolution 20x20, and (2) with a finer mesh, producing high-resolution (HR) data of spatial resolution 100x100. These data points can be treated as images with the quantities of interest as their channels and can be used to train machine learning models to learn a mapping from the LR images as inputs to the HR images as outputs.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Airborne Release Fractions from Surrogate Nuclear Waste Fires Containing Lanthanide Nitrates and Depleted Uranium Nitrate in 30% Tributyl Phosphate in Kerosene

Airborne contaminants from fires containing nuclear waste represent significant health hazards and shape the design and operation of nuclear facilities. Much of the data used to formulate DOE-HDBK-3010-94, “Airborne Release Fractions/Rates and Respirable Fractions for Nonreactor Nuclear Facilities,” from the U.S. Department of Energy, were taken over 40 years ago. The objectives of this study were to reproduce experiments from Pacific Northwest Laboratories conducted in June 1973 employing current aerosol measurement methods and instrumentation, develop an enhanced understanding of particulate formation and transport from fires containing nuclear waste, and provide modeling and experimental capabilities for updating current standards and practices in nuclear facilities. A special chamber was designed to conduct small fires containing 25 mL of flammable waste containing lutetium nitrate, ytterbium nitrate, or depleted uranium nitrate. Carbon soot aerosols showed aggregates of primary particles ranging from 20 to 60 nm in diameter. In scanning electron microscopy, ~200-nm spheroidal particles were also observed dispersed among the fractal aggregates. The 200-nm spherical particles were composed of metal phosphates. Airborne release fractions (ARFs) were characterized by leaching filter deposits and quantifying metal concentrations with mass spectrometry. The average mass-based ARF for 238 U experiments was 1.0 × 10 -3 with a standard deviation of 7.5 × 10 -4 . For the original experiments, DOE-HDBK-3010-94 states, “Uranium ARFs range from 2 × 10 -4 to 3 × 10 -3 , an uncertainty of approximately an order of magnitude.” Therefore, current measurements were consistent with DOE-HDBK-3010-94 values. ARF values for lutetium and ytterbium were approximately one to two orders of magnitude lower than 238 U. Furthermore, metal nitrate solubility may have varied with elemental composition and temperature, thereby affecting ARF values for uranium surrogates (Yb and Lu). In addition to ARF data, solution boiling temperatures and evaporation rates can also be deduced from experimental data.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Data Generation for Machine Learning Interatomic Potentials and Beyond

The field of data-driven chemistry is undergoing an evolution, driven by innovations in machine learning models for predicting molecular properties and behavior. Recent strides in ML-based interatomic potentials have paved the way for accurate modeling of diverse chemical and structural properties at the atomic level. The key determinant defining MLIP reliability remains the quality of the training data. A paramount challenge lies in constructing training sets that capture specific domains in the vast chemical and structural space. This Review navigates the intricate landscape of essential components and integrity of training data that ensure the extensibility and transferability of the resulting models. We delve into the details of active learning, discussing its various facets and implementations. We outline different types of uncertainty quantification applied to atomistic data acquisition and the correlations between estimated uncertainty and true error. The role of atomistic data samplers in generating diverse and informative structures is highlighted. Furthermore, we discuss data acquisition via modified and surrogate potential energy surfaces as an innovative approach to diversify training data. The Review also provides a list of publicly available data sets that cover essential domains of chemical space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Uncertainties in Density and Simulation Parameters for Radiographic Reconstructions Using Machine Learning

We will develop new and improved methods that will enable a fuller and more extensive use of experimental data, such as from radiographic imaging, towards better characterizing and reducing uncertainties in predictive modeling of weapons performance. We will achieve this by leveraging recent developments in the areas of computational imaging, statistical and machine learning, and reduced order modeling. Key new aspects of our approach include (a) a coupling of deep learning based density reconstruction with fast hydrodynamics simulators that will permit the development of certain guarantees on extrapolatability and bounds on certain other hydrodynamics-related para- metric uncertainties and (b) a dual approach towards better characterizing uncertainties in density reconstruction using deep learning based surrogates to accelerate Bayesian reconstructions on the one hand and using variational inference and Bayesian machine learning on the other hand.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Continued Investigations of Respirable Release Fractions for Stress Corrosion Crack-Like Geometries

