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Modeling the Effect of Evaporative Flux and Colloidal Aggregation on Crud Deposition

During the last few years lot of research has been conducted to investigate and predict the Crud deposition in PWRs. One of the common findings of various experimental and computational studies is that thickness or amount of crud deposits is directly related to evaporative flux maps. Evaporation driven deposition profile on the surfaces takes different forms, i.e. from ring to disk shapes during initial stages and in the form of porous to impervious continuous layers covering the hot fuel surface at the later stages. The amount and thickness of these deposits although are directly related to evaporative flux, the relationship is much complex and can be dependent upon several other factors. A popular problem relating evaporative flux to particulate deposition has been well studied in the form of drying of sessile colloidal drops. It was proposed that, this phenomenon is due to a geometrical constraint: the free surface, constrained by a pinned contact line squeezes the fluid outwards to compensate for evaporative losses and thereby transporting particles to the contact line. Later on a quantitative relationship between evaporative flux and deposition rate was proposed and validated by the same group, which showed power-law relationship. Deposition studies conducted with controlled concentration of particles with subcooled nucleate boiling also showed a power-law relationship rather than a simpler linear relationship whereas physics of evaporation would tend to concentrate particles at linear rate. In a typical subcooled nucleate boiling system, bubble growth and departure time is of the order 1-2 ms, measured experimentally. Diffusion time constant for dilute spherical metallic colloids such as crud particulates, generally present as particulate in process piping, range from 0.0025-2.5 sec in water for a size range 0.1-1.0 μm. Colloidal behavioral characteristics during the growth of bubbles can be computed with escape time constant at collision, which is dependent on effective Hamaker constant. For minimum effective Hamaker constant of Hematite is -2.5 kT and diffusion time constant τ = 0.0025 sec, escape time constant is computed as Kramer rule, τexp[A/kT] magnitude is 0.03 sec or 30 ms. This clearly indicates that evaporation will cause particles to come together and they cannot escape at a fast enough rate which would lead them to form agglomerates. Therefore both effects of evaporative flux in conjunction with the agglomeration kinetics must be considered for modeling the crud deposition if the evaporative flux is known. In this paper, we propose a phenomenological model of colloidal transport and aggregation with evaporative flux. The dynamic of particles interactions while drying of sessile colloidal drops is developed by coupling general transport equation with Smoluchowshki Coagulation equation. Crud deposition on the nuclear fuel has been a serious problem with severe consequences in nuclear power plants. In several studies it has been consistently reported that crud deposition is directly related to evaporative flux on the nuclear fuel surfaces. However, it has not been established how to quantify the deposition rates of crud type particulates if the evaporative flux is known. This complex multiphysics problem is similar to coffee-ring effect, where the governing physics is understood more clearly. In this work, a simplified geometry is used to model the effects of evaporative flux acting at a boundary on the colloidal concentration. The effect of this condition on change in concentration is shown numerically. Further, agglomeration is suspected to play a significant role in high evaporative flux such as bubble nucleation. The coagulation kinetics is modeled using uniform particle distribution and the effective total concentration of colloids including original particles and agglomerates is studied. Once this model is validated with a simple separate effect experiments, it can be integrated to large scale PWR models of evaluating evaporative flux and chemistry models developed by Electrical Power Research Institute (EPRI). (authors)

42 ENGINEERING↗

Effect of Solvent on the Local Structure, Dynamics, and Vibrational Density of States in Sn-BEA Zeolite

