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DOE OSTI2018

Conditions for translation and scaling invariance of the neutron diffusion equation

Lie group methods are applied to the time-dependent, monoenergetic neutron diffusion equation in materials with spatial and time dependence. To accomplish this objective, the underlying 2nd order partial differential equation (PDE) is recast as an exterior differential system so as to leverage the isovector symmetry analysis approach. Some of the advantages of this method as compared to traditional symmetry analysis approaches are revealed through its use in the context of a 2nd order PDE. In this context, various material properties appearing in the mathematical model (e.g., a diffusion coefficient and macroscopic cross section data) are left as arbitrary functions of space and time. The symmetry analysis that follows is restricted to a search for translation and scaling symmetries; consequently the Lie derivative yields specific material conditions that must be satisfied in order to maintain the presence of these important similarity transformations. The principal outcome of this work is thus the determination of analytic material property functions that enable the presence of various translation and scaling symmetries within the time-dependent, monoenergetic neutron diffusion equation. The results of this exercise encapsulate and generalize many existing results already appearing in the literature. While the results contained in this work are primarily useful as phenomenological guides pertaining to the symmetry behavior of the neutron diffusion equation under certain assumptions, they may eventually be useful in the construction of exact solutions to the underlying mathematical model. Furthermore, the results of this work are also useful as a starting point or framework for future symmetry analysis studies pertaining to the neutron transport equation and its many surrogates.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1994

Axial and centrifugal pump meanline performance analysis

A meanline pump flow modeling method has been developed to provide a fast capability for modeling pumps of cryogenic rocket engines. Based on this method, a meanline pump flow code (PUMPA) has been written that can predict the performance of pumps at off-design operating conditions, given the loss of the diffusion system at the design point. The design point rotor efficiency is obtained from empirically derived correlations of loss to rotor specific speed. The rapid input setup and computer run time for the meanline pump flow code makes it an effective analysis and conceptual design tool. The map generation capabilities of the PUMPA code provide the information needed for interfacing with a rocket engine system modeling code.

Veres, Joseph P.↗

DOE OSTI2019

Validation of Wichner Predictive Model for Chronic Oxidation by Moisture of Nuclear Graphite

This document reports the results of multi-year extensive research on chronic oxidation of nuclear graphite by traces of moisture that might be present in the helium coolant of high-temperature gas-cooled reactors (HTGRs). The research focuses on four grades of nuclear graphite that are considered potential candidates for component fabrication in advanced nuclear reactors. The four grades are (1) PCEA (medium-fine grain, extruded, manufactured by GrafTech Inc., USA); (2) NBG-17 (medium-fine grain, vibrationally molded, manufactured by SGL Carbon, Germany/France); (3) IG-110 (microfine grain, isostatically molded, manufactured by Toyo Tanso, Japan); and (4) 2114 (microfine grain, isostatically pressed, manufactured by Mersen, USA). The experimental part of this research comprised three objectives that were consistently pursued for each graphite material: (1) accelerated oxidation tests in well-controlled conditions (temperature, gas composition) and analysis of chemical kinetic models and of their parameters for each graphite grade; (2) measurements of water vapor transport rates from H 2 O/He mixtures through thin graphite slabs for estimation of the water effective diffusivity specific to each material; (3) controlled oxidation of graphite specimens in H 2 O/He mixtures and characterization of the effects of oxidation temperatures on the density profiles of oxidized layers. These three groups of experimental results were interpreted using the model developed by Wichner et al. for predicting the penetration depth of oxidants (moisture or oxygen) as a function of oxidation conditions. Basically, starting from the kinetic and transport properties of each graphite grade, the ultimate goal was predicting the stable density profile in the oxidized layer and its dependence on the oxidation temperature. The profiles obtained this way were then compared against direct observations of oxidized layers in specimens obtained in well-controlled oxidation conditions. The general agreement between predictions and observations validated the general applicability of the Wichner model. The results obtained in this project were presented at annual Department of Energy–Advanced Reactor Technologies program reviews and at specialist meetings and conferences and were published in Oak Ridge National Laboratory (ORNL) reports and in professional journals. The results published in 2018 had an immediate impact in 2019, when a group from three US universities used ORNL kinetic data as input information in a complex simulation of chronic oxidation by moisture using the same graphite grades during long-time operation in a modular high-temperature gas-cooled reactor. Their conclusion, in line with the conclusions obtained at the end of this project, was that chronic graphite oxidation by moisture during normal operation conditions of an HTGR will be limited to a thin surface layer of graphite blocks at the reactor bottom, where the highest temperatures are. That will not affect the integrity of graphite components and reactor safety, provided the impurity concentration in the helium coolant is rigorously controlled and maintained at the design specifications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1996

