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DOE OSTI2013

GLOBAL DRAG-INDUCED INSTABILITIES IN PROTOPLANETARY DISKS

We use the Fokker-Planck equation and model the dispersive dynamics of solid particles in annular protoplanetary disks whose gas component is more massive than the particle phase. We model particle-gas interactions as hard sphere collisions, determine the functional form of diffusion coefficients, and show the existence of two global unstable modes in the particle phase. These modes have spiral patterns with the azimuthal wavenumber m = 1 and rotate slowly. We show that in ring-shaped disks, the phase-space density of solid particles increases linearly in time toward an accumulation point near the location of pressure maximum, while instabilities grow exponentially. Therefore, planetesimals and planetary cores can be efficiently produced near the peaks of unstable density waves. In this mechanism, particles migrating toward the accumulation point will not participate in the formation of planets, and should eventually form a debris ring like the main asteroid belt or classical Kuiper Belt objects. We present the implications of global instabilities to the formation of ice giants and terrestrial planets in the solar system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Removing Numerical Pathologies in a Turbulence Parameterization Through Convergence Testing

Abstract Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB's equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e., clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, nonlinear artificial diffusion employed for improving numerical stability can introduce unintended small‐scale features into the solution of the model equations. Smoothing the limiters and using linear artificial diffusion reduces the noise and restores the expected first‐order convergence in CLUBB's solutions. These model reformulations enhance our confidence in the trustworthiness of solutions from CLUBB by eliminating the unphysical oscillations in high‐resolution simulations. The improvements in the results at coarser, near‐operational grid spacing and timestep are also seen in cumulus cloud and dry turbulence tests. In addition, convergence testing is proven to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set.

58 GEOSCIENCES↗

DOE OSTI2016

Report on simulation of fission gas and fission product diffusion in UO 2

In UO 2 nuclear fuel, the retention and release of fission gas atoms such as xenon (Xe) are important for nuclear fuel performance by, for example, reducing the fuel thermal conductivity, causing fuel swelling that leads to mechanical interaction with the clad, increasing the plenum pressure and reducing the fuel–clad gap thermal conductivity. We use multi-scale simulations to determine fission gas diffusion mechanisms as well as the corresponding rates in UO 2 under both intrinsic and irradiation conditions. In addition to Xe and Kr, the fission products Zr, Ru, Ce, Y, La, Sr and Ba have been investigated. Density functional theory (DFT) calculations are used to study formation, binding and migration energies of small clusters of Xe atoms and vacancies. Empirical potential calculations enable us to determine the corresponding entropies and attempt frequencies for migration as well as investigate the properties of large clusters or small fission gas bubbles. A continuum reaction-diffusion model is developed for Xe and point defects based on the mechanisms and rates obtained from atomistic simulations. Effective fission gas diffusivities are then obtained by solving this set of equations for different chemical and irradiation conditions using the MARMOT phase field code. The predictions are compared to available experimental data. The importance of the large Xe U3O cluster (a Xe atom in a uranium + oxygen vacancy trap site with two bound uranium vacancies) is emphasized, which is a consequence of its high mobility and high binding energy. We find that the Xe U3O cluster gives Xe diffusion coefficients that are higher for intrinsic conditions than under irradiation over a wide range of temperatures. Under irradiation the fast-moving Xe U3O cluster recombines quickly with irradiation-induced interstitial U ions, while this mechanism is less important for intrinsic conditions. The net result is higher concentration of the Xe U3O cluster for intrinsic conditions than under irradiation. We speculate that differences in the irradiation conditions and their impact on the Xe U3O cluster can explain the wide range of diffusivities reported in experimental studies. However, all vacancy-mediated mechanisms underestimate the Xe diffusivity compared to the empirical radiation-enhanced rate used in most fission gas release models. We investigate the possibility that diffusion of small fission gas bubbles or extended Xe-vacancy clusters may give rise to the observed radiation-enhanced diffusion coefficient. These studies highlight the importance of U divacancies and an octahedron coordination of uranium vacancies encompassing a Xe fission gas atom. The latter cluster can migrate via a multistep mechanism with a rather low effective barrier, which together with irradiation-induced clusters of uranium vacancies, gives rise to the irradiation-enhanced diffusion coefficient observed in experiments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2019

