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DOE OSTI2012

Oscillating plasma bubbles. I. Basic properties and instabilities

Plasma bubbles are created in an ambient discharge plasma. A bubble is a plasma volume of typically spherical shape, which is separated from the ambient plasma by a negatively biased grid of high transparency. Ions and electrons from the ambient plasma flow into the bubble volume. In steady state the flow of particles and currents is divergence-free, which is established by the plasma potential inside the bubble. The grid has two sheaths, one facing the ambient plasma, the other the bubble plasma. The inner sheath is observed to become unstable, causing the plasma potential in the bubble to oscillate. The instability arises from an excess of ions and a deficiency of electrons. Its frequency is in the range of the ion plasma frequency but depends on all parameters which influence the charge density in the sheath. When the grid voltage is very negative, electrons cannot enter the outer sheath, and the inner sheath becomes a virtual anode which reflects ions such that the bubble interior is empty. When an electron source is placed into the bubble it can neutralize the ions and the bubble refills. Without plasma sources or sinks the bubble plasma is extremely sensitive to perturbations by probes. Modified current-voltage characteristics of Langmuir and emissive probes are demonstrated. A sequence of papers first describes the basic steady-state properties, then the time evolution of bubbles, the effects of electron sources in bubbles, and the role of the grid and bubble geometry. The physics of plasma bubbles is important to several fields of basic plasma physics such as sheaths, sheath instabilities, diagnostic probes, electrostatic confinement, and current and space charge neutralization of beams.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

The role of irradiation-enhanced interstitial diffusion in over-pressurizing fission gas bubbles in UO 2

Fission gas bubbles in UO 2 nuclear fuel have been observed to exhibit pressures in excess of the equilibrium bubble pressure; however, the cause of bubble over-pressurization has not yet been demonstrated. The mechanical interaction between a bubble and the surrounding matrix or grain boundary depends on the internal pressure of the bubble and local stress state, such that over-pressurized bubbles are thought to be responsible for fragmentation and pulverization, when exposed to a temperature ramp. Here, in this work, we investigate the role of U interstitials, produced through irradiation, in over-pressurizing bubbles by using a combined molecular dynamics (MD) and cluster dynamics approach. Firstly, the energies for the capture of interstitials and vacancies by bubbles have been determined from MD as a function of the ratio of gas atoms to vacancies that make up the bubble. Secondly, these reaction energies have been implemented in the cluster dynamics code Centipede to predict bubble over-pressurization as a function of temperature for typical fission rates. It was found that there is a transition from low pressure bubbles (at high temperatures) to high pressure bubbles (at lower temperatures). The cause of this behavior was shown to be the creation of irradiation-induced interstitials that are highly mobile relative to vacancies at low temperature; whereas, vacancies are sufficiently mobile at high temperatures to limit bubble pressures. This result supports the hypothesis that over-pressurized bubbles form during steady-state operation and that this behavior is highly sensitive to the local pellet temperature.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

First demonstration of a scintillating xenon bubble chamber for detecting dark matter and coherent elastic neutrino-nucleus scattering

A 30-g xenon bubble chamber, operated at Northwestern University in June and November 2016, has for the first time observed simultaneous bubble nucleation and scintillation by nuclear recoils in a superheated liquid. This chamber is instrumented with a CCD camera for near-IR bubble imaging, a solar-blind photomultiplier tube to detect 175-nm xenon scintillation light, and a piezoelectric acoustic transducer to detect the ultrasonic emission from a growing bubble. The time of nucleation determined from the acoustic signal is used to correlate specific scintillation pulses with bubble-nucleating events. We report on data from this chamber for thermodynamic "Seitz" thresholds from 4.2 to 15.0 keV. The observed single- and multiple-bubble rates when exposed to a $^{252}$Cf neutron source indicate that, for an 8.3-keV thermodynamic threshold, the minimum nuclear recoil energy required to nucleate a bubble is $19\pm6$ keV (1$\sigma$ uncertainty). This is consistent with the observed scintillation spectrum for bubble-nucleating events. We see no evidence for bubble nucleation by gamma rays at any of the thresholds studied, setting a 90% C.L. upper limit of $6.3\times10^{-7}$ bubbles per gamma interaction at a 4.2-keV thermodynamic threshold. This indicates stronger gamma discrimination than in CF$_3$I bubble chambers, supporting the hypothesis that scintillation production suppresses bubble nucleation by electron recoils while nuclear recoils nucleate bubbles as usual. Finally, these measurements establish the noble-liquid bubble chamber as a promising new technology for the detection of weakly interacting massive particle dark matter and coherent elastic neutrino-nucleus scattering.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1994