The formation of a stress corrosion crack (SCC) in the canister wall of a dry cask storage system (DCSS) has been identified as a potential issue for the long-term storage of spent nuclear fuel. The presence of an SCC in a storage system could represent a through-wall flow path from the canister interior to the environment. Modern, vertical DCSSs are of particular interest due to the commercial practice of using relatively high backfill pressures (up to approximately 800 kPa) in the canister to enhance internal natural convection. This pressure differential offers a comparatively high driving potential for blowdown of any particulates that might be present in the canister. In this study, the rates of gas flow and aerosol transmission of a spent fuel surrogate through an engineered microchannel with dimensions representative of an SCC were evaluated experimentally using coupled mass flow and aerosol analyzers. The microchannel was formed by mating two gage blocks with a linearly tapering slot orifice nominally 13 μm (0.005 in.) tall on the upstream side and 25 μm (0.0010 in.) tall on the downstream side. The orifice is 12.7 mm (0.500 in.) wide by 8.89 mm (0.350 in.) long (flow length). Surrogate aerosols of cerium oxide, CeO 2 , were seeded and mixed with either helium or air inside a pressurized tank. The aerosol characteristics were measured immediately upstream and downstream of the simulated SCC at elevated and ambient pressures, respectively. These data sets are intended to demonstrate a new capability to characterize SCCs under well-controlled boundary conditions. Modeling efforts were also initiated that evaluate the depletion of aerosols in a commercial dry storage canister. These preliminary modeling and ongoing testing efforts are focused on understanding the evolution in both size and quantity of a hypothetical release of aerosolized spent fuel particles from failed fuel to the canister interior and ultimately through an SCC.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Data‐driven variational method for discrepancy modeling: Dynamics with small‐strain nonlinear elasticity and viscoelasticity

Abstract The effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.

Masud, Arif↗

Comparison of mercury (Hg) bioaccumulation with mono- and mixed Lemna minor and Spirodela polyrhiza cultures

Mercury (Hg) is a prevalent and harmful contaminant that persists in the environment. For phytoremediation, it is important to discover which plants can bioaccumulate meaningful amounts of Hg while also tolerating its toxicity. Additionally, increasing biodiversity could create a more resilient and self-sustaining system for remediation. This study explores whether mixed populations of Lemna minor and Spirodela polyrhiza can better bioaccumulate and tolerate Hg than monocultures. Mono- and mixed cultures of L. minor and S. polyrhiza were grown in mesocosms of 0.5 μg/L or 100 μg/L Hg ( HgCl2) spiked water for 96 h. Change in weight of duckweed was used to assess Hg tolerance. Diffusive gradients in thin-films (DGTs) were used as surrogate monitoring devices for bioavailable levels of Hg. For biomass growth, the mixed culture of the L. minor was greater than the monoculture at the high dose. The L. minor accumulated more Hg in the mixed culture at the low dose while the S. polyrhiza was higher in the mixed at the high dose. Hg speciation in water was modeled using Windermere Humic Aqueous Model 7 (WHAM7) to compare the bioavailable species indicated by the DGTs. Potentially due to the controlled conditions, the WHAM7 output of bioavailable Hg was almost 1:1 to that estimated by the DGTs, indicating good predictive capability of geochemical modeling and passive sampler DGT on metal bioavailability. Altogether, the mixed cultures statistically performed as well as or better than the monocultures when tolerating and bioaccumulating Hg. However, there needs to be further work to see if the significant differences translate into practical differences worth the extra resources to maintain multiple species.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

Implementation of stacked ensemble machine learning for the detection of surrogate plutonium contamination in soil via LIBS

Supervised machine learning methods have demonstrated increased utility for the quantification of lanthanide and actinide elements in atomic spectroscopy applications. This study implements laser-induced breakdown spectroscopy (LIBS) for the identification of plutonium surrogate material (CeO 2 ) in soil matrices by training supervised machine learning methods on the recorded spectral data. A bagged ensemble using Random Forest yields the highest sensitivity predictions with a detection limit of 0.015 wt.% CeO 2 . However, high precision in Ce content prediction required the use of a stacked ensemble regression, which provided the superlative Ce quantification model with an error of 0.107% and a detection limit of 0.022 wt.%. Furthermore, the high performance of the stacked ensemble demonstrates its potential to enhance the accuracy and sensitivity of nuclear contaminant detection using field-deployable spectroscopic analyzers in real-world scenarios.

