Bubble Deformation Research Articles

Bubbly flow simulation with particle-center-averaged Euler-Euler model: Fixed polydispersity and bubble deformation

Bubble size and deformation are important factors for the closure models required in Euler-Euler simulations of bubbly flows. To properly simulate polydisperse bubbly flows where the bubble size spectrum may cover a range of several millimeters, several velocity groups with different sizes have to be considered. To this end, the theory for the particle-center-averaged Euler-Euler model is generalized for the simulation with multiple bubble velocity groups. Furthermore, bubble deformation effects have been included in appropriate bubble force models. The particle-center-averaged Euler-Euler model provides additional freedom to consider the bubble shape during the conversion between the bubble number density and the gas volume fraction. Therefore, the theory is also generalized to consider an oblate ellipsoidal bubble shape in simulations. A bubbly pipe flow is used to validate the theory and to demonstrate the improvements of the proposed generalizations.

Two-group bubble interfacial area concentration correlation for upward bubbly to churn flows in vertical rod bundle flow channels

The detailed understanding and accurate modeling of the upward two-phase flows in vertical rod bundle flow channels are significant for various industrial applications, such as performing the optimal design and evaluating the transient and accident scenarios for BWR (Boiling Water Reactor) and PWR (Pressurized Water Reactor) systems. The interfacial area concentration (IAC) describing the available interfacial area for the transfer of mass, momentum, and energy between two phases plays an important role in the two-phase flow simulation in the frequently-used thermal-hydraulics system codes. Although various IAC correlations utilizing the drag-based two-group bubble categorization, namely two-group bubble IAC correlations, have been proposed to predict the IAC changes in the two-phase flow ranging from bubbly to churn flows in simple-geometry flow channels, the two-group bubble IAC correlation for rod bundle flow channels is still underdeveloped. This study performed a survey on the existing representative two-group bubble IAC correlations for simple-geometry flow channels and collected 425 experimental IAC data taken in various vertical rod bundle flow channels. The predictive abilities of these two-group bubble IAC correlations were evaluated with the collected experimental IAC data. The evaluations showed that no existing correlations can consistently maintain satisfied predictive ability throughout the upward bubbly to churn flows in vertical rod bundle flow channels. In view of this fact, this study proposed a new two-group IAC correlation for vertical rod bundle flow channels. Specifically, the group-2 bubble void fraction model was proposed by physically analyzing the changing characteristics of the group-2 bubbles in different flow regimes. The Sauter mean diameter model of group-1 bubbles was derived by (a) selecting the distorted small bubble as the representative group-1 bubble for the bubbly, cap-bubbly and churn flows and (b) selecting the spherical small bubble as the representative group-1 bubble for the finely dispersed bubbly flow. The Sauter mean diameter model of group-2 bubbles was proposed by treating the cap-bubble as the representative group-2 bubble and taking into account the bubble deformation caused by the surrounding rods. The proposed two-group bubble IAC correlation has been checked against the collected existing experimental IAC data and the proposed correlation exhibited reliable predictive abilities in the bubbly to churn flows in various rod bundle flow channels with the mean relative deviation of 0.233, 0.212, 0.247, 0.222 and 0.234 for bubbly, finely dispersed bubbly, cap-bubbly, churn and all data, respectively.

The lift force on deformable and freely moving bubbles in linear shear flows

This paper provides a comprehensive explanation for the lift force acting on a freely deformable bubble rising in a linear shear flow and examines how the lift force scales with the undisturbed shear rate in cases governed by different lift force mechanisms. Four distinct flow mechanisms are identified from previous studies, and the associated bubble-induced vorticity dynamics are outlined. We provide a theoretical framework to qualitatively explain the lift force acting on a bubble in terms of moments of the bubble-induced vorticity. We support our theoretical framework with three-dimensional multiphase direct numerical simulations to illustrate how the vorticity dynamics associated with the four mechanisms generate the lift force. These findings provide a comprehensive explanation for the behaviour of the lift force in a wide range of relevant governing parameters. Additionally, our simulation results show how differently the lift force scales with the shear rate, depending on the dominating lift force mechanism. These results indicate that the shear rate should, in general, be accounted for in highly viscous flows (low Galilei numbers) or at significant bubble deformations (moderate-to-high Eötvös numbers) when modelling the lift force coefficient.

