Bubble Velocity Research Articles

Phase field simulation of single bubble behavior under magnetic field

By combining the continuum equation with the momentum equation, phase field and magnetic field, a three-dimensional multi-field coupled model of the single bubble rising dynamics in the gas–liquid two-phase flow is established. The phase field method is used to capture the two-phase interface and simulate the movement of the gas–liquid interface. Compare the model with the numerical simulation under the Level Set method, it turns out that the simulation effect of the model established by the phase field method is better. The effects of different magnetic field intensity on the rise velocity of bubble and bubble deformation under vertical and horizontal magnetic field are analyzed. The results show that the bubble stretches along the magnetic field line under the action of the magnetic field, and the degree of bubble deformation is proportional to the intensity of the magnetic field. The rising speed of the bubble is affected by the magnetic field, which speeds up the overall rising speed of the bubble in the vertical direction and slows down the rising speed of the bubble in the horizontal direction.

Intrusive effects of dual-tip conductivity probes on bubble measurements in a wide velocity range

High-velocity air-water flows in hydraulic structures, such as spillways and low-level outlets, are characterised by high turbulence levels and strong self-aeration. In air-water flows, the void fraction varies from values close to zero at the invert up to near unity in the upper spray region. Because of the strong aeration, non-intrusive optical measurement techniques can only be applied to a limited extent, and intrusive phase-detection probes are widely used to estimate air-water flow properties, including void fraction, interfacial velocity, and chord sizes. However, these probes are often used without independent validation. Herein, this study systematically investigated the uncertainties of phase-detection probe measurements of individual bubbles traveling at a wide range of velocities (up to 7.5 m/s) in a vertically upward bubbly pipe flow. Velocities and chord times of air bubbles were simultaneously measured with an intrusive dual-tip conductivity probe and stereo-view high-speed videos, and a comparative analysis identified various effects of bubble-probe interactions on the measurement accuracy of the bubble velocities. The bubble deceleration due to these bubble-probe interactions were quantified. For standard interactions (i.e., bubbles undergoing no significant deformation and slowing down), the velocity estimates compared well with a theoretical model (errors less than 2 %), while larger errors were found for non-standard interactions such as those characterised by crawling, drifting, and waking mechanisms. In addition, a novel correction scheme for chord times was proposed, improving the accuracy of chord length, bubble size and void fraction estimations in air-water flows.

Quantification and correlation analysis of bubble characteristics and heat transfer performance in direct contact heat exchanger

In this work, a combination of morphological processing and watershed algorithm is proposed to measure bubble size, based on which an improved frame difference method is proposed to obtain bubble velocities with an F1 score of 0.96. Empirical equations for the boiling properties of flow in immiscible fluids and their influencing factors are developed. Correlation equations for the Nusselt (Nu) number and Colburn (j) factor are developed, with mean deviations of 5.42% and 5.47%, respectively. The results show that the increase in bubble rise rate and the trend of bubble growth become slower with the increase in the flow rate of the dispersed phase. In contrast, the temperature of the continuous phase has a negative correlation on the bubble growth and almost no effect on the bubble velocity. In addition, the heat transfer coefficient, which increases with the increase of the flow rate of the dispersed phase, has a negative correlation with the initial temperature difference. The main objective of this study is to provide a new method for measuring bubble parameters during direct contact boiling heat transfer and to provide new ideas for studying direct contact boiling heat transfer.

The role of the water–air and pulp-froth interfaces on particle detachment: Impact of particle size, type, contact angle and bubble rise velocity

Although the pulp-froth interface is thought to be very important to particle detachment and therefore overall flotation recovery, experimental evidence to back this is contradictory with recent observation indicating that detachment may not be as rigorous as previously thought. We investigate the effect of the interface (air–water and froth-water) on particle detachment as function of particle size, density, hydrophobicity, and bubble sizes. Bubbles were loaded with particles of size classes between 53 µm and 1018 µm and were allowed to collide with the a given interface while videos of the interaction were taken. using a high-speed video camera. The results from the experiments indicate that particles attached to bubbles do not detach when a loaded bubble collides with the interfaces. Further, the particle properties - (size and type of the particles, and contact angle) and bubble had no influence on particle detachment at the interface. However, the particles attached as agglomerates dropped off upon impact and as a result of bubble shape deformations. Further, observations from the water froth interface show that the impact upon collision can significantly shake of particles from within the froth while the particles on the bubble remain attached. Under our experimental conditions, coalescence was also observed not to be as rapid, with loaded bubbles remaining in contact with the water-froth interface for not less than 26 s.

