Bubble Rise Research Articles

Distributed Physics-Informed machine learning strategies for two-phase flows

This study delves into applying Distributed Learning Machines (DLM), a subset of Physics-Informed Neural Networks (PINN), in tackling benchmark challenges within two-phase flows. Specifically, two variants of DLM, namely Distributed Physics-Informed Neural Networks (DPINN) and Transfer Physics-Informed Neural Networks (TPINN), are studied. The DLM architecture strategically divides the global domain into distinct non-overlapping sub-domains, with interconnected solutions facilitated by interface conditions embedded in the loss function. Forward and inverse benchmark problems in two-phase flows are explored: (a) bubble in a reversing vortex and (b) Bubble Rising under Buoyancy. The Volume of Fluid (VOF) method handles interface transport in both scenarios, with the inverse problem incorporating interface-position data during the training phase. The forward problem highlights the effectiveness of DPINN in capturing the interface using a simple transport equation. The distinctive contribution of this work lies in its exploration of the inverse problem, offering insights into the scalability of distributed architectures when dealing with a system of governing equations. Following the validation of an initial PINN model against Computational Fluid Dynamics (CFD) data, the study extends to DPINN and TPINN. A parametric study optimizes network hyperparameters, emphasizing the regularization of loss terms within the DPINN loss function. A self-adaptive weighting strategy based on a Gaussian probabilistic model dynamically adjusts loss weights during training to overcome challenges associated with manual parameter tuning. The evaluation of accuracy against CFD data and published results underscore the efficacy of DLMs in addressing two-phase flow problems. Additionally, the computational efficiency of distributed networks is explored compared to traditional PINNs.

Numerical study of bubble rise in plunging breaking waves

During the occurrence of plunging wave breaking, a substantial number of multi-scale bubbles are generated. These submerged bubbles persist for extended periods and contribute to the distinct acoustic and optical characteristics of the wake. In this study, we utilize high-fidelity simulations, combined with the adaptive refinement strategy to accurately track bubbles of multi-scales during the entire rising stage. Unlike previous studies, our emphasis is specifically on investigating the process of bubble rising during plunging wave breaking. Comprehensive statistical analyses are performed and characteristics of bubbles across various scales are also provided. Our findings reveal that most bubbles are concentrated in small scales, while larger bubbles rapidly ascend to the surface or undergo fragmentation into smaller bubbles through breaking cascades eventually. A distinct stratification of bubble size distribution along the depth direction is observed. Bubble velocity distributions are also important characteristics that are frequently neglected in studies of plunging wave breaking. Bubbles primarily spread along the spanwise direction, with a uniform distribution of velocity in this dimension. The velocity distribution of bubbles displays asymmetric tails that extend to higher velocities, and within this high-velocity regime, a power law behavior is observed, similar to the size distributions. Ultimately, the flow field is left with only a few small bubbles, moving at an exceedingly low speed. Furthermore, dynamical evolution of bubble rise in plunging wave breaking is described in detail and we analyze the intricate interactions between bubbles and turbulent flows. We observe that vortices are predominantly generated in close proximity to the bubbles, and bubble motion plays a crucial role in initiating turbulent flows. Simultaneously, these vortices contribute to the fragmentation of large-scale bubbles, transforming them into smaller counterparts due to turbulent fluctuations.

