Implementing bubbly mercury material model (R-P model) in the pulse simulation to predict strain on the Spallation Neutron Source target vessel with gas injection
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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Sensitivity Analysis of Tunable Equation of State Material Model In Pulsed Mercury Target Simulation
A pulsed neutron spallation target is subjected to very short but intense loads from repeated proton pulses. Approximately 60% of the energy from each proton pulse is deposited into the mercury target material and the stainless-steel target structure, leading to a high-pressure region in both the stationary target structure and the flowing mercury. The high-pressure region propagates and leads to fluid-structure interaction. The resultant loading on the target structure containing liquid mercury is difficult to predict, although various simulation approaches and material models for the mercury have been tried. To date, the best match of simulation to experimental data is obtained by using an equation of state (EOS) material model with a specified tensile cutoff pressure, which simulates the cavitation threshold. The inclusion of a threshold to represent cavitation is key to the successful predictions of stress waves triggered by the high-energy pulse striking the mercury and vessel. However, recent measurements of target structure strain show that significant discrepancies remain between the measured and simulated strain values in the EOS mercury model. These differences grow when noncondensable helium gas is intentionally injected into the flowing mercury to reduce the loading on the structure. An EOS-based proportional–integral–derivative (PID) mercury model has been proposed to reduce the gap between the measured and simulated vessel strain responses for targets with gas injection. The conceptual and numerical description and initial investigation of the PID model are presented in previous work. Further studies of this PID model — including the sensitivity of the structure’s strain response to model parameters (the tensile cutoff, PID parameters Kp, Ki, and Kd) — are reported in this article. Results show the strain response is more sensitive to changes in the tensile cutoff value than to changes in the model parameters Kp, Ki, and Kd. These results will aid in future work where the model parameters will be optimized to match simulation data to strain measurements.
Lin, Lianshan↗
Material Model Parameters Optimization in Liquid Mercury Target Dynamics Simulation With Machine Learning Surrogates
A pulsed spallation target is subjected to very short (∼0.7μs) but intense loads (23.3 kJ) from repeated proton pulses, which knock away neutrons from the mercury atoms’ nuclei for a wide range application in physics, engineering, medicine, petroleum exploration, biology, chemistry, etc. The effect of this pulsed loading on the stainless-steel target module which contains the flowing mercury target material is difficult to predict not only due to its short but intense explosive-like physical reaction, but also the nonlinear material behavior of the liquid mercury in the structure. Injecting small helium bubbles in the mercury has been an efficient method of mitigating the pressure wave at high power level stage. However, prediction of the resultant loading on the target is more difficult when helium gas is intentionally injected into the mercury. A 2-phase material model that incorporates the Rayleigh-Plesset (R-P) model is expected to address this complex multi-physics dynamics problem by including the bubble dynamics in the liquid mercury. A parameter sensitivity study was firstly employed to understand their impact on the simulation strains. The investigated parameters included E, μ, γ, σ, n, VFgas, and gas cumulative volume curve control parameters a and b. Verification and validation results from sparse polynomial expansions (SPE) method and directional Gaussian smoothing (DGS) optimization show that the surrogate model had training error of ∼7% and validation error of ∼15%, indicating that machine learning methods and surrogate models can help optimize the uncertain parameters in the complex 2-phase material model. This approach is expected to fill the knowledge gap between unknown liquid-gas mixture material model and measured vessel strain responses.