ICAT: A numerical scheme to minimize numerical diffusion in advection-dispersion modeling and its application in identifying flow channeling

The advection-dispersion equation for scalar transport is essential for the numerical modeling of many fluid dynamics problems. However, solutions from numerical schemes always suffer from numerical diffusion and/or oscillation. In this study, we develop an Intra-Cell Advection Tracking (ICAT) scheme to minimize numerical diffusion and preserve monotonicity for advection-dispersion modeling. The key idea is to introduce “queues” in each discretized cell, and using a sequential transport rule and a flow distribution mechanism to track the scalar transport in these queues temporally and spatially. The capability and limitations of ICAT are first investigated through three test cases. Compared with the results obtained from other numerical schemes, the results from ICAT show substantially reduced numerical diffusion and agree better with analytical solutions. We also employ ICAT to simulate the transport process of a conservative tracer in a fracture with a highly heterogeneous aperture distribution. We report discrete flow channels in the fracture are better discerned by ICAT than by other numerical schemes, indicating the suitability of ICAT for modeling tracer transport in channelized flow fields.

15 GEOTHERMAL ENERGY↗

NASA NTRS1978

Numerical simulation of warm fog and its application to warm fog prediction and modification

The considered theoretical model describes the evolution of potential temperature, water vapor content, liquid water content, and horizontal and vertical winds as determined by the processes of vertical turbulent transfer and horizontal advection for momentum, energy, and moisture, as well as radiation cooling, growth of water droplets based on microphysical processes, and drop sedimentation. The mathematical model is two-dimensional in the X-Z plane. The diffusivity coefficient is the same for liquid water droplets as for vapor. The fundamental equations governing the macrophysical processes of the evolution of wind components, water vapor content, liquid water content, and potential temperature under the influences of vertical turbulent diffusion transfer, turbulent momentum transfer, and turbulent energy transfer are expressed by three sets of conservation equations.

Hung, R. J.↗

DOE OSTI2023

Thermo4PFM: Facilitating Phase-field simulations of alloys with thermodynamic driving forces

Phase-field modeling is a popular front-tracking approach used to model solidification. Its time-evolution equations are often coupled to alloy composition and/or thermal diffusion in high-resolution multiphysics approaches. Materials thermodynamic properties tabulated in CALPHAD databases can be used for phase-field modeling to parameterize bulk energies of alloys. In addition, they can be naturally integrated into models such as the Kim-Kim-Suzuki (KKS) model where driving forces depend on the differences between chemical potentials of co-existing phases. In that case, a small system of coupled nonlinear equations needs to be solved at every point in space where the phase-field order parameter is to be updated and evolved in time. Here we present Thermo4PFM, a solver for the KKS equations for binary and ternary alloys, with two or three phases, and parameterized with CALPHAD models. Thermo4PFM is open source, written in C++, and can take advantage of Graphics Processing Units (GPU) accelerators. Using OpenMP offload capabilities for C++ classes, an excellent performance is demonstrated on GPU using the LLVM compiler. CALPHAD data is read from simple JSON files using an open source parser from the boost library.

36 MATERIALS SCIENCE↗

DOE OSTI2015

The hysteresis response of soil CO 2 concentration and soil respiration to soil temperature