Lewis acid zeolites are attractive catalysts for epoxidation and biomass valorization, as they are highly active and selective in the liquid phase and can operate at or near ambient conditions. While a rich experimental literature exists on liquid-phase Lewis acid zeolite catalysis, our understanding of the molecular organization and solvent dynamics in the vicinity of Lewis acid sites with differing metal site speciation remains limited. In this work, we investigate the molecular coordination and diffusion of two common solvents (methanol and water) around the closed and open Sn-BEA zeolite active sites using molecular dynamics simulations with a machine-learned interatomic potential trained on ab initio molecular dynamics trajectories. Molecular dynamics simulations reveal that introducing active sites significantly enhances local order in the first and second solvation shells compared to the pure silica case. For methanol, both closed and open active sites are singly coordinated, while more than two water molecules coordinate the open site. In contrast to methanol, we observed that water molecules dissociate, leading to the formation of additional Sn-OH and silanol groups away from the active site. The diffusion coefficients of water and methanol are functions of the solvent population in the pore. Here, our work provides insights into how active site speciation in Lewis acid zeolites affects solvent coordination, diffusion, and vibrational signature. This information is foundational for catalyst design and optimization of liquid-phase catalytic processes in zeolites. It also demonstrates the suitability of machine-learned interatomic potentials for modeling reactive systems, enabling sufficiently long trajectories for appropriate statistical averaging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling the Size Distribution and Chemical Composition of Secondary Organic Aerosols during the Reactive Uptake of Isoprene-Derived Epoxydiols under Low-Humidity Condition

Reactive uptake of isoprene epoxydiols (IEPOX), which are isoprene oxidation products, onto acidic sulfate aerosols is recognized to be an important mechanism for the formation of isoprene-derived secondary organic aerosol (SOA). While a mechanistic understanding of IEPOX-SOA formation exists, several processes affecting their formation remain uncertain. Evaluating mechanistic IEPOX-SOA models with controlled laboratory experiments under longer atmospherically relevant timescales is critical. Here, we implement our latest understanding of IEPOX-SOA formation within a box model to simulate the measured reactive uptake of IEPOX on polydisperse ammonium bisulfate seed aerosols within an environmental Teflon chamber. The model is evaluated with single-particle measurements of size distribution, volume, density, and composition of aerosols due to IEPOX-SOA formation at timescales of hours. Additionally, we find that the model can simulate the growth of particles due to IEPOX multiphase chemistry, as reflected in increases of the mean particle size and volume concentrations, and a shift of number size distribution to larger sizes. The model also predicts the observed evolution of particle number mean diameter and total volume concentrations at the end of the experiment. We show that in addition to self-limiting effects of IEPOX-SOA coatings, accounting for the molar balance between inorganic and organic sulfate and mass accommodation coefficient of IEPOX are important parameters governing modeling of IEPOX-SOA formation. Thus, models which do not account for the molar sulfate balance and/or diffusion limitations within IEPOX-SOA coatings are likely to predict too high IEPOX-SOA formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Geomechanical characterization of Rock Valley carbonates

In Rock Valley, Nevada, the USA, past earthquake sequences and shallow faulting in Paleozoic carbonates remain poorly understood. Carbonates are typically more ductile rocks that do not experience large stress drops or fracture coalescence, which contradicts previous observations in the region. As part of the Source Physics Experiment, an effort has been made to experimentally characterize the petrophysical and geomechanical properties of carbonates from Rock Valley. Well core and outcrop samples were used to determine the difference between shallow-buried Tertiary limestones and deeply buried Paleozoic limestones and dolostones. The carbonates possessed porosities between 3 and 9%, with V P and V S in the Tertiary carbonates around 2700 and 1800 m/s, respectively, and 6000 and 3100 m/s, respectively, in the Paleozoic carbonates. Microstructural characterization revealed that the Paleozoic carbonates contained significantly more pre-existing damage and alteration than the Tertiary carbonates, though the deformation varies from localized to diffuse. Unconfined Brazilian tests and triaxial tests with confining pressures between 0 and 50 MPa showed that, although samples all experienced failure, the dolostones typically failed at greater stresses and possessed greater E/ν ratios than the limestones. Furthermore, the Hoek–Brown failure criterion was used to construct failure envelopes with the compressive and tensile failure tests. Velocity, density, and porosity measurements were used to construct a hypothetical velocity-depth profile and compare the results with the theoretical petrophysical measurements. Using brittleness analysis, the likely failure conditions were determined to be low-porosity dolomitic rock for fault nucleation in the Paleozoic basement.

