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Diffusion, Fluxes, Friction Forces, and Joule Heating in Two-Temperature Multicomponent Magnetohydrodynamics

The relationship between Joule heating, diffusion fluxes, and friction forces has been studied for both total and electron thermal energy equations, using general expressions for multicomponent diffusion in two-temperature plasmas with the velocity dependent Lorentz force acting on charged species in a magnetic field. It is shown that the derivation of Joule heating terms requires both diffusion fluxes and friction between species which represents the resistance experienced by the species moving at different relative velocities. It is also shown that the familiar Joule heating term in the electron thermal energy equation includes artificial effects produced by switching the convective velocity from the species velocity to the mass-weighted velocity, and thus should not be ignored even when there is no net energy dissipation.

Chang, C. H.↗

Development of physics-consistent conditional diffusion model to overcome data scarcity in critical heat flux

Deep generative modeling provides a powerful pathway to overcome data scarcity in energy-related applications where experimental data are often limited. By learning the underlying probability distribution of the training dataset, deep generative models, such as the diffusion model, can generate high-fidelity synthetic samples that statistically resemble the training data. Such synthetic data generation can significantly enrich the size and diversity of the available training data, and more importantly, improve the robustness of downstream machine learning models in predictive tasks. The objective of this paper is to investigate the effectiveness of diffusion models for overcoming data scarcity in nuclear energy applications. By leveraging a public dataset on critical heat flux which covers a wide range of commercial nuclear reactor operational conditions, we developed a diffusion model that can generate an arbitrary amount of synthetic samples. Since a vanilla diffusion model can only generate samples randomly, we also developed a conditional diffusion model capable of generating targeted critical heat flux data under user-specified thermal-hydraulic conditions. The performance of the diffusion model was evaluated based on its ability to capture empirical feature distributions and pair-wise correlations, as well as to maintain physical consistency. The results showed that both the diffusion model and conditional diffusion model can successfully generate realistic and physics-consistent critical heat flux data. Furthermore, uncertainty quantification results demonstrate that the conditional diffusion model is highly effective in augmenting critical heat flux data while maintaining acceptable levels of uncertainty.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The distribution of Martian ground ice at other epochs

The past orbital evolution of Mars is examined in relation to changes in ice stability as well as the condensation, sublimation, and diffusion of atmospheric water in an exchange with the regolith. The Martian obliquity has undergone significant oscillations in its recent past. During periods of high obliquity, the solar energy would have been distributed such that the equatorial and midlatitude regions would have been colder that at present and the polar regions would have been warmer. Warmer polar regions would result in the sublimation of more polar cap water into the atmosphere and thus higher atmospheric water abundances. This combination of effects would have resulted in ground ice being stable globally. During periods of low obliquity the opposite would have occurred. Modeling results of the regolith thermal behavior and the molecular diffusion of water vapor within the regolith and in exchange with the atmosphere have shown significant quantities of ground ice can form at all latitudes within the top 50 cm to 1 m of the regolith during periods of high obliquity. The amount of ice that forms can be as much as the regolith pores can hold. During low obliquity most or all of this ice sublimes and diffuses away. Below this depth a longer-term stability is observed at some latitudes where ice steadily increases in concentration regardless of orbital oscillations that occur.

Mellon, M. T.↗

Conversion of Magnetic Energy to Plasma Kinetic Energy During Guide Field Magnetic Reconnection in the Laboratory

Here, we present laboratory measurements showing the two-dimensional (2D) structure of energy conversion during magnetic reconnection with a guide field over the electron and ion diffusion regions, resolving the separate energy deposition on electrons and ions. We find that the electrons are energized by the parallel electric field at two locations, at the X line and around the separatrices. On the other hand, the ions are energized ballistically by the perpendicular electric field in the vicinity of the high-density separatrices. An energy balance calculation by evaluating the terms of the Poynting theorem shows that 40% of the magnetic energy is converted to particle energy, 2/3 of which is transferred to ions and 1/3 to electrons. Further analysis suggests that the energy deposited on particles manifests mostly in the form of thermal kinetic energy in the diffusion regions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Coherent X-rays reveal the influence of cage effects on ultrafast water dynamics

