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DOE OSTI2024

Severe Convective Storms in Limited Instability Organized by Pattern and Distribution

Abstract Severe convection occurring in high-shear, low-CAPE (HSLC) environments is a common cool-season threat in the southeastern United States. Previous studies of HSLC convection document the increased operational challenges that these environments present compared to their high-CAPE counterparts, corresponding to higher false-alarm ratios and lower probability of detection for severe watches and warnings. These environments can exhibit rapid destabilization in the hours prior to convection, sometimes associated with the release of potential instability. Here, we use self-organizing maps (SOMs) to objectively identify environmental patterns accompanying HSLC cool-season severe events and associate them with variations in severe weather frequency and distribution. Large-scale patterns exhibit modest variation within the HSLC subclass, featuring strong surface cyclones accompanied by vigorous upper-tropospheric troughs and northward-extending regions of instability, consistent with prior studies. In most patterns, severe weather occurs immediately ahead of a cold front. Other convective ingredients, such as lower-tropospheric vertical wind shear, near-surface equivalent potential temperature (θ e ) advection, and the release of potential instability, varied more significantly across patterns. No single variable used to train SOMs consistently demonstrated differences in the distribution of severe weather occurrence across patterns. Comparison of SOMs based on upper and lower quartiles of severe occurrence demonstrated that the release of potential instability was most consistently associated with higher-impact events in comparison to other convective ingredients. Overall, we find that previously developed HSLC composite parameters reasonably identify high-impact HSLC events. Significance Statement Even when atmospheric instability is not optimal for severe convective storms, in some situations they can still occur, presenting increased challenges to forecasters. These marginal environments may occur at night or during the cool season, when people are less attuned to severe weather threats. Here, we use a sorting algorithm to classify different weather patterns accompanying such storms, and we distinguish which specific patterns and weather system features are most strongly associated with severe storms. Our goals are to increase situational awareness for forecasters and to improve understanding of the processes leading to severe convection in marginal environments.

Meteorology & Atmospheric Sciences↗

DOE OSTI2022

Machine learning changes the rules for flux limiters

Learning to integrate non-linear equations from highly resolved direct numerical simulations has seen recent interest for reducing the computational load for fluid simulations. Here, we focus on determining a flux-limiter for shock capturing methods. Focusing on flux limiters provides a specific plug-and-play component for existing numerical methods. Since their introduction, an array of flux limiters has been designed. Using the coarse-grained Burgers' equation, we show that flux-limiters may be rank-ordered in terms of their log-error relative to high-resolution data. We then develop a theory to find an optimal flux-limiter and present flux-limiters that outperform others tested for integrating Burgers' equation on lattices with [Formula: see text], and 2x, 3x, 4x, and 8x coarse-grainings. We train a continuous piecewise linear limiter by minimizing the mean-squared misfit to six-grid point segments of high-resolution data, averaged over all segments. While flux limiters are generally designed to have an output of φ(r) = 1 at a flux ratio of r = 1, our limiters are not bound by this rule and yet produce a smaller error than standard limiters. Here we find that our machine learned limiters have distinctive features that may provide new rules-of-thumb for the development of improved limiters. Additionally, we use our theory to learn flux-limiters that outperform standard limiters across a range of values (as opposed to at a specific fixed value) of coarse-graining, number of discretized bins, and diffusion parameter. This demonstrates the ability to produce flux limiters that should be more broadly useful than standard limiters for general applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Probabilistic flux limiters