Computational fluid dynamics modeling and mass transfer study of an in situ gas production process

AbstractThe oxidation of cyclohexanone with nitric acid in microreactors, as a representative chemical reaction with in situ gas production, was selected as the model reaction for computational fluid dynamics (CFD) modeling. The reaction kinetics was coupled with the CFD model by user‐defined functions (UDFs) to obtain the velocity field of liquid phase, the concentration field of products, and the temperature field of gas–liquid phases during the reaction process. The simulation results were then validated by the experimental data. Based on the established model, the fluid flow behavior and mass transfer characteristics during the in situ gas production process in a microreactor were further analyzed. Finally, the effects of channel diameter and bubble velocity on gas–liquid interfacial mass transfer were investigated. This work provides an effective method for studying in situ gas production processes through modeling and simulation, which is valuable in the design and optimization of tubular reactors.

Comparison of bubble parameters in natural and chemical surfactant solutions: a force analysis

The authors have investigated the potential of a plant-based natural surfactant in the modification of various bubble parameters. Bubble dynamics at the orifice were studied in natural surfactant solutions extracted from the plant Sapindus mukorossi at concentrations below and above its critical micellar concentration (CMC). The results were compared to the ones obtained with Sodium Dodecyl Sulfate solutions. The CMC values of Sapindus mukorossi and Sodium Dodecyl Sulfate are 7.5 × 10−3 g/cc and 2.39 × 10−3 g/cc, respectively. A photographic method was employed to observe bubble formation at the orifice. The results show that biosurfactants, like chemical surfactants, have a comparable effect on bubble density, size, and rise velocity. Experimentally determined bubble radius, volume, and radial velocity were used to calculate various forces contributing to the bubble dynamics. The buoyancy, pressure, and surface tension forces were significantly stronger in magnitude in comparison to the gas momentum, viscous drag, and added mass forces. Our findings suggest that the significance of various dynamic forces involved in bubble growth dynamics varies according to the bubble generation frequency regimes. We report for the first time the potential of Sapindus mukorossi in altering bubble properties and surface forces at the orifice and its usage in various bubble-related industrial applications.

Fate of bubble clusters rising in a quiescent liquid

We use experiments to study the evolution of bubble clusters in a swarm of freely rising, deformable bubbles. A new machine learning-aided algorithm allows us to identify and track bubbles in clusters and measure the cluster lifetimes. The results indicate that contamination in the carrier liquid can enhance the formation of bubble clusters and prolong the cluster lifetimes. The mean bubble rise velocities conditioned on the bubble cluster size are also explored, and we find a positive correlation between the cluster size and the rise speed of the bubbles in the cluster, with clustered bubbles rising up to $20\,\%$ faster than unclustered bubbles.

Numerical simulation of the motion and interaction of bubble pair rising in a quiescent liquid

In the present study, the motion and interaction of a bubble pair rising in a stationary liquid are simulated in two dimensions using the volume of fluid method (VOF) in the open-source CFD package OpenFOAM. For validation, the single bubble rising for different regimes was simulated. Comparing the present study results and previous numerical and experimental results showed that the results have a good agreement. In the present study, the bubble pair is arranged along a horizontal line, and results showed that in 2D domain four different interactions happen between the bubble pair rising based on the Bond (Bo) and Morton (Mo) numbers which are: coalescence, bouncing, zigzagging, and breakup. The simulations are done at three different slopes of the line connecting the center of two bubbles (θ=[0°, 45°, and 90°]), which shows the different arrangements of bubble pairs. At θ=90°, due to the attraction created by the wake of the leading bubble, the trailing bubble gets a significant acceleration in its motion, and will coalesce in the absence of surfactants. The results showed that the value of the trailing bubble velocity increases with decreasing the separation distance between the bubbles. Also, the rising velocity of the trailing bubble is always greater than the velocity of a single bubble due to the attraction effect of the leading bubble’s wake. The drag force of a trailing bubble decreases with decreasing the separation distance between the bubbles. Finally, a general criterion based on dimensionless numbers of Bo and Mo is presented to determine the type of interaction between bubble pair.