Global, Collisional Model of High-Energy Photoelectrons

A previously-developed colissional, interhemispheric flux tube model for photoelectrons (PE) has been extended to three dimensions by including transport due to vector E x vector B and magnetic gradient-curvature drifts. Using this model, initial calculations of the high-energy (greater then 50 eV) PE distribution as a function of time, energy, pitch angle, and spatial location in the equatorial plane, are reported for conditions of low geomagnetic activity. To explore both the dynamic and steady behaviors of the model, the simulation starts with the abrupt onset of photoelectron excitation, and is followed to steady state conditions. The results illustrate several features of the interaction of photoelectrons with typical magnetospheric plasmas and fields, including collisional diffusion of photoelectrons in pitch angle with flux tube filling, diurnal intensity and pitch angle asymmetries introduced by directional sunlight, and energization of the photoelectron distribution in the evening sector. Cross-field drift is shown to have a long time scale, taking 12 to 24 hours to reach a steady state distribution. Future applications of the model are briefly outlined.

Khazanov, G. V.↗

DOE OSTI2016

Laser-material interaction during atom probe tomography of oxides with embedded metal nanoparticles

Here, oxide-supported metal nano-particles are of great interest in catalysis but also in the development of new large-spectrum-absorption materials. The design of such nano materials requires three-dimensional characterization with a high spatial resolution and elemental selectivity. The laser assisted Atom Probe Tomography (La-APT) presents both these capacities if an accurate understanding of laser-material interaction is developed. In this paper, we focus on the fundamental physics of field evaporation as a function of sample geometry, laser power, and DC electric field for Au nanoparticles embedded in MgO. By understanding the laser-material interaction through experiments and a theoretical model of heat diffusion inside the sample after the interaction with laser pulse, we point out the physical origin of the noise and determine the conditions to reduce it by more than one order of magnitude, improving the sensitivity of the La-APT for metal-dielectric composites.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Extending the range of validity of Fourier's law into the kinetic transport regime via asymptotic solution of the phonon Boltzmann transport equation

We derive the continuum equations and boundary conditions governing phonon-mediated heat transfer in the limit of a small but finite mean-free path from the asymptotic solution of the linearized Boltzmann equation in the relaxation time approximation. Our method uses the ratio of the mean-free path to the characteristic system length scale, also known as the Knudsen number, as the expansion parameter to study the effects of boundaries on the breakdown of the Fourier description. We show that, in the bulk, the traditional heat conduction equation using Fourier's law as a constitutive relation is valid at least up to second order in the Knudsen number for steady problems and first order for time-dependent problems. Yet, this description does not hold within distances on the order of a few mean-free paths from the boundary; this breakdown is a result of kinetic effects that are always present in the boundary vicinity and require solution of a Boltzmann boundary layer problem to be determined. Matching the inner, boundary layer solution to the outer, bulk solution yields boundary conditions for the Fourier description as well as additive corrections in the form of universal kinetic boundary layers; both are found to be proportional to the bulk-solution gradients at the boundary and parametrized by the material model and the phonon-boundary interaction model (Boltzmann boundary condition). Our derivation shows that the traditional no-jump boundary condition for prescribed temperature boundaries and the no-flux boundary condition for diffusely reflecting boundaries are appropriate only to zeroth order in the Knudsen number; at higher order, boundary conditions are of the jump type. We illustrate the utility of the asymptotic solution procedure by demonstrating that it can be used to predict the Kapitza resistance (and temperature jump) associated with an interface between two materials. All results are validated via comparisons with low-variance deviational Monte Carlo simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Exploration of a Reacting Jet-in-Crossflow in a High-Pressure Axial Stage Combustor