The stable numerical integration of shocks in compressible flow simulations relies on the reduction or elimination of Gibbs phenomena (unstable, spurious oscillations). A popular method to virtually eliminate Gibbs oscillations caused by numerical discretization in under-resolved simulations is to use a flux limiter. A wide range of flux limiters have been studied in the literature, with recent interest in their optimization via machine learning methods trained on high-resolution datasets. The common use of flux limiters in numerical codes as plug-and-play blackbox components makes them key targets for design improvement. Even for deterministic dynamical models, numerical uncertainty is introduced via coarse-graining required by insufficient computational power to solve all scales of motion. Conventional flux limiters are deterministic and lack the capacity to address uncertainties, both aleatoric (inherent randomness) and epistemic (modeling uncertainty due to limited knowledge), which arise in coarse-grained numerical simulations. Here, we introduce a conceptually distinct type of flux limiter that is designed to handle the effects of randomness in the model and uncertainty in model parameters. Unlike traditional single-function flux limiters, these new probabilistic flux limiters incorporate multiple flux limiting functions, each applied with a learned probability drawn from high-resolution data to mitigate the effects of uncertainty in numerical simulations. This approach departs from traditional single-function limiters by explicitly modeling and incorporating uncertainty into the shock capturing process. Using the example of Burgers' equation as a testbed, we show that a machine learned, probabilistic flux limiter may be used in a shock capturing code to more accurately capture shock profiles. In particular, we show that our probabilistic flux limiter outperforms standard limiters and can be successively improved upon (up to a point) by expanding the set of probabilistically chosen flux limiting functions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Zero-pairing and zero-temperature limits of finite-temperature Hartree-Fock-Bogoliubov theory

Recently, variational Hartree-Fock-Bogoliubov (HFB) mean-field equations were shown to possess a mathematically well-defined zero-pairing limit, independently of the closed- or open-shell character of the system under consideration. This limit is non-trivial for open-shell systems such that HFB theory does {\it not} reduce to the Hartree-Fock (HF) formalism in all cases. The present work extends this analysis to finite-temperature HFB (FTHFB) theory by investigating the behavior of this more general formalism in the combined zero-temperature and zero-pairing limits. The zero-pairing and zero-temperature limits of the FTHFB statistical density operator constrained to carry an arbitrary (integer) number of particles A on average is worked out analytically and realized numerically using a two-nucleon interaction. While the FTHFB density operator reduces to the projector corresponding to a pure HF Slater determinant for closed-shell nuclei, the FTHFB formalism does not reduce to the HF theory in all cases in the zero-temperature and zero-pairing limits, i.e. for open-shell nuclei. However, the fact that a nucleus can be of open-shell character in these joint limits is necessarily the result of some symmetry restrictions. Whenever it is the case, the non-trivial description obtained for open-shell systems is shown to depend on the order with which both limits are taken, i.e. the two limits do not commute for these systems. When the zero-temperature limit is performed first, the FTHFB density operator is demoted to a projector corresponding to a pure state made out of a linear combination of a finite number of Slater determinants with different (even) numbers of particles. When the zero-pairing limit is performed first, the FTHFB density operator remains a statistical mixture of a finite number of Slater determinants with both even and odd particle numbers. While the entropy (pairing density) is zero in the first (second) case, it does not vanish in the second (first) case in spite of the temperature (pairing) tending towards zero. The difference between both limits can have striking consequences for the (thermal) expectation values of observables. For instance, the particle-number variance does not vanish in either case and has limiting values that differ by a factor of two in both cases. In conclusion, while in the textbook situation associated with closed-shell nuclei Hartree-Fock-Bogoliubov (finite-temperature Hartree-Fock) theory reduces to Hartree-Fock theory in the zero-pairing (zero-temperature) limit, the present analysis demonstrates that a non trivial and unexpected limit is obtained for this formalism in open-shell systems. This result sheds a new light on certain aspects of this otherwise very well-studied many-body formalism.