Investigation of Taylor bubble dynamics in annular conduits with counter-current flow

This study numerically investigates counter-current slug flow by considering the motion of a Taylor bubble in annular conduits with downward-flowing liquids using the Volume-of-Fluid method implemented in the commercial computational fluid dynamics software ANSYS Fluent (Release 19.2). The translational velocity of a counter-current ascending or co-current descending Taylor bubble in vertical concentric annuli and the corresponding distribution parameter (C0) are analyzed. The latter is correlated in terms of Eötvös number (Eo) and inverse viscosity number (Nf) within the range of Eo between 40 and 400 and Nf between 40 and 320. The proposed correlation provides an accurate fit to the numerical data with an average error of 2.64%, and is successfully compared with published numerical findings. In general, the smooth and stable shape of the bubble is disrupted as the counter-current flow velocity (Frl) increases above a critical value, leading to the formation of surface waves and the displacement of the bubble tip away from the annular gap center and towards the outer pipe. C0 increases with Eo and Nf, plateauing at high values of Eo. The effects of annulus inclination (θ) and eccentricity (ε) on bubble rise velocity are examined within the common range of θ and ε encountered during the drilling of oil, gas, or geothermal wells, i.e. 0° ≤ θ ≤ 60° and 0 ≤ ε ≤ 0.7, and their impact on the C0. The increasing Frl and θ lead to a streamlined bubble with pointed nose and thus a reduction in the wrap angle (θwrap), ultimately leading to reduced drag compared to the vertical annulus case and a decrease in C0. As the ε increases, which is accompanied by an increase in the degree of bubble eccentricity, the corresponding C0 decreases. For a constant Eo = 100 and Nf = 160 with inclination angle of θ = 40°and eccentricity of ε = 0.5, the C0 < 1 is observed.

Bubble detection in liquid metal by perturbation of eddy currents: Model and experiments

A model has been developed to predict the response of an eddy current flow meter (ECFM) to the passage of a non-conductive inclusion moving in a cylindrical tube filled with a liquid metal. The model can be solved analytically for small inclusion diameters and moderate AC frequencies of the excitation signal. This condition is expressed as vbSω≪1, where vb is the dimensionless inclusion volume and Sω is a function of the ratio between the characteristic length of the system and the penetration depth of the magnetic field. The magnetic induction equation for this problem has also been solved numerically. A very good agreement between the analytical model and numerical solutions has been found for vbSω≪1. Two experimental setups have been designed. First, the ECFM model has been validated by comparing the response due to the passage of traveling beads of known diameters in a low melting point alloy. In a second experiment, the diameters of ascending argon bubbles have been estimated with the ECFM model. The numerical model predicts the gas volume with very good accuracy in the range of bubble diameters studied, between 1.5 and 6 mm, while the analytical model only deviates significantly from the experimental data when vbSω≳0.1. Moreover, we establish that the ECFM can also measure the radial deviation of the bubble trajectory, and the results are consistent with the theoretical limit for isolated bubbles between the regimes of oscillating/zigzag motion of ellipsoidal bubbles and non-oscillating motion of spherical bubbles. Another observation is that the dependence of the ECFM response on the shape of the bubble is negligible; indeed, the ECFM response is well approximated by a linear relation with the bubble volume as is assumed in the analytical model. Finally, an estimation of the terminal rising velocity of bubbles was also carried out.