Brittleness↗

Pressure solution creep of random packs of spheres

Abstract We performed numerical calculations of compaction in aggregates of spherical grains, using Lehner and Leroy's (2004, hereinafter LL) constitutive model of pressure solution at grain contacts. That model is founded on a local definition of the thermodynamic driving force and leads to a fully coupled formulation of elastic deformation, dissolution, and diffusive transport along the grain boundaries. The initial geometry of the aggregate was generated by random packing of spheres with a small standard deviation of the diameters. During the simulations, isostatic loading was applied. The elastic displacements at the contacts were calculated according to Digby's (1981) nonlinear contact force model, and deformation by dissolution was evaluated using the LL formulation. The aggregate strain and porosity were tracked as a function of time for fixed temperature, applied effective pressure, and grain size. We also monitored values of the average and standard deviation of total load at each contact, the coordination number for packing, and the statistics of the contact dimensions. Because the simulations explicitly exclude processes such as fracturing, plastic flow, and transport owing to surface curvature, they can be used to test the influence of relative changes in the kinetics of dissolution and diffusion processes caused by contact growth and packing rearrangements. We found that the simulated strain data could be empirically fitted by two successive power laws of the form, ε x ∝ t ξ , where ξ was equal to 1 at very early times, but dropped to as low as 0.3 at longer times. The apparent sensitivity of strain rate to stress found in the simulations was much lower than predicted from constitutive laws that assume a single dominant process driven by average macroscopic loads. Likewise, the apparent activation enthalpy obtained from the simulated data was intermediate between that assumed for dissolution and diffusion, and, further, tended to decrease with time. These results are similar to the experimental observations of Visser et al.'s (2012), who used an aggregate geometry and physical conditions closely resembling the present numerical simulations.

Bernabé, Y.↗

Analytical model of the effect of misfit dislocation character on the bubble-to-void transition in metals

Here, this paper addresses the role of misfit dislocations in the nucleation and growth of nanoscale He bubbles at interfaces. In a recent work, we studied the nanoscale effects on the capillarity equation and on equilibrium conditions. We proposed an expression for surface energy and for the equation of state, EOS, for He in bubbles, which have a size dependence that captures the role of the interface forces, which become relevant at the nanoscale. Here we determine the EOS for several twist grain boundaries in Fe and Cu and incorporate these results into the rate equation that determines the bubble-to-void transition, focusing on the influence of interface dislocations on the evaporation rate of vacancies. We find a significant effect of the magnitude of the Burgers vector of the dislocations on the critical radius for the transition. In conclusion, these results give a quantitative way to characterize grain boundaries in their ability to capture He and alter the onset of swelling.

36 MATERIALS SCIENCE↗

Defect Production and Microstructural Feature Impact for Radiation Damage in Additively Manufactured 316 Stainless Steel

This milestone presents multi-scale modeling research results for additively manufactured 316 stainless steel. A combination of phase field, cluster dynamics, molecular dynamics, and density functional theory with machine learning is used, allowing for predictions of radiation-driven microstructural evolution in additively manufactured 316 stainless steel over a range of temperatures, damage rates, neutron spectra, and microstructures, and supporting the development of combined ion and neutron irradiation for material qualification. Informed by ion irradiation and neutron irradiation results across the Advanced Materials and Manufacturing Technologies program, we investigate the unique aspects of radiation-driven microstructure evolution in additively manufactured 316 stainless steel. In particular, we focus on understanding the impact of carbon concentration (varying, for example, between the 316L and 316H standards) on void formation; radiation-induced segregation at dislocation cells and grain boundaries; and the evolution of dislocation loops and network dislocation populations. We find that the unique characteristics of the additively manufactured microstructures must be accounted for in understanding the evolution of dislocation populations under thermal and irradiation conditions, such as the variation in sink strengths arising due to the variation in dislocation density. We also find that the radiation-induced segregation of Cr and Ni to grain boundaries and cell walls differs due to the differences in their defect sink biases. We also find that increasing the Ni content can slow vacancy diffusion, which may provide a mechanism for the observed reduction in transient swelling rate for austenitic Fe-Cr-Ni alloys with increasing Ni content. In addition, ion irradiations have shown that increasing carbon content in 316 SS results in a larger population of smaller voids, suggesting reduced vacancy diffusion. Our results show that the carbon content of additively manufactured 316 SS has a significant impact on the migration rate of defect clusters. The presence of carbon atoms results in carbon-vacancy trapping, significantly reducing the diffusion rate of vacancies. Carbon atoms may also be trapped near the surface of a void, which may reduce void growth by trapping vacancies that diffuse toward the void.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Recalescence and Segregation Phenomena During Equiaxed Dendritic Solidification of Fe-C Alloy

