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Bubble Departure Diameter and Bubble Release Frequency Measurement from TAMU Subcooled Flow Boiling Experiment

The bubble departure diameter and bubble release frequency were obtained through the analysis of TAMU subcooled flow boiling experimental data. The numerous images of bubbles at departure were analyzed for each experimental condition to achieve the reliable statistics of the measured bubble parameters. The results are provided in this report with simple discussion.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Experimental study on bubble dynamics and wall heat transfer arising from a single nucleation site at subcooled flow boiling conditions – Part 2: Data analysis on sliding bubble characteristics and associated wall heat transfer

In this second of two companion papers presents an analysis of sliding bubble and wall heat transfer parameters measured during subcooled boiling in a square, vertical, upward flow channel. Bubbles were generated only from a single nucleation site for better observation of both the sliding bubbles’ characteristics and their impact on wall heat transfer through optical measurement techniques. Specific interests include: (i) bubbles departure and subsequent growth while sliding, (ii) bubbles release frequency, (iii) coalescence of sliding bubbles, (iv) sliding bubbles velocity, (v) bubbles size distribution and (vi) wall heat transfer influenced by sliding bubbles. Our results showed that sliding bubbles involve two distinct growth behaviors: (i) at low mass fluxes, sliding bubbles grew fast near the nucleation site, subsequently shrank, and then grew again, (ii) as mass flux increased, however, sliding bubbles grew more steadily. The bubbles originating from the single nucleation site coalesced frequently while sliding, which showed close relation with bubbles release frequency. The sliding bubble velocity near the nucleation site consistently decreased by increasing mass flux, while the observation often became reversed as the bubbles slid downstream due to the effect of interfacial drag. The sliding bubbles moved faster than the local liquid (i.e., ur<0) at low mass flux conditions, but it became reversed as the mass flux increased. The size distribution of sliding bubbles followed Gaussian distribution well both near and far from the nucleation site. The standard deviation of bubble size varied insignificantly through sliding compared to the changes in mean bubble size. Lastly, the sliding bubbles enhanced the wall heat transfer and the effect became more noticeable as inlet subcooling/mass flux decreased or wall heat flux increased. Particularly, the sliding bubble characteristics such as bubble growth behavior observed near the nucleation site played a dominant role in determining the ultimate level of wall heat transfer enhancement within the test channel.

42 ENGINEERING↗

A Multi-scale Mathematical Model of Growth and Coalescence of Bubbles Beneath the Anode in an Aluminum Reduction Cell

Modeling of bubble shapes is challenging because of the wide range of length scales in aluminum reduction cells. A 3D multi-scale mathematical model was developed to understand the nucleation, growth and coalescence of bubbles beneath the anode and to investigate the transition of bubbles from the micro- to macro level. The motion of micro-bubbles is examined using the discrete bubble model (DBM) within a Lagrangian reference. An algorithm for the transition from discrete micro-bubbles to large bubbles, which are fully resolved by the volume of fluid (VOF) approach, is achieved using a user-defined function. The two-way coupling between discrete bubbles and continuous fluids is achieved by inter-phase momentum exchange. The model involves three kinds of bubble coalescence: micro-bubble coalescence is taken into account by the DBM; large bubbles swallowing up micro-bubbles are solved by the discrete-continuum transition model; the coalescence between large bubbles is handled by the VOF method. Numerical results show that the coverage and thickness of bubbles agree well with the experimental data in the literature. Bubble thickness stops increasing when the bubble elongates with the anode bottom, which is 4.0 to 4.5 mm. Meanwhile, two asymmetrical thick heads can be observed under the anode. Bubble release frequency increases with increasing current density.

36 MATERIALS SCIENCE↗

Nucleate boiling performance evaluation of cavities at mesoscale level

Nucleate boiling heat transfer (NBHT) from enhanced structures is an effective way to dissipate high heat flux. Here, a 3D multi-relaxation-time (MRT) phase-change lattice Boltzmann method in conjunction with conjugated heat transfer treatment is proposed and then applied to the study of cavities behaviours for nucleation on roughened surfaces for an entire ebullition cycle without introducing any artificial disturbance. The bubble departure diameter, departure frequency and total boiling heat transfer rate are also explored. We demonstrate that the cavity shapes show significant influence on the features of NBHT. The total heat transfer rate increases with the cavity mouth and cavity base area while decreases with the increase in cavity bottom wall thickness. The cavity with low wetting can enhance the heat transfer and improve the bubble release frequency.