Reconstruction and prediction of rising bubble by Lagrange DMD in data-driven

Dynamic mode decomposition (DMD) is a widely used data-driven modeling method for understanding complex flow systems, however, it is inadequate to deal with translation problems such as bubble rising. The Lagrangian DMD formed by the DMD combined with translation information has shown preliminary promise for solving simple translation problems (convection dominated). This paper aims to use a data-driven method to predict the 2D bubble rising process and try to improve the Lagrangian DMD modeling ability. In the simple case without bubble deformation, Lagrangian DMD shows significantly better reconstruction and prediction results than DMD. However, in a complex case with bubble deformation, Lagrangian DMD cannot provide satisfactory prediction results. After adding velocity prediction to the Lagrangian DMD method, the prediction of bubble rising has been improved.

Numerical simulation of bubble rising in porous media using lattice Boltzmann method

Rising bubble systems in porous media exist in a variety of industrial processes. However, the flow characteristics of the issue are not well understood. In this work, the rising of bubble/bubbles through two types of porous structures, namely, in-line structured pore and staggered structured pore, are studied using a large density ratio lattice Boltzmann model. The effects of Eötvös number, pore shape, viscosity ratio, initial bubble number, and arrangement manner of the initial bubbles on the bubble deformation, bubble rising velocity, residual bubble mass, bubble perimeter, and the number of bubble breakups are investigated. It is found that as the Eötvös number increases, the bubbles are more easily broken during the process of passing through the porous media, the shapes of the sub-bubbles deviate from the original ones more and more, the bubble perimeter increases, and the difference between the bubble dynamics obtained by the in-line and staggered porous media decreases. Compared to the results of circular and rectangular pores, the bubble rising through the diamondoid pore has a more considerable deformation, which causes a slower rising speed. Furthermore, in the case that two bubbles are originally placed under the porous medium, the bubble deformation is greater and the bubble fracture times increase if the initial bubbles are aligned vertically. The findings of this work can contribute to the understanding of gas–liquid two-phase flow in porous media.

Simulation of single bubble dynamic process in pool boiling process under microgravity based on phase field method

We use the phase field method to track the gas–liquid interface based on the gas–liquid two-phase flow in the pool boiling process, and study the bubble nucleation, growth, deformation, departure and other dynamic behaviors on the heating surface under microgravity. By simulating the correlation between liquid undercooling and bubble dynamics, we find that the bubble growth time increases with the increase of liquid undercooling, but the effect of liquid undercooling on bubble height is not significant. Meanwhile, the gas–liquid–solid three-phase contact angle and the gravity level will also have an effect on the bubble growth time and bubble height. With the increase of the contact angle, the bubble growth time and bubble height when the bubble departs also increase. While the effect of gravity level is on the contrary, the smaller the gravity level is, the larger the bubble height and bubble growth time when the bubble separates.

Experimental observations and modelling of sub-Hinze bubble production by turbulent bubble break-up

We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale$d_{H}$, the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes$d_0$much larger than$d_{H}$(probing up to$d_0/d_{H} = 8.3$), the size distribution of bubbles smaller than$d_{H}$follows$N(d) \propto d^{-3/2}$, with$d$the bubble diameter. The capillary instability of ligaments involved in the deformation of the large bubbles is shown visually to be responsible for the creation of the small bubbles. Turning to dynamical, three-dimensional measurements of individual break-up events, we describe the break-up child size distribution and the number of child bubbles formed as a function of$d_0/d_{H}$. Then, to model the evolution of a population of bubbles produced by turbulent bubble break-up, we propose a population balance framework in which break-up involves two physical processes: an inertial deformation to the parent bubble that sets the size of large child bubbles, and a capillary instability that sets the size of small child bubbles. A Monte Carlo approach is used to construct the child size distribution, with simulated stochastic break-ups constrained by our experimental measurements and the understanding of the role of capillarity in small bubble production. This approach reproduces the experimental time evolution of the bubble size distribution during the disintegration of large air cavities in turbulence.

The dynamics of a bubble in the internal fluid flow of a pipeline

In the aeronautical and marine engineering fields, bubbles are often carried in the pipelines of filling systems and marine risers. Under the action of internal flow, air bubbles seriously threaten device security. Therefore, to analyze the motion and deformation of a bubble in the internal fluid flow of a pipeline, we establish a corresponding boundary element numerical model based on the potential flow theory. A comparison of the numerical model results with the experimental results verifies the accuracy of the model. Subsequently, we simulate the dynamics of a bubble under the action of the internal flow, and the influence of the velocity, pipe radius, and surface tension on the bubble movement are discussed. When the dimensionless flow velocity exceeds 0.3, the bubbles will be seriously deformed. Different flow velocity directions cause different deformations of the annular bubbles in the later stages. Additionally, the channel limits bubble deformation. If the pipe radius is greater than 5, the effect of the pipe on the bubble is negligible. We also find that surface tension keeps the bubbles morphologically stable under internal flow. When the surface tension coefficient exceeds 2.45 × 10−4, it will not make the bubble toroidal.