Guest investigator program study: Physics of equatorial plasma bubbles

Plasma bubbles are large-scale (10 to 100 km) depletions in plasma density found in the night-time equatorial ionosphere. Their formation has been found to entail the upward transport of plasma over hundreds of kilometers in altitude, suggesting that bubbles play significant roles in the physics of many of the diverse and unique features found in the low-latitude ionosphere. In the simplest scenario, plasma bubbles appear first as perturbations in the bottomside F layer, which is linearly unstable to the gravitationally driven Rayleigh-Taylor instability. Once initiated, bubbles develop upward through the peak of the F layer into its topside (sometimes to altitudes in excess of 1000 km), a behavior predicted by the nonlinear form of the same instability. While good general agreement has been found between theory and observations, little is known about the detailed physics associated with plasma bubbles. Our research activity centered around two topics: the shape of plasma bubbles and associated electric fields, and the day-to-day variability in the occurrence of plasma bubbles. The first topic was pursued because of a divergence in view regarding the nonlinear physics associated with plasma bubble development. While the development of perturbations in isodensity contours in the bottomside F layer into plasma bubbles is well accepted, some believed bubbles to be cylinder-like closed regions of depleted plasma density that floated upward leaving a turbulent wake behind them (e.g., Woodman and LaHoz, 1976; Ott, 1978; Kelley and Ott, 1978). Our results, summarized in a paper submitted to the Journal of Geophysical Research, consisted of incoherent scatter radar measurements that showed unambiguously that the depleted region is wedgelike and not cylinderlike, and a case study and modeling of SM-D electric field instrument (EFI) measurements that showed that the absence of electric-field perturbations outside the plasma-depleted region is a distinct signature of wedge-shaped plasma bubbles. The second topic was pursued because the inability to predict the day-to-day occurrence of plasma bubbles indicated inadequate knowledge of the physics of plasma bubbles. An understanding of bubble formation requires an understanding of the roles of the various terms in the linearized growth rate of the collisional Rayleigh-Taylor instability. In our study, we examined electric-field perturbations found in SM-D EFI data and found that the seeding is more likely to be produced in the E region rather than the F region. The results of this investigation are presented in the Appendix of this report and will be submitted for publication in the Journal of Geophysical Research.

Tsunoda, Roland T.↗

NASA NTRS2000

Generation of Bubbly Suspensions in Low Gravity

Generation of a uniform monodisperse bubbly suspension in low gravity is a rather difficult task because bubbles do not detach as easily as on Earth. Under microgravity, the buoyancy force is not present to detach the bubbles as they are formed from the nozzles. One way to detach the bubbles is to establish a detaching force that helps their detachment from the orifice. The drag force, established by flowing a liquid in a cross or co-flow configuration with respect to the nozzle direction, provides this additional force and helps detach the bubbles as they are being formed. This paper is concerned with studying the generation of a bubbly suspension in low gravity in support of a flight definition experiment titled "Behavior of Rapidly Sheared Bubbly Suspension." Generation of a bubbly suspension, composed of 2 and 3 mm diameter bubbles with a standard deviation <10% of the bubble diameter, was identified as one of the most important engineering/science issues associated with the flight definition experiment. This paper summarizes the low gravity experiments that were conducted to explore various ways of making the suspension. Two approaches were investigated. The first was to generate the suspension via a chemical reaction between the continuous and dispersed phases using effervescent material, whereas the second considered the direct injection of air into the continuous phase. The results showed that the reaction method did not produce the desired bubble size distribution compared to the direct injection of bubbles. However, direct injection of air into the continuous phase (aqueous salt solution) resulted in uniform bubble-diameter distribution with acceptable bubble-diameter standard deviation.