Lin, Lianshan↗
Assessment of simulated and observed cavitation-induced erosion damage in Spallation Neutron Source target vessels
Cavitation-induced erosion damage in different Spallation Neutron Source (SNS) target designs are simulated using explicit finite element–based techniques and compared with observations of erosion in targets after operation. The efficacy of the previously developed method, called saturation time, was evaluated using erosion-damaged samples from new target designs. A new metric called maximum bubble size was implemented under the rationale that larger cavitation bubbles will collapse more intensely. The maximum cavitation bubble size over 1 ms of simulated time was calculated based on the Rayleigh–Plesset equation for each element integration point and presented as a contour map at the vessel surface for assessing with erosion observations. SNS targets are now operated with helium gas injection to reduce cavitation damage. A simulation method using a material model for the mixture of mercury and gas bubbles was recently developed and used to account for the effect of small gas bubbles on the structural response of the target vessel. Furthermore, this work compares the new method's results with observed cavitation damage. Maps of the calculated maximum bubble size for targets operated with and without gas injection were compared with photographs of erosion damage observed in SNS targets. The patterns in maximum bubble size maps correlated well with observations of erosion patterns in target vessels after service. Advantages and challenges of the maximum bubble size simulation technique are provided, and differences between results from the previous and the newly proposed metric are discussed.
Jiang, Hao↗
Benchmarking and Exploring Parameter Space of the 2-Phase Bubble Tracking Model for Liquid Mercury Target Simulation
High intensity proton pulses strike the Spallation Neutron Source (SNS)’s mercury target to provide bright neutron beams. These strikes deposit extensive energy into the mercury and its steel vessel. Prediction of the resultant loading on the target is difficult when helium gas is intentionally injected into the mercury to reduce the loading and to mitigate the pitting damage on the vessel. A 2-phase material model that incorporates the Rayleigh-Plesset (R-P) model is expected to address this complex multi-physics dynamics problem by including the bubble dynamics in the liquid mercury. We present a study comparing the measured target strains in the SNS target station with the simulation results of the solid mechanics simulation framework. We investigate a wide range of various physical model parameters, including the number of bubble families, bubble size distribution, viscosity, surface tension, etc. to understand their impact on simulation accuracy. Our initial findings reveal that using 8-10 bubble families in the model renders a simulation strain envelope that covers the experimental ones. Further optimization studies are planned to predict the strain response more accurately.
Lin, Lianshan↗
Calibration of the 2-Phase Bubble Tracking Model for Liquid Mercury Target Simulation with Machine Learning Surrogate Models
The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory is one of the most powerful accelerator-driven neutron sources in the world. The intense protons strike on SNS's mercury target to provide bright neutron beams, which also leads to severe fluid-structure interactions inside the target. Prediction of resultant loading on the target is difficult particularly when helium gas is injected into mercury to reduce the loading and mitigate the pitting damage on vessel walls. A 2-phase material model that incorporates the Rayleigh-Plesset (R-P) model is expected to address this multi-physics problem. However, several uncertain parameters in the R-P model require intensive simulations to determine their optimal values. With the help of machine learning and the measured target strain, we have studied the major uncertain parameters in this R-P model and developed a framework to identify optimal parameters that significantly reduce the discrepancy between simulations and experimental strains. The preliminary results show the possibility of using this mercury/helium mixture and surrogate models to predict a better match of target strain response when the helium gas is injected.