Here, the dynamics of liquid water feature a variety of time scales, ranging from extremely fast ballistic-like thermal motion, to slower molecular diffusion and hydrogen-bond rearrangements. Here, we utilize coherent X-ray pulses to investigate the sub-100 fs equilibrium dynamics of water from ambient conditions down to supercooled temperatures. This novel approach utilizes the inherent capability of X-ray speckle visibility spectroscopy to measure equilibrium intermolecular dynamics with lengthscale selectivity, by measuring oxygen motion in momentum space. The observed decay of the speckle contrast at the first diffraction peak, which reflects tetrahedral coordination, is attributed to motion on a molecular scale within the first 120 fs. Through comparison with molecular dynamics simulations, we conclude that the slowing down upon cooling from 328 K down to 253 K is not due to simple thermal ballistic-like motion, but that cage effects play an important role even on timescales over 25 fs due to hydrogen-bonding.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Numerical Tool for the Design of Enhanced Geothermal Reservoirs based on Modeling of Thermo-Hydro-Mechanical Processes and Explicit Representation of 3D Discrete Fracture Networks

This project has developed a coupled thermo-hydro-mechanical numerical modeling tool for prediction of energy production from Enhanced Geothermal Reservoirs (EGS). The tool is unique because it can explicitly represent thousands of pre-existing natural fractures. The capabilities developed in this project were built on the already existing expertise of Itasca arising from thirty years of research and development in discrete element modeling of fractured rocks. A thermal module suitable for analysis of different heat transfer mechanisms in fractured rocks percolated by fluids was developed and coupled with the already existing hydro-mechanical calculation in 3DEC, a commercial software for analysis of jointed rock based on the discrete element method (DEM). The heat transfer module simulates heat conduction, heat advection by moving fluid in rock fractures, and convective heat exchange at the fracture walls between the rock and the moving fluid. Techniques for spatial discretization of heat transfer in EGS-type problems were evaluated, and a boundary layer meshing approach was developed. Also, given the significant differences in time scale of physical processes involved, temporal integration schemes for coupled advection-diffusion processes and coupled thermal-hydro-mechanical processes were developed by taking advantage of both implicit and explicit time integration and also optimizing the coupling intervals. These improvements were necessary for modeling EGS reservoirs. Also, the DFN capacities in 3DEC were extended to include a larger number of fractures. Research was carried out on approaches to simplify the DFN so that the model can meet computational demands, while preserving thermo-hydro-mechanical characteristics of the DFN. The developed modules were coupled with the already existing capabilities of 3DEC. The results were presented as a submitted conference paper (Riahi et al., 2018a). A series of benchmark and test examples showed the developed capabilities. Finally, the developed tool was tested for a large-scale reservoir model for longer periods of injection and production. The thermal draw-down curves were generated and presented. The project successfully met all the milestones laid out in the proposal. Results demonstrated the feasibility of developing a fast and reliable software for the EGS community to use for assessment and prediction of reservoir performance. Some of its applications include assessment of stimulated volume and produced temperature and power. It can also be used for improved engineering, design and optimization of EGS reservoirs as well as other unconventional resources such as shale gas. Finally, the 3D analysis presented in this study showed that simulating EGS reservoirs with tens of thousands of fractures is feasible, and confirmed that the developed tool can serve toward meeting the goals and objectives of Geothermal Technologies Office in overcoming technical barriers associated with commercial EGS development.

15 GEOTHERMAL ENERGY↗

Flexible machine-learning interatomic potential for simulating structural disordering behavior of Li 7 La 3 Zr 2 O 12 solid electrolytes

Batteries based on solid-state electrolytes, including Li 7 La 3 Zr 2 O 12 (LLZO), promise improved safety and increased energy density; however, atomic disorder at grain boundaries and phase boundaries can severely deteriorate their performance. Machine-learning (ML) interatomic potentials offer a uniquely compelling solution for simulating chemical processes, rare events, and phase transitions associated with these complex interfaces by mixing high scalability with quantum-level accuracy, provided that they can be trained to properly address atomic disorder. To this end, we report the construction and validation of an ML potential that is specifically designed to simulate crystalline, disordered, and amorphous LLZO systems across a wide range of conditions. The ML model is based on a neural network algorithm and is trained using ab initio data. Performance tests prove that the developed ML potential can predict accurate structural and vibrational characteristics, elastic properties, and Li diffusivity of LLZO comparable to ab initio simulations. As a demonstration of its applicability to larger systems, we show that the potential can correctly capture grain boundary effects on diffusivity, as well as the thermal transition behavior of LLZO. Here these examples show that the ML potential enables simulations of transitions between well-defined and disordered structures with quantum-level accuracy at speeds thousands of times faster than ab initio methods.