The present work investigates a reacting methane jet in a vitiated cross flow at five atmospheres. The experiments are run at temperatures and velocities relevant to real world gas turbines. High speed chemiluminescence is utilized to obtain flame behavior and visualize flame trajectories. Experimental results are compared with a corresponding RANS CFD model. The characteristics of a diffusion methane jet injected into a vitiated crossflow are explored at various momentum flux ratios and test section inlet boundary conditions. Temperature and velocity measurements are made at the inlet of the test section to ensure uniform boundary conditions for the axial stage. The effect of different momentum flux ratios on flame stabilization mechanisms and jet trajectories are presented. Momentum flux ratios are varied from 0.5-107; at lower momentum flux ratios the diffusion flame is less stable and burns downstream in the shear layer between the jet and crossflow. At higher momentum flux ratios, the diffusion flame burns more upstream and exhibits improved stability compared to the lower momentum flux ratio cases.

03 NATURAL GAS↗

DOE OSTI2014

A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces

In this study, we present a new numerical model for crystal growth in a vertical solidification system. This model takes into account the buoyancy induced convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. Two novel phase-field models are developed to model the crystal growth interface in vertical gradient furnaces with two temperature profile setups: 1) fixed wall temperature profile setup and 2) time-dependent temperature profile setup. A semi-implicit lattice kinetics solver based on the Boltzmann equation is employed to model the unsteady incompressible flow. This model is used to investigate the effect of furnace operational conditions on crystal growth interface profiles and growth velocities. For a simple case of macroscopic radial growth, the phase-field model is validated against an analytical solution. Crystal growth in vertical gradient furnaces with two temperature profile setups have been also investigated using the developed model. The numerical simulations reveal that for a certain set of temperature boundary conditions, the heat transport in the melt near the phase interface is diffusion dominant and advection is suppressed.

Lin, Guang↗

NASA NTRS1978

Design and subscale tests of a diffuser system for a Mach 4 scramjet test facility

A fixed-geometry diffuser system was designed for use in Mach 4 free-jet tests of a hydrogen-burning modular scramjet engine. The scramjet engine has a rectangular cross section that blocks up to 33 percent of the existing tunnel nozzle exit area and swept leading edges of the scramjet produce an asymmetric downward flow that sharply increases when the scramjet inlet unstarts. Effects of these conditions on the operation of the diffuser system are not accurately predictable. An experimental investigation has therefore been conducted in unheated air using a subscale model of the tunnel-scramjet-diffuser system to substantiate the design. Test results showed that the preliminary design had to be modified to obtain an acceptable configuration of the nozzle exit, test cabin, and diffuser that would provide shock-free flow at the scramjet inlet for simulated Mach 4 flight at altitudes from 16,764 to 20,422 meters.

Andrews, E. H., Jr.↗

NASA NTRS1981

A study of atmospheric diffusion from the LANDSAT imagery

LANDSAT multispectral scanner data of the smoke plumes which originated in eastern Cabo Frio, Brazil and crossed over into the Atlantic Ocean, are analyzed to illustrate how high resolution LANDSAT imagery can aid meteorologists in evaluating specific air pollution events. The eleven LANDSAT images selected are for different months and years. The results show that diffusion is governed primarily by water and air temperature differences. With colder water, low level air is very stable and the vertical diffusion is minimal; but water warmer than the air induces vigorous diffusion. The applicability of three empirical methods for determining the horizontal eddy diffusivity coefficient in the Gaussian plume formula was evaluated with the estimated standard deviation of the crosswind distribution of material in the plume from the LANDSAT imagery. The vertical diffusion coefficient in stable conditions is estimated using Weinstock's formulation. These results form a data base for use in the development and validation of meso scale atmospheric diffusion models.