20 ≤ A ≤ 38↗

DOE OSTI2023

Density limits as disruption forecasters for spherical tokamaks

Fusion power output from spherical tokamaks would benefit from increased confined plasma density, but there exists a limit on the density before confinement is lost and the plasma current is disrupted. This density limit has long been characterized by a simple, global Greenwald limit proportional to the plasma current and inversely proportional to the cross sectional area of the plasma. It is shown that in the database of discharges from the National Spherical Tokamak Experiment (NSTX) and Mega Ampere Spherical Tokamak (MAST) spherical tokamaks, the likelihood of disruption does increase above the Greenwald limit, and especially in the plasma current rampdown phase. The physics of the density limit has been recently theoretically explored through local criteria. Several of these are tested using the disruption event characterization and forecasting (DECAF TM ) code for their potential effectiveness as disruption warning signals. For a limited set of NSTX discharges, a local island power balance criteria was found to be less reliable, presently, than the Greenwald limit. For this work, an empirical critical edge line density and a boundary turbulent transport limit were both tested for MAST-U, which has an electron density profile measurement with high spatial resolution in the outer part of the plasma. Both were found to have similar dependencies on key plasma parameters. In a limited set of MAST-U discharges that appear to disrupt due to rising density at values under the Greenwald limit, crossing of the boundary turbulent transport limit occurred close to the time of disruption. Finally, these limits were evaluated for their potential use in real-time, and it was found that with the necessary real-time inputs and with refinement through further testing, these limits could be implemented in a real-time disruption forecasting system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Global patterns of terrestrial nitrogen and phosphorus limitation

Nitrogen (N) and phosphorus (P) limitation constrains the magnitude of terrestrial carbon uptake in response to elevated carbon dioxide and climate change. However, global maps of nutrient limitation are still lacking. Here we examined global N and P limitation using the ratio of site-averaged leaf N and P resorption efficiencies of the dominant species across 171 sites. We evaluated our predictions using a global database of N- and P-limitation experiments based on nutrient additions at 106 and 53 sites, respectively. Globally, we found a shift from relative P to N limitation for both higher latitudes and precipitation seasonality and lower mean annual temperature, temperature seasonality, mean annual precipitation and soil clay fraction. Excluding cropland, urban and glacial areas, we estimate that 18% of the natural terrestrial land area is significantly limited by N, whereas 43% is relatively P limited. The remaining 39% of the natural terrestrial land area could be co-limited by N and P or weakly limited by either nutrient alone. This work provides both a new framework for testing nutrient limitation and a benchmark of N and P limitation for models to constrain predictions of the terrestrial carbon sink.

58 GEOSCIENCES↗

DOE OSTI2023

Reciprocal transplants reveal asymmetric local adaptation of Himalayan Rhododendron approaching elevational range limit

Abstract As plant species expand their upper limits of distribution under current warming, some retain both traditional climate space and biotic environment while others encounter novel conditions. The latter is the case for Rhododendron campanulatum , a woody shrub that grows both above and below treeline at our study site in the Eastern Himalayas where a very conspicuous, stable treeline was defined by a nearly contiguous canopy of tall Abies spectabilis trees, many of which are over a century old. Prior work showed that treeline had remained static in this region while R. campanulatum expanded its elevational range limit. We tested local adaptation of R. campanulatum by performing reciprocal transplants between the species' current elevational range limit (4023 m above sea level [asl]) and just above treeline (3876 m asl). Contrary to expectation, the coldest temperatures of late winter and early mid‐spring were experienced by plants at the lower elevation: R. campanulatum at species' limit (upper site) were covered by snow for a longer period (40 more days) and escaped the coldest temperatures suffered by conspecifics at treeline (lower site). The harsher spring conditions at treeline likely explain why leaves were smaller at treeline (15.3 cm 2 ) than at species limit (21.3 cm 2 ). Contrary to results from equivalent studies in other regions, survival was reduced more by downslope than by upslope movement, again potentially due to extreme cold temperatures observed at treeline in spring. Upslope transplantation had no effect on mortality, but mortality of species limit saplings transplanted downslope was three times higher than that of residents at both sites. A general expectation is that locals should survive better than foreign transplants, but survival of locals and immigrants at our species limit site was identical. However, those species limit saplings that survived the transplant to treeline grew faster than both locals at treeline and the transplants at species limit. Overall, we found asymmetric adaptation: Compared with treeline saplings, those at species limit (147 m above treeline) were more tolerant of extremes in the growing season but less tolerant of extremes in winter and early mid‐spring, displaying local adaptation in a more complex manner than simply home advantage, and complicating predictions about impacts of future regional climate change.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Evidence of vapor shielding effect on heat flux loaded on flowing liquid lithium limiter in EAST