Direct measurements of gas flux at seep sites using a broadband split-beam echosounder

Measurement of methane gas flux from oceanic seep sites is challenging, given the ephemeral nature and the heterogeneous spatial distribution of seeps. Acoustic systems offer a solution, as they make synoptic measurements of the water column, and the gas bubbles are strong acoustic scatterers. Here, we present a method to directly estimate gas flux using a calibrated broadband split-beam echosounder. The vertical range resolution of the broadband system facilitates discrimination of individual bubbles in the acoustic record. By comparing measurements of bubble target strength to an analytical scattering model, bubble radii can be directly measured from the acoustic data. Concurrently, split-aperture processing allows for the precise tracking of bubbles as they rise from the seafloor for measurement of bubble rise velocity. Together, the observations of bubble radius and rise velocity offer a measure of gas flux, requiring nothing more than a vessel transiting over a seep site. Application of this method to seep data collected on the East Siberian Arctic Shelf shows good agreement between resulting measurements of bubble radii (0.68–8.40 mm) with those made using optical sensors, and bubble rise velocities (4–36 cm/s) are consistent with published measurements and models. Extrapolating from single bubbles measurements, our estimates of regional methane flux (2.9 × 104 kg/year) suggest that carbon emissions in this region may be lower than previously believed.

Experimental study of boiling heat transfer of inclined down-ward facing heated curved wall under low flow and pressure conditions

This study aims to investigate the behavior of bubbles and the mechanisms of heat transfer in a downward-facing curved channel under boiling flow conditions. A curved wall, representing a portion of the external surface geometry of a nuclear light water reactor vessel, is used to examine the influence of channel curvature on boiling phenomena. Experiments are conducted across a range of heat fluxes to understand the behavior of bubbles and slugs at different thermal loads on the curved surface. High-speed videography is employed to visualize bubble dynamics and their impact on heat transfer. The study quantifies parameters such as slug bubble velocity, length, width, and frequency, and examines their dependence on heat flux. The findings reveal that under a heat flux range of 30 to 100 kW/m2, the bubble motion and dynamics exhibit varying patterns, with the generation of smaller and faster bubbles. At approximately 150–200 kW/m2, a transition phase occurs, alternating between isolated nucleates and the formation of large slugs. Beyond 200 kW/m2, in the slug boiling regime, bubbles undergo substantial transformations, characterized by the emergence of larger vapor structures and more intricate boiling patterns. The resulting heat transfer rate is, thus, affected by the dynamics and behavior of these vapor structures, as well as the streamwise evolving thermal boundary layer and the surface curvature of the heater.

Gas-liquid hydrodynamics of a fractal flow mixer

Gas-liquid hydrodynamics of a micro-structured device (fractal flow mixer) was experimentally investigated. Experiments were conducted for a range of liquid-to-gas superficial velocity ratios (VSL/VSG). High-speed imaging was used to identify the flow regimes inside the microchannels of the device at different VSL/VSG. At different VSL/VSG, two or more flow regimes were observed simultaneously in different micro-channels. Consequently, a new flow regime map was developed. An optical probe was used to measure the bubble mean size and velocity. The effect of the VSL/VSG towards the bubble mean size, mean velocity, and frequency were analyzed. The bubble mean size decreases with the increase of the VSL/VSG, which can be attributed to the uniform shearing of gas slugs across all channels. To check the consistency of the fractal flow mixer in producing gas bubbles over a single experiment run, the global relative standard deviation (RSD) was used. The fractal flow mixer was able to generate equal flow distribution across the 16 outlets and maintain a Taylor flow over a range of VSL/VSG. . However, depending on the VSL/VSG, the GB and GS vary to a certain extent, governed by the capillary effect and the back-pressure.

