Phase-field simulation of intergranular fission gas bubble growth in U3Si2
Presentation on simulations of U3Si2 fission gas bubble interconnection for TMS 2020 conference.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
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Theoretical Model of Helium Bubble Growth and Density in Plasma-Facing Metals
We present a theoretically-motivated model of helium bubble density as a function of volume for high-pressure helium bubbles in plasma-facing tungsten. The model is a good match to the empirical correlation we published previously [Hammond et al., Acta Mater. 144, 561–578 (2018)] for small bubbles, but the current model uses no adjustable parameters. The model is likely applicable to significantly larger bubbles than the ones examined here, and its assumptions can be extended trivially to other metals and gases. We expect the model to be broadly applicable and useful in coarse-grained models of gas transport in metals.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Modeling of Vapor Bubble Growth Under Nucleate Boiling Conditions in Reduced Gravity
A dynamic model is developed to describe the evolution of a vapor bubble growing at a nucleation site on a superheated surface under arbitrary gravity. The bubble is separated from the surface by a thin microlayer and grows due to the evaporation from the microlayer interface. The average thickness of the microlayer increases as the bubble expands along the surface if the evaporation rate is lower than some critical value. The corresponding threshold value of the surface temperature has to be associated with the burn-out crisis. Two main reasons make for bubble separation, which are the buoyancy force and a force caused by the vapor momentum that comes to the bubble with vapor molecules. The latter force is somewhat diminished if condensation takes place at the upper bubble surface in subcooled liquids. The action of the said forces is opposed by inertia of the additional mass of liquid as the bubble center rises above the surface and by inertia of liquid being expelled by the growing bubble in radial directions. An extra pressure force arises due to the liquid inflow into the microlayer with a finite velocity. The last force helps in holding the bubble close to the surface during an initial stage of bubble evolution. Two limiting regimes with distinctly different properties can be singled out, depending on which of the forces that favor bubble detachment dominates. Under conditions of moderately reduced gravity, the situation is much the same as in normal gravity, although the bubble detachment volume increases as gravity diminishes. In microgravity, the buoyancy force is negligible. Then the bubble is capable of staying near the surface for a long time, with intensive evaporation from the microlayer. It suggests a drastic change in the physical mechanism of heat removal as gravity falls below a certain sufficiently low level. Inferences of the model and conclusions pertaining to effects caused on heat transfer processes by changes in bubble hydrodynamics induced by gravity are discussed in connection with experimental evidence, both available in current and in as yet unpublished literature.
Buyevich, Yu A.↗
Helium Bubble Growth and Retention Characteristics in Aging Palladium Tritide
The helium-related characteristics of aged palladium tritide, including tritium loss, the formation of He bubbles from tritium decay-induced He atoms, and He thermal desorption behavior are computed using a continuum model of bubble evolution that incorporates the log-normal bubble spacing distribution deduced from 3 He nuclear magnetic resonance (NMR) measurements. This spacing distribution produces significant differences between mean (expectation) values of the bubble size and pressure and the average (median) values of these aging characteristics obtained by a previous calculation. The new calculations find much of the He is retained in a large quantity of smaller bubbles with higher bubble pressures, improving the overall stability of the bubbles and extending the age of He retention. By contrast, the integrated tritide material characteristics of swelling and tritium pressure are found relatively insensitive to details of the bubble spacing distribution. Inter-bubble fracture is predicted to begin with small, closely-spaced bubbles and progress to include larger bubbles near the onset of rapid He release. The critical concentration for this onset increases almost linearly with material tensile strength and decreases with shear modulus. Release of He from the aging solid is modeled as a growing network of fractured inter-bubble ligaments. For small particle or small grain material, the physical size of the fracture cluster, relative to the material dimensions, becomes important. In contrast with normal aging, inter-bubble fracture occurring during thermal desorption appears to begin with large, widely-spaced bubbles, indicating elevated temperature techniques may be of limited use for evaluating development of the bubble fracture network.