For this study, a lithium (Li) vapour layer was formed around a flowing liquid Li limiter to shield against the plasma incident power and reduce limiter heat flux in the EAST tokamak. The results revealed that after a plasma operation of a few seconds, the layer became clear, which indicated a strong Li emission with a decrease in the limiter surface temperature. This emission resulted in a dense vapour around the limiter, and Li ions moved along the magnetic field to form a green shielding layer on the limiter. The plasma heat flux loaded on the limiter, measured by the probe installed on the limiter, was approximately 52% lower than that detected by a fast-reciprocating probe at the same radial position without the limiter in EAST. Additionally, approximately 42% of the parallel heat flux was dissipated directly with the enhanced Li radiation in the discharge with the liquid metal infused trenches (LIMIT) limiter. This observation revealed that the Li vapour layer exhibited an excellent shielding effect to liquid Li on plasma heat flux, which is a possible benefit of liquid-plasma-facing components in future fusion devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

A Two-Stage Current Limiting Control Strategy for Direct-Droop-Controlled Grid-Forming Inverters

This paper presents a two-stage current limiting control strategy with fault ride-through capability for the direct-droop-controlled grid-forming (GFM) inverters. The proposed approach comprises Stage 1 and Stage 2 current limiting controls. During faults, Stage 1 current limiting control instantly clamps the inverter output current magnitude to its maximum transient limit by blocking the switching pulses to the insulated-gate bipolar transistors (IGBTs) with the help of a hysteresis loop control, and Stage 2 current limiting control limits the inverter output current magnitude to its steady-state limit by regulating the amplitude and frequency of the modulating waveform utilizing the active and reactive current limiting control loops. By implementing the current limiting actions in two stages, this approach can effectively limit the over-current within a few cycles after the fault occurrence and ensure synchronism to the grid after long-term fault events. The efficacy of the proposed control approach is validated through electromagnetic transient (EMT) simulation results conducted on a single GFM inverter-based test system and the IEEE 39-bus test system with multiple GFM inverters in the PSCAD platform.

Mohiuddin, Sheik Mohammad↗

DOE OSTI2020

Microbial carbon limitation: The need for integrating microorganisms into our understanding of ecosystem carbon cycling

Abstract Numerous studies have demonstrated that fertilization with nutrients such as nitrogen, phosphorus, and potassium increases plant productivity in both natural and managed ecosystems, demonstrating that primary productivity is nutrient limited in most terrestrial ecosystems. In contrast, it has been demonstrated that heterotrophic microbial communities in soil are primarily limited by organic carbon or energy. While this concept of contrasting limitations, that is, microbial carbon and plant nutrient limitation, is based on strong evidence that we review in this paper, it is often ignored in discussions of ecosystem response to global environment changes. The plant‐centric perspective has equated plant nutrient limitations with those of whole ecosystems, thereby ignoring the important role of the heterotrophs responsible for soil decomposition in driving ecosystem carbon storage. To truly integrate carbon and nutrient cycles in ecosystem science, we must account for the fact that while plant productivity may be nutrient limited, the secondary productivity by heterotrophic communities is inherently carbon limited. Ecosystem carbon cycling integrates the independent physiological responses of its individual components, as well as tightly coupled exchanges between autotrophs and heterotrophs. To the extent that the interacting autotrophic and heterotrophic processes are controlled by organisms that are limited by nutrient versus carbon accessibility, respectively, we propose that ecosystems by definition cannot be ‘limited’ by nutrients or carbon alone. Here, we outline how models aimed at predicting non‐steady state ecosystem responses over time can benefit from dissecting ecosystems into the organismal components and their inherent limitations to better represent plant–microbe interactions in coupled carbon and nutrient models.