Nahra, Henry K.↗

NASA NTRS1995

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.↗

DOE OSTI2023

Pressure fields produced by single-bubble collapse near a corner

Damage produced by repeated bubble collapse to neighboring rigid objects in hydraulic systems is an important consequence of cavitation. Although bubble collapse near a single wall has received significant attention in the past, few studies exist on the dynamics of bubbles collapsing near a corner, i.e., two flat rigid surfaces intersecting at a right angle. In this work we quantify the pressure fields produced by a single bubble collapsing near two perpendicular rigid walls. Using a high-order accurate shock- and interface-capturing method to solve the three-dimensional compressible Navier-Stokes equations for gas and liquid flows, we simulate the dynamics of a single bubble collapsing at different initial stand-off distances from the two walls. In contrast to a bubble collapsing near a single wall, the collapse of bubbles within a critical stand-off distance is not symmetric about the bisecting plane due to the interaction between the bubble and the second wall. The second wall affects the pressure produced during the collapse in the following ways: (i) For bubbles initially located sufficiently close to both walls, the reentrant jet produced during collapse no longer points in the direction normal to the closest wall but at an angle toward the corner, (ii) the part of the emitted shock with the highest amplitude propagates in line with the jet, and (iii) the bubble migrates in that same direction during its collapse with a dependence on the stand-off distance, consistent with predictions made using Kelvin impulse. The location of maximum pressure along the walls is measured for the different initial stand-off distances. Using acoustic arguments, we find a semiempirical relationship to predict the initial stand-off distances for which the maximum pressure occurs in the corner. Here we find that when the bubble is sufficiently close to equidistant from each boundary, the maximum pressure is observed in the corner due to the water-hammer and implosion shocks reflecting off the boundaries and intersecting in the corner. We also show that when bubbles are initially attached to either wall the wall pressure produced can be significantly increased compared to bubbles detached from either wall.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

A phase field study of the thermal migration of gas bubbles in UO 2 nuclear fuel under temperature gradient

Phase field models are developed to study the gas bubble migration in uranium dioxide nuclear fuel in which a large temperature gradient exists during the operation. In this work, thermal diffusion mechanism for nanosized gas bubbles and vapor transport process for micron-sized gas bubbles are considered, respectively. In both cases, gas bubbles migrate to the high-temperature area. Due to the velocity difference between leading and trailing edges of the gas bubbles, nanosized gas bubbles are elongated along the temperature gradient direction when thermal diffusion is dominated. Micron-sized gas bubbles are either compressed along temperature gradient direction to form lenticular shape bubbles or elongated along temperature gradient direction, depending on the location of the gas bubbles within the fuel pellet. Initial gas bubble radius has no significant effect on the gas bubble migration velocity for both thermal diffusion and vapor transport mechanisms. We notice that the shape change of the gas bubble due to vapor transport mechanism has no significant effect on the migration velocity. Furthermore, the center cavity formation is also captured by our model which is due to the migration and accumulation of lenticular gas bubbles at the center of the fuel pellet. The modeling results compare well with experimental observations and theoretical analysis in the literature.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Numerical analysis of coalescence-induced bubble departure for enhanced boiling heat transfer