Migration dynamics of an initially spherical deformable bubble in the vicinity of a corner

Three-dimensional numerical simulations are performed to study the migration dynamics of a deformable bubble that is spherical at an initial time near a corner formed by two vertical walls. Near-wall dynamics of this rising bubble are studied by investigating its path, wake, shape and velocity. A finite volume approach coupled with VOF (volume-of-fluid) method is adopted to solve the incompressible Navier–Stokes equation and track the gas–liquid interface. From the study, it is found that bubble inertia is dictated by initial bubble–walls interaction as bubble progressively migrates away in a diagonal direction from both the vertical walls in three-dimensional space. This influenced bubble inertia, in turn, affects the conformity of the bubble to a specific bubble regime. Five regimes are identified based on the bubble's migrating trajectory among which three of them are fully developed-steady, zigzag, and spiral and two of them are transitional-steady to zigzag and zigzag to spiral. The point of complete transformation of bubble from steady to zigzag transition to fully developed path instability is evaluated by varying a certain dimensionless parameter, Galilei number Ga. It is found that the path instability occurs at a lower Ga than what it is for the unbounded situations, and the onset of planar zigzag motion is not the result of vortex shedding rather the critical amount of wake accumulation on bubble surface and bubble inertia modulated by walls. Furthermore, the overall dynamics found in the current study show distinguishable characteristics when compared to single wall and unbounded situations.

Experimental study of influence of liquid viscosity in horizontal slug flow

Slug flow is present in many industrial processes, including the ones related to the petroleum industry. Such flow pattern is characterized by the periodic passage of liquid slugs that may or may not be aerated and elongated bubbles that flow atop a liquid film. Most of the existing models for slug flow have been developed for two-phase water–air flows but, in oil and gas production, the liquid phase is often substantially more viscous than water. The aim of this article is to evaluate the effect of the liquid viscosity increase on slug flow. To achieve this goal, an experimental study on liquid–gas flows in a 26-mm ID, 8.65-m long horizontal pipe was developed. Water and mixtures of water and glycerin (μL≈5.46, 10.27, 15.39, 20.33 and 30.37 cP) made the working liquids. The experimental results from the high-speed camera and resistivity sensors enabled a detailed investigation of elongated bubble characteristics and slug flow parameters. The elongated bubble nose deformation, the appearance of plunging jets and the deformation of the dispersed bubbles are associated to dimensionless numbers. Experimental results show that the dispersed bubble deformation in the slug, the number of fragmented bubbles in the slug and the elongated bubble velocity increase as the mixture velocity and the liquid viscosity increase. The effects on the slug frequency and slug length depend on the superficial velocities of the fluids.

Slug bubble deformation and its influence on bubble breakup dynamics in microchannel

The deformation of moving slug bubbles and its influence on the bubble breakup dynamics in microchannel were studied. Three bubble morphologies were found in the experiment: slug, dumbbell and grenade shapes. The viscosity effect of continuous phase aggravates the velocity difference between the fluid near the wall and the bubble, resulting in that the continuous phase near the bubble head flows towards and squeezes the bubble tail, which causes the deformation of bubbles. Moreover, the experimental results show that the deformation of bubbles could significantly prolong the bubble breakup period at the downstream Y-junction. There exists the critical capillary number Ca Cr for the asymmetric breakup of grenade bubbles, Ca Cr increases with the rise of flow rate and viscosity of the continuous phase.

