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DOE OSTI2022

Impact of carbonation on leaching of constituents from a cementitious waste form for treatment of low activity waste at the DOE Hanford site

Carbonation can be a major aging process during disposal of alkaline cementitious waste forms and can impact constituent leaching by changes in material alkalinity, pore structure, and controlling mineral phases. The effect of carbonation on the leaching of major and trace constituents from Cast Stone, a cementitious waste form developed to treat high salt content low activity waste, was studied through a combination of leaching experiments and reactive transport simulations. Diffusive transport of constituents in the waste form was evaluated using reactive transport modeling of diffusion-controlled leaching test results and a geochemical speciation model derived from pH-dependent leaching. Comparisons between Cast Stone materials aged under nitrogen, air, and 2% carbon dioxide in nitrogen showed that carbonation impacts solubility, physical retention and observed diffusivity of major and trace constituents. Carbonation under 2% CO 2 decreased the diffusion-controlled leaching of chromium by two orders of magnitude. Finally, modeling results suggest that carbonation may also decrease solubility of technetium while changes to microstructure by carbonation increases effective diffusivity of constituents in Cast Stone.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2015

On the statistical and transport properties of a non-dissipative Fermi-Ulam model

The transport and diffusion properties for the velocity of a Fermi-Ulam model were characterized using the decay rate of the survival probability. The system consists of an ensemble of non-interacting particles confined to move along and experience elastic collisions with two infinitely heavy walls. One is fixed, working as a returning mechanism of the colliding particles, while the other one moves periodically in time. The diffusion equation is solved, and the diffusion coefficient is numerically estimated by means of the averaged square velocity. Our results show remarkably good agreement of the theory and simulation for the chaotic sea below the first elliptic island in the phase space. From the decay rates of the survival probability, we obtained transport properties that can be extended to other nonlinear mappings, as well to billiard problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Comparison of DeePMD, MTP, GAP, ACE and MACE Machine‐Learned Potentials for Radiation‐Damage Simulations: A User Perspective

Accurate and efficient interatomic potentials are essential for molecular dynamics (MD) simulations of radiation damage, gas diffusion, and phase stability in complex ceramics such as LiAlO 2 , especially under extreme conditions relevant to tritium production. Here, we evaluate the performance of six machine-learned interatomic potentials (MLIPs), moment tensor potential (MTP), Gaussian approximation potential, deep potential (DeePMD), atomic cluster expansion (ACE), message-passing ACE (multilayer atomic cluster expansion (MACE) pretrained) and MACE (trained from-scratch), all trained on the same density functional theory dataset with inclusion of tritium. The MLIPs are benchmarked against traditional Buckingham and ReaxFF potentials in terms of energy accuracy, density predictions, thermal equilibration behavior, threshold displacement energy (E d ), tritium diffusivity, and computational cost. Among the models, MTP shows the best overall balance between efficiency and accuracy, with low force and energy errors and realistic E d values for Li and Al. The ACE and MACE (pretrained and trained from scratch) models exhibit high E d (>200 eV) and unphysical pair interactions. DeePMD underestimates Ed due to overly repulsive behavior even at equilibrium distances. All models over-estimate tritium diffusion but the pretrained MACE model behaves well during tritium-diffusion simulations up to 500 K, maintaining diffusivities in the physically consistent 10 −11 m 2 /s range. Finally, we quantify the computational cost of each potential in large-scale atomic/molecular massively parallel simulator, finding that only MTP is more efficient than traditional empirical potentials, while others are significantly more expensive. These findings explain the trade-offs between accuracy and computational cost in MLIP development and provide essential guidance for use in high-throughput radiation damage and gas diffusion simulations in nuclear ceramics.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Application of community data to surface complexation modeling framework development: Iron oxide protolysis

This study presents a comprehensive community data-driven surface complexation modeling framework for simulating potentiometric titration of mineral surfaces. Compiled community data for ferrihydrite, goethite, hematite, and magnetite are fit to produce representative protolysis constants that can reproduce potentiometric titration data collected from multiple literature sources. Using this framework, the impact of surface complexation model type and surface site density (SSD) on the fit quality and protolysis constants can be readily evaluated. For example, the non-electrostatic model yielded a poor data fit compared to diffuse double layer model and constant capacitance models due to the absence of known surface charge effects. Regardless of the choice of iron oxide mineral, pK a1 decreased with increasing SSD while the opposite tendency was observed for pK a2 . This newly developed framework demonstrates a method to reconcile community data-wide potentiometric titration data using Findable, Accessible, Interoperable, Reusable data principles to produce mineral protolysis constants that improve robustness of surface complexation models for applications in metal sorption and reactive transport modeling. The framework is readily expandable (as community data increase) and extensible (as the number of minerals increase). The framework provides a path forward for developing self-consistent, comprehensive, and updateable surface complexation databases for surface complexation and reactive transport modeling.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