Boiling heat transfer plays a crucial role in a wide range of applications, such as power generation, refrigeration, electronics cooling, and pharmaceutics. Among the various factors that influence boiling heat transfer, the dynamics of vapor bubble nucleation, growth, and departure from the heated surface stand out as particularly important. An emerging phenomenon that can promote the departure of bubbles smaller than the Fritz diameter is coalescence-induced departure. If the dynamics of this process are fully understood, then surfaces can be engineered to promote faster bubble departure and substantially increase the performance of boiling heat transfer. Further, this work expands on published results by presenting a detailed numerical analysis of bubble coalescence and departure for a range of initial bubble diameters and size ratios between coalescing bubbles. Analysis of the results is focused on explaining how the release of surface energy and bubble surface dynamics lead to bubble departure, as well as fundamentally distinguishing capillary–inertial jumping and buoyant–inertial departure mechanisms across different bubble sizes and size ratios. The results show that both the initial sizes of the coalescing bubbles and the ratio between their sizes can determine whether the merged bubble will leave the surface through capillary–inertial jumping or buoyant departure. Below a certain bubble size, the release of surface energy by the merger is not sufficient to propel the merged bubble from the surface.

42 ENGINEERING↗

DOE OSTI2014

Shock response of He bubbles in single crystal Cu

With large-scale molecular dynamics simulations, we investigate shock response of He nanobubbles in single crystal Cu. For sufficient bubble size or internal pressure, a prismatic dislocation loop may form around a bubble in unshocked Cu. The internal He pressure helps to stabilize the bubble against plastic deformation. However, the prismatic dislocation loops may partially heal but facilitate nucleation of new shear and prismatic dislocation loops. For strong shocks, the internal pressure also impedes internal jetting, while a bubble assists local melting; a high speed jet breaks a He bubble into pieces dispersed among Cu. Near-surface He bubbles may burst and form high velocity ejecta containing atoms and small fragments, while the ejecta velocities do not follow the three-dimensional Maxwell-Boltzmann distributions expected for thermal equilibrium. The biggest fragment size deceases with increasing shock strength. With a decrease in ligament thickness or an increase in He bubble size, the critical shock strength required for bubble bursting decreases, while the velocity range, space extension and average velocity component along the shock direction, increase. Small bubbles are more efficient in mass ejecting. Compared to voids and perfect single crystal Cu, He bubbles have pronounced effects on shock response including bubble/void collapse, Hugoniot elastic limit (HEL), deformation mechanisms, and surface jetting. HEL is the highest for perfect single crystal Cu with the same orientations, followed by He bubbles without pre-existing prismatic dislocation loops, and then voids. Complete void collapse and shear dislocations occur for embedded voids, as opposed to partial collapse, and shear and possibly prismatic dislocations for He bubbles. He bubbles lower the threshhold shock strength for ejecta formation, and increase ejecta velocity and ejected mass.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Linear oscillation of gas bubbles in a viscoelastic material under ultrasound irradiation

Acoustically forced oscillation of spherical gas bubbles in a viscoelastic material is studied through comparisons between experiments and linear theory. An experimental setup has been designed to visualize bubble dynamics in gelatin gels using a high-speed camera. A spherical gas bubble is created by focusing an infrared laser pulse into (gas-supersaturated) gelatin gels. The bubble radius (up to 150 μm) under mechanical equilibrium is controlled by gradual mass transfer of gases across the bubble interface. The linearized bubble dynamics are studied from the observation of spherical bubble oscillation driven by low-intensity, planar ultrasound driven at 28 kHz. It follows from the experiment for an isolated bubble that the frequency response in its volumetric oscillation was shifted to the high frequency side and its peak was suppressed as the gelatin concentration increases. The measurement is fitted to the linearized Rayleigh–Plesset equation coupled with the Voigt constitutive equation that models the behavior of linear viscoelastic solids; the fitting yields good agreement by tuning unknown values of the viscosity and rigidity, indicating that more complex phenomena including shear thinning, stress relaxation, and retardation do not play an important role for the small-amplitude oscillations. Moreover, the cases for bubble-bubble and bubble-wall systems are studied. The observed interaction effect on the linearized dynamics can be explained as well by a set of the Rayleigh–Plesset equations coupled through acoustic radiation among these systems. This suggests that this experimental setup can be applied to validate the model of bubble dynamics with more complex configuration such as a cloud of bubbles in viscoelastic materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2012

Enhanced Generic Phase-field Model of Irradiation Materials: Fission Gas Bubble Growth Kinetics in Polycrystalline UO 2