25 ENERGY STORAGE↗

A mathematical and numerical framework for the analysis of compressible thermal convection in gases at very high temperatures

The relevance of non-equilibrium phenomena, nonlinear behavior, gravitational effects and fluid compressibility in a wide range of problems related to high-temperature gas-dynamics, especially in thermal, mechanical and nuclear engineering, calls for a concerted approach using the tools of the kinetic theory of gases, statistical physics, quantum mechanics, thermodynamics and mathematical modeling in synergy with advanced numerical strategies for the solution of the Navier–Stokes equations. The reason behind such a need is that in many instances of relevance in this field one witnesses a departure from canonical models and the resulting inadequacy of standard CFD approaches, especially those traditionally used to deal with thermal (buoyancy) convection problems. Starting from microscopic considerations and typical concepts of molecular dynamics, passing through the Boltzmann equation and its known solutions, we show how it is possible to remove past assumptions and elaborate an algorithm capable of targeting the broadest range of applications. Moving beyond the Boussinesq approximation, the Sutherland law and the principle of energy equipartition, the resulting method allows most of the fluid properties (density, viscosity, thermal conductivity, heat capacity and diffusivity, etc.) to be derived in a rational and natural way while keeping empirical contamination to the minimum. Special attention is deserved as well to the well-known pressure issue. With the application of the socalled multiple pressure variables concept and a projection-like numerical approach, difficulties with such a term in the momentum equation are circumvented by allowing the hydrodynamic pressure to decouple from its thermodynamic counterpart. The final result is a flexible and modular framework that on the one hand is able to account for all the molecule (translational, rotational and vibrational) degrees of freedom and their effective excitation, and on the other hand can guarantee adequate interplay between molecular and macroscopic-level entities and processes. Performances are demonstrated by computing some incompressible and compressible benchmark test cases for thermal (gravitational) convection, which are then extended to the high-temperature regime taking advantage of the newly developed features.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Influence of heat and particle fluxes nonlocality on spatial distribution of plasma density in two-chamber inductively coupled plasma sources

This study presents 2D simulations of the two-chamber inductively coupled plasma source where power is supplied in the small discharge chamber and extends by electron thermal conductivity mechanism to the big diffusion chamber. Depending on pressure, two main scenarios of plasma density and its spatial distribution behavior were identified. One case is characterized by the localization of plasma in the small driver chamber where power is deposed. Another case describes when the diffusion chamber becomes the main source of plasma with maximum of the electron density. The differences in spatial distribution are caused by local or non-local behavior of electron energy transport in the discharge volume due to different characteristic scale of heat transfer with electronic conductivity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Novel K rattling: A new route to thermoelectric materials?

We have performed ab initio molecular dynamics simulations to study the alkali-metal dynamics in the Al-doped (KAl{sub 0.33}W{sub 1.67}O{sub 6} and RbAl{sub 0.33}W{sub 1.67}O{sub 6}) and undoped (KW{sub 2}O{sub 6} and RbW{sub 2}O{sub 6}) defect pyrochlore tungstates. The K atoms exhibit novel rattling dynamics in both the doped and undoped tungstates while the Rb atoms do not. The KAl{sub 0.33}W{sub 1.67}O{sub 6} experimental thermal conductivity curve shows an unusual depression between ∼50 K and ∼250 K, coinciding with two crossovers in the K dynamics: the first at ∼50 K, from oscillatory to diffusive, and the second at ∼250 K, from diffusive back to oscillatory. We found that the low-temperature crossover is a result of the system transitioning below the activation energy of the diffusive dynamics, whereas the high-temperature crossover is driven by a complex reconstruction of the local potential around the K atoms due to the cage dynamics. This leads to a hardening of the K potential with increasing temperature. This unusual reconstruction of the potential may have important implications for the interpretation of finite-temperature dynamics based on zero-temperature potentials in similar materials. The key result is that the novel K rattling, involving local diffusion, leads to a significant reduction in the thermal conductivity. We suggest that this may open a new route in the phonon engineering of cage compounds for thermoelectric materials, where the rattlers are specifically selected to reduce the lattice thermal conductivity by the mechanism of local diffusion.