Interaction of Two Gas Bubbles Rising One after Another in a Liquid

Interaction of Two Gas Bubbles Rising One after Another in a Liquid

Development of a simplified one-dimensional CDA bubble model

Sodium-cooled fast reactors (SFRs) have high safety with an extremely low probability of a core disruptive accident (CDA). However, from a defense-in-depth perspective, the CDA sequence is still worth studying. Severe accidents in SFRs, such as unprotected loss of flow, might lead to a CDA during which fuel and some fission products could be instantly released from a large CDA bubble through potential leak paths in the top shield structure. Therefore, a reasonable prediction of dynamic behavior of a large-scale bubble within the sodium pool is vital for accurately evaluating the migration of source terms. In this study, we propose a simplified one-dimensional CDA bubble model that can handle heat and mass transfer in two-phase multicomponent materials in different computational domains during the rising of bubbles through the sodium pool toward the cover-gas region. In this model, an entrainment model based on the Rayleigh–Taylor instability and Kelvin–Helmholtz instability was used to explain the coolant entrainment through the gas/liquid boundary and jet fragmentation. The model also addresses the mitigation effect of non-condensable gases on the condensation of fuel, steel and sodium vapor at bubble interface. We evaluated the model using a past experiment on the expansion of a two-phase, large bubble with high pressure in a stagnant liquid pool conducted by Purdue University in the late 1970 s using a 1/7-scale model of Clinch River Breeder Reactor. Good agreement with the experimental data demonstrates that the developed model can reasonably represent the essential characteristics of dynamic behavior of a large, high-pressure bubble with heat and mass transfer in two-phase multicomponent materials. This is valuable for evaluating the migration of the source terms, which will be carried out in future studies.

Machine learning enhanced exploration of bubble dynamics beneath a horizontal wall

A better understanding of the dynamic behavior of a single bubble rising and impacting on a horizontal substrate is crucial, yet it has traditionally been constrained by the necessity for demanding experiments and extensive time-consuming simulations. This work develops a machine learning-enhanced model to determine characteristic quantities for the dynamic behavior of rising bubbles beneath the horizontal wall based on Computational Fluid Dynamics (CFD) simulation. We establish an unprecedentedly extensive dataset from accurate CFD modeling, covering a vast range of values for input parameters: Galilei number (1∼100), Bond number (0.001∼20), and rising distance (0.1R∼40R). Three popular regression models (Support Vector Regression, Back Propagation Neural Network, and Random Forest) are trained to capture key features for the first bounce of a bubble after collision, exhibiting promising predictive capacity, generalization, and interpretability. Our current approach facilitates the generation of dense datasets, enabling finer interpolation and detection of the physical properties of the unknown fluids. This pioneering data-driven methodology paves the way for advancing our understanding and prediction of bubble dynamics, marking a significant contribution to fluid dynamics research.

Modeling electrolysis in reduced gravity: producing oxygen from in-situ resources at the moon and beyond

Molten Regolith Electrolysis, as an in situ resource utilization (ISRU) technology, has the potential to enable the production of oxygen and metallic alloys on the Lunar surface; opening new doors in Cis-Lunar, and eventually Martian space exploration. This research studies the fundamental physics which govern the formation, growth, detachment, and rise of electrolytic bubbles. To this end, computational fluid dynamic (CFD) models were developed and run, to simulate water electrolysis, molten salt electrolysis (MSE), and molten Lunar regolith (MRE) electrolysis across multiple reduced gravity levels. The results demonstrate that reduced gravity, electrode surface roughness (possibly due to surface degradation), fluid properties, and electrode orientation can all affect electrolytic efficiency and possibly even stall electrolysis by delaying bubble detachment. The findings of this research must be considered when designing and operating electrolysis systems at reduced gravity levels.

Gas Seepage and Pockmark Formation From Subsurface Reservoirs: Insights From Table‐Top Experiments

AbstractPockmarks are morphological depressions commonly observed in ocean and lake floors. Pockmarks form by fluid (typically gas) seepage thorough a sealing sedimentary layer, deforming and breaching the layer. The seepage‐induced sediment deformation mechanisms, and their links to the resulting pockmarks morphology, are not well understood. To bridge this gap, we conduct laboratory experiments in which gas seeps through a granular (sand) reservoir, overlaid by a (clay) seal, both submerged under water. We find that gas rises through the reservoir and accumulates at the seal base. Once sufficient gas over‐pressure is achieved, gas deforms the seal, and finally escapes via either: (a) doming of the seal followed by dome breaching via fracturing; (b) brittle faulting, delineating a plug, which is lifted by the gas seeping through the bounding faults; or (c) plastic deformation by bubbles ascending through the seal. The preferred mechanism is found to depend on the seal thickness and stiffness: in stiff seals, a transition from doming and fracturing to brittle faulting occurs as the thickness increases, whereas bubble rise is preferred in the most compliant, thickest seals. Seepage can also occur by mixed modes, such as bubbles rising in faults. Repeated seepage events suspend the sediment at the surface and create pockmarks. We present a quantitative analysis that explains the tendency for the various modes of deformation observed experimentally. Finally, we connect simple theoretical arguments with field observations, highlighting similarities and differences that bound the applicability of laboratory experiments to natural pockmarks.