74 ATOMIC AND MOLECULAR PHYSICS↗
Incorporating bubble growth volume feedback to improve simulation of the response of a structure containing liquid and gas to sudden energy input
The SNS target module is a stainless-steel structure that contains and directs mercury. The mercury is struck with short, intense proton pulses to create neutrons. The pulses deposit energy and cause loads on the target structure and mercury cavitation. Helium bubbles are introduced into the mercury to reduce loads and cavitation. This gas complicates the prediction of the target module’s physical response. The current method used to simulate the structural response to the proton pulse incorporates a simple but effective approach to approximate mercury cavitation effects. This method cannot account for the changes from injected non-condensable gas. The ability to model the target vessel response is a prerequisite for estimating its life. Known approaches for simulating a bubbly fluid mixture’s response are computationally expensive and impractical for detailed engineering models. A constitutive model is proposed for target mercury with injected gas bubbles, with the intent of providing more accurate mercury–vessel response behavior without the computing costs required to track individual bubbles. The model’s assumptions and a computational model embodiment are described. The bubbly mercury computational model is subjected to test problems to assess its potential utility. Here, the model was able to better predict the effect of gas on wave propagation.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Corrigendum and Addendum: Helium flux effects on bubble growth and surface morphology in plasma-facing tungsten from large-scale molecular dynamics simulations (2019 Nucl. Fusion 59 066035)
Two of the simulations discussed in a prior article (Hammond et al 2019 Nucl. Fusion 59 066035) were affected by a simulation glitch. We repeated the affected calculations and discuss them here. Here, the overall conclusions are essentially unchanged, though the details are different. In particular, observations that we referred to as ‘concerted bursting’ were caused primarily by non-physical heating and cooling applied by the thermostat after most atoms’ velocities were deleted (for reasons that are not known for certain). The phenomenon of one bubble bursting and causing another nearby bubble to burst does exist, though its effects are much less spectacular in the absence of non-physical driving forces. The observation of an interconnected network of sub-surface cavities formed by burst bubbles is real, and the observation of holes on the surface 1–2 nm in diameter is also confirmed.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Bridging scales in multiscale bubble growth dynamics with correlated fluctuations using neural operator learning
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Rayleigh-Plesset equation↗
Molecular Dynamics Modeling and Experimental Assessment of Helium Bubble Growth and Surface Morphology Evolution
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Cusentino, Mary Alice [Sandia National Laboratorie↗
On the application of the source theory to the solution of problems involving phase change. i - growth and collapse of bubbles.
Growth of vapor bubble in liquid mixtures and growth and collapse of noncondensing, nonsoluble gas in pure liquid determined by approximate solutions derived from forster source theory
GAS PHASE↗
CFD Predictions of Boiling Regime Transitions during Line Chilldown validated against a 1G LN2 Experiment
Introduction Before filling a propellant tank on the ground or in Space, the transfer line between the donor and receiver tanks must be cooled down preferably by sacrificing a minimum amount of the cryogenic fluid. The cryogenic line chill-down process involves a transition between different flow boiling regimes, namely, film boiling, transition film boiling, and nucleate boiling which are complex and may be quite gravity-dependent. Capturing these boiling phenomena and predicting the transition between them in a CFD framework is new and challenging both for 1g and microgravity applications. Materials & Methods The present work addresses this challenge by employing a two-phase Eulerian approach in the context of a homogeneous fluid mixture together with the Lee phase change model to capture the film boiling regime of the chill-down process using ANSYS Fluent®. The nucleate boiling regime is predicted by incorporating an in-house developed sub-grid model that accounts for bubble nucleation, bubble growth, bubble departure diameter, and their shedding frequency. The sub-grid model is encoded and implemented into Fluent via a user-defined function for the wall-fluid heat flux calculations. The mathematical formulation and numerical implementation of the CFD model are described in detail. The coupled CFD-Subgrid model is validated against published experimental data for liquid nitrogen chill-down of a heated stainless-steel pipe in 1g. Results Numerical simulation results show good agreements between the CFD predictions of the wall temperature evolution, rewetting temperature, and transition between film and nucleate boiling, with the experimental measurements published by Darr et al [2] for several different LN2 flowrates in the vertical pipe orientation. The CFD predictions for the wall temperature distribution indicate a rapid quenching of the wall at two upstream and downstream temperature sensing locations as compared to the experimental measurement. The only tuning parameter in the CFD model is the Lee mass transfer coefficient. The CFD Model predicts the Liedenfrost rewetting temperature in close agreement with the experiment. This marks a transition between stable and transitionary flow boiling regimes. The CFD-predicted boiling curve for the downstream sensor location is also compared against its experimental counterpart and indicates that the model is able to predict all the key temperature and heat flux parameters during the transitions from stable to transitionary film boiling to nucleate boiling in close agreement with the experiment. A sequence of predicted volume fraction, and temperature contours depicting these transitions will be presented.