42 ENGINEERING↗

Boiling Closure Model Validation/Development Effort with TAMU Experimental Data

This report describes a model validation and developmental effort in INL based on the analysis of experimental data taken from TAMU subcooled flow boiling facility. This report first describes briefly the test loop, experimental strategy, measurement techniques, data quality achieved, and test boundary conditions. Then, two main topics are discussed based on the experimental observation, bubble departure frequency and sliding bubble characteristics. The comparison of experimental data with the prediction of bubble departure frequency models shows that the predictive capability of existing models depends strongly on flow conditions. Also, the best performance region of each bubble departure frequency model could be determined from this analysis. Another critical achievement through this study is that the limitation of existing CFD boiling models dealing with sliding bubble effect was clearly identified. Specifically, the experimental observation indicates that the wall area influenced by sliding bubbles is not just a function of bubble size, but also depends strongly on sliding bubble trajectory and sliding distance. As a result, the bubble influence factor ( K ) for the small size of sliding bubbles was often found substantially higher than those reported in literature. In this regard, an effort is currently being made in INL to develop a new model to predict the sliding bubble effect on wall heat transfer based on the insight achieved from TAMU subcooled flow boiling experiment.

42 ENGINEERING↗

A model for trapping and re-solution regarding intra-granular bubbles in UO 2 , linked to atomic-scale simulations

In the literature, a clear definition of the irradiation re-solution frequency of gas from bubbles in the UO 2 fuel is absent. Moreover, for intra-granular bubbles, a detailed calculation of the cumulated displaced gas quantities in function of the distance from the radius of the bubble after a re-solution event has never been published. The assessment of these two elements is very useful if we want to increase the adherence of fission gas release codes to our present knowledge of the behavior of fission gases. Hence, we suggest to link the definition of the re-solution frequency to atomic-scale simulations. Furthermore, we present the cumulated displaced gas quantities obtained from Molecular Dynamics calculations, from which we have derived a re-solution profile that can be exploited to better consider the irradiation re-solution phenomenon inside Fission Gas Release codes. On top of that, we have built a new trapping/re-solution model for intra-granular bubbles linked to Molecular Dynamics simulations that can be easily incorporated into Fission Gas Release codes. In conclusion, we also check that the model is properly built through the comparison of the new model against a reference.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Dynamic Behavior of Natural Seep Vents: Analysis of Field and Laboratory Observations and Modeling (Final Scientific/Technical Report)