Experiments show that inter-granular and intra-granular gas bubbles have different growth kinetics which results in heterogeneous gas bubble microstructures in irradiated nuclear fuels. A science-based model predicting the heterogeneous microstructure evolution kinetics is desired, which enables one to study the effect of thermodynamic and kinetic properties of the system on gas bubble microstructure evolution kinetics and morphology, improve the understanding of the formation mechanisms of heterogeneous gas bubble microstructure, and provide the microstructure to macroscale approaches to study their impact on thermo-mechanical properties such as thermo-conductivity, gas release, volume swelling, and cracking. In our previous report 'Mesoscale Benchmark Demonstration, Problem 1: Mesoscale Simulations of Intra-granular Fission Gas Bubbles in UO 2 under Post-irradiation Thermal Annealing', we developed a phase-field model to simulate the intra-granular gas bubble evolution in a single crystal during post-irradiation thermal annealing. In this work, we enhanced the model by incorporating thermodynamic and kinetic properties at grain boundaries, which can be obtained from atomistic simulations, to simulate fission gas bubble growth kinetics in polycrystalline UO 2 fuels. The model takes into account of gas atom and vacancy diffusion, vacancy trapping and emission at defects, gas atom absorption and resolution at gas bubbles, internal pressure in gas bubbles, elastic interaction between defects and gas bubbles, and the difference of thermodynamic and kinetic properties in matrix and grain boundaries. We applied the model to simulate gas atom segregation at grain boundaries and the effect of interfacial energy and gas mobility on gas bubble morphology and growth kinetics in a bi-crystal UO 2 during post-irradiation thermal annealing. The preliminary results demonstrate that the model can produce the equilibrium thermodynamic properties and the morphology of gas bubbles at grain boundaries for given grain boundary properties. More validation of the model capability in polycrystalline is underway.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Experimental observations of shock-wave-induced bubble collapse and hot-spot formation in nitromethane liquid explosive

We studied the collapse of individual helium gas bubbles in the homogeneous explosive nitromethane (NM) to investigate effects of hot-spot formation on the detonation process. A bubble was injected into a NM sample, and a shock wave from an explosive detonator compressed the bubble, creating a localized hot spot. We measured shock and detonation wave speeds with optical velocimetry, and we used a high-speed camera to image the shock propagation and the pre- and post-bubble collapse processes. An infrared camera image showed the residual radiance temperature distribution after the bubble collapse, and an optical fiber pyrometer measured the time-resolved thermal radiance. We measured the optical spectra of light emitted from detonating NM without a bubble and from a collapsing bubble in shocked, undetonated NM. We estimated temperatures of the detonation fronts and of the hot spots formed by bubble collapse. To study the incipient detonation process, we performed all bubble collapse experiments at pressures below the threshold for creating a sustained detonation. Where the bubble collapsed, we observed an opaque, thermally emissive region believed to be chemical reaction products. Chemical reactions in NM can be produced with lower shock pressures (~1 GPa) when a helium bubble is present than without a bubble (~10 GPa). We used hydrodynamic modeling to predict shock wave propagation, extent of chemical reaction, and subsequent temperature rise from the collapsing bubble. Simulations using a temperature-dependent Arrhenius burn model gave much better results than reactive burn models that depend only on pressure and density.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2005