Shape deformations and instabilities of single bubble rising in liquid metals

In this study, a computational fluid dynamics simulation was used to study single bubble flow in liquid metal. Until now, bubble trajectory and shape [Mougin, G. and Magnaudet, J., “Path instability of a rising bubble,” Phys. Rev. Lett. 88, 014502 (2002)] stability problems in liquid metal have only been insufficiently analyzed in the literature. Because of the difficulty of such an experimental validation, no universal correlations on terminal velocity, shape aspect ratio, and drag force coefficient have been produced to date. The existing bubble shape parameter and terminal velocity correlations with dimensionless numbers are still debatable, mostly because experimental validation is very challenging. The objective of this study was to develop new correlations between bubble stability and bubble deformation in liquid metals. An in-house code, PSI-BOIL, has been used for the simulations. A single bubble rising in a quiescent liquid has been simulated for three different sets of materials (nitrogen+mercury, argon+GaInSn, and argon+steel). The obtained results suggest that shape instability phenomena take place in the bubble dynamics in liquid metals for Eötvös numbers >1.7. Small bubbles (Eo < 1.7) maintain a stable ellipsoidal shape, while the shape and velocity of larger bubbles (Eo > 1.7) tend to oscillate with bubbles rising via non-rectilinear trajectories. The inviscid approximation works well for bubbles in liquid metals. It has been confirmed that the dynamics and the shape of small bubbles (Eo < 1.7) in liquid metals are only controlled by the Weber number.

The left-right symmetrical and asymmetrical deformations in a three-bubble system

This paper studies the simplest system that can possess left-right symmetrical and asymmetrical surroundings, three bubbles in a line. Assuming that the deformations are small, the surfaces of bubbles are described by a combination of the first three Legendre polynomials, that is, spherical symmetrical mode P0, L-R antisymmetrical mode P1, and symmetrical mode P2. A dynamical model is built to describe aspherical oscillations of central and two side bubbles. It is found that when three identical bubbles are separated uniformly, the central bubble only has a P2 component and P1 component tends to zero, while two side bubbles have both P1 and P2 components. When three identical bubbles are separated by different distances, they can be degenerated into a two-bubble system and a free bubble. The bubble deformations contain both P1 and P2 components in the two-bubble system, while both aspherical components P1 and P2 of the free bubble tend to zero. If side bubbles are different in ambient radii but located symmetrically on the left and right of the central bubble, the side bubble pulsated more strongly plays an important role on the deformation of the central one.

Three-dimensional phase-field lattice-Boltzmann simulations of a rising bubble interacting with obstacles: Shape quantification and parameter dependence

Exploring the bubble dynamics in the presence of obstacles can improve understanding of mechanism, design, and operation of multiphase flow. However, large deformation and complex hydrodynamics during the bubble–obstacle interaction pose challenges for shape quantification and parameter dependence. In this work, the bubble–obstacle interaction is investigated by employing a conservative phase-field lattice-Boltzmann model implemented on a parallel platform. Two shape parameters, which are the combination of the bubble geometrical parameters, are defined to characterize the bubble deformation during rising, impacting, and sliding process. The effects of the flow parameters (Reynolds, Eötvös, and Morton numbers) and the obstacle geometry settings (size and layout) are discussed, and a multilinear correlation is established to obtain a thorough evaluation. The difference induced by spatial dimension is further discussed to illustrate the necessity of simulating three-dimensional liquid–gas flow. The results can help decode the intricate bubble dynamics and lay a foundation for developing physically informed models for predicting the bubble–obstacle interaction.

Interaction of a rigid buoyant sphere and a deforming bubble with a vortex ring: The role of deformability

Bubbly turbulent flows involve complex interactions between the water and the bubbles in which bubble deformation is known to play an important role. We experimentally investigate an idealization, namely, the interaction of a deforming air bubble and a rigid buoyant particle (non-deforming bubble) with a single vortex ring. On the bubble/particle dynamics side, after capture by the low-pressure vortex core, the bubble undergoes large azimuthal expansion within the ring, unlike the particle. This difference in the shape of the bubble compared to the particle, within the ring, leads to distinct differences in the ring time evolution, which brings us insight into the role of deformability in these interactions.

Numerical study of bubble induced mixing in stratified fluids

Direct numerical simulations of up to 146 bubbles rising in unbounded stratified fluids using finite-volume/front-tracking method are performed. Both the bubble dynamics and destratification effects caused by the bubble motion are analyzed. The importance of bubble deformability and bubble Reynolds numbers on the induced background mixing are studied by varying the Eo¨tvo¨s number in the range 1.55 to 4.95 and Reynolds number in the range 25 to 200. Highly deformable, high Reynolds number bubbles undergo path instabilities and give rise to higher levels of mixing. Liquid and bubble velocity fluctuations and pseudo-turbulence caused by the bubble motion are examined and are seen to play an important role in mixing statistics. An increase in turbulent kinetic energy (TKE) levels with void fraction is noted. TKE levels are seen to decrease slightly as the stratification strength is increased, indicating increasing stability and resistance to destratification. The dependence of mixing parameters on the void-fraction of bubbles and stratification strength of the liquid is also presented. An increase in buoyancy flux across pycnoclines is observed as void fraction increases. A similar increase in vertical mass flux is observed for a decrease in stratification strength. The bubble dispersion and wake flow patterns are seen to strongly influence mixing properties.