Diurnal hysteresis between soil temperature (T s ) and both CO 2 concentration ([CO 2 ]) and soil respiration rate (R s ) were reported across different field experiments. However, the causes of these hysteresis patterns remain a subject of debate, with biotic and abiotic factors both invoked as explanations. Here, to address these issues, a CO 2 gas transport model is developed by combining a layer-wise mass conservation equation for subsurface gas phase CO 2 , Fickian diffusion for gas transfer, and a CO 2 source term that depends on soil temperature, moisture, and photosynthetic rate. Using this model, a hierarchy of numerical experiments were employed to disentangle the causes of the hysteretic [CO 2 ]-T s and CO 2 flux T s (i.e., F-T s ) relations. Model results show that gas transport alone can introduce both [CO 2 ]-T s and F-T s hystereses and also confirm prior findings that heat flow in soils lead to [CO 2 ] and F being out of phase with T s , thereby providing another reason for the occurrence of both hystereses. The area (A hys ) of the [CO 2 ]-T s hysteresis near the surface increases, while the A hys of the Rs-Ts hysteresis decreases as soils become wetter. Moreover, a time-lagged carbon input from photosynthesis deformed the [CO 2 ]-T s and R s -T s patterns, causing a change in the loop direction from counterclockwise to clockwise with decreasing time lag. An asymmetric 8-shaped pattern emerged as the transition state between the two loop directions. Lastly, tracing the pattern and direction of the hysteretic [CO 2 ]-T s and R s -T s relations can provide new ways to fingerprint the effects of photosynthesis stimulation on soil microbial activity and detect time lags between rhizospheric respiration and photosynthesis.

58 GEOSCIENCES↗

DOE OSTI2016

Modeling the Capacitive Deionization Process in Dual-Porosity Electrodes

In many areas of the world, there is a need to increase water availability. Capacitive deionization (CDI) is an electrochemical water treatment process that can be a viable alternative for treating water and for saving energy. A model is presented to simulate the CDI process in heterogeneous porous media comprising two different pore sizes. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A two steps volume averaging technique is used to derive the averaged transport equations in the limit of thin electrical double layers. A one-equation model based on the principle of local equilibrium is derived. The constraints determining the range of application of the one-equation model are presented. The effective transport parameters for isotropic porous media are calculated solving the corresponding closure problems. The source terms that appear in the average equations are calculated using theoretical derivations. The global diffusivity is calculated by solving the closure problem.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2018

Fluctuating Hydrodynamics and Debye-Hückel-Onsager Theory for Electrolytes

We apply fluctuating hydrodynamics to strong electrolyte mixtures to compute the concentration corrections for chemical potential, diffusivity, and conductivity. We show these corrections to be in agreement with the limiting laws of Debye, Hückel, and Onsager. We compute explicit corrections for a symmetric ternary mixture and find that the co-ion Maxwell-Stefan diffusion coefficients can be negative, in agreement with experimental findings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Real-Time Observation of the Diffusion Mechanism Progression from Liquid to Solid State of Transition Metal Complexes

Copper complexes have recently shown remarkable performance upon conversion from liquid-based to solid-state hole transport materials (HTMs) in mesoscopic solar cells; however, the diffusion mechanism is not clear. Here, we apply an in situ solidification analysis of the charge diffusion and find that the dominant mechanism of [Cu(dmbpy) 2 ] 2+/+ (dmbpy = 6,6'-dimethyl-2,2'-bipyridine) changes from ionic to electronic diffusion. Through use of the modified Dahms–Luff equation, a fast self-exchange rate constant of hole-hopping in the HTM of 8.3 × 10 8 (±5 × 10 7 ) M –1 s –1 is calculated, which indicates a small reorganization energy of 0.47 eV. These findings present a new methodology to analyze the transport mechanism of solids, reveal the mechanism of charge transport in molecular-based HTMs, and offer insight into ways to control the flow of charge in optoelectronic systems

14 SOLAR ENERGY↗

DOE OSTI2026

Effects of Dissolution Regimes on Flow Channelization and Solute Transport in 3D Fracture Networks: Insights From Graph‐Based Reactive Transport Modeling

We investigate how mineral dissolution reshapes flow pathways and solute transport in three‐dimensional discrete fracture networks using a computationally efficient graph‐based reactive transport model. The DFNs are inspired by field‐site observations of fractured carbonate and represent realistic connectivity and structural heterogeneity. Flow is simulated with the Reynolds equation, and dissolution follows first‐order kinetics with diffusive limitations captured through an effective mass‐transfer coefficient. By systematically varying two key dimensionless parameters, the effective Damköhler number (Da), governing reaction versus advection rates, and a transport parameter (Da), analogous to the Thiele modulus, distinct flow channelization regimes emerge: mildly channelized at low G, highly channelized at intermediate Da, and extreme wormhole formation at high Da and low G. Eulerian and Lagrangian analyses, including breakthrough curves, particle tortuosity, dispersivity, and flow channeling indicators quantitatively characterize the progression of dissolution‐driven network restructuring. Across all regimes, initial fracture heterogeneity persists. The results underscore how the interplay between this initial structure, advection, reaction, and diffusion critically shapes subsurface flow pathways, with implications for applications ranging from groundwater remediation to enhanced geothermal systems.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2014