The growth of a single rising bubble in viscous solution and the resulting volatile removal

In the foam devolatilization, volatiles are removed accompanying with the growth of rising bubbles, and determining the amount of removed volatile is important in the design of devolatilization device. In this work, acetone and polydimethylsiloxane were used as the volatile and polymer respectively to study the single bubble growth process in the foam devolatilization. The variation of single bubble spherical equivalent radius and rising velocity in viscous solution were experimentally determined, and the effects of operational parameters (i.e., polymer viscosity, vacuum degree, solution temperature and volatile concentration) on bubble growth were evaluated. By analyzing the mechanics of bubble devolatilization, and based on the mass transfer boundary layer theory, the mass of removed volatile during bubble rising is determined, together establishing a correlation to predict the volatile removal amount.

Numerical Study of Geometric Characteristics and Coalescence and Breakup Behavior during the Rise of Multiple Parallel Bubbles

Numerical Study of Geometric Characteristics and Coalescence and Breakup Behavior during the Rise of Multiple Parallel Bubbles

A lattice Boltzmann model for incompressible gas and liquid two-phase flows combined with free-surface method

A novel lattice Boltzmann (LB) model is proposed to study the gas and liquid two-phase flows with large density and viscosity ratios. In the model, both the gas and liquid phases are considered as viscous incompressible fluids, which are governed separately by the two-relaxation-time LB equations. They are coupled by a momentum exchange method at the interface. The interaction between the gas and liquid phases is explicitly described and naturally involved in the model. The interfacial conditions in the model are validated by the benchmarks of the layered Poiseuille flow and the Laplace law. The feasibility of combining this model with the bubble model and the wetting scheme is proven through transient flow problems of single bubble rising and capillary intrusion. The validity of this model is confirmed by more complex flows including solid–liquid–gas coupling and droplet breaking problems by simulating shearing a droplet on a substrate and a droplet falling on a liquid film. The results demonstrate that the present model can be used to describe both the gas and the liquid flows. This work provides a solution to model the simulation of the dynamical behaviors of multi-phase flows.

An experimental study of the dynamics and mass transfer of a rising bubble

In this work, the rise characteristics of shrinking CO2 and non-shrinking N2 bubbles in distilled water for a wide range of bubble sizes in ellipsoidal and wobbly regime (deq = 1.5 mm to 6.5 mm) have been investigated. For these bubbles, their size, trajectory, and rise velocity have been measured using a moving camera system, while the dissolved CO2 is qualitatively studied using a planar laser-induced fluorescence (P-LIF) technique. We explore the interplay between hydrodynamics and mass transfer using well-studied regimes in bubble behaviour. Our results show that the interrelation between mass transfer and bubble rise dynamics is quasi-steady in nature and strongly dependent on wake-induced effects: shape and path oscillations. Based on an analogy of the two phenomena, we conclude that the behaviour of smaller bubbles (<2 mm) as immobile spheres from a mass transfer perspective is not related to the mobility of the interface, but a lack of surface renewal of dissolved gas at the interface. We propose a mechanistic correlation for calculating the mass transfer coefficient, kL, in this regime of bubble size, using the knowledge of the drag coefficient.