Measurement of the Shear Lift Force on a Bubble in a Channel Flow

Two-phase flow systems play vital roles in the design of some current and anticipated space applications of two-phase systems which include: thermal management systems, transfer line flow in cryogenic storage, space nuclear power facilities, design and operation of thermal bus, life support systems, propulsion systems, In Situ Resource Utilization (ISRU), and space processes for pharmaceutical applications. The design of two-phase flow systems for space applications requires a clear knowledge of the behaviors of the dispersed phase (bubble), its interaction with the continuous phase (liquid) and its effect on heat and mass transfer processes, The need to understand the bubble generation process arises from the fact that for all space applications, the size and distribution of bubbles are extremely crucial for heat and mass transfer control. One important force in two-phase flow systems is the lift force on a bubble or particle in a liquid shear flow. The shear lift is usually overwhelmed by buoyancy in normal gravity, but it becomes an important force in reduced gravity. Since the liquid flow is usually sheared because of the confining wall, the trajectories of bubbles and particles injected into the liquid flow are affected by the shear lift in reduced gravity. A series of experiments are performed to investigate the lift force on a bubble in a liquid shear flow and its effect on the detachment of a bubble from a wall under low gravity conditions. Experiments are executed in a Poiseuille flow in a channel. An air-water system is used in these experiments that are performed in the 2.2 second drop tower. A bubble is injected into the shear flow from a small injector and the shear lift is measured while the bubble is held stationary relative to the fluid. The trajectory of the bubble prior, during and after its detachment from the injector is investigated. The measured shear lift force is calculated from the trajectory of the bubble at the detachment point. These values for the shear lift are then compared with the theoretical predictions from various published works on shear lift in the open literature, which include asymptotic solutions at low bubble Reynolds number, potential flow predictions and numerical studies that deal with intermediate bubble Reynolds numbers.

Nahra, Henry K.↗

DOE OSTI2016

Spacer Grid and Mixing Vanes Effects Study on Two-phase Flow Using Bubble Tracking Simulations

In Light Water Reactor (LWR) cores, the nuclear fuel rods are arranged together as rod bundles in a triangular or square pattern. The fuel rod bundles are supported by the spacer grids with mixing vanes. An understanding of spacer grid and mixing vanes effect is important since it has a direct impact on the turbulence structure in the flow and the heat removal efficiency from the fuel rod surface. Although a considerable amount of literature has been published on the experimental investigation of spacer grid and mixing vanes effect, the measurements were mainly focused on single-phase flow. The influence of spacer grid and mixing vanes on two-phase flow is yet to be fully understood. Some preliminary research efforts have been invested in nuclear community. For example, Wheeler et al. experimentally studied the effects of spacer grid in air-water two-phase flow. Although mixing vanes are not considered, they presented interesting results of time-averaged two-phase flow quantities at upstream and downstream locations of the spacer grid. Over the past decades, the rapid development of High-Performance Computing (HPC) is allowing for the increasingly larger-scale high-fidelity simulations. Thanks to this favorable historical trend, Direct Numerical Simulation (DNS), integrated with Interface Tracking Methods (ITM), has been emerging as a valuable tool to complement and expand our ability to understand the two-phase flow phenomenon. Meanwhile, in order to make best use of the large-scale two-phase flow simulations, advanced data analysis techniques are being developed, as they enable the extraction of detailed parameters about individual bubble behavior. The level set ITM is utilized in our DNS flow solver, which makes use of a signed distance field. The gas-liquid interface is modeled by the zero level set. The level set method can be readily used to distinguish different phases based on the sign of corresponding level set value (e.g. the sign is positive in the liquid phase while negative in the gas phase.). However, the traditional level set approach is not able to collect calculated values and associate with specific bubbles when multiple (even thousands of) bubbles present in the simulations of two-phase flow. This drawback hinders the collection of useful bubble information, which can give us valuable insights about bubbly flows. For example, how the different local fluid conditions could affect bubble interfacial forces, bubble deformation level, and eventually the bubble distribution throughout the whole domain. A bubble tracking methodology has been developed to address the drawbacks and improve the data collection efficiency of level set based two-phase flow simulations. In the present work, a single Pressurized Water Reactor (PWR) subchannel with reduced size spacer grid and mixing vanes is chosen as the computational domain. The springs and dimples of the spacer grid are not represented for simplicity in the present investigation. The bubble tracking methodology is applied to the simulations of two-phase bubbly flow through spacer grid and mixing vanes region. In the intended simulation, the liquid turbulence will be fully resolved by DNS while the two-phase behaviors are captured by level set ITM. Bubble tracking data are to be processed to investigate the spacer grid and mixing vanes effect on two-phase bubbly flow. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2017