36 MATERIALS SCIENCE↗

Directional solidification in an imperfect furnace

The upward directional solidification of a binary alloy in which the rejected solute is more dense than the solvent is considered. The system is stably stratified both thermally and solutally. If heat is lost through the sidewalls, horizontal thermal gradients drive a steady double-diffusive convection. Solidification cells with small aspect ratios (width/length) A are considered, and asymptotic solutions to the steady double-diffusive system are obtained as A tends to 0 under the assumption heat losses are also small. When the thermal Grashof number is large, buoyancy boundary layers are at the sidewalls. The shape of the crystal-melt interface is determined by the coupled effects of local thermodynamic equilibrium, diffusion and convection.

Brattkus, K.↗

Diffusion Barrier Selection from Refractory Metals (Zr, Mo and Nb) via Interdiffusion Investigation for U-Mo RERTR Fuel Alloy

U-Mo alloys are being developed as low enrichment monolithic fuel under the Reduced Enrichment for Research and Test Reactor (RERTR) Program. Diffusional interactions between the U-Mo fuel alloy and Al-alloy cladding within the monolithic fuel plate construct necessitate incorporation of a barrier layer. Fundamentally, a diffusion barrier candidate must have good thermal conductivity, high melting point, minimal metallurgical interaction, and good irradiation performance. Refractory metals, Zr, Mo, and Nb are considered based on their physical properties, and the diffusion behavior must be carefully examined first with U-Mo fuel alloy. Solid-to-solid U-10wt.%Mo vs. Mo, Zr, or Nb diffusion couples were assembled and annealed at 600, 700, 800, 900 and 1000 degrees C for various times. The interdiffusion microstructures and chemical composition were examined via scanning electron microscopy and electron probe microanalysis, respectively. For all three systems, the growth rate of interdiffusion zone were calculated at 1000, 900 and 800 degrees C under the assumption of parabolic growth, and calculated for lower temperature of 700, 600 and 500 degrees C according to Arrhenius relationship. The growth rate was determined to be about 10 3 times slower for Zr, 10 5 times slower for Mo and 10 6 times slower for Nb, than the growth rates reported for the interaction between the U-Mo fuel alloy and pure Al or Al-Si cladding alloys. Zr, however was selected as the barrier metal due to a concern for thermo- mechanical behavior of UMo/Nb interface observed from diffusion couples, and for ductile-to-brittle transition of Mo near room temperature.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Neutron capture of UO 2 targets prepared by spin-coating assisted combustion synthesis

Two uranium dioxide (UO 2 ) targets of (414 ± 23) nm and (1092 ± 93) nm thicknesses were prepared on 6061 aluminum alloy and puratronic grade aluminum backing materials. The targets were deposited with a novel method combining spin coating and solution combustion synthesis (SCS). The target layers consisted of small (3–7 nm) UO 2 grains and uniformly distributed ultra-small (1–3 nm) pores. The prepared targets were tested at the Los Alamos National Laboratory’s LANSCE facility for neutron irradiation damage and suitability for neutron capture experiments. The samples showed no signs of target material loss after the irradiation. However, irradiation caused a significant increase in the grain size (4–10 nm), as well as upward mass diffusion and coalescence of the pores due to the thermal spikes. The magnesium in the aluminum 6061 alloy backing also diffused into the UO 2 layer during neutron irradiation. The structural changes in the target after the irradiation do not affect the data from neutron capture. As a result, the new method can be used more broadly to prepare other actinide targets for nuclear physics experiments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Neutron Diffraction Measurement of Residual Stresses in “OSU Plate”