Hydrodynamic modifications in vertical bubble plumes by a grid-screen

Air injection through a single circular nozzle has been used for aeration enhancement, oxygen transfer, and mixing in natural lakes and reservoirs. A series of laboratory experiments with different hydrodynamic conditions was carried out to improve mixing capacity and entrainment in vertically discharged bubble plumes. Hydrodynamic modifications were performed by inserting a grid-screen with different openings and distances from the nozzle and hydrodynamic modifications were examined for different air discharges. Bubble plume characteristics such as bubble concentration and velocity were measured along the vertical axis of the plume using an accurate Refractive Bubble Index (RBI) probe. Utilizing bubble concentration and bubble velocity data, the hydrodynamic forces such as buoyancy, drag, added mass, and surface tension were calculated before and after the grid-screen to evaluate modification by a grid-screen. The bubble induced force acting on the grid-screen was then calculated by implementing the momentum transfer at the vicinity of the grid-screen. The effects of grid-screen openings, the location of grid-screen respect to the nozzle, and air discharge on the contributed forces were examined to design the optimum operation condition. The results indicated that the grid-screen size and its distance from the nozzle decreased the buoyancy and drag forces after the grid-screen by 49% and 42%, respectively. Non-linear correlations between the hydrodynamic forces and bubble Reynolds number were proposed indicating that all contributing forces increased with increasing bubble Reynolds number. Empirical models were also developed for prediction of surface tension and bubble induced forces on the grid-screen.

Bubble behavior in a vacuum fluidized bed

Bubble behavior in a vacuum fluidized bed was investigated in this work. Experimental results showed that bubble diameter and rise velocity increased with declining the pressure, whereas bubble density decreased. The evolution of bubble density with bed height could be divided into three stages on the basis of the corresponding net-coalescence rates. The decrease in bubble density in the bottom region accelerated as the pressure decreased, whereas the increase in bubble density in the top region was gentle. Increasing the vacuum degree enlarged the variation in bubble size, resulting in the decline of operating stability in the fluidized bed. A new correlation that considered the effect of operating pressure on bubble behaviors exhibited accurate prediction in the vacuum fluidized bed. Bubble velocity was proportional to bubble diameter for small bubbles, and bed structure obviously affected the rise velocity of large bubbles. The distribution of the bubble aspect ratio was positively skewed and many bubbles had a tendency to become slender as the operating pressure decreased.

Numerical study of bubble rise in a three-dimensional sinusoidal channel

The bubble formation phenomenon and its movement have numerous applications in the shipbuilding, nuclear, mechanical, and ocean industries. Thus, a complete understanding of bubble rise is of immense importance in the fields mentioned above. Although, even after a plethora of research, a significant understanding of bubble wobbling and path instability still needs to be achieved. Furthermore, the complexity increases when a bubble rises in complex channels. Although various two-dimensional studies have attempted to report the bubble wobbling in the complex channels, a three-dimensional study on it still needs to be explored. Thus, in the present study, we attempted to report the bubble rise tendency in a three-dimensional sinusoidal channel. As bubble rise velocity plays a significant role in bubble wobbling, we attempted to study the bubble's path instability and rising velocity at different Reynolds numbers (Re) and Bond numbers (Bo). The maximum bubble rise velocity was observed to increase with Reynolds number (Re) while it decreases with an increase in Bond number (Bo). Furthermore, the wobbling tendency was also less in three-dimensional cases compared to previously reported two-dimensional studies. The bubble wobbling was reported to increase with the Reynolds number with a more periodic nature of the velocity profile. Bubble wobbling increased with an increase in a Bond number less than 9. The multi-phase simulation was performed on the open-source solver Gerris. The present study unveiled various aspects of bubble rise in three-dimensional sinusoidal channels and highlighted the role of rising velocity in the path instability of bubble rise.

Using Multiscale Direct Simulation Approach to Understanding Transports Behavior Inside PEM Water Electrolyzer

In this work, numerical modeling techniques were developed to predict oxygen bubble evolution through complex pore geometries to provide information of gas transport pathways inside saturated porous transport layers (PTL). Each PTL undergoes an image processing technique that uses X-ray CT images to generate accurate 3D microstructures. An example of a generated PTL structure is shown in Figure 1.Historically, meshing of the complex geometry was tedious and non-automated. Due to the random particle size across the geometry, a constant base size for meshing resulted in an inadequate mesh for accurate predictions. The Lattice-Boltzmann method is therefore more commonly used because a lattice is easier than a finite volume mesh to generate. Although sufficiently fine lattices adhered to the topology of the physical structure, simulations required a timestep between 1e-8 and 1e-10 seconds, resulting in long computational time.Meshing techniques have improved and can now be applied to complex geometries. Using the finite volume method accompanied with an adaptive mesh and adaptive time scale, provides an accurate representation of the PTL structure and larger timesteps. A volume of fluid (VoF) method was used to model two phase flow, using liquid water and gaseous oxygen, through different PTL structures. Evolution, growth, size, velocity, and surface interaction of oxygen bubbles through microstructures were studied as also shown in Figure 2. Findings from the work will provide better understanding of oxygen evolution through saturated PTLs Figure 1