Effect of Slotted Anode on Gas Bubble Behaviors in Aluminum Reduction Cell

In the aluminum reduction cells, gas bubbles are generated at the bottom of the anode which eventually reduces the effective current contact area and the system efficiency. To encourage the removal of gas bubbles, slotted anode has been proposed and increasingly adopted by some industrial aluminum reduction cells. Nonetheless, the exact gas bubble removal mechanisms are yet to be fully understood. A three-dimensional (3D) transient, multiphase flow mathematical model coupled with magnetohydrodynamics has been developed to investigate the effect of slotted anode on the gas bubble movement. The Eulerian volume of fluid approach is applied to track the electrolyte (bath)–molten aluminum (metal) interface. Meanwhile, the Lagrangian discrete particle model is employed to handle the dynamics of gas bubbles with considerations of the buoyancy force, drag force, virtual mass force, and pressure gradient force. The gas bubble coalescence process is also taken into account based on the O’Rourke’s algorithm. The two-way coupling between discrete bubbles and fluids is achieved by the inter-phase momentum exchange. Numerical predictions are validated against the anode current variation in an industrial test. Comparing the results using slotted anode with the traditional one, the time-averaged gas bubble removal rate increases from 36 to 63 pct; confirming that the slotted anode provides more escaping ways and shortens the trajectories for gas bubbles. Furthermore, the slotted anode also reduces gas bubble’s residence time and the probability of coalescence. Moreover, the bubble layer thickness in aluminum cell with slotted anode is reduced about 3.5 mm (17.4 pct), so the resistance can be cut down for the sake of energy saving and the metal surface fluctuation amplitude is significantly reduced for the stable operation due to the slighter perturbation with smaller bubbles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

The effect of stress on the migration of He gas bubbles under a thermal gradient in Fe by phase-field modeling

Here a phase-field model is parameterized to study the effect of elastic stresses on the migration of He gas bubbles in Fe under a temperature gradient. Stresses caused by the gas bubble pressure and residual stress in the Fe matrix are considered. The dependence of He bubble migration velocity on the magnitude of the residual stress, average temperature, temperature gradient, and bubble size is measured. In agreement with a theoretical model based on surface diffusion, simulation results demonstrate that He bubbles move towards the high temperature region with velocities in Fe that are orders of magnitude faster than previously reported in UO 2 . It is found that local stresses in the matrix caused by the He bubble have negligible effect on the bubble migration process; however, residual stresses in the Fe matrix, potentially caused by processing or irradiation, can modestly modify bubble kinetics through pressure dependence of the He diffusion coefficients. Compressive residual stress decreases diffusion coefficients for bulk and surface diffusion mechanisms, thus reducing the migration velocity of the gas bubble. In contrast, tensile residual stress increases the diffusion coefficients, resulting in an increase in the gas bubble migration velocity. This pressure dependence is also consistent with a theoretical model. This phase field model lays the foundation for analysis of bubble coalescence-induced fracture in He bubble-containing steels.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Atomistic simulations of He bubbles in Beryllium

Formation of He bubbles can have a significant effect on the microstructural evolution and properties of irradiated materials. In this report, we use atomistic simulations based on machine learning potentials to investigate the fundamental behavior of He bubbles in Be, with a specific focus on the shape, stability, and diffusivity of bubbles. Stability of He bubbles is quantified in terms of formation energies, which are determined as a function of the ratio of He/V. We find that He bubbles become unstable with respect to plastic deformation through punch-out dislocations around the bubble when the He/V ratio is larger than ~1.25, and the punch-out process induces the change of the regular bubble shape. In general, the bubble shape of He in Be is found to be ellipsoid-like. It is also found that for a fixed He/V ratio, the bubble attracts vacancies to become larger in size. If the bubble size is constant, the bubble attracts additional He atoms until the punch-out reaction occurs. The dominant diffusion mechanism of He bubbles changes from surface diffusion to volume diffusion as the temperature is increased, with a crossover occurring at about 900 K.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