CQL3D-Hybrid-FOW modeling of the temporal dynamics of NSTX NBI+HHFW discharges

The CQL3D Fokker-Planck code[1] has been upgraded to include physics of finite-orbit-width (FOW) guiding-center orbits[2,3], as compared with the previous zero-orbit-width (ZOW) model, and a recent first-order orbit calculation[2]. The Fast Ion Diagnostic FIDA[4,5] signal resulting from neutral beam (NBI) and high harmonic fast wave (HHFW) RF power injected into the NSTX spherical tokamak can now be modeled quite accurately, using ion distributions from the CQL3D-Hybrid-FOW code, a rapidly executing variant that includes FOW+gyro-orbit losses to the plasma edge, FOW effects on NBI injection and HHFW diffusion, but does not include neoclassical radial diffusion. Accurate simulation of prompt fast ion (FI) losses is a key feature of the marked modeling improvement relative to previous ZOW results. By comparing NBI-only and NBI+HHFW shots, independent confirmation of the usual 35% edge loss of HHFW in NSTX is obtained. Further, HHFW prompt losses from the plasma core are shown to be 3X as large (>25%) as the NBI-only case. The modulated NBI and time-dependent background plasma variations and charge exchange losses of fast ions are accounted for, and the temporal neutron variation is in approximate agreement with NSTX observations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Optimizing white light luminescence in Dy{sup 3+}-doped Lu{sub 3}Ga{sub 5}O{sub 12} nano-garnets

Trivalent dysprosium-doped Lu{sub 3}Ga{sub 5}O{sub 12} nano-garnets have been prepared by sol-gel method and characterized by X-ray powder diffraction, high-resolution transmission electron microscopy, dynamic light scattering, and laser excited spectroscopy. Under a cw 457 nm laser excitation, the white luminescence properties of Lu{sub 3}Ga{sub 5}O{sub 12} nano-garnets have been studied as a function of the optically active Dy{sup 3+} ion concentration and at low temperature. Decay curves for the {sup 4}F{sub 9/2} level of Dy{sup 3+} ion exhibit non-exponential nature for all the Dy{sup 3+} concentrations, which have been well-fitted to a generalized energy transfer model for a quadrupole-quadrupole interaction between Dy{sup 3+} ions without diffusion. From these data, a simple rate-equations model can be applied to predict that intense white luminescence could be obtained from 1.8 mol% Dy{sup 3+} ions-doped nano-garnets, which is in good agreement with experimental results. Chromaticity color coordinates and correlated color temperatures have been determined as a function of temperature and are found to be within the white light region for all Dy{sup 3+} concentrations. These results indicate that 2.0 mol% Dy{sup 3+} ions doped nano-garnet could be useful for white light emitting device applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Shear-induced aggregation or disaggregation in edible oils: Models, computer simulation, and USAXS measurements

The effects of shear upon the aggregation of solid objects formed from solid triacylglycerols (TAGs) immersed in liquid TAG oils were modeled using Dissipative Particle Dynamics (DPD) and the predictions compared to experimental data using Ultra-Small Angle X-ray Scattering (USAXS). The solid components were represented by spheres interacting via attractive van der Waals forces and short range repulsive forces. A velocity was applied to the liquid particles nearest to the boundary, and Lees-Edwards boundary conditions were used to transmit this motion to non-boundary layers via dissipative interactions. The shear was created through the dissipative forces acting between liquid particles. Translational diffusion was simulated, and the Stokes-Einstein equation was used to relate DPD length and time scales to SI units for comparison with USAXS results. The SI values depended on how large the spherical particles were (250 nm vs. 25 nm). Aggregation was studied by (a) computing the Structure Function and (b) quantifying the number of pairs of solid spheres formed. Solid aggregation was found to be enhanced by low shear rates. As the shear rate was increased, a transition shear region was manifested in which aggregation was inhibited and shear banding was observed. Aggregation was inhibited, and eventually eliminated, by further increases in the shear rate. The magnitude of the transition region shear, $\dot{γ}_t$, depended on the size of the solid particles, which was confirmed experimentally.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Pitch-angle scattering of energetic particles with adiabatic focusing