Dejesusparada, N.↗

DOE OSTI2018

Use of Physics Based Management Optimization for Groundwater Remedy Design - 18671

Numerical modeling coupled with formal mathematical optimization techniques was used to design a groundwater remedy strategy to address a carbon tetrachloride (CCl{sub 4}) plume covering several square miles. The optimization approach, methodology, and project costs are described. The site consists of a large grain elevator in Nebraska. CCl{sub 4} was used as a fumigant and subsequently impacted soils and groundwater. Remedy design focused on the more diffuse plume, which extended approximately 4.5 miles down gradient of the source area. An eleven-layer model was developed and calibrated to observed groundwater conditions. This model was linked with formal optimization techniques to identify the best design capable of meeting client specified requirements and well location limitations. The planned system included requirements on the location of extraction and injection wells, total system flow rate, number of management periods, and specific constraints limiting further plume expansion. A separate trinitrotoluene (TNT) contaminant plume from a third party was located vertically above the leading edge of the CCl{sub 4} plume within the same aquifer. A further constraint imposed was that the design could not affect or cause additional migration of the TNT plume. Optimal system design was determined using HydroGeoLogic's Physics Based Management Optimization (PBMO{sup TM}) system. Over 38,000 candidate solutions consisting of different combinations of pumping and injection wells locations and rates, were evaluated through flow modeling coupled with either particle tracking or fully convective-dispersive transport simulations to determine the optimal design. Planning for installation of the optimal design is underway. Simulations were completed on a distributed computing platform consisting of 3 Quad Core PCs. Flow and particle tracking simulations required less than 2 minutes per simulation. Coupled flow and transport simulation run times were generally between 30-40 minutes per simulation. The total costs for developing the groundwater flow model and completing the subsequent optimal design were approximately $400,000. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2025

Probabilistic Diffusion Models Advance Extreme Flood Forecasting

Extreme floods pose escalating risks in a changing climate, yet forecasting remains challenging due to peak flow underestimation and high uncertainty. We introduce diffusion-based runoff model (DRUM), a probabilistic deep learning (DL) approach that advances extreme flood forecasting across representative basins in the contiguous United States. DRUM outperforms state-of-the-art benchmarks, enhancing nowcasting skill for the top 1‰ of flows in 72.3% of studied basins. Under operational scenarios, DRUM extends reliable lead times by nearly a full day for 20- and 50-year floods. When evaluated with measured precipitation, an ideal condition, recall improves by 0.3–0.4 and the early warning window extends by 2.3 days for 50-year floods. The enhancement potential varies regionally, with precipitation-driven flood zones in the eastern and northwestern US benefiting most, gaining 3–7 days in lead time. These findings highlight the transformative potential of diffusion models as a cutting-edge generative AI technique for advancing hydrology and broader Earth system sciences.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2022

2020 Innovation Fair Project: Is Midlatitude Ground Ice on Mars Habitable for Life?

The objective of this project was to perform a modeling study to evaluate whether midlatitude ground ice on Mars that could support life in geologically recent times. Recent studies from Mars orbital imaging, ground penetrating radar data, and infrared thermal data have revealed that large areas of Mars at latitudes higher than 40o N host near surface ground ice. Past climate cycles driven by orbital oscillations are expected to result in the distribution of ground ice changing over geologically recent history. The insolation at any location on Mars varies over time due to quasi-periodic changes in its orbital parameters (obliquity, eccentricity, perihelion longitude). The last 2 MY Mars obliquity varied between 15o and 35o but 5 MY ago varied between 24o and 48o with the average obliquity being 36o. The current low obliquity Mars atmosphere is dryer than average conditions. Recent work (Mellon and Sizemore Icarus (2022) 371;114667) has shown that repeatedly over the last 2 MY ground ice was present even at low Northern latitudes. The ice table depth is controlled by diffusive equilibrium with water vapor in the atmosphere, which also varies with orbital parameters. Determining the surface temperature and water vapor abundance requires a sophisticated climate model that was developed at NASA Ames, and results of high obliquity climate simulations will be used in the study. Work is underway to evaluate the subsurface thermal conditions in ice-rich areas of Mars during high obliquity periods to determine whether, where, and when the subsurface ice becomes warm enough to support metabolic processes or growth of terrestrial organisms.