Examining Graphite Degradation in Molten Salt Environments: A Chemical, Physical, and Material Analysis

Molten-salt reactors (MSRs) are Generation IV nuclear reactors that use liquid salt as a coolant and/or fuel. In several MSR designs, graphite serves as a moderator and/or reflector. However, due to limited experimental data and operational experience, our understanding of graphite behavior in molten salt environments remains incomplete. This report aims to identify the degradation mechanisms of nuclear graphite in MSRs, detail the mechanisms of each factor, and provide an initial assessment of their impact on the structural integrity of graphite components. This assessment is based on an extensive literature review and insights from subject matter experts. Furthermore, given the limited data, a modeling strategy using existing Grizzly software is proposed for a more thorough analysis where appropriate. Additionally, it presents mitigation strategies where applicable. The report covers physical degradation mechanisms such as infiltration, erosion, and abrasion, as well as chemical degradation mechanisms including fluorination, intercalation, corrosion, and oxidation. Molten salt can infiltrate the porous structure of graphite, leading to several detrimental effects. Entrapment of fissile products within the graphite pores can cause radiation damage and could pose challenges in the handling and disposal of contaminated components. The differential thermal expansion between the infiltrated salt and graphite, along with internal stress from pressurized molten salt and volumetric heating, can compromise the structural integrity of graphite. To mitigate these effects, employing ultra-fine graphite grades and applying sealants and coatings are effective strategies. A computational model based on coupled solid mechanics and heat transfer phenomena could be used to predict the internal stresses using Grizzly software. In pebble-bed MSRs, graphite fuel pebbles can cause abrasion against reactor components due to friction and wear. The severity of wear is influenced by various factors such as temperature, environment, and the presence of lubricants. Tribological studies reveal that higher temperatures and molten salt environments, such as FLiBe, significantly reduce wear rates compared to dry conditions. Additionally, the chemical composition of the salt can further optimize graphite's tribological performance. Long-term wear effects can be modeled by incorporating surface defects into the geometry and predict stresses under thermal and radiation effects using Grizzly software. Chemical degradation of graphite in a molten salt environment can occur through fluorination and intercalation. Fluorination can occur via replacement of hydrogen or oxygen atoms, or at the active sites, but does not cause structural degradation. Intercalation, on the other hand, can lead to exfoliation, where layers of graphite separate and peel away, damaging the graphite. Protective coatings can enhance graphite's resistance to intercalation. Graphite generally exhibits good chemical stability in molten salt environments, though it can corrode under specific conditions, particularly in the presence of impurities or oxidants. Studies have shown that protective coatings, such as plasma-sprayed partially stabilized zirconia (PSZ), can effectively prevent such degradation. Corrosion behavior varies significantly with different graphite grades and coating applications, underscoring the need for detailed studies on uncoated and coated graphite to understand and mitigate corrosion mechanisms in MSRs. Research indicates that the presence of oxidants and impurities can accelerate graphite degradation in molten salts, making it essential to explore acceptable impurity limits. Oxidation is another critical degradation mechanism, leading to weight loss and structural damage due to the formation of CO and CO 2 from the reaction of carbon atoms with oxygen. This process creates new porosity and compromises graphite's integrity. While extensive research on graphite oxidation has been conducted for gas-cooled reactors, studies specific to MSRs are limited. Findings from the coal industry suggest that molten alkali metal salts can significantly accelerate graphite oxidation, a hypothesis worth exploring for fluoride salts in MSRs. Understanding oxidation behavior in MSRs is vital for developing protective measures. The analysis of post-irradiated graphite from the MSRE experiment demonstrated exceptional chemical compatibility with molten fluoride salt, suggesting that the extent of chemical attack on graphite largely depends on the salt's infiltration capability. Therefore, the use of ultra-fine grade graphite could help mitigate chemical degradation effects. Existing oxidation modeling capabilities in Grizzly, which use reaction-diffusion equations to model graphite-air interactions, could be adapted to simulate the chemical degradation effects of graphite in molten salt environments.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Turbulent Processes that Influence Boundary-Layer Cloud Structure (Final Technical Report)