Recalescence and segregation are two characteristic phenomena for the equiaxed dendritic solidification of alloys. The present work developed a two-dimensional dendritic model with cellular automaton (CA) method to investigate influence mechanisms of thermal conditions on recalescence and segregation behaviors of Fe-0.82wt pct C alloy. The released latent heat reduces the undercooling around the equiaxed dendrite, and thus eases its growth velocity. The predicted steady growth velocity agrees well with the analytical results as the melt undercooling is 9 K. Additionally, the present CA model can ensure the growth consistence of equiaxed dendrites in the undercooled melt. With improving the convective heat transfer coefficients applied around the domain boundaries, the temperature recalescence in the domain center becomes more significant, and the corresponding solid fractions enhance. It is because that the stronger cooling promotes the solidification, resulting in more latent heat released. Accordingly, the heat dissipation can be neutralized. Moreover, a deeper undercooling for the temperature recalescence is needed under a stronger cooling condition. With the increase of both the cooling rate and the convection coefficient, secondary arms of the equiaxed dendrite become more developed. At the lower cooling rate range, the segregation ratio in the domain enlarges with the improvement of the cooling rate. However, it gets weaker under the condition with super cooling intensity due to the expansion of the low concentration region. As the convection coefficient is enhanced, the solute segregation in the domain gets less pronounced.

36 MATERIALS SCIENCE↗

Poole-Frenkel-effect as dominating current mechanism in thin oxide films—An illusion?!

In many of the publications, over 50 per year for the last five years, the Poole-Frenkel-effect (PFE) is identified or suggested as dominating current mechanism to explain measured current–electric field dependencies in metal-insulator-metal (MIM) thin film stacks. Very often, the insulating thin film is a metal oxide as this class of materials has many important applications, especially in information technology. In the overwhelming majority of the papers, the identification of the PFE as dominating current mechanism is made by the slope of the current–electric field curve in the so-called Poole-Frenkel plot, i.e., logarithm of current density, j, divided by the applied electric field, F, versus the square root of that field. This plot is suggested by the simplest current equation for the PFE, which comprises this proportionality (ln(j/F) vs. F{sup 1/2}) leading to a straight line in this plot. Only one other parameter (except natural constants) may influence this slope: the optical dielectric constant of the insulating film. In order to identify the importance of the PFE simulation studies of the current through MIM stacks with thin insulating films were performed and the current–electric field curves without and with implementation of the PFE were compared. For the simulation, an advanced current model has been used combining electronic carrier injection/ejection currents at the interfaces, described by thermionic emission, with the carrier transport in the dielectric, described by drift and diffusion of electrons and holes in a wide band gap semiconductor. Besides the applied electric field (or voltage), many other important parameters have been varied: the density of the traps (with donor- and acceptor-like behavior); the zero-field energy level of the traps within the energy gap, this energy level is changed by the PFE (also called internal Schottky effect); the thickness of the dielectric film; the permittivity of the dielectric film simulating different oxide materials; the barriers for electrons and holes at the interfaces simulating different electrode materials; the temperature. The main results and conclusions are: (1) For a single type of trap present only (donor-like or acceptor-like), none of the simulated current density curves shows the expected behavior of the PFE and in most cases within the tested parameter field the effect of PFE is negligibly small. (2) For both types of traps present (compensation) only in the case of exact compensation, the expected slope in the PF-plot was nearly found for a wider range of the applied electric field, but for a very small range of the tested parameter field because of the very restricting additional conditions: first, the quasi-fermi level of the current controlling particle (electrons or holes) has to be 0.1 to 0.5 eV closer to the respective band limit than the zero-field energy level of the respective traps and, second, the compensating trap energy level has to be shallow. The conclusion from all these results is: the observation of the PFE as dominating current mechanism in MIM stacks with thin dielectric (oxide) films (typically 30 nm) is rather improbable!.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