Lin, Lianshan↗
Dielectric Screening Modulates Semiconductor Nanoplatelet Excitons
The influence of external dielectric environments is well understood for 2D semiconductor materials but overlooked for colloidally grown II–VI nanoplatelets (NPLs). In this work, we synthesize MX (M = Cd, Hg; X = Se, Te) NPLs of varying thicknesses and apply the Elliott model to extract exciton binding energies—reporting values in good agreement with prior methods and extending to less studied cadmium telluride and mercury chalcogenide NPLs. Here, we find that the exciton binding energy is modulated both by the relative effect of internal vs external dielectric and by the thickness of the semiconductor material. An analytical model shows dielectric screening increases the exciton binding energy relative to the bulk by distorting the Coulombic potential across the NPL surface. We further confirm this effect by decreasing and recovering the exciton binding energy of HgTe NPLs through washing in polarizable solvents. Our results illustrate NPLs are colloidal analogues of van der Waals 2D semiconductors and point to surface modification as an approach to control photophysics and device properties.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
High Pressure Melting Curve of Fe‐Si: Implication for the Thermal Properties in Mercury's Core
The motion of liquid iron (Fe) alloy materials in the outer core drives the dynamo, which generates Mercury's magnetic field. The assessment of core models requires laboratory measurements of the melting temperature of Fe alloys at high pressure. Here, we experimentally determined the melting curve of Fe9wt%Si and Fe17wt%Si up to 17 GPa using in situ and ex situ measurements of intermetallic fast diffusion that serves as the melting criterion in a large-volume press. Our determined melting slopes are comparable with previous studies up to about 17 GPa. However, when extrapolated, our melting slopes significantly deviate from previous studies at higher pressures. For Mercury's core with a model composition of Fe9wt%Si, the melting temperature-depth profile determined in our study is lower by ∼150–250 K when compared with theoretical calculations. Using the new melting curve of Fe9wt%Si and the electrical resistivity values from a previous study of Fe8.5wt%Si, we estimate that the electronic thermal conductivity of liquid Fe9wt%Si is 30 Wm −1 K −1 at the Mercury's CMB pressure of 5 GPa and 37 Wm −1 K −1 at an assumed ICB of 21 GPa, corresponding to heat flux values of 23 mWm −2 and 32 mWm −2 , respectively. These values provide new constraints on the core models.
58 GEOSCIENCES↗
Status of Mercury and Imp: Two Monte Carlo Transport Codes Developed Using Shared Infrastructure at Lawrence Livermore National Laboratory
The Monte Carlo Transport Project at Lawrence Livermore National Laboratory develops two Monte Carlo transport codes used in production by a sizable internal user community. Mercury is a Monte Carlo particle transport code used to model the interaction of neutrons, gammas, and light ions with a material. Imp is an implicit Monte Carlo thermal x-ray photon transport code used to model the interaction of x-ray photons with a material. This paper describes the two codes and highlights recent developments.
Pozulp, Michael↗
Derivation of heterogeneous material distributions and their sensitivity to HM-coupled two-phase flow models exemplified with the LASGIT experiment
Abstract Advective gas transport in bentonite, a possible buffer material in repositories for radioactive materials, is difficult to simulate in numerical continuum models, partly due to the complicated microstructure of bentonite. To generate reliable models of repositories nevertheless, spatially distributed heterogeneous material properties can be used to allow localization of gas flow. In this study, a pore-size-dependent stochastic approach of the gas entry pressure is derived from Mercury Intrusion Porosimetry, which is used to replicate measurements from the LASGIT experiment. In addition, three benchmark tests are simulated to investigate the dependence of heterogeneous distributions of material properties on the mesh discretization, the temporal dependence, and the coupling between the processes influenced by the heterogeneous parameters. The numerical modeling results of the LASGIT experiment show that the onset of gas flow into the system and the subsequent increase in pressure and stress can be well reproduced using heterogeneous distributions. Compared to a model with homogeneous material properties, heterogeneous distributions may allow the generation of dilatancy-controlled microfractures—an important feature with regard to the advective gas flow in bentonites. However, it can be observed that the heterogeneous distributions in LASGIT are less significant, as technical gaps or differences in material types could have a greater impact.