Understanding turbulent transport of charged particles in magnetized plasmas often requires a model for the description of random variations in the particle's pitch angle. The Fokker-Planck coefficient of pitch-angle scattering, which is used to describe scattering parallel to the mean magnetic field, is therefore of central importance. Whereas quasi-linear theory assumes a homogeneous mean magnetic field, such a condition is often not fulfilled, especially for high-energy particles. Here, a new derivation of the quasi-linear approach is given that is based on the unperturbed orbit found for an adiabatically focused mean magnetic field. The results show that, depending on the ratio of the focusing length and the particle's Larmor radius, the Fokker-Planck coefficient is significantly modified but agrees with the classical expression in the limit of a homogeneous mean magnetic field.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Thermalization at low temperatures via weakly damped multisite baths

We study the thermalization properties of one-dimensional open quantum systems coupled to baths at their boundary. The baths are driven to their thermal states via Lindblad operators, while the system undergoes Hamiltonian dynamics. We specifically consider multisite baths and investigate the extent to which the late-time steady state resembles a Gibbs state at some controllable temperature set by the baths. We study three models: a noninteracting fermion model accessible via free-fermion technology, and two interacting models, the XZ model and the chiral clock model, which are accessible via tensor network methods. We show that, by tuning towards the weak coupling and slow relaxation limits, one can engineer low temperatures in the bulk of the system provided the bath size is big enough. Here, we use this capability to study energy transport in the XZ model at lower temperatures than previously reported. Our work paves the way for future studies of interacting open quantum systems at low temperatures.

1-dimensional spin chains↗

DOE OSTI2017

Use of Cloud Radar Doppler Spectra to Evaluate Stratocumulus Drizzle Size Distributions in Large-Eddy Simulations with Size-Resolved Microphysics

Abstract A case study of persistent stratocumulus over the Azores is simulated using two independent large-eddy simulation (LES) models with bin microphysics, and forward-simulated cloud radar Doppler moments and spectra are compared with observations. Neither model is able to reproduce the monotonic increase of downward mean Doppler velocity with increasing reflectivity that is observed under a variety of conditions, but for differing reasons. To a varying degree, both models also exhibit a tendency to produce too many of the largest droplets, leading to excessive skewness in Doppler velocity distributions, especially below cloud base. Excessive skewness appears to be associated with an insufficiently sharp reduction in droplet number concentration at diameters larger than ~200 μm, where a pronounced shoulder is found for in situ observations and a sharp reduction in reflectivity size distribution is associated with relatively narrow observed Doppler spectra. Effectively using LES with bin microphysics to study drizzle formation and evolution in cloud Doppler radar data evidently requires reducing numerical diffusivity in the treatment of the stochastic collection equation; if that is accomplished sufficiently to reproduce typical spectra, progress toward understanding drizzle processes is likely.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Analysis of Tempered Fractional Operators

Tempered fractional operators are useful in models for subsurface transport and diffusion due to their ability to capture anomalous diffusion: a behavior which the classical partial differential equation models cannot describe. We analyze tempered fractional operators within the nonlocal vector calculus framework in order to assimilate them to the rigorous mathematical structure developed for nonlocal models. First, we show they are special instances of generalized nonlocal operators in correspondence of a proper choice of nonlocal kernels. Then, we work towards showing tempered fractional operators are equivalent to truncated fractional operators. These truncated operators are useful because they are less computationally intensive than the tempered operators.

97 MATHEMATICS AND COMPUTING↗