47 OTHER INSTRUMENTATION↗

Toward DMC Accuracy Across Chemical Space with Scalable Δ-QML

In the past decade, quantum diffusion Monte Carlo (DMC) has been demonstrated to successfully predict the energetics and properties of a wide range of molecules and solids by numerically solving the electronic many-body Schrödinger equation. With O(N 3 ) scaling with the number of electrons N, DMC has the potential to be a reference method for larger systems that are not accessible to more traditional methods such as CCSD(T). Assessing the accuracy of DMC for smaller molecules becomes the stepping stone in making the method a reference for larger systems. We show that when coupled with quantum machine learning (QML)-based surrogate methods, the computational burden can be alleviated such that quantum Monte Carlo (QMC) shows clear potential to undergird the formation of high-quality descriptions across chemical space. We discuss three crucial approximations necessary to accomplish this: the fixed-node approximation, universal and accurate references for chemical bond dissociation energies, and scalable minimal amons-set-based QML (AQML) models. Numerical evidence presented includes converged DMC results for over 1000 small organic molecules with up to five heavy atoms used as amons and 50 medium-sized organic molecules with nine heavy atoms to validate the AQML predictions. Finally, numerical evidence collected for Δ-AQML models suggests that already modestly sized QMC training data sets of amons suffice to predict total energies with near chemical accuracy throughout chemical space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

From electronic structure to model application of key reactions for gasoline/alcohol combustion: Hydrogen-atom abstractions by $CH_3\dot{O}$ radical

H-atom abstraction by methoxy radical ($CH_3\dot{O}$) plays an important role in capturing the kinetics of reactions between gasoline components and alcohols. This study focuses on determining the reaction rates and thermodynamic properties of methoxy radical reactions with five gasoline fuel components: n-heptane, iso-octane, 1-hexene, cyclopentane and toluene. Electronic structure calculations were per-formed for all the stationary points with M06-2X/6 -311 ++ g(d,p) method. G3 composite method with atomization method is used for determining Δ f H 0 of all the closed shell and radical species, using which the necessary thermodynamic data of all the species was determined. Coupled cluster theory QCISD(T)/cc-pVXZ (where X = D and T) and Møller-Plesset perturbation theory MP2/cc-pVXZ (where X = D, T and Q) were used to calculate single point energies. Subsequently, rate constants for all hydrogen atom ab-straction channels have been performed using conventional transition state theory with unsymmetric tunneling corrections. A systematic comparison of rates for abstraction from different sites within the same species and same site from different species is done in order to get insights into this reaction class. Here, the computed thermodynamic properties and rate constants were incorporated into a recent gasoline mechanism to investigate the impact of the calculations performed in this work. A shift in predicted NTC (negative temperature coefficient) behavior and significant reduction in model reactivity is observed upon incorporating the rates calculated herein.

33 ADVANCED PROPULSION SYSTEMS↗

Mitigating the noise of DESI mocks using analytic control variates

In order to address fundamental questions related to the expansion history of the Universe and its primordial nature with the next generation of galaxy experiments, we need to model reliably large-scale structure observables such as the correlation function and the power spectrum. Cosmological N-body simulations provide a reference through which we can test our models, but their output suffers from sample variance on large scales. Fortunately, this is the regime where accurate analytic approximations exist. To reduce the variance, which is key to making optimal use of these simulations, we can leverage the accuracy and precision of such analytic descriptions using Control Variates (CV). The power of control variates stems from utilizing inexpensive but highly correlated surrogates of the statistics one wishes to measure. The stronger the correlation between the surrogate and the statistic of interest, the larger the variance reduction delivered by the method. We apply two control variate formulations to mock catalogs generated in anticipation of upcoming data from the Dark Energy Spectroscopic Instrument (DESI) to test the robustness of its analysis pipeline. Our CV-reduced measurements offer a factor of 5-10 improvement in the measurement error compared with the raw measurements. We explore the relevant properties of the galaxy samples that dictate this reduction and comment on the improvements we find on some of the derived quantities relevant to Baryon Acoustic Oscillation (BAO) analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

APOLLO: a facility-scale differentiable virtual accelerator for Fermilab

As the design complexity of modern accelerators grows, there is more interest in using advanced simulations that have fast execution time or yield additional insights like gradients. The FAST/IOTA facility has been working on implementing and experimentally validating an end-to-end digital twin that is both fast and gradient-aware, allowing for rapid prototyping of new software and experiments with minimal beam time costs. Our framework integrates physics and ML codes for linac and ring simulation through a set of generic interfaces between surrogate and physics-based sections. To reproduce device inputs and outputs, system state is exposed as a deterministic discrete event simulator. Because Fermilab is undergoing control system transition, both EPICS and ACNET frontends are supported. Recently, we have begun transitioning to a new community lattice standard, PALS, as well as developing standardized infrastructure for data ingest and normalization to prepare for model calibration during FAST proton injector commissioning. We discuss implementation details as well as challenges, and future plans to extend modelling to main complex proton accelerators like PIPII and Booster.