Environmental Sciences & Ecology↗
Activity model for 36 elements in Fe-Ni-Si-S-C liquids with application to terrestrial planet accretion and mantle geochemistry: New data for Ru, Re, Pt, Os, Ti, Nb, and Ta
Understanding siderophile element partitioning between metal and silicate melts under diverse conditions can be used to place important constraints on the materials and conditions of planetary accretion and core formation, as well as post core formation processes. However, the effects of Si on the partitioning and activity coefficients for these elements are not well known, despite Si likely being one of the dominant light elements in Earth’s core. To address this gap in understanding, we have undertaken a systematic study of the highly siderophile elements Re, Pt, Os, and Ru, and the refractory lithophile elements Nb, Ta and Ti at 1600 °C and 1 GPa, to derive epsilon interaction parameters for these elements in FeSi metallic liquids. Positive epsilon interaction parameters were measured for Nb, Ta, Ti, Ru, Re, Pt, and Os, indicating that dissolved Si in Fe liquids causes a decrease in their metal/silicate partition coefficients (or ‘silicophobic’ behavior). Furthermore, ε$_{Re, Os, or Ru}^{Si}$ > ε$_{Re, Os, or Ru}^{S}$ which means Si causes a larger decrease in D(metal/silicate) than S, and the chalcophile behavior expected from some elements will be completely masked by the presence of Si in a metallic liquid. The new parameters are used to update an activity model that now includes 36 siderophile elements in Fe-Ni-Si-S-C liquids (27 trace elements considered here). Systematic assessment of these 27 elements shows which have the strongest affinity for Si, C, and S, and also how activity coefficients for these elements would vary during accretion and core formation in Earth, Mars, and Mercury of widely differing fO 2 and core compositional conditions. The activity model is combined with new partitioning expressions for Mo, W, Cr, Re Ru, Pt, and Os and applied to aspects of post core formation mantle geochemistry of Earth, Mars, and Mercury. Our updated expressions show that the BSE Mo/W ratio can easily be achieved with metal/silicate partitioning during growth of the Earth, whereas Re, Os and Ru become lower than and highly fractionated compared with BSE values during core formation and accretion, and thus nearly 99% of their BSE abundances are likely contributed by late accretion. Ru isotopes should be a very good indicator of the source material for the late accretion. The high Pt/Os and Re/Os developed in a deepening magma ocean during the growth of the Earth, indicates 186 Os and 187 Os isotopes could be coupled if this ancient material remained isolated and subsequently became entrained in mantle plumes and measured in surficial lavas. The extent to which this occurred will be limited by the low Os content of this ancient material, thus requiring mixing as a major component in plume sources. Martian mantle Hf/W ratio stays low during accretion and core formation modelling, suggesting that W isotope anomalies are more likely due to solid/liquid silicate fractionation than to core formation. Finally, Ti contents measured by MESSENGER at Mercury’s surface can be explained by segregation of either a metallic core (IW-6 to -8) or metallic core + sulfide (IW-4 to -7.5) followed by mantle melting.
38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
Mercury Modeling of TREAT Big-BUSTER Free Field Characterization Experiments
This report summarizes modeling of Big-BUSTER free field characterization (FFC) experiments at the Idaho National Laboratory (INL) Transient Reactor Test Facility (TREAT) reactor performed from December 20th, 2023, to February 22nd, 2024. TREAT is an air-cooled graphite moderated research reactor that can be used to study material response to neutron irradiation. The BUSTER (Broad Use Specimen Transient Experiment Rig) refers to a containment module for placing experiments in the reactor core. The Big-BUSTER is an analogous platform for a modified core configuration with a larger experimental cavity.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Cavitation-induced erosion in liquid metal spallation targets – A comparison between a predictive method and measured erosion damage to stainless steel target modules at the Spallation Neutron Source
Neutrons are produced for neutron scattering instruments at the Spallation Neutron Source by bombarding liquid mercury with a pulsed high-energy proton beam. The liquid mercury target material flows through a replaceable stainless-steel target vessel and cavitates during operation due to the extremely high heating rate caused by each proton pulse. Cavitation-induced erosion damage to the mercury-facing surfaces of target vessels is a key concern for target lifetime and has been the subject of considerable research. While numerous experiments have studied and modeled the progression of cavitation erosion damage to liquid metal target containers, direct quantitative measurements of actual erosion of a spallation target vessel were previously not available. Recently, the erosion damage to multiple target vessels operated at the Spallation Neutron Source was measured using a high-resolution laser scanning system, which provided an opportunity to study the efficacy of a cavitation damage progression model. In this paper, a cavitation progression modeling procedure developed using empirical observations is compared to measurements of samples from target vessels after operation. We discuss the strengths and limitations of the technique and propose methods for improving future modeling and predictive accuracy.