Carol R Stoker↗

DOE OSTI2019

M3MS-19IN0101201 Modeling Intra-granular Fission Gas Bubble Evolution in Uranium Dioxide during Transients

The SciDAC milestone M3MS-19IN0101201 on Modeling Intra-granular Fission Gas Bubble Evolution in Uranium Dioxide during Transients was completed with the development, testing and implementation in the Bison code of an engineering model for intra-granular fission gas bubble evolution that is applicable to transient conditions. The model extends the previous work on modeling bubble evolution during normal operating conditions to include additional complexity that arises during transient situations, in particular, the so-called intra-granular bubble coarsening. This phenomenon refers to the appearance of a second population of coarsened bubbles with diameters of tens to hundreds of nm, which co-exist with nanometric bubbles present also during normal operating conditions and are responsible for a large portion of transient fuel swelling. The developed model considers growth of bubbles along dislocations, associated with the absorption of vacancies available in the dislocation core region, and favored by pipe diffusion of fission gas atoms. The model also utilizes the formulation for the gas atom resolution rate developed in the present SciDAC project through molecular dynamics simulations by other institutions. The present work therefore demonstrates an operational multiscale approach, based on collaboration within the project. The model is validated to an extensive experimental dataset of ramp tested uranium dioxide fuel samples. Additionally, we present new applications of the base model for bubble evolution during normal operating conditions to Bison engineering simulations of Cr2O3-doped fuel rods irradiated in the Halden reactor. Simulation results in terms of integral fission gas release in the fuel rods are compared to the available experimental data, pointing out significant improvements in the engineering predictions compared to application of the empirical model that was available in Bison before the SciDAC developments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2016

String flash-boiling in gasoline direct injection simulations with transient needle motion

A computational study was performed to investigate the influence of transient needle motion on gasoline direct injection (GDI) internal nozzle flow and near-field sprays. Simulations were conducted with a compressible Eulerian flow solver modeling liquid, vapor, and non-condensable gas phases with a diffuse interface. Variable rate generation and condensation of fuel vapor were captured using the homogeneous relaxation model (HRM). The non-flashing (spray G) and flashing (spray G2) conditions specified by the Engine Combustion Network were modeled using the nominal spray G nozzle geometry and transient needle lift and wobble were based upon ensemble averaged x-ray imaging preformed at Argonne National Lab. The minimum needle lift simulated was 5 μm and dynamic mesh motion was achieved with Laplacian smoothing. The results were qualitatively validated against experimental imaging and the experimental rate of injection profile was captured accurately using pressure boundary conditions and needle motion to actu- ate the injection. Needle wobble was found to have no measurable effect on the flow. Low needle lift is shown to result in vapor generation as fuel rushes past the needle. In conclusion, the internal injector flow is shown to contain many transient and interacting vortices which cause perturbations in the spray angle, fluctuations in the mass flux, and frequently result in string flash-boiling.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2020

Growth and Properties of Vapor Diffused Nb3Sn Coating for Superconducting Radiofrequency Accelerator Cavity Applications