Aluminum-clad U10Mo (including zirconium diffusion layer) fuel assembly plates are bound to be in a state of residual stress due to the mismatch of thermal expansion of the constituent phases. Due to the geometry of the plates, i.e. thin beams, it is expected that the stress will predominantly be in-plane. The thermal expansion of the aluminum cladding, zirconium diffusion layer and U10Mo foil are roughly α Al =22x10 -6 /K, α Zr =5x10 -6 /K, and α U10Mo =10x10 -6 /K. Note that the coefficient of thermal expansion of the zirconium is quoted as that in the a direction in the hexagonal close packed crystal structure because of the strong texture in the rolled zirconium foil, in which the a-axis are strongly preferred in the in-plane direction. During cooling from the hot isostatic pressing (HIP’ing) temperature, the zirconium contracts considerably less than the U10Mo, which in turn, contracts less than the aluminum. Because the aluminum dominates in terms of volume fraction, it is expected that the U10Mo foil and zirconium bonding layer will be in a residual stress state of in-plane compression at room temperature after bonding. This has been verified for the U10Mo foil in a mini fuel plate using x-ray diffraction at the Advanced Photon Source, but measurements of the stress state of the aluminum and zirconium were not possible at the APS. Also, the APS measurements were limited to mini size fuel plates Neutron diffraction experiments of residual stress on the “OSU plate” were completed on the Spectrometer for Materials Research at Temperature and Stress (SMARTS) at the Lujan Center at LANSCE between 2/19-21/2013. Longitudinal and transverse residual strain profiles were measured on an Al-clad U10-Mo OSU plate. Residual strains from the aluminum cladding, the zirconium bonding layer and the U10Mo fuel foil were recorded.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Process-dependent anisotropic thermal conductivity of laser powder bed fusion AlSi10Mg: impact of microstructure and aluminum-silicon interfaces

Purpose AlSi10Mg alloy is commonly used in laser powder bed fusion due to its printability, relatively high thermal conductivity, low density and good mechanical properties. However, the thermal conductivity of as-built materials as a function of processing (energy density, laser power, laser scanning speed, support structure) and build orientation, are not well explored in the literature. This study aims to elucidate the relationship between processing, microstructure, and thermal conductivity. Design/methodology/approach The thermal conductivity of laser powder bed fusion (L-PBF) AlSi10Mg samples are investigated by the flash diffusivity and frequency domain thermoreflectance (FDTR) techniques. Thermal conductivities are linked to the microstructure of L-PBF AlSi10Mg, which changes with processing conditions. The through-plane exceeded the in-plane thermal conductivity for all energy densities. A co-located thermal conductivity map by frequency domain thermoreflectance (FDTR) and crystallographic grain orientation map by electron backscattered diffraction (EBSD) was used to investigate the effect of microstructure on thermal conductivity. Findings The highest through-plane thermal conductivity (136 ± 2 W/m-K) was achieved at 59 J/mm 3 and exceeded the values reported previously. The in-plane thermal conductivity peaked at 117 ± 2 W/m-K at 50 J/mm 3 . The trend of thermal conductivity reducing with energy density at similar porosity was primarily due to the reduced grain size producing more Al-Si interfaces that pose thermal resistance. At these interfaces, thermal energy must convert from electrons in the aluminum to phonons in the silicon. The co-located thermal conductivity and crystallographic grain orientation maps confirmed that larger colonies of columnar grains have higher thermal conductivity compared to smaller columnar grains. Practical implications The thermal properties of AlSi10Mg are crucial to heat transfer applications including additively manufactured heatsinks, cold plates, vapor chambers, heat pipes, enclosures and heat exchangers. Additionally, thermal-based nondestructive testing methods require these properties for applications such as defect detection and simulation of L-PBF processes. Industrial standards for L-PBF processes and components can use the data for thermal applications. Originality/value To the best of the authors’ knowledge, this paper is the first to make coupled thermal conductivity maps that were matched to microstructure for L-PBF AlSi10Mg aluminum alloy. This was achieved by a unique in-house thermal conductivity mapping setup and relating the data to local SEM EBSD maps. This provides the first conclusive proof that larger grain sizes can achieve higher thermal conductivity for this processing method and material system. This study also shows that control of the solidification can result in higher thermal conductivity. It was also the first to find that the build substrate (with or without support) has a large effect on thermal conductivity.

Engineering↗