Transient behavior of a molten salt fast reactor under two-phase flow conditions with helium bubbling
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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↗
Hydrate Formation on Marine Seep Bubbles and the Implications for Water Column Methane Dissolution
Abstract Methane released from seafloor seeps contributes to a number of benthic, water column, and atmospheric processes. At seafloor seeps within the methane hydrate stability zone, crystalline gas hydrate shells can form on methane bubbles while the bubbles are still in contact with the seafloor or as the bubbles begin ascending through the water column. These shells reduce methane dissolution rates, allowing hydrate‐coated bubbles to deliver methane to shallower depths in the water column than hydrate‐free bubbles. Here, we analyze seafloor videos from six deepwater seep sites associated with a diverse range of bubble‐release processes involving hydrate formation. Bubbles that grow rapidly are often hydrate‐free when released from the seafloor. As bubble growth slows and seafloor residence time increases, a hydrate coating can form on the bubble's gas‐water interface, fully coating most bubbles within ∼10 s of the onset of hydrate formation at the seafloor. This finding agrees with water‐column observations that most bubbles become hydrate‐coated after their initial ∼150 cm of rise, which takes about 10 s. Whether a bubble is coated or not at the seafloor affects how much methane a bubble contains and how quickly that methane dissolves during the bubble's rise through the water column. A simplified model shows that, after rising 150 cm above the seafloor, a bubble that grew a hydrate shell before releasing from the seafloor will have ∼5% more methane than a bubble of initial equal volume that did not grow a hydrate shell after it traveled to the same height.
54 ENVIRONMENTAL SCIENCES↗
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↗
Understanding the effect of minor alloying elements on helium bubble formation in ferritic-martensitic steels
Ferritic-martensitic steels are promising structural materials for advanced nuclear reactors. To minimize long-term radioactivity, reduced-activation ferritic-martensitic steels have been developed by substituting high-activation elements like Ni and Mo with low-activation elements such as W. However, the impact of these alloying modifications on helium bubble formation, which plays a key role in material swelling, remains unclear. Here, in this study, we compared helium bubble formation in ferritic-martensitic steel T91 and reduced-activation ferritic-martensitic steel F82H. Both materials were irradiated with sequential 100 keV, 150 keV, and 200 keV helium ions to a dose of 0.5 dpa and a helium concentration of 9,000 appm at 500°C. The helium bubbles in F82H exhibited a larger average size and a lower density than those in T91, suggesting differences in minor alloying elements may influence the bubble growth. Here, to investigate the effects of these alloying elements, we characterized radiation-induced segregation near bubbles and grain boundaries. Prominent Ni-Mn-Si enriched clusters were found near bubbles in T91, while only Mn-Si enriched clusters were found near bubbles in F82H. In addition, the obvious Cr enrichment near grain boundaries was absent around bubbles in both steels. The different segregation trends among elements revealed the variations in element diffusion mechanisms and the different sink biases between bubbles and grain boundaries. Cr enrichment near grain boundaries is mostly driven by interstitial-mediated diffusion. However, since bubble growth relies on net vacancy flux, vacancy-mediated diffusion plays a dominant role in controlling element segregation near bubbles. Therefore, Cr enrichment was not found near bubbles. Because of preferential vacancy-drag diffusion for Ni, Si and Mn, these elements were enriched near bubbles. Due to the strong binding energies of vacancies with these solute atoms, the vacancy diffusivity can be reduced near these solutes. Therefore, the more prominent Ni-Si-Mn clustered near helium bubbles in T91 lead to stronger suppression of helium bubble growth compared to F82H.
36 MATERIALS SCIENCE↗
Plasma breakdown in bubbles passing between two pin electrodes
The ignition of plasmas in liquids has applications from medical instrumentation to manipulation of liquid chemistry. Formation of plasmas directly in a liquid often requires prohibitively large voltages to initiate breakdown. Producing plasma streamers in bubbles submerged in a liquid with higher permittivity can significantly lower the voltage needed to initiate a discharge by reducing the electric field required to produce breakdown. The proximity of the bubble to the electrodes and the shape of the bubbles play critical roles in the manner in which the plasma is produced in, and propagates through, the bubble. In this paper, we discuss results from a three-dimensional direct numerical simulation (DNS) used to investigate the shapes of bubbles formed by injection of air into water. Comparisons are made to results from a companion experiment. A two-dimensional plasma hydrodynamics model was then used to capture the plasma streamer propagation in the bubble using a static bubble geometry generated by the DNS The simulations showed two different modes for streamer formation depending on the bubble shape. In an elliptical bubble, a short electron avalanche triggered a surface ionization wave (SIWs) resulting in plasma propagating along the surface of the bubble. In a circular bubble, an electron avalanche first traveled through the middle of the bubble before two SIWs began to propagate from the point closest to the grounded electrode where a volumetric streamer intersected the surface. In an elliptical bubble approaching a powered electrode in a pin-to-pin configuration, we experimentally observed streamer behavior that qualitatively corresponds with computational results. Optical emission captured over the lifetime of the streamer curve along the path of deformed bubbles, suggesting propagation of the streamer along the liquid/gas boundary interface. Plasma generation supported by the local field enhancement of the deformed bubble surface boundaries is a mechanism that is likely responsible for initiating streamer formation.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Quantitatively Monitoring Bubble-Flow at a Seep Site Offshore Oregon: Field Trials and Methodological Advances for Parallel Optical and Hydroacoustical Measurements
Two lander-based devices, the Bubble-Box and GasQuant-II, were used to investigate the spatial and temporal variability and total gas flow rates of a seep area offshore Oregon, United States. The Bubble-Box is a stereo camera–equipped lander that records bubbles inside a rising corridor with 80 Hz, allowing for automated image analyses of bubble size distributions and rising speeds. GasQuant is a hydroacoustic lander using a horizontally oriented multibeam swath to record the backscatter intensity of bubble streams passing the swath plain. The experimental set up at the Astoria Canyon site at a water depth of about 500 m aimed at calibrating the hydroacoustic GasQuant data with the visual Bubble-Box data for a spatial and temporal flow rate quantification of the site. For about 90 h in total, both systems were deployed simultaneously and pressure and temperature data were recorded using a CTD as well. Detailed image analyses show a Gaussian-like bubble size distribution of bubbles with a radius of 0.6–6 mm (mean 2.5 mm, std. dev. 0.25 mm); this is very similar to other measurements reported in the literature. Rising speeds ranged from 15 to 37 cm/s between 1- and 5-mm bubble sizes and are thus, in parts, slightly faster than reported elsewhere. Bubble sizes and calculated flow rates are rather constant over time at the two monitored bubble streams. Flow rates of these individual bubble streams are in the range of 544–1,278 mm 3 /s. One Bubble-Box data set was used to calibrate the acoustic backscatter response of the GasQuant data, enabling us to calculate a flow rate of the ensonified seep area (~1,700 m 2 ) that ranged from 4.98 to 8.33 L/min (5.38 × 10 6 to 9.01 × 10 6 CH 4 mol/year). Such flow rates are common for seep areas of similar size, and as such, this location is classified as a normally active seep area. For deriving these acoustically based flow rates, the detailed data pre-processing considered echogram gridding methods of the swath data and bubble responses at the respective water depth. The described method uses the inverse gas flow quantification approach and gives an in-depth example of the benefits of using acoustic and optical methods in tandem.
54 ENVIRONMENTAL SCIENCES↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗
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↗