Evaporation Condensation↗
Force Balance Model Assessment for Mechanistic Prediction of Sliding Bubble Velocity in Vertical Subcooled Boiling Flow
The bubble sliding after departing from nucleation site is frequently observed in flow boiling systems and, the crucial impact on wall heat transfer has been evidenced through many experiments. As a result, the heat transfer modeling associated with sliding bubble has become one of the subjects of great attention in CFD boiling heat transfer community. The modeling efforts are primarily aimed at improving the existing Heat Flux Partitioning (HFP) model via the implementation of sliding bubble-induced heat transfer. The performance of HFP model depends inherently on the fidelity of sub-models used to predict the fundamental bubble parameters (e.g., bubble departure/lift-off diameter). In the same context, the accurate prediction of sliding bubble parameters (e.g., sliding bubble growth, sliding bubble velocity) is essential to achieving the successful heat transfer modeling associated with sliding bubble. Of many sliding bubble parameters, this paper deals with the sliding bubble velocity. Specifically, the force balance model was assessed in view of the sliding bubble velocity prediction. The parametric effect of key sub-models (e.g., drag force, bubble growth models) used in the force balance equation was investigated. The experimental data from Maity (2000) and Yoo et al. (2016) were used for demonstrating the model predictive performance. It was found that the force balance model proposed in this study was able to predict well the bubble sliding velocity based on the accurate prediction of bubble growth during sliding. The predictive performance was proven with the experimental data measured under various subcooled boiling conditions of both water and refrigerant (NOVEC-7000) flowing upward in vertical channels.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
A quantitative phase-field model for gas bubble evolution in UO2
Due to the large formation energy of vacancies and noble gas atoms in the form of interstitials or substitutional atoms in nuclear fuel (UO2), the thermodynamic equilibrium concentrations of these species are very low in the nuclear fuel matrix even at very high temperatures, which imposes difficulties upon the quantitative study of bubble evolution via the phase-field method. In this study, a quantitative phase-field model is proposed to deal with this problem. The system’s free energy density is derived according to the principles of thermodynamics, with consideration of the elastic effect and with the use of real material parameters from experiments. The model is useful for the study of the kinetics of gas bubble growth with very dilute concentrations of vacancy and gas atoms in the matrix. This model is applied to study single bubble growth and multiple bubble growth under various concentrations of vacancy and gas atoms and at various temperatures. The elastic effect and the effects of the generation rate of vacancies and gas atoms on bubble growth are analyzed.
low defect concentration, nuclear fuel, gas bubble↗
Defect cluster and nonequilibrium gas bubble associated growth in irradiated UMo fuels – a cluster dynamics and phase field model
Irradiation examination shows that gas bubble swelling kinetics is much faster after irradiation-induced recrystallization than that prior recrystallization in UMo fuels. It implies that gas bubbles in coarse grains and small recrystallized grains have different growth behavior. In this work, a phase-field model of gas bubble evolution integrating microstructure dependent cluster dynamics has been developed, for the first time, to study the gas bubble swelling behavior in the recrystallization zone of UMo fuels. Generation, diffusion, reaction, sink, emission and clustering of vacancies and interstitials are described by the cluster dynamics model while a phase-field model is used to describe the evolution of non-equilibrium gas bubbles including nucleation and growth. With the coupled model, the effect of defect generation rate, clustering rate, interstitial emission and sink rates on grain boundaries on the gas bubble evolution are systematically simulated. A set of model parameters (defect generation rate, clustering rate, interstitial emission and sink rates) is determined by comparing measured and simulated gas bubble swelling kinetics. The results demonstrate that interstitial clustering is one of the important physical mechanisms which results in a fast gas bubble swelling kinetics in the recrystallization zone. The developed model can also be extended to study the associated growth of defect and second phase precipitates often observed in irradiated materials.