Function of Solidification Pressure on the Rising and Breakup of Nitrogen Bubbles in Molten Steel

Function of Solidification Pressure on the Rising and Breakup of Nitrogen Bubbles in Molten Steel

Experimental study of interfacial mass transfer from single CO2 bubbles ascending in stagnant water

The study focuses on the interfacial mass transfer from single CO2 bubbles with initial diameter in the range of 0.7−3.0 mm in a vertical column with stagnant deionized water. The objective is to enhance the understanding of the intricate phenomena involved in interfacial mass transfer by examining the individual effects of the liquid-side mass transfer coefficient and the bubble size. The liquid-side mass transfer coefficient is found in this study to be influenced by both the initial bubble diameter and on the bubble age, i.e., the time the bubble is exposed to the liquid influences the obtained liquid-side mass transfer coefficient. Existing literature suggests that bubbles of diameter <2−3 mm behave as rigid spheres with immobile interface and reduced internal gas circulation, which negatively impact the interfacial mass transfer. The results obtained from this study show that the maximum value of the liquid-side mass transfer coefficient is obtained for bubbles of diameter 2.1−2.3 mm. For bubbles with a mean diameter ≤1.4 mm, the mean liquid-side mass transfer coefficient decreases with decreasing mean bubble diameter. A Lagrangian model description is used with various correlations for the liquid-side mass transfer coefficients to perform numerical simulations of the change in bubble volume during the bubble rise. The existing correlations for the liquid-side mass transfer coefficient give very different simulation results and fail to accurately capture the transient evolution of the bubble as it exposes to the mass transfer phenomenon and hydrostatic pressure gradient. The correlation for the liquid-side mass transfer coefficient proposed by Clift et al. (1978) is modified in this work, and the experimentally obtained data are well predicted by the new modified correlation.

Study of hydrodynamic processes in a two-phase layer above a submerged perforated sheet

To study the hydrodynamics of a two-phase flow over a submerged perforated sheet (SPS) and the entrainment of water droplets from the water-air interface, a “Bubbler” installation was built. The main observation tool was video recording of the process followed by data analysis. An SPS with two holes was used. Three experiments were performed with different air flow rates. A general picture of air flow was established: the rise of bubbles in the water volume under the SPS, the formation of an air blanket, air bubbling in the layer of water above the SPS, the formation and jump of water drops upward. For each air flow rate, the size of the bubbles in the two-phase layer and the size of the resulting droplets were determined. It was found that with increasing air flow, these parameters increase.

Generalized prediction for self-starting performance of two-dimensional hypersonic inlets

The acceleration self-starting performance of a hypersonic inlet is pivotal for ensuring the stable operation of a scramjet. While the geometric configuration of the internal contraction section (ICS) considerably influences the inlet's self-starting performance, the current prediction model solely considers the internal contraction ratio. To encompass the entire geometric configuration's influence on ICS, a generalized prediction model for the acceleration self-starting Mach number of critical hard unstart two-dimensional hypersonic inlets is proposed. This model calculates the theoretical reattachment pressure rise of the main separation bubble within the actual unstarted flow structure of the hypersonic inlet. Additionally, it computes the theoretical pressure rise assuming the main separation bubble is in a critical state. By comparing these pressures, the model evaluates whether the main separation bubble can be sustained under given incoming flow conditions, predicting the self-starting Mach number. This modeling approach offers broad adaptability to various ICS configurations and incoming flow Reynolds numbers. Each step of the prediction model and the final computational results underwent rigorous evaluation through unsteady numerical simulations. Remarkably, the prediction results demonstrated exceptional alignment with simulation outcomes, surpassing the accuracy of previous prediction methods.

Multi-fluid simulation of pool scrubbing in the bubble rise region of PECA experiment

Multi-fluid simulation of pool scrubbing in the bubble rise region of PECA experiment