Many models of the atmosphere simulate vertical profiles of observable fields, such as temperature, moisture, and vertical velocity. To assess the realism of such model output, it is important to evaluate the modeled profiles against observations. However, many extant evaluations consist of comparing time averaged profiles from the model and the observations. Such time averages can smooth out unrealistic features that appear in instantaneous profiles. In this way, the time averages may obscure certain model errors from detection. For instance, many models misrepresent turbulent processes, leading to profiles that are too smoothed out or too noisy. E.g., if a model has coarse vertical resolution and overly strong diffusion, then the model may be unable to produce observed sharp peaks. On the other hand, a model may have artificial approximations that produce spurious jumps in the vertical. Much can be learned by browsing through instantaneous snapshots of model output. But the volume of output produced by a global model is far too great to rely purely on visual inspection. In addition, we need a way to statistically characterize the profiles, so that anomalies can be detected more conveniently.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1987

Theoretical approach to oxygen atom degradation of silver

Based on available Rutherford backscattering spectrometry (RBS), proton induced X-ray emission (PIXE) and ellipsometry data obtained on silver specimens subjected to atomic oxygen attack in low Earth orbit STS flight 41-G, a theory was developed to model the oxygen atom degradation of silver. The diffusion of atomic oxygen in a microscopically nonuniform medium is an essential constituent of the theory. The driving force for diffusion is the macroscopic electrochemical potential gradient developed between the specimen surface exposed to the ambient and the bulk of the silver specimen. The longitudinal electric effect developed parallel to the gradient is modified by space charge of the diffusing charged species. Lateral electric fields and concentration differences also exist due to the nonuniform nature of the medium. The lateral concentration differences are found to be more important than the lateral electric fields in modifying the diffusion rate. The model was evaluated numerically. Qualitative agreement exists between the kinetics predicted by the theory and kinetic data taken in ground-based experiments utilizing a plasma asher.

Fromhold, Albert T., Jr.↗

NASA NTRS1991

NASA/DOD Aerospace Knowledge Diffusion Research Project. Paper 12: The diffusion of federally funded aerospace Research and Development (R&D) and the information seeking behavior of US aerospace engineers and scientists

The present exploration of the diffusion of federally-funded R&D via the information-seeking behavior of scientists and engineers proceeds under three assumptions: (1) that knowledge transfer and utilization is as important as knowledge production; (2) that the diffusion of knowledge obtained through federally-funded R&D is necessary for the maintenance of U.S. preeminence in the aerospace field; and (3) that federally-funded NASA and DoD technical reports play an important, albeit as-yet undefined, role in aerospace R&D diffusion. A conceptual model is presented for the process of knowledge diffusion that stresses the role of U.S. government-funded technical reports.

Pinelli, Thomas E.↗

DOE OSTI2025

External Magnetic Field Suppression of Carbon Diffusion in Iron

External magnetic fields reduce diffusion of carbon in BCC iron, but the physical mechanism is not understood. Using DFT calculations with magnetic moments sampled from a Heisenberg model, we calculate diffusivities of carbon in iron at high temperatures and with field. Our model reproduces the measured suppression of diffusivity from field. Here, we find that increasing magnetic disorder flattens the electron density of states compared with the ferromagnetic case, which distorts the octahedral cages around carbon, lowering the activation barrier to diffusion; an applied field reverses these trends.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Verification of Modelica-Based Models with Analytical Solutions for Tritium Diffusion

Here, tritium transport in metal and molten salt fluids combined with diffusion through high-temperature structural materials is an important phenomenon in both magnetic confinement fusion (MCF) and molten salt reactor (MSR) applications. For MCF, tritium is desirable to capture for fusion fuel. For MSRs, uncaptured tritium potentially can be released to the environment. In either application, quantifying the time- and space-dependent tritium concentration in the working fluid(s) and structural components is necessary.Whereas capability exists specifically for calculating tritium transport in such systems (e.g., using TMAP for fusion reactors), it is desirable to unify the calculation of tritium transport with other system variables such as dynamic fluid and structure temperature combined with control systems such as those that might be found in a system code. Some capability for radioactive trace substance transport exists in thermal-hydraulic systems codes (e.g., RELAP5-3D); however, this capability is not coupled to species diffusion through solids. Combined calculations of tritium transport and thermal-hydraulic solution have been demonstrated with TRIDENT but only for a specific type of MSR.Researchers at Oak Ridge National Laboratory have developed a set of Modelica-based dynamic system modeling tools called TRANsient Simulation Framework Of Reconfigurable Models (TRANSFORM) that were used previously to model advanced fission reactors and associated systems. In this system, the augmented TRANSFORM library includes dynamically coupled fluid and solid trace substance transport and diffusion. Results from simulations are compared against analytical solutions for verification.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1999