Hu, Shenyang↗
Evolution of highly multimodal Rayleigh–Taylor instabilities
Rayleigh–Taylor (RT) instabilities are important fluid instabilities that arise in inertial confinement fusion (ICF) capsule implosions, and many other contexts. Multi-mode coupling is observed in experiments and plays a substantial role in material mix from RT instabilities. In this work, we study the evolution of highly multimodal perturbations (power law distribution) that approximate those found at manufactured material interfaces. We use simulations of over 2000 different perturbations in the LANL code xRAGE to identify distinct phases in the processes of bubble growth and bubble merger which can be visualized in a 2D phase portrait with clear regimes of mode growth and decay. Our results show that the dynamic evolution of the instability strongly depends on the mode of the perturbations and mode interactions. The merger process accelerates bubble growth. A non-Markovian region and a transition of the instability from: (1) initial exponential growth to (2) linear growth and to (3) quadratic growth and asymptotic behavior, are clearly captured in the phase space. We have developed a quantitative model of bubble growth that reproduces the dynamic behavior of ensembles of perturbations. Implications for ICF capsules designed for robustness against instabilities are discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A Mechanistic Study of Nucleate Boiling Heat Transfer Under Microgravity Conditions
Experimental studies of growth and detachment processes of a single bubble and multiple bubbles formed on a heated surface have been conducted in the parabola flights of KC-135 aircraft. Distilled water and PF5060 were used as the test liquids. A micro-fabricated test surface was designed and built. Artificial cavities of diameters 10 microns, 7 microns and 4 microns were made on a thin polished Silicon wafer that was electrically heated by a number of small heating elements on the back side in order to control the surface superheat. Bubble growth period, bubble size and shape from nucleation to departure were measured under subcooled and saturation conditions. Significantly larger bubble departure diameters and bubble growth periods than those at earth normal gravity were observed. Bubble departure diameters as large as 20 mm for water and 6 mm for PF5060 were observed as opposed to about 3 mm for water and less than 1 mm for PF5060 at earth normal gravity respectively. It is found that the bubble departure diameter can be approximately related to the gravity level through the relation D(sub d) proportional 1/g(exp 1/2). For water,the effect of wall superheat and liquid subcooling on bubble departure diameter is found to be small.The growth periods are found to be very sensitive to liquid subcooling at a given wall superheat. However,the preliminary results of single bubble dynamics using PF5060 showed that the departure diameter increases when wall superheat is elevated at the same gravity and subcooling. Growth period of single bubbles in water has been found to vary as t(sub g) proportional g(exp -.93). For water, when the magnitude of horizontal gravitational components was comparable to that of gravity normal to the surface, single bubbles slid along the heater surface and departed with smaller diameter at the same gravity level in the direction normal to the surface. For PF5060, even a very small horizontal gravitational component caused the sliding of bubble along the surface. The numerical simulation has been carried out by solving under the condition of axisymmetry, the mass, momentum, and energy equations for the vapor and the liquid phases. In the model the contribution of micro-layer has been included and instantaneous shape of the evolving vapor-liquid interface is determined from the analysis. Consistent with the experimental results, it is found that effect of reduced gravity is to stretch the growth period and bubble diameter It is found that effect of reduced gravity is to stretch the growth period and bubble diameter at departure. The numerical simulations are in good agreement with the experimental data for both the departure diameters and the growth periods. In the study on dynamics of multiple bubbles, horizontal merger of 2,3 4,and 5 bubbles was observed. It is found that after merger of 2 and 3 bubbles the equivalent diameter of the detached bubble is smaller than that of a single bubble departing at the same gravity level. During and after bubble merger, liquid still fills the space between the vapor stems so as to form mushroom type bubbles. The experimental and numerical studies conducted so far have brought us a step closer to prediction of nucleate boiling heat fluxes under low gravity conditions. Preparations for a space flight are continuing.