The desire to reduce construction and operating costs of future SRF accelerators motivates the search for higher-performing alternative materials. Nb3Sn (Tc ~ 18.3 K and Hsh ~ 425 mT) is the front runner. The tin vapor diffusion process is currently the technique of choice to produce promising Nb3Sn-coated cavities. Understanding Nb3Sn nucleation and growth in this process is essential to progress. Samples representing different stages of Nb3Sn formation have been produced and studied to elucidate the effects of nucleation, growth, process conditions, and impurities. Nb3Sn films with thickness from a few hundred nm up to ~15 µm were grown and characterized. The microscopic examination of samples suggests the mechanisms of thin film nucleation and growth. Broadly, nucleation deposits tin as a thin surface phase and, under some conditions, a few hundred nanometer sized particles as well. Conditions that impair nucleation promote the formation of defects, such as ?patches?, in subsequent coating growth. Analysis of coated samples is consistent with the model of Nb3Sn grown in which tin diffuses via grain boundaries to Nb3Sn-Nb interface, where the growth Nb3Sn into the niobium bulk takes place. Similar scaling laws are found for grain growth and layer thickness. Non-parabolic layer growth is consistent with significant grain growth, which reduces the number of Sn-transport channels. Examination of patchy region in Nb3Sn coating revealed it to be large single crystalline grains, pointing to impeded Nb3Sn layer growth due to low grain boundary density, resulting in a significantly thin coating in those areas. Examination of RF loss regions from a coated cavity, identified with a thermometry mapping system showed patchy regions and carbonus defects were associated with strong local field-dependent surface resistance. RF measurements of coated cavities were combined with material characterization of witness samples and coated-cavity cutouts to improve the coating process. Understanding obtained and applied to cavity coatings, resulted in single-cell Nb3Sn cavities with a quality factor of ~2 ×1010 up to 15 MV/m accelerating gradient at 4 K, without "Wuppertal" Q-slope. We have also produced Nb3Sn-coated CEBAF 5-cell cavities with accelerating gradients useful for accelerator cryomodules. This dissertation will discuss the genesis of the Nb3Sn coating in a typical tin vapor diffusion process, effects of different process parameters, and its consequences to the coating of single-cell and multi-cell SRF cavities.

Pudasaini, Uttar↗

DOE OSTI2021

Transport Upscaling under Flow Heterogeneity and Matrix-Diffusion in Three-Dimensional Discrete Fracture Networks

For this work, we investigate the combined effects of network scale flow variability and retention due to matrix-diffusion on the scaling behavior of transport through fractured media. Two of the principal mechanisms controlling the transport of solutes through fractured low-permeability media are broad distributions of flow velocities and retention times in the solid matrix. We study the relative impact of these two processes under different initial conditions using a set of three-dimensional discrete fracture network simulations. We use these simulations to develop and calibrate an upscaled continuous time random walk (CTRW) approach for advective transport based on an Ornstein-Uhlenbeck model for the particle velocities that accounts for the fracture-matrix coupling using a compound Poisson process. This CTRW model can be conditioned on the initial solute distribution and allows to observe late-time scaling behavior at distances beyond what is feasible to observe using high-fidelity direct numerical simulations. We determine that the initial distribution of particles leads to marked differences in the persistent long-term scale behavior in the solute travel time distributions, even those undergoing retention due to matrix diffusion through implementation and analysis of the model.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

Evolution Models of Helium White Dwarf–Main-sequence Star Merger Remnants

It is predicted that orbital decay by gravitational-wave radiation and tidal interaction will cause some close binary stars to merge within a Hubble time. The merger of a helium-core white dwarf with a main-sequence (MS) star can produce a red giant branch star that has a low-mass hydrogen envelope when helium is ignited and thus become a hot subdwarf. Because detailed calculations have not been made, we compute post-merger models with a stellar evolution code. We find the evolutionary paths available to merger remnants and find the pre-merger conditions that lead to the formation of hot subdwarfs. We find that some such mergers result in the formation of stars with intermediate helium-rich surfaces. These stars later develop helium-poor surfaces owing to diffusion. Combining our results with a model population and comparing to observed stars, we find that some observed intermediate helium-rich hot subdwarfs can be explained as the remnants of the mergers of helium-core white dwarfs with low-mass MS stars.

79 ASTRONOMY AND ASTROPHYSICS↗