H I-to-H{sub 2} transition layers in the star-forming region W43

The process of atomic-to-molecular (H i-to-H{sub 2}) gas conversion is fundamental for molecular-cloud formation and star formation. 21 cm observations of the star-forming region W43 revealed extremely high H i column densities, of 120–180 M{sub ⊙} pc{sup −2}, a factor of 10–20 larger than predicted by H i-to-H{sub 2} transition theories. We analyze the observed H i with a theoretical model of the H i-to-H{sub 2} transition, and show that the discrepancy between theory and observation cannot be explained by the intense radiation in W43, nor be explained by variations of the assumed volume density or H{sub 2} formation rate coefficient. We show that the large observed H i columns are naturally explained by several (9–22) H i-to-H{sub 2} transition layers, superimposed along the sightlines of W43. We discuss other possible interpretations such as a non-steady-state scenario and inefficient dust absorption. The case of W43 suggests that H i thresholds reported in extragalactic observations are probably not associated with a single H i-to-H{sub 2} transition, but are rather a result of several transition layers (clouds) along the sightlines, beam-diluted with diffuse intercloud gas.

79 ASTRONOMY AND ASTROPHYSICS↗

Theoretical Analysis of the EPR Spectrum Saturation Effect with Account for Spectral Diffusion in a System with a Gaussian Distribution of Spin Resonance Frequencies

We have analyzed the effect of saturation of the EPR spectrum for the model situation when a set of resonance frequencies of spin packets is described by a Gaussian distribution and spectral diffusion, which is a random process without correlation, exists. We have obtained the form of the spectrum for arbitrary values of magnetic–resonant parameters: relaxation times for the longitudinal and transverse components of the magnetization vector of the system, the spectral diffusion rate, the dispersion of the Gaussian distribution of resonance frequency, and the magnetic induction of the microwave field. We have derived an analytic expression for the saturation curve of the EPR spectrum. Detailed analysis of the dependence of the spectrum saturation curve on the spin system parameters is performed for the optimal case when the microwave field frequency coincides with the average frequency of the Gaussian distribution for resonance frequencies. The value of the microwave field induction at which the peak of the saturation curve is attained has been determined for arbitrary values of the paramagnetic relaxation time, spectral diffusion rate, and dispersion of the Gaussian spin frequency distribution. We have formulated the algorithm for determining the spin–lattice relaxation time using the experimentally determined microwave field induction for which the saturation curve passes through the peak. It should be noted that numerical calculations have been performed for parameters typical of EPR spectroscopy. The general analytic expression derived for the shape of the spectrum in the saturation conditions and qualitative conclusions concerning the effect of spectral diffusion on the saturation of stationary spectra obtained in this study can also be used in other fields of spectroscopy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Recovery of lithium and cobalt from waste lithium ion batteries of mobile phone

Graphical abstract: Recovery of valuable metals from scrap batteries of mobile phone. - Highlights: • Recovery of Co and Li from spent LIBs was performed by hydrometallurgical route. • Under the optimum condition, 99.1% of lithium and 70.0% of cobalt were leached. • The mechanism of the dissolution of lithium and cobalt was studied. • Activation energy for lithium and cobalt were found to be 32.4 kJ/mol and 59.81 kJ/mol, respectively. • After metal recovery, residue was washed before disposal to the environment. - Abstract: In view of the stringent environmental regulations, availability of limited natural resources and ever increasing need of alternative energy critical elements, an environmental eco-friendly leaching process is reported for the recovery of lithium and cobalt from the cathode active materials of spent lithium-ion batteries of mobile phones. The experiments were carried out to optimize the process parameters for the recovery of lithium and cobalt by varying the concentration of leachant, pulp density, reductant volume and temperature. Leaching with 2 M sulfuric acid with the addition of 5% H{sub 2}O{sub 2} (v/v) at a pulp density of 100 g/L and 75 °C resulted in the recovery of 99.1% lithium and 70.0% cobalt in 60 min. H{sub 2}O{sub 2} in sulfuric acid solution acts as an effective reducing agent, which enhance the percentage leaching of metals. Leaching kinetics of lithium in sulfuric acid fitted well to the chemical controlled reaction model i.e. 1 − (1 − X){sup 1/3} = k{sub c}t. Leaching kinetics of cobalt fitted well to the model ‘ash diffusion control dense constant sizes spherical particles’ i.e. 1 − 3(1 − X){sup 2/3} + 2(1 − X) = k{sub c}t. Metals could subsequently be separated selectively from the leach liquor by solvent extraction process to produce their salts by crystallization process from the purified solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Magnetic Prandtl number dependence of the kinetic-to-magnetic dissipation ratio