(Invited) Bubble Trouble: Simulation of Molten Oxide Electrolysis in Reduced Gravity

Molten Oxide Electrolysis (MOE) is a leading contender for processing extra-terrestrial minerals because it produces oxygen and liquid metal without the use of consumables. During electrolysis a gravitational field stratifies gas, electrolyte, and metal from each other by density. Processing on the moon, with ~1/6g, or Mars, with ~1/3g, will reduce the buoyancy force slowing bubble velocity and lowering convection intensity. Low thermal conductivity, (~1Wm-1K-1) and high viscosity, (~1Pa⋅s) of molten regolith contribute to thermal and chemical transport being dominated by convection, even as convection velocity decreases. We explore MOE system dynamics in Earth’s (1g), Mars’ (1/3g), and the Moon’s (1/6g) gravity through simulations that include composition and temperature dependent material properties and two phase flow. We implement the level set method to track the interface between the bubble laden flow near the anode and the bubble free flow far from the anode. By grouping bubble dynamics into the material properties of the fluid near the anode we relax the requirements for a fine mesh to track individual bubble-fluid interfaces, and are able to use a mesh that is finer than that required for a bubbly flow mixture model. Thus, all physics can be captured on one mesh. This is particularly relevant because bubble sizes for proposed systems are 1/10 to 1/100 of the system scale. While other simulations have been presented and experiments performed in micro and zero gravity for gas evolving electrolysis systems, none have investigated the downward facing electrode, heat transfer, or species diffusion. The focus of this work is to address this gap in the literature through simulation. Here, multiphysics simulation is supported by inspection of dimensionless groups and observations from other electrolysis systems. This work demonstrates that combining heat and mass transfer with temperature and composition dependent material properties is critical to designing MOE and other electrolysis systems for earth and beyond.

Bubble Formation and Motion in Liquids—A Review

In flotation, a bubble acts as a carrier for attached particles. The properties of the gas–liquid interface of the bubble are one of the main factors determining the bubble motion and flotation efficiency. Monitoring of the bubble motion may deliver interesting information about the state of the gas–liquid interface. In the case of pure liquids, a bubble surface is fully mobile, while the presence of surface-active substances (e.g., surfactants) causes diminishing bubble velocity due to the retardation of the interface fluidity. The theoretical prediction of the terminal velocity value for the bubble has been investigated for over a century, delivering a number of various models describing bubble motion in a liquid. This narrative review is devoted to the motion of the bubble in stagnant liquids and is divided into three main sections describing: (i) experimental techniques for tracking bubble motion, (ii) bubble motion and shape deformation in clean water, and (iii) bubble motion in solutions of surface-active substances.

Isothermal and non-isothermal growth of a vapor bubble in pool boiling – Effect of translational velocity of bubble

In the present work, we have numerically simulated the effect of bubble translation on the growth of a vapor bubble in a pool of superheated liquid based on the isothermal and non-isothermal model. The isothermal growth uses the ODE solver and the non-isothermal growth the PDE-ODE solver. The overall model at present considers the forces acting on the bubble to compute the bubble motion and the energy balance at the bubble surface to include the effect of bubble size on its motion. Thus, it computes equivalent bubble radius and bubble velocity simultaneously. The numerical simulation shows a remarkable improvement by our method over the previous numerical model while validating with the experimental and numerical results on bubble growth with the phase motion. The improved model has significantly reduced the deviation from the experiments reported in literature on the growth of a moving bubble. The aspect ratio of the bubble is computed to see the shape change of the bubble and is used to model the drag force accurately. It has been shown that the model of the isothermal growth can better explain the bubble growth at the initial stage, and the model of the non-isothermal growth at the final stage. The non-isothermal growth of bubble is accompanied by the slowdown of the bubble translation in the superheated liquid.