Analysis of X-Ray Microradiographs of Al-Au Interface Quench Profile using Modeling of Solidification Including Double-Diffusion and Convection in the Melt

Experimental data on Al-0.8Au horizontal solidification of a 1 mm thick specimen in a BN crucible shows the effect of growth rate on the solidification interface shape. For translation rates below 0.5 micron/s the interface maintains a plain and flat shape. When the translation rate is 3 to 5 micron/s or more, the interface appearance changes to two planar zones, with the zone closer to the bottom having higher inclination. The interface shapes were measured by first quenching in place during growth. X-ray microscopy shows the interface shape within the quenched sample by viewing through the side of the specimen. In order to provide theoretical explanation of the phenomena, numerical modeling was undertaken using finite element code FIDAP. Double diffusion convection in Al-0.8Au melt and crystal-melt interface curvature during directional solidification was analyzed numerically. Actual thermophysical properties of Al-0.8Au including the binary Al-Au phase diagram were used. Although convection in the sample is weak, for the slower translation rate convection and diffusion is sufficient for the redistribution of initial compositional stratification caused by gravity. When translation rate is raised, neither convection nor diffusion can provide proper mixing so that solidification temperatures differ significantly near the bottom within the bulk of the sample. As a result, the solid-liquid interface appears to have two planar zones with different inclination.

Bune, Andris V.↗

NASA NTRS2007

The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation

A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

Campbell, Joel↗

NASA NTRS1993

Application of a Reynolds stress turbulence model to a supersonic radiating hydrogen-air diffusion flame

A second-order differential Reynolds Stress turbulence model has been applied to the Favre-averaged Navier-Stokes equations for the study of supersonic flows with finite-rate chemistry and radiation. An assumed Beta Probability Density Function is applied to account for the chemical source terms and the radiative flux terms in the conservation equations. A seven-species, seven-reaction finite rate chemistry mechanism is used to simulate the combustion process. The tangent slab approximation is used in radiative flux formulation. A pseudo-gray gas model is used to represent the absorption-emission characteristics of the participating species. The turbulence/radiation interaction is achieved via a new formulation. The resulting formulation is validated by comparison with experimental data on reacting supersonic axisymmetric jets. Results obtained for specific conditions indicate that the effect of chemical reaction on the turbulence is significant. Also, the radiative heat transfer is enhanced by the turbulence.

Chandrasekhar, R.↗

DOE OSTI2026

Development and assessment of models for turbulent Rayleigh-Taylor mixing using the macroscopic forcing method

Reynolds-Averaged Navier Stokes (RANS) simulations are a popular method for designing ICF experiments, and accurate mixing models are crucial for these simulations to give good predictions. To this end, the present work seeks to demonstrate the Macroscopic Forcing Method (MFM) as a tool for both improving existing RANS models as well as assessing RANS model forms. First, MFM analysis from Lavacot et al. (Phys. Rev. Fluids, 2025) is used to develop the k–L–F model, an extension of the k–L model of Dimonte and Tipton (Phys. Fluids, 2006) that incorporates nonlocality through addition of a turbulent species flux transport equation. MFM is then applied to the k–L–F model along with the k–L and BHR–4 models to assess their forms and compare the model-implied eddy diffusivity moments to those measured from high-fidelity simulations. Furthermore, the analysis reveals that models incorporating nonlocality (k–L–F and BHR–4) match the high-fidelity simulation data better than purely local models (k–L), both in terms of mean fields and eddy diffusivity moments. However, all of the considered RANS models struggle to match temporal moments at high Atwood numbers, highlighting the importance of temporal nonlocality in these regimes and the need for additional improvement even among models incorporating nonlocality.

general physics↗

NASA NTRS1987

Diffusive shock acceleration - Comparison of a unified shock model to bow shock observations

A comparison is made between recent AMPTE/IRM observations of diffuse ions detected upstream of the earth's bow shock when the interplanetary magnetic field was nearly parallel to the solar wind direction and a known collisionless quasi-parallel shock model. These observations, which provide the proton spectrum for all of velocity space, give a direct measure of the shock acceleration efficiency and show how thermal solar winds are injected into the diffusive shock acceleration mechanism. The model accurately describes the proton spectrum; moreover, it predicts the shock structure, the complete particle spectrum, the relative velocity distributions of different ion species in the down stream region, and the enhancement of heavy ions over protons relative to the unshocked solar wind.