Using direct numerical simulations of three-dimensional hydromagnetic turbulence, either with helical or non-helical forcing, we show that the kinetic-to-magnetic energy dissipation ratio always increases with the magnetic Prandtl number, i.e., the ratio of kinematic viscosity to magnetic diffusivity. This dependence can always be approximated by a power law, but the exponent is not the same in all cases. For non-helical turbulence, the exponent is around 1/3, while for helical turbulence it is between 0.6 and 2/3. In the statistically steady state, the rate of energy conversion from kinetic into magnetic by the dynamo must be equal to the Joule dissipation rate. We emphasize that for both small-scale and large-scale dynamos, the efficiency of the energy conversion depends sensitively on the magnetic Prandtl number, and thus on the microphysical dissipation process. To understand this behavior, we also study shell models of turbulence and one-dimensional passive and active scalar models. We conclude that the magnetic Prandtl number dependence is qualitatively best reproduced in the one-dimensional model as a result of dissipation via localized Alfvén kinks.

79 ASTRONOMY AND ASTROPHYSICS↗

Investigation of Mass Transfer and Sorption in CO 2 /Brine/Rock Systems via In Situ FT-IR

CO 2 geological storage in deep saline formations is considered a promising method to mitigate anthropogenic CO 2 emissions and, thereby, minimize changes to the Earth’s atmosphere. A fundamental understanding of CO 2 mass transfer and sorption phenomena in brine-saturated reservoir formations is necessary to understand the long-term fate of injected CO 2 as it is subjected to different (physical, dissolution, and mineral) trapping mechanisms. In this work, we investigate CO 2 sorption in brine-saturated and dry Mt. Simon sandstone samples via in-situ Fourier Transform infrared spectroscopy (FT-IR) at elevated pressures, ranging from 0.3 MPa to 8.3 MPa, at a temperature of 50 ⁰C. The FT-IR spectra of bulk-phase CO 2 were simultaneously recorded under the same conditions. For bulk-phase CO 2 , we observed, in agreement with past studies, a doublet peak at 2361 cm -1 and 2336 cm -1 and another peak (ν 2 bending mode) at 667 cm -1 . With increasing pressure, the position of the peak at 667 cm -1 remains invariant, however, when crossing into the supercritical region the doublet peak degenerates onto a single peak at 2336 cm -1 with a barely visible shoulder at 2361 cm -1 . The bulk CO 2 data provide a perfect fit for Beer’s law for the whole range of pressure conditions. For the dry sample, the IR spectrum is experimentally indistinguishable from the bulk CO 2 spectrum, signifying that if physical adsorption occurs to any significant extent, the adsorbed CO 2 molecules are not substantially more rotationally constrained than the dense bulk CO 2 molecules. For the brine-saturated sample, we observe a strong band centered at 2342 cm -1 and a small companion peak at 2360-2361 cm -1 that degenerates into a barely visible shoulder peak at the higher pressures. The 2342 cm -1 band has been previously observed by other investigators for CO 2 dissolved in bulk water/brine as well during its adsorption on a variety of other wet natural porous media. We observe no peaks corresponding to bicarbonate or carbonate bulk species, which correlates well with the prior literature on similar low-pH aqueous solutions. The integrated peak area for the CO 2 sorbed in the brine-saturated sample correlates linearly with its solubility in the same bulk brine, as measured separately via a PVT-cell approach. Here, this validates the accuracy of both techniques, and the potential of the FT-IR method to be used in the study of mass transfer and adsorption in such systems. To that effect, a simple mathematical model is presented to analyze the FT-IR data to determine the CO 2 effective diffusivity in the brine-saturated sandstone sample.