In this project, we have analyzed data collected by the U.S. Department of Energy (DOE), National Energy Technology Laboratory (NETL) in a high pressure water tunnel (HPWT) and data from two research cruises to natural seeps in the Gulf of Mexico to adapt and validate a numerical model to predict the dynamics of natural seeps in the deep oceans. The HPWT data include video observations of the shrinkage rate of individual methane and natural gas bubbles under simulated deep-water conditions. Field data were collected during two cruises by the Gulf Integrated Spill Research (GISR) Consortium led by Texas A&M University and funded by the Gulf of Mexico Research Initiative (GoMRI). These data included in situ observations from a remotely operated vehicle (ROV) of gas bubbles at two natural seep sites in the Gulf and acoustic observations of the natural seep bubble flares in the ocean water column. The acoustic data were from multibeam echosounders, one mounted in a forward-looking orientation on the ROV and another mounted down-looking in the haul of the ship. All of these laboratory and field data were focused on the dynamics of natural gas bubbles at temperatures and pressures favorable for clathrate hydrate formation between the gas and water. Our analyses of this data focused on understanding the mechanisms responsible for gas bubble dissolution within the hydrate stability zone (HSZ) of the oceans. Ice-like hydrate shells may form on the bubble-water interface under these conditions, and it was unknown how this might affect the mass transfer of gas into the ocean. We were able to extract bubble shrinkage rates from the HPWT datasets. Using this data we determined that mass transfer coefficients with and without a hydrate shell match empirical values for bubbles in contaminated systems (so-called dirty bubbles contaminated by naturally occurring surfactants). We also showed that free gas, and not gas hydrate, is the dominant dissolving phase when the hydrate sub-cooling is below 11 degree Celsius (temperature difference between hydrate the hydrate formation temperature and ambient temperator) or the pressure is reducing as bubbles rise through the ocean water column. Using this mass transfer model, our numerical model of bubble dissolution matched the over 200 HPWT experiments with an average error of 10% for predicting the bubble size at the end of an experiment. From field data in the literature, we also observed that gas bubbles dissolve faster when they are initially released, following mass transfer coefficients for so-called clean-bubbles (those not yet contaminated by surfactants). Shortly after release within the HSZ, a hydrate shell forms on the bubble-water interface, and the mass transfer reduces to rates matching those of dirty bubbles. We correlated this transition time from clean to dirty bubble behavior with the initial bubble surface area and the hydrate sub-cooling. With this model for hydrate formation time and using the mass transfer coefficients deduced from the HPWT data, we validated our numerical model for predicting the rise heights of natural seep flares in the oceans. Flare heights are commonly observed in haul-mounted acoustic multibeam data. The numerical model predicts bubbles to rise high in the ocean water column owing to the slower mass transfer rates for dirty bubbles that accompany the majority of their rise time. We found that the numerical model predictions matched the observed flare heights within 5% to 10% accuracy when we compared the rise heights of the largest bubbles released from the seafloor with the bubbles acoustically visible in the multibeam data. Bubbles become acoustically transparent as they shrink to sizes of order 1 mm in diameter for the multibeam frequencies used in the field. The forward-looking multibeam on the ROV also provided data on the lateral spreading of bubbles in natural seep flares. Our analysis of this data showed that spreading follows a diffusion process, with the effective diffusivity correlating with the wobbling length scale of these ellipsoidal bubbles. When we apply this diffusivity in a random displacement model of bubble spreading, our numerical simulations match closely the lateral spread observed by the M3 in the ocean water column. Finally, we compared the seep model predictions for the acoustic properties of these natural seep plumes with that observed by the acoustic instruments in the field. The M3 and EM 302 observations were converted to relative values of target strength using a calibration we obtained in the laboratory for the M3 and using an algorithm from the manufacturer for the EM 302. Comparing the numerical seep model to these data, we obtain good agreement over the whole height of rise of these bubble flares. This further validates the numerical model. Overall, our validated seep model captures the key dynamics of gas bubbles released from natural seeps in the oceans and helps to predict the fate of methane in the water column.

03 NATURAL GAS↗

Long-Term Measurements of Methane Ebullition From Thaw Ponds

Arctic regions are experiencing rapid warming, leading to permafrost thaw and formation of numerous water bodies. Although small ponds in particular are considered hot spots for methane (CH 4 ) release, long-term studies of CH 4 efflux from these surfaces are rare. We have collected an extensive data set of CH 4 ebullition (bubbling) measurements from eight small thaw ponds (<0.001 km 2 ) with different physical and hydrological characteristics over four summer seasons, the longest set of observations from thaw ponds to date. The measured fluxes were highly variable with an average of 20.0 mg CH 4 · m -2 · day -1 (median: 4.1 mg CH 4 · m -2 · day -1 , n = 2,063) which is higher than that of most nearby lakes. The ponds were categorized into four types based on clear and significant differences in bubble flux. We found that the amount of CH 4 released as bubbles from ponds was very weakly correlated with environmental variables, like air temperature and atmospheric pressure, and was potentially more related to differences in physical characteristics of the ponds. Using our measured average daily bubble flux plus the available literature, we estimate circumpolar thaw ponds <0.001 km 2 in size to emit between 0.2 and 1.0 Tg of CH 4 through ebullition. Our findings exemplify the importance of high-frequency measurements over long study periods in order to adequately capture the variability of these water bodies. Through the expansion of current spatial and temporal monitoring efforts, we can increase our ability to estimate CH 4 emissions from permafrost pond ecosystems now and in the future.