Soong, Jennifer L.↗

DOE OSTI2024

Correlation of the L-mode density limit with edge collisionality

The "density limit'' is one of the fundamental bounds on tokamak operating space, and is commonly estimated via the empirical Greenwald scaling. This limit has garnered renewed interest in recent years as it has become clear that ITER and many tokamak pilot plant concepts must operate near or above the widely-used Greenwald limit to achieve their objectives. Evidence has also grown that the Greenwald scaling - in its remarkable simplicity - may not capture the full complexity of the disruptive density limit. In this study, we assemble a multi-machine database to quantify the effectiveness of the Greenwald limit as a predictor of the L-mode density limit and identify alternative stability metrics. We find that a two-parameter dimensionless boundary in the plasma edge, $\nu_{*\rm, edge}^{\rm limit} = 3.0 \beta_{T,{\rm edge}}^{-0.4}$, achieves significantly higher accuracy (true negative rate of 97.7\% at a true positive rate of 95\%) than the Greenwald limit (true negative rate 86.1\% at a true positive rate of 95\%) across a multi-machine dataset including metal- and carbon-wall tokamaks (AUG, C-Mod, DIII-D, and TCV). The collisionality boundary presented here can be applied for density limit avoidance in current devices and in ITER, where it can be measured and responded to in real time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Unified Model of Current-Limiting Grid-Forming Inverters for Large-Signal Analysis

Grid-forming (GFM) inverters can hardly withstand any overloading. As such, GFM inverters need a current limiter in their control system to avoid hardware damage during overloading or grid disturbances. When the current limiter is engaged for inverter protection, however, it dynamically changes the inverter output impedance, which can significantly affect the system behavior against large disturbances. For example, when the current limiter curtails the output power, the primary controller of the GFM inverter-which generates the voltage and angle reference-is prone to losing synchronization with the grid. This can cause large-signal instability in the network. This paper presents a unified GFM current-limiter model to gain a deeper understanding of the impact of the GFM inverter current limiting on large-signal instability and other system behaviors. The unified model captures several well-known current limiters for GFM inverters, and it reveals their large-signal equivalence characterized by the limiter angle. We use the unified model to present in-depth insights into the driving forces that cause large-signal instability in GFM inverter-driven grids. Further, this paper illustrates that the unified model can be used as a tool for assessing the system-level impacts of various GFM current-limiter designs during grid disturbances. Using numerical, analytical, electromagnetic transient models, and a hardware setup, the validity of the unified model is evaluated.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Data for: Spatial access and resource limitations control carbon mineralization in soils

This dataset contains data and code used for the paper "Spatial access and resource limitations control carbon mineralization in soils", https://doi.org/10.1016/j.soilbio.2021.108427. Core-scale soil carbon fluxes are ultimately regulated by pore-scale dynamics of substrate availability and microbial access. These are constrained by physicochemical and biochemical phenomena (e.g. spatial access and hydrologic connectivity, physical occlusion, adsorption-desorption with mineral surfaces, nutrient and resource limitations). We conducted an experiment to determine how spatial access and resource limitations influence core-scale water-soluble soil organic matter (SOM) mineralization, and how these are regulated by antecedent moisture conditions. Intact soil cores were incubated at field-moist vs. drought conditions, after which they were saturated from above (to simulate precipitation) or below (to simulate groundwater recharge). Soluble carbon (acetate) and nitrogen (nitrate) forms were added to some cores during the rewetting process to alleviate potential nutrient limitations. Soil respiration was measured during the incubation, after which pore water was extracted from the saturated soils and analyzed for water soluble organic carbon concentrations and characterization. Our results showed that carbon (C) amendments increased the cumulative carbon dioxide (CO2) evolved from the soil cores, suggesting that the soils were C-limited. Drought and rewetting increased soil respiration, and there was a greater abundance of complex aromatic molecules in pore waters sampled from these soils. This newly available substrate appeared to alleviate nutrient limitations on respiration, because there were no further respiration increases with subsequent C and N amendments. We had hypothesized that respiration would be influenced by wetting direction, as simulated precipitation would mobilize C from the surface. However, as a main effect, this response was seen only in the C-amended soils, indicating that surface-C may not have been bioavailable. At the pore scale (pore water samples), drought and the C, N amendments caused a net loss of identified molecules when the soils were rewet from below, whereas wetting from above caused a net increase in identified molecules, suggesting that fresh inputs stimulated the C-and N-limited microbial populations present deeper in the soil profile. Our experiment highlights the complex and interactive role of antecedent moisture conditions, wetting direction, and resource limitations in driving core-scale C fluxes.This dataset contains a compressed (.zip) archive of the data and R scripts used for this manuscript. The dataset includes files in .csv format, which can be accessed and processed using MS Excel or R. This archive can also be accessed on GitHub at https://github.com/kaizadp/TES_spatial_access_2021 (DOI: 10.5281/zenodo.5522938).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