Dhir, V. K.↗
Steam chugging analysis in single-vent vapor injection
A complete cycle of the periodic steam chugging phenomenon is analyed. Steam velocity and pressure variations in the vent are described by one-dimensional conservation equations. This is coupled either to the water slug model when water is in the vent, or, the infinite pool spherical bubble model at the vent exit during bubble growth. An isolated spherical bubble model is used for computing the collapse pressures. Comparisons of the model predictions with the UCLA 1/12-scale and the Japan 1/6-scale data indicate that the vent-pipe model predicts the vent-clearing times and the bubble growth times well. In addition, the predicted maximum chugging heights compared well with those measured in the Japan data. On bubble collapse pressures, the comparison with the spherical bubble model predictions is only fair. The model generally overpredicts the magnitude of the spikes. On examining the effects of pool subcooling and steam mass flux, general agreement is found between the predicted trends and those measured.
Lee, C. K. B.↗
Investigation of Mechanisms Associated with Nucleate Boiling Under Microgravity Conditions
The focus of the present work is to experimentally study and to analytically/numerically model the mechanisms of growth of bubbles attached to, and sliding along, a heated surface. To control the location of the active cavities, the number, the spacing, and the nucleation superheat, artificial cavities will be formed on silicon wafers. In order to study the effect of magnitude of components of gravitational acceleration acting parallel to, and normal to the surface, experiments will be conducted on surfaces inclined at different angles including a downward facing surface. Information on the temperature field around bubbles, bubble shape and size, and bubble induced liquid velocities will be obtained through the use of holography, video/high speed photography and hydrogen bubble techniques, respectively. Analytical/numerical models will be developed to describe the heat transfer including that through the micro-macro layer underneath and around a bubble. In the micro layer model capillary and disjoining pressures will be included. Evolution of the interface along with induced liquid motion will be modelled. Subsequent to the world at normal gravity, experiments will be conducted in the KC-135 or the Lear jet especially to learn about bubble growth/detachment under low gravity conditions. Finally, an experiment will be defined to be conducted under long duration of microgravity conditions in the space shuttle. The experiment in the space shuttle will provide microgravity data on bubble growth and detachment and will lead to a validation of the nucleate boiling heat transfer model developed from the preceding studies performed at normal and low gravity (KC-135 or Lear jet) conditions.
Dhir, Vijay K.↗
Multiscale modeling for high burnup structure formation and associated pulverization
This report summarizes the lower length scale modeling work performed in the fiscal year 2023 under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to capture the microstrutural evolution and associated pulverization criteria in the high burnup regions. This year, the resolution mechanisms within the cluster dynamics code has been updated and it influence on the bubble growth in HBS regions at the mesoscale is studied. To improve the accuracy of phase-field models of fission gas bubble growth, a new Helmholtz free energy for high-density Xe gas is derived from a virial equation of state. Two previously used strategies for representing net vacancy production in phase-field models of fission gas bubble growth are compared with each other and with analytical models of bubble growth. The vacancy source only model is found to be more convenient to parameterize realistically compared with the vacancy source+sink model. Furthermore, the phase-field-fracture simulation have been performed using MD- informed failure stress values and realistic HBS structure obtained from the phase-field simulations. We also present the uncertainty bands on prediction of the critical stress to account for the effect of the lower length scale variabilities on the failure criteria at the mesoscale. It is observed that pulverization may occur in partially restructured regions with restructuring fraction as low as 17%. In light of this, an update to the BISON’s pulverization criteria is recommended.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