Physics-informed neural networks for heat transfer prediction in two-phase flows

This paper presents data-driven simulations of two-phase fluid processes with heat transfer. A Physics-Informed Neural Network (PINN) was applied to capture the behaviour of phase interfaces in two-phase flows and model the hydrodynamics and heat transfer of flow configurations representative of established numerical test cases. The developed PINN approach was trained on simulation data derived from physically based Computational Fluid Dynamics (CFD) simulations with interface capturing. The present study considers fundamental problems, including tracking the rise of a single gas bubble in a denser fluid and exploring the heat transfer in the wake of a bubble rising close to a heated wall. Tracking of a rising bubble phase interface of fluids with disparate properties was performed, revealing a maximum error of only 5.2% at the interface edge and a maximum error of 2.8% at the position of the centre of mass. Inferred (hidden variable) flows are studied in addition to a purely extrapolative inverse isothermal bubble case. When no velocity data was supplied, velocity field predictions remained accurate. Rise of an inferred isothermal bubble with unseen fluid properties was found to produce a maximum mean-squared error of 0.28 and centre of mass error of 1.25%. For the case of the rising bubble with a hot wall, the maximum error in the temperature domain using specified boundary conditions was 6.8%, while the bubble position analysis reveals a maximum positional error of 3.6%. These results demonstrate that PINN is agnostic to geometry and fluid properties when studying the combined effects of convection and buoyancy on two-phase flows for the first time. This work serves as a starting point for PINN in multiphase cases involving heat transfer over a range of geometries. Eventually, PINN will be used in such cases to provide solutions for forward, inverse, and extrapolative cases. Each of which represent a dramatic saving in computational cost compared to traditional CFD.

Flash boiling and pressure recovery phenomenon during venting from liquid ammonia tank ullage

Liquid ammonia stored at elevated pressures undergoes phase change during tank venting. The paper describes a CFD model able to reproduce the INERIS experiment performed using 12 m3 volume tank when 300 kg of ammonia were vented during 460 s from the ullage through the pipe to the atmosphere. The model is based on the volume-of-fluid method combined with Lee’s model for mass transfer between phases. Extensive calibration trials were conducted to examine the impact of surrounding temperature conditions. It allowed to establish the range of time relaxation parameter values of Lee evaporation-condensation model specific for liquid ammonia tank venting. Simulations reproduced accurately the experimentally measured final pressure in the tank and the amount of ammonia released during venting. Liquid ammonia boiling is triggered by reduction of pressure and takes place throughout the liquid causing the pressure recovery phenomenon. Numerical simulations demonstrated that pressure recovery phenomenon is driven by the characteristic time delay associated with the rise of vapour bubbles generated by flash boiling and the subsequent release of evaporated ammonia into the tank ullage space. The developed CFD model can be used as a contemporary tool for safety engineering and development of tank management strategies for liquid ammonia storage.

The bubble size and rise velocity of bubble‐induced three‐phase inverse fluidized bed (BIFB)

AbstractThe bubble size and rise velocity were investigated in detail using a new telecentric photographic probe in a pilot‐scale bubble‐induced three‐phase inverse fluidized bed (BIFB). By the influence of the bubble flow behavior, the particle bed goes through four different flow regimes with increasing gas velocity in BIFB. An obvious normal bubble size distribution caused by bubble coalescence and breakup was observed. A parameter of “size span” was proposed to describe the distribution width of bubble size. The average bubble size increases with the axial distance from the column bottom and with the gas velocity until reaching a relatively stable size. The radial distributions of the average bubble size are almost uniform but experience a decreasing trend near the column wall. The bubble rise velocity increases with the bubble size and the gas velocity. An empirical equation was established to predict successfully the bubble rise velocity in BIFB.

Rising of asymmetric bubble through milli-tubes: Experimental, theoretical and numerical analysis

Appearance of Taylor bubble is ubiquitous in two-phase fluid flow through millimeter-sized tubes. Precise control over bubble generation and stability in those tubes are instrumental in unit processes in fine chemical industries. In this article, we systematically study the role of wall surface wettability in the structure and dynamics of the gaseous bubble flowing through water across milli-tubes. Specifically, from imaging experiments, we find that in a non-wettable milli-tube, the bubble loses its axial symmetry to reduce contact of the liquid phase with the tube wall. Moreover, we observe that the bubble speed is significantly higher in hydrophobic-coated tubes in comparison to the tubes without coating. Computational simulation balancing the viscous, gravitational, and surface forces recovers the observed effect of surface wettability on bubble shape and velocity. Finally, we establish the observed quantitative correlation between the bubble velocity and the surface wettability using an analytical model. Altogether, integrating experiments, numerical simulation, and theoretical analysis, we demonstrated the significant influence of wall-surface wettability in the shape and velocity of the Taylor bubble through milli-tubes.