58 GEOSCIENCES↗

Effects of high-energy particles on accretion flows onto a supermassive black hole

We study the effects of high-energy particles (HEPs) on the accretion flows onto a supermassive black hole and luminosities of escaping particles such as protons, neutrons, gamma rays, and neutrinos. We formulate a one-dimensional model of the two-component accretion flow consisting of thermal particles and HEPs, supposing that some fraction of the released energy is converted to the acceleration of HEPs. The thermal component is governed by fluid dynamics while the HEPs obey the moment equations of the diffusion-convection equation. By solving the time evolution of these equations, we obtain advection-dominated flows as the steady state solutions. The effects of the HEPs on the flow structures turn out to be small even if the pressure of the HEPs dominates over the thermal pressure. For a model in which the escaping protons take away almost all the energy released, the HEPs have a large enough influence to make the flow have a Keplerian angular velocity at the inner region. We calculate the luminosities of the escaping particles for these steady solutions. The escaping particles can extract the energy from about 10{sup −4} M-dot c{sup 2} to 10{sup −2} M-dot c{sup 2}, where M-dot is the mass accretion rate. The luminosities of the escaping particles depend on parameters such as the injection Lorentz factors, the mass accretion rates, and the diffusion coefficients. We also discuss some implications on the relativistic jet production by the escaping particles.

79 ASTRONOMY AND ASTROPHYSICS↗

Cluster Dynamics Simulations of Intra-Granular Fission Gas Bubble Size and Pressure Evolution in UO 2

Fission gases such as xenon (Xe) play a critical role in determining the behavior and response of nuclear fuel. Given that Xe has little solubility in UO 2 , it accumulates and forms bubbles, which significantly impact fuel performance. Intra- and inter-granular bubble nucleation and growth can lead to fuel swelling, and once bubbles interconnect at grain boundaries, fission gas can be released into the plenum. At low temperatures, limited uranium vacancy mobility can restrict swelling, therefore causing the bubbles to become highly pressurized. Consequently, this can induce micro-cracking, promote fission gas release (increasing the likelihood of cladding failure), and even lead to fuel pulverization under accident conditions such as a loss of coolant accident. As bubble evolution is strongly influenced by local temperature and fission rate, markedly different behavior occurs across the radial profile of the fuel pellet. Capturing the mechanisms that underpin bubble evolution is therefore important to predict these behaviors in the fuel. Previous models describing important mechanisms informed by lower length scale simulations have been developed under the NEAMS program. These can describe the evolution of a single bubble type (i.e., single value for radius and pressure) at each position in the pellet, for instance using the Centipede cluster dynamic code. However, in reality, a full distribution in bubble sizes and pressures exists within the microstructure at a given position in the pellet. To address this the cluster dynamics code Xolotl, which can predict Xe and vacancy phase space (i.e., bubble distributions) for intra-granular bubbles, has been used before. Prior work benchmarked the Xolotl code against the Centipede cluster dynamics code to ensure compatibility and to verify that mobile defect properties are adequately transferred between the two codes, along with some physics improvements. In this work, we go further by introducing a physics-based set of improvements that will allow us to accurately predict bubble size distributions and internal bubble pressures under representative UO 2 irradiation conditions. The improvements include (i) coupling bubble-defect reaction energies to a virial equation of state (EOS), (ii) including a bubble surface tension contribution, (iii) incorporating radiation-induced re-solution of Xe and vacancies, (iv) enabling pressure-driven dislocation loop punching through an effective emission of interstitial clusters informed by interstitial loop energetics, (v) accounting for radiation induced athermal diffusion of Xe, and (vi) implementing a Booth-type grain boundary sink representation for all mobile defects and defect clusters. After these modifications, we observe good agreement of Xolotl fission gas bubble size and concentration predictions with legacy experimental measurements. Additionally, it allows the distribution of Xe bubble pressures and radius to also be predicted and compared to data produced through the Advanced Fuels Campaign (AFC) program. Here, we have done this by running simulations under conditions similar to the AFC post-irradiation examination (PIE) samples irradiated at North Anna 2 light water reactor (LWR). Our results shows excellent agreement with these experimental measurements.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