LANSCE CCL Performance Limits

This report summarizes the performance limits of the LANSCE Coupled-Cavity Linac (CCL). These results are captured or summarized directly from the references cited. This report was written in support of the LANSCE Modernization Project (LAMP). Many factors contribute to the performance limits of the CCL accelerator system. One performance limit is set by the CCL mechanical structure and available cooling. Heating of the structure is ultimately linked to the operating RF duty factor of the CCL. Another performance limit is set by the maximum RF and beam duty factors that can be supported by the 805-MHz klystrons and associated HVDC power supplies. The RF and HVDC systems also set limits for the maximum peak beam current that can be accelerated in the CCL. And finally, a maximum beam current limit is set by the beam dynamics determined by the details of the CCL physics design (number of cells per CCL tank, accelerating gradients, magnetic focusing lattice, beam losses, etc.). This limit can be informed by both simulation results and beam measurement data, if available. A detailed explanation of each performance limit is given in the sections below. The results are summarized in the table below. In all cases, it is assumed that the CCL and the RF system are operating in their nominal beam production configuration – nominal magnet set points and nominal cavity fields, unless otherwise specified.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Spatial access and resource limitations control carbon mineralization in soils

Core-scale soil carbon fluxes are ultimately regulated by pore-scale dynamics of substrate availability and microbial access. These are constrained by physicochemical and biochemical phenomena (e.g. spatial access and hydrologic connectivity, physical occlusion, adsorption-desorption with mineral surfaces, nutrient and resource limitations). We conducted an experiment to determine how spatial access and resource limitations influence core-scale SOM mineralization, and how these are regulated by antecedent moisture conditions. Intact soil cores were incubated at field-moist vs. drought conditions, after which they were saturated from above (to simulate precipitation) or below (to simulate groundwater recharge). Soluble C (acetate) and N (nitrate) forms were added to some cores during the rewetting process to alleviate potential nutrient limitations. Respiration showed evidence of C-limitation, as C amendments increased the cumulative CO 2 evolved. Drought and rewetting increased soil respiration, and these soils also exhibited increased complex aromatic molecules in porewater. This newly available substrate appeared to alleviate nutrient limitations on respiration, because there were no further respiration increases with subsequent C and N amendments. We expected that respiration would be influenced by wetting direction, as simulated precipitation would mobilize C from the surface. However, as a main effect, this response was seen only in the C-amended soils, indicating that surface-C may not have been bioavailable. At the pore scale (porewater samples), compared to the baseline soils, drought and the C, N amendments caused a net loss of identified molecules when the soils were rewet from below, whereas wetting from above caused a net increase in identified molecules. This indicates that as soils were wet from below, the fresh inputs simulated the C-and N-limited microbial populations present deeper in the soil profile. Furthermore, our experiment highlights the complex and interactive role of antecedent moisture conditions, wetting direction, and resource limitations in driving core-scale C fluxes.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Effect of microphase separation on the limiting current density in hybrid organic-inorganic copolymer electrolytes