Kuklev, Nikita [Fermilab]↗

Absolute Templating of M(111) Cluster Surrogates by Galvanic Exchange

The precise preparation of monodisperse nanomaterials is among the most fundamental tasks in inorganic synthesis and materials science. Achieving this goal by galvanic exchange is hardly predictable, and often results in major structural changes and polydisperse mixtures. Here, taking advantage of the enhanced stability imparted by ambiphilic carbenes, we report and rationalize the absolute templating — the complete exchange of metals in a template — of group 11 clusters across the entire coinage metal family by means of galvanic exchange. We further delineate that these species provide a molecular model for better understanding the reduction of CO 2 at M(111) coinage metal surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hydrogen uptake in graphite matrix at high temperature

Tritium management is a critical challenge for the next generation of nuclear reactors, such as Fluoride Salt Cooled High Temperature Reactors (FHRs) and High Temperature Gas-cooled Reactors (HTGRs), due to the higher production rate (up to 10,000 times) than conventional Light Water Reactors (LWRs). Graphitic materials employed as moderator, reflector, and fuel pebbles offer a potential pathway for tritium recovery by serving as a sink for tritium. Prediction of uptake capacity under reactor relevant conditions remains a challenge due to a lack of low partial pressure data and significant inter-grade variability of graphite. This study addresses these gaps by providing a comprehensive characterization of hydrogen (as a tritium surrogate) uptake and release behavior in the A3-3 graphite matrix (GM) used in fuel pebbles. Uptake measurements are performed at reactor relevant temperatures of 600- 800 °C, 1-200 Torr hydrogen pressure, and 15-120 min equilibration time, followed by thermal desorption spectroscopy up to 1100 °C. Uptake experiments at different equilibration times demonstrate the role of kinetics in hydrogen uptake, which can be modeled as a diffusion-with-trapping process. In the thermodynamics limit, the Sips adsorption model is shown to capture the uptake in A3-3 GM well. Our campaign provides a set of new results for hydrogen uptake in A3-3, including limiting uptake capacity at 600 °C, apparent diffusion coefficient at 600 °C, and the first estimates of the FHR/HTGR relevant (600 °C, 20 Pa partial pressure) equilibrium uptake capacity and time to saturation. Desorption data highlights a new site for hydrogen uptake, not observed in nuclear graphite, which we attribute to the non-graphitized binder. Using the Kissinger method, we estimate activation energy for release from the desorption peaks, confirming the activation energy for release from the basal planes and providing the first estimate for the activation energy of release from the binder.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Understanding power and energy utilization in large scale production physics simulation codes

Power is an often-cited reason for the move to advanced architectures on the path to Exascale computing. Here, this is due to practical considerations related to delivering enough power to successfully site and operate these machines, as well as concerns about energy usage while running large simulations. Since obtaining accurate power measurements can be challenging, it may be tempting to use the processor thermal design power (TDP) as a surrogate due to its simplicity and availability. However, TDP is not indicative of typical power usage while running simulations. Using commodity and advanced technology systems at Lawrence Livermore and Sandia National Labs, we performed a series of experiments to measure power and energy usage in running simulation codes. These experiments indicate that large scale Lawrence Livermore simulation codes are significantly more efficient than a simple processor TDP model might suggest.

HPC↗

Flame kinetics at scramjet-engine-relevant conditions: Role of prompt dissociation of weakly-bound radicals

Combustion in high-speed ram-based propulsion engines occurs under distinct thermodynamic conditions of high reactant temperatures (greater than 1000 K) and relatively low pressures (<5 atm). There is a lack of fundamental flame measurements at such conditions that result in adiabatic flame temperatures (T ad ) exceeding 2500 K. In this work, we have measured laminar flame speeds of oxygen-enriched CH 4 /oxidizer mixtures at sub-atmospheric conditions to probe kinetics at high T ad using the isobaric spherically expanding flame approach. Simulations with recent kinetic models revealed increasing differences between data and model predictions with increasing T ad , reaching up to 25 %. Kinetic analyses reveal that at the thermodynamic conditions in these O 2 -enriched flames, i.e., lower pressures and higher T ad , the effects of HCO prompt dissociation are accentuated. In addition to HCO, the prompt dissociations of CH 2 OH and C 2 H 5 are also considered. Here, the prompt dissociations of all three radicals were evaluated and their effects considered in flame speed simulations. Reaction path analysis for the present flames revealed that approximately half of the reaction flux for HCO formation undergoes prompt dissociation to H + CO. Furthermore, these analyses also revealed that the pathways and sensitive reactions are similar between oxygen-enriched fuel/oxidizer mixtures and preheated fuel/air mixtures, if both have similar T ad . Thus, flames of oxygen-enriched mixtures could be a surrogate to probe the flame chemistry of highly preheated mixtures at relatively low pressures that are often encountered in ram-based propulsion engine combustors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Pertechnetate/perrhenate–capped Zr/Hf–Dihydroxide Dimers: Elucidating Zr–TcO 4 Co–Mobility in the Nuclear Fuel Cycle