54 ENVIRONMENTAL SCIENCES↗

Report on simulation of fission gas and fission product diffusion in UO 2

In UO 2 nuclear fuel, the retention and release of fission gas atoms such as xenon (Xe) are important for nuclear fuel performance by, for example, reducing the fuel thermal conductivity, causing fuel swelling that leads to mechanical interaction with the clad, increasing the plenum pressure and reducing the fuel–clad gap thermal conductivity. We use multi-­scale simulations to determine fission gas diffusion mechanisms as well as the corresponding rates in UO 2 under both intrinsic and irradiation conditions. In addition to Xe and Kr, the fission products Zr, Ru, Ce, Y, La, Sr and Ba have been investigated. Density functional theory (DFT) calculations are used to study formation, binding and migration energies of small clusters of Xe atoms and vacancies. Empirical potential calculations enable us to determine the corresponding entropies and attempt frequencies for migration as well as investigate the properties of large clusters or small fission gas bubbles. A continuum reaction-­diffusion model is developed for Xe and point defects based on the mechanisms and rates obtained from atomistic simulations. Effective fission gas diffusivities are then obtained by solving this set of equations for different chemical and irradiation conditions using the MARMOT phase field code. The predictions are compared to available experimental data. The importance of the large Xe U3O cluster (a Xe atom in a uranium + oxygen vacancy trap site with two bound uranium vacancies) is emphasized, which is a consequence of its high mobility and high binding energy. We find that the Xe U3O cluster gives Xe diffusion coefficients that are higher for intrinsic conditions than under irradiation over a wide range of temperatures. Under irradiation the fast-­moving Xe U3O cluster recombines quickly with irradiation-induced interstitial U ions, while this mechanism is less important for intrinsic conditions. The net result is higher concentration of the Xe U3O cluster for intrinsic conditions than under irradiation. We speculate that differences in the irradiation conditions and their impact on the Xe U3O cluster can explain the wide range of diffusivities reported in experimental studies. However, all vacancy-­mediated mechanisms underestimate the Xe diffusivity compared to the empirical radiation-­enhanced rate used in most fission gas release models. We investigate the possibility that diffusion of small fission gas bubbles or extended Xe-­vacancy clusters may give rise to the observed radiation-­enhanced diffusion coefficient. These studies highlight the importance of U divacancies and an octahedron coordination of uranium vacancies encompassing a Xe fission gas atom. The latter cluster can migrate via a multistep mechanism with a rather low effective barrier, which together with irradiation-induced clusters of uranium vacancies, gives rise to the irradiation-enhanced diffusion coefficient observed in experiments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Soft interface instability and gas flow channeling in low-permeability deformable media

Understanding gas percolation through a clay layer or a shale formation is of great importance for the development of a geologic repository for nuclear waste disposal, a subsurface system for gas storage, and an engineering approach for hydrocarbon extraction from unconventional reservoirs. Gas injection experiments have revealed complex dynamic behaviours of gas percolation through water saturated compacted bentonite, characterized by a high breakthrough pressure, rapid breakthrough, a pressure/stress decay after the breakthrough, a relatively high migration rate, high-frequency periodic/nonperiodic variations in flow rate, stepwise rate reductions during relaxation, and low gas saturation over the whole process, all indicating channelling nature of the processes. Using linear stability analyses, we show that this channelling can autonomously emerge from the instability of the deformable interface between the injected gas and the compacted bentonite matrix driven by local stress concentration, pore dilation, and hydrologic gradient. Channel patterns formed would possess a fractal geometry. We further show that, once a percolating channel is established, the gas injected would percolate through the channel in a chain of gas bubbles, also due to the interface instability, resulting in periodic/chaotic variations in gas flow rate. Our work provides a unified explanation for key features observed for gas percolation in low-permeability deformable media. The work also suggests a possibility of designing an engineered barrier system for a nuclear waste repository that can have controllable gas release while limit water transport.

Bentonite↗