Hybrid organic-inorganic block copolymer electrolytes are of interest to enable batteries containing lithium metal anodes. The conductive block is a standard polymer electrolyte of poly(ethylene oxide) and the mechanically rigid block is an inorganic poly(acryloisobutyl polyhedral oligomeric silsesquioxane) polymer. Here, in this paper, we compare a poly(acryloisobutyl polyhedral oligomeric silsesquioxane)-b-poly(ethylene oxide)-b-poly(acryloisobutyl polyhedral oligomeric silsesquioxane) (POSS-PEO-POSS) triblock copolymer and a poly(ethylene oxide)-b- poly(acryloisobutyl polyhedral oligomeric silsesquioxane) (PEO-POSS) diblock copolymer mixed with lithium bis(trifluoromethanesulfonyl)imide salt. We have experimentally measured the limiting current density in lithium symmetric cells containing hybrid organic-inorganic electrolytes at 90 °C. The cells were polarized at a large range of applied current density. The diblock copolymer electrolyte exhibited a clear plateau in cell potential at all current densities below the limiting current density. At low applied current density, the triblock copolymer electrolyte also exhibited a clear plateau in cell potential. At currents approaching the limiting current density, the triblock copolymer electrolyte exhibited an underdamped potential profile. The cell potential did not reach a plateau at current densities above the limiting current in both systems. The diblock and triblock copolymer electrolytes were fully characterized using electrochemical methods to determine the ionic conductivity, cation current fraction, salt diffusion coefficient, and open circuit voltage as a function of salt concentration. Cell potential and salt concentration as functions of position in the cell at various current densities were calculated using Newman's concentrated solution theory. The theoretical limiting current density was calculated to be the current density at which salt is depleted at the cathode. We see quantitative agreement between experimental measurements and theoretical predictions for the limiting current density in the diblock copolymer electrolyte which has an ordered structure at all salt concentrations, while the experimental limiting current density is lower than the theoretical prediction for the triblock copolymer electrolyte, which exhibits a disordered morphology at high salt concentrations.

25 ENERGY STORAGE↗

DOE OSTI2021

Overview of the Tolerance Limit Calculations with Application to TSURFER

To establish confidence in the results of computerized physics models, a key regulatory requirement is to develop a scientifically defendable process. The methods employed for confidence, characterization, and consolidation, or C3, are statistically involved and are often accessible only to avid statisticians. This manuscript serves as a pedagogical presentation of the C3 process to all stakeholders—including researchers, industrial practitioners, and regulators—to impart an intuitive understanding of the key concepts and mathematical methods entailed by C3. The primary focus is on calculation of tolerance limits, which is the overall goal of the C3 process. Tolerance limits encode the confidence in the calculation results as communicated to the regulator. Understanding the C3 process is especially critical today, as the nuclear industry is considering more innovative ways to assess new technologies, including new reactor and fuel concepts, via an integrated approach that optimally combines modeling and simulation and minimal targeted validation experiments. This manuscript employs intuitive, analytical, numerical, and visual representations to explain how tolerance limits may be calculated for a wide range of configurations, and it also describes how their values may be interpreted. Various verification tests have been developed to test the calculated tolerance limits and to help delineate their values. The manuscript demonstrates the calculation of tolerance limits for TSURFER, a computer code developed by the Oak Ridge National Laboratory for criticality safety applications. The goal is to evaluate the tolerance limit for TSURFER-determined criticality biases to support the determination of upper, subcritical limits for regulatory purposes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Evaluation of the Simplified Assessment Peak Equivalent Stress Design Limit Probability of Failure

The ASME Boiler and Pressure Vessel Code Section III Division 5 Subsection HH Subpart A (HHA) outlines requirements and qualification methods for graphite core components in high temperature reactor environments. One such structural qualification method is the Simplified Assessment outlined in HHA-3220, which represents a comparison of service level specific equivalent stresses to allowable stress values derived from target probability of failures (POFs). The target POF is based on the structural reliability class (SRC) for the components and service condition of interest, and is used to establish design limits for combined membrane and peak equivalent stresses. Combined membrane stress limits are derived from two parameter Weibull distribution fits of the graphite grade specific tensile strength data and the target POF. The combined membrane stress limits are then scaled based on the ratio of flexural strength to tensile strength (referred hereinafter as Rtf) to establish the corresponding peak equivalent stress limits. It is desired that the target POF is at least maintained for both combined membrane and peak equivalent design limits, especially with the use of Rtf. The assessment presented herein examines tensile and flexural data for medium and fine grade graphites relative to the calculated combined membrane and peak equivalent stress limits per HHA-3220 and illustrates the simplified assessment method results in anticipated, or at least conservative, peak equivalent design stress limits.

36 - MATERIALS SCIENCE↗