Spent nuclear fuel contains heavy element fission products that must be separated for effective reprocessing for a safe and sustainable nuclear fuel cycle. 93 Zr and 99 Tc are high-yield fission products that co-transport in liquid-liquid extraction processes. Here we seek atomic-level information of this co-extraction process, as well as fundamental knowledge about Zr IV (and Hf IV ) aqueous speciation in the presence of topology-directing ligands such as pertechnetate (TcO 4 – ) and non-radioactive surrogate perrhenate (ReO 4 – ). In this context, we show that the flat tetrameric oxyhydroxyl-cluster [M IV 4 (OH) 8 (H 2 O) 16 ] 8+ (and related polymers) is dissociated by perrhenate/pertechnetate to yield isostructural dimers, M 2 (OH) 2 (XO 4 – ) 6 (H 2 O) 6 • 3H 2 O (M=Zr/Hf IV ; X=Re/Tc VII ), elucidated by single-crystal X-ray diffraction. We used these model compounds to understand the pervasive 93 Zr- 99 Tc coextraction with further speciation studies in water, nitric acid, and tetrabutylphosphate (TBP) -kerosene; where the latter two media are relevant to nuclear fuel reprocessing. SAXS (small angle X-ray scattering), compositional evaluation, and where experimentally feasible, ESI-MS (electrospray ionization mass spectrometry) showed that perrhenate/pertechnetate influence Zr/Hf IV -speciation in water. Here, in Zr-XO 4 solvent extraction studies to simulate fuel reprocessing, we provide evidence that TcO 4 – enhances extraction of Zr IV , and compositional analysis of the extracted metal-complexes (Zr-ReO 4 study) is consistent with the crystallized Zr IV 2 (OH) 2 (Re VII O 4 – ) 6 (H 2 O) 6 •dimer.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Design and Analysis of a Mutual Inductance Level Sensor for Liquid Metals

Here, this article describes the design and analysis of an electromagnetic level sensor for use in high-temperature liquid metal systems. The mutual inductance level sensor (MILS) described in this work was fabricated using two single-conductor mineral insulated cables wrapped in a bifilar fashion around a stainless steel tube core and was housed in an isolating thimble that preserved the pressure boundary of the test vessel. Two sensor variations were fabricated that differ only in active length, 1016 and 1778 mm. Experimental data were collected using the 1016-mm sensor (MILS-MKII-040) that demonstrated a sensitivity of 9.2 μ V/mm in a room temperature testing stand that used solid aluminum as a surrogate for liquid metal. Experimental data were collected using the 1778-mm sensor (MILS-MKII-070) that demonstrated a sensitivity of 6.9 μ V/mm in the high-temperature (300 ° C) liquid sodium environment at the mechanisms engineering test loop (METL) of Argonne National Laboratory. The sensor performance was found to be repeatable over the course of several months, with roughly ±1% deviation from nominal output. Finite element models were developed in COMSOL Multiphysics that fully describe each test setup, and the models were validated using experimental data. The validated COMSOL models were used to perform an array of analyses that examined the performance of the sensor in differing environments. Maximizing the coil diameter inside the isolating thimble was found to maximize the signal and sensitivity of the sensor. An optimal operating frequency was found near 1000 Hz using both experimental data and COMSOL. The influence of a metallic thimble surrounding the sensor and a metallic sensor core was quantified and found to be negligible at the optimal operating frequency. The sensitivity of the sensor was quantified when monitoring the level of additional liquid metals. These include lead, lead-bismuth eutectic (LBE), sodium-potassium alloy (NaK), and lithium (in addition to sodium). The sensitivities were quantified using liquid metal properties at 350 ° C and 650 ° C. The geometry of the test stand model, all material properties used in the model, and the results are presented in a manner that allows the reader can replicate the model and perform additional analyses.

COMSOL↗