Ellison, Donald C.↗

DOE OSTI2023

Theoretical estimates of flammability bounds for thin condensed fuel diffusion flames in microgravity using detailed models of chemistry and radiation

Recently, U-shape flammability maps have been constructed showing minimal oxygen vs. flame strain for opposed flame spread in micro-gravity by Olson and Ferkul. The U-shape defines the limiting flammability bounds from radiative extinction and flame blow-off. Here, the minimum of the U corresponds to the minimum possible oxidizer concentration where burning can occur, and is an important quantity of interest for fire safety. While high strain extinction bounds have been well analyzed, low strain radiative extinction has not. To estimate low strain extinction, in this study an analytical theory is developed based on thin flame theory coupled with a heat and mass transfer model for solid fuels. A reaction progress variable based on the Damköhler number is adapted in the theory to account for incomplete combustion at high strain rates and enable the capturing of the full flammability map. The analytical model is compared to a one dimensional numerical model w/ detailed chemical kinetics and coupled radiation heat transfer in planar and spherical geometries. The flammability maps are then qualitatively compared to experimental extinguishment data compiled by Olson and Ferkul for cylindrical rods of PMMA showing similar trends. The results show the newly developed analytics capture the radiative extinction bound compared to the numerical model and qualitatively agrees with microgravity data.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

NASA NTRS1983

A computational method for subsonic compressible flow in diffusers

Integral methods are used to model subsonic flow in planar diffusers operating with or without stall. Turbulent boundary layers are computed with a lag-entrainment method employing new correlations for shape factor and skin friction, which are based on a Coles-Van Driest velocity profile. The inviscid flow is modeled as one dimensional and is easily coupled with the boundary layer method to yield equations that can be solved by integrating in the downstream direction. Analysis of the equations describing flow in a diffuser shows that the boundary layer separation singularity may not be eliminated by viscous-inviscid interaction; a modified interaction scheme is used to guarantee a non-singular equation set. The nature of this singularity offers an explanation for the apparent universality of asymmetric stall in planar diffusers. Results for several flows demonstrate the accuracy and range of applicability of the method.

Childs, R. E.↗

DOE OSTI2016

Experimental Studies and Model Analysis of Noble Gas Fractionation in Porous Media

Core Ideas Ambient noble gases in porous media fractionate from through‐flow of other gases. CO 2 fluxes and noble‐gas fractionation are measured in simple sandbox experiments. Modeled fractionation provides indirect proxy, e.g., of steady CO 2 leakage fluxes. The noble gases, which are chemically inert under normal terrestrial conditions but vary systematically across a wide range of atomic mass and diffusivity, offer a multicomponent approach to investigating gas dynamics in unsaturated soil horizons, including transfer of gas between saturated zones, unsaturated zones, and the atmosphere. To evaluate the degree to which fractionation of noble gases in the presence of an advective–diffusive flux agrees with existing theory, a simple laboratory sand column experiment was conducted. Pure CO 2 was injected at the base of the column, providing a series of constant CO 2 fluxes through the column. At five fixed sampling depths within the system, samples were collected for CO 2 and noble gas analyses, and ambient pressures were measured. Both the advection–diffusion and dusty gas models were used to simulate the behavior of CO 2 and noble gases under the experimental conditions, and the simulations were compared with the measured depth‐dependent concentration profiles of the gases. Given the relatively high permeability of the sand column (5 × 10 −11 m 2 ), Knudsen diffusion terms were small, and both the dusty gas model and the advection–diffusion model accurately predicted the concentration profiles of the CO 2 and atmospheric noble gases across a range of CO 2 flux from ∼700 to 10,000 g m −2 d −1 . The agreement between predicted and measured gas concentrations demonstrated that, when applied to natural systems, the multi‐component capability provided by the noble gases can be exploited to constrain component and total gas fluxes of non‐conserved (CO 2 ) and conserved (noble gas) species or attributes of the soil column relevant to gas transport, such as porosity, tortuosity, and gas saturation.

54 ENVIRONMENTAL SCIENCES↗