Experimental and Numerical Studies on Fixed Steel Sheets Subjected to Underwater Explosion.

This study presents underwater explosion tests with three different TNT charge weights to investigate the dynamic responses of a fixed steel sheet. A finite element model was established and benchmarked by comparing the bubble development and deformation distribution from the tests. The steel sheet shows a deformation process of hogging, sagging, and hogging again, due to the actions of shock waves, bubble expansion, bubble collapse, and bubble pulsation. The air may be sucked into the bubble during the hogging process, making the bubble collapse earlier and resulting in a relatively lower sagging deformation for large charge weights of TNT. The deformation caused by bubble pulsation is larger than that by the shock waves, owing to the large time duration of bubble pulsation. A parametric analysis was conducted to study the influence of steel grade, plate thickness, detonation distance, and the shape and position of charges on the dynamic behavior of steel plates subjected to underwater explosions. It shows that the damage to the steel plate gradually decreases, with the increase in steel strength, plate thickness, and detonation distance. The influence of the shape and position of charges is limited. The largest deformation is observed when the detonation distance increases to bubble radius.

A single bubble rising in the vicinity of a vertical wall: A numerical study based on volume of fluid method

Single bubble rising in the close vicinity of a vertical wall is one of the focuses in the field of gas-liquid two-phase flow. In this work, three-dimensional direct numerical simulation based on volume of fluid (VOF) and adaptive mesh refinement method is performed to investigate the bubble rising and wake structures near a vertical wall. The bubble migration trajectory, deformation, velocity and wake structures were analyzed under various Galileo numbers and initial wall distances. Bubbles with a Galileo number of 8.8 significantly migrate away from the wall, which is driven by the repulsive force as a result of the suppression of the vortex diffusion on the bubble surface. As the Galileo number increases, the asymmetry of the shedding vortex tends to play a vital role on the repulsive force, which is exacerbated by the presence of the vertical wall. A periodic shedding of the vortex appears behind the bubble when the Galileo number reaches at 95. Meanwhile, the bubble trajectory changes from rectilinear to spiral along with a periodic oscillation. Due to the interaction between the vertical wall and the bubble wake, a transition from a rectilinear rising path to a spiral rising path is more likely to occur compared to that without a vertical wall. The presence of a vertical wall contributes to bubble-rising oscillations. A decrease of the bubble terminal velocity due to viscous effect near the vertical wall is observed for bubbles at low Galileo numbers. However, the viscous effect is less pronounced as the Galileo number increases.

Experimental and simulation analysis of bubble deformation in foaming polypropylene

This paper investigates the bubble deformation in bubble growth using a self-made in situ visual injection molding device. The results show that the deformation degree of independent bubbles is kept within 0.015. Under the frame rate of 25 frames per second (FPS), it is found that adjacent bubbles with the same average diameter simultaneously pass through the deformation critical point, while adjacent bubbles with different average diameters can’t pass through the critical deformation point at the same time. The interaction in the process of adjacent bubble growth is simulated by finite element software, radial migration of bubbles is suppressed, the hoop stretch of bubbles is enhanced, and the deformation sequence of adjacent bubbles is determined by bubble radius and bubble pressure. On the basis of the bubble influence zone model and the bubble deformation model, a bubble deformation response model is established, used to reflect adjacent bubbles’ deformation response speed.

Numerical study of surfactant effects on the rise of a single bubble and two coaxial bubbles

A hybrid lattice Boltzmann and finite difference method is presented for two-phase flows with unequal densities and insoluble surfactants. This method simulates two-phase flows through an improved lattice Boltzmann color-gradient model, which is developed from the previous density ratio model but considers surfactant effect by incorporating dynamic surface tension and Marangoni stress, and solves surfactant transport by a finite difference method. We first use it to simulate a single bubble rise and explore the surfactant roles on bubble motion and deformation for varying Bond (Bo) and Galilei (Ga) numbers. Results show that the addition of surfactants always retards bubble motion and deformation but the retarding effect decreases with increasing Bo. As Ga increases, the retarding effect of surfactants