36 MATERIALS SCIENCE↗
Incorporating bubble growth volume feedback to improve simulation of the response of a structure containing liquid and gas to sudden energy input
The SNS target module is a stainless-steel structure that contains and directs mercury. The mercury is struck with short, intense proton pulses to create neutrons. The pulses deposit energy and cause loads on the target structure and mercury cavitation. Helium bubbles are introduced into the mercury to reduce loads and cavitation. This gas complicates the prediction of the target module’s physical response. The current method used to simulate the structural response to the proton pulse incorporates a simple but effective approach to approximate mercury cavitation effects. This method cannot account for the changes from injected non-condensable gas. The ability to model the target vessel response is a prerequisite for estimating its life. Known approaches for simulating a bubbly fluid mixture’s response are computationally expensive and impractical for detailed engineering models. A constitutive model is proposed for target mercury with injected gas bubbles, with the intent of providing more accurate mercury–vessel response behavior without the computing costs required to track individual bubbles. The model’s assumptions and a computational model embodiment are described. The bubbly mercury computational model is subjected to test problems to assess its potential utility. Here, the model was able to better predict the effect of gas on wave propagation.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Lab Scale Mercury Dissolution Testing
Researchers at the Savannah River National Laboratory were requested by Savannah River Mission Completion to perform laboratory testing and modeling designed to understand why the Defense Waste Processing Facility (DWPF) is not collecting elemental mercury (Hg 0 ) despite long boiling times designed to recover Hg 0 . In response to a Technical Task Request, a Task Technical and Quality Assurance Plan was written and approved to authorize this work.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Defense Waste Processing Facility Nitric-Glycolic Flowsheet Chemical Process Cell Chemistry: Part 2
The conversions of nitrite to nitrate, the destruction of glycolate, and the conversion of glycolate to formate and oxalate were modeled for the Nitric-Glycolic flowsheet using data from Chemical Process Cell (CPC) simulant runs conducted by Savannah River National Laboratory (SRNL) from 2011 to 2016. The goal of this work was to develop empirical correlation models to predict these values from measurable variables from the chemical process so that these quantities could be predicted a-priori from the sludge or simulant composition and measurable processing variables. The need for these predictions arises from the need to predict the REDuction/OXidation (REDOX) state of the glass from the Defense Waste Processing Facility (DWPF) melter. This report summarizes the work on these correlations based on the aforementioned data. Previous work on these correlations was documented in a technical report covering data from 2011-2015. This current report supersedes this previous report. Further refinement of the models as additional data are collected is recommended. The glass REDOX depends on the concentrations of nitrate and manganese (oxidants), and of glycolate, formate, oxalate, carbon, and antifoam (reductants) in the melter feed. The waste sludge contains nitrite, nitrate, manganese (Mn), and oxalate. Virtually all of the nitrite is converted to nitrate or NO+NO 2 +N 2 O gases in the CPC. The portion of the nitrite converted to nitrate increases the amount of nitrate in the sludge. The amount of glycolate in the final melter feed depends on the amount of the glycolic acid feed that is destroyed. Similarly, the amounts of formate and oxalate formed during the decomposition of glycolic acid are required. The material balance on carbon was found to not close in most cases. Generally, there was less carbon at the end of testing compared to the inputs. The most uncertain product variable was glycolate, so material balances were performed where the glycolate concentration was adjusted, usually upward, to close the balance. Correlation versus the original, as-measured, data was generally poor, but correlation against the material balance adjusted values was greatly improved. It was also shown that the correlation of the measured REDOX versus the predicted REDOX was much better when the material balance adjusted glycolate values were used. Three data series were primarily used during the regressions of the data; these series were 1) Sludge Batch 9 NG flowsheet simulant runs NG51-62 (SB9-NG); 2) Scaled Runs + Bounding Hydrogen Runs (SR+BH); and 3) Runs GN43-50 and 57 (43-50,57). The glycolate destruction was found to correlate with acid stoichiometry (AS), percent reducing acid (PRA), and for some data series, headspace to simulant volume ratio (HSV), mercury (Hg), and nitrate. Although glycolate destruction for pairs of data series (e.g., [SB9-NG] and [SR+BH]) were found to depend on HSV, the combination of all three data series was not found to have significant dependence on this variable. The best model for glycolate destruction depended on AS, nitrate, and Hg. This model predicted the product glycolate compositions of the data to within 92-106%. The conversion of glycolate to formate was high when noble metals and Hg were not present, with values up to 100%. When noble metals and Hg were present, this conversion ranged from zero to 7%, and was dependent on AS. Lower AS gave higher conversions to formate. The conversion to oxalate was found to depend on the AS and the initial concentration of nitrite. An alternative fit versus AS and the form of ruthenium (Ru) used is a possible alternative. This fit was somewhat less statistically significant. This second model predicts that more oxalate is formed when Ru-nitrosyl nitrate is used rather than Ru chloride. The conversion of glycolate to oxalate ranged from zero to 6%. The conversion of nitrite to nitrate depended primarily on AS and PRA, with HSV and Hg being significant when these variables were varied. For multiple series of data, nitrite was also needed to SRNL-STI-2017-00172 5HYLVLRQ viL distinguish between data series, and the effect of HSV became insignificant. The best model for nitrite to nitrate conversion depended on AS, PRA, nitrite, and Hg. The 95% confidence intervals on the predicted values of glycolate destruction, glycolate to oxalate conversion, and nitrite to nitrate conversion were used to determine the uncertainty in the predicted REDOX when starting with only the composition of the sludge, AS, and PRA. Using the 95% confidences on an individual value (that is the confidence in getting a particular value for one single test as opposed to what the mean would be for multiple tests), the uncertainty in the predicted REDOX was calculated. The uncertainty in the actual product composition glycolate, oxalate, formate, and nitrate concentrations translated to an uncertainty in the REDOX value of ±0.1,which is approximately the uncertainty claimed in the REDOX model itself.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Eddy Current Flow Meter Measurements and Modeling Validation
The goal of the eddy current flow meter (ECFM) is to monitor velocities and temperatures of conductive liquid metals. The ECFM can also detect voids in two-phase liquid metal flows. Measurement of these flows can greatly improve the accuracy of the empirical formulas used for fluid dynamics near the reactor core and aid in mapping any non-uniformities in fluid flow such as estimates of temperature and phase. While the eventual goal is to develop the ECFM for the liquid sodium surrounding the Versatile Test Reactor (VTR) core, this report focuses on modeling and experimental validation of ECFM for a moving solid test rod and for liquid mercury in the Target Test Facility (TTF) flow loop to better understand and further develop ECFM measurement capabilities by validating model predictions with benchmark experiments. Eventually the models could be used to design and optimize future ECFMs for specific applications such as monitoring flow within the VTR pool.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
TNSL Overview
Thermal neutron scattering law (TNSL) data describe low-energy neutrons scattering off of bound materials, and can have a significant impact on modeling any system with slow neutrons, including nuclear reactors. Previous work to introduce TNSL data to neutron transport codes at LLNL focused on COG and TART [1], with the limitation that these codes require highly specialized data processing and formatting. We have recently increased efforts to process TNSL data with the central LLNL nuclear data processing code FUDGE, to be stored in the generalized nuclear database structure (GNDS) for use in any general transport code with the ability to read GNDS data. The first step in this effort is to verify that the TNSL processing with FUDGE yields results comparable to results obtained using the LANL nuclear data processing code NJOY. The next step is to verify the transport of thermal neutrons in Mercury (a Monte Carlo code) and Ardra (a deterministic code) against one another, as well as against the LANL Monte Carlo neutron transport code MCNP. This verification step has not been completed, due to a number of discrepancies between results obtained using differently processed data. There is ongoing effort to understand differences between FUDGE and NJOY. Finally, we map out our current capability to validate TNSL data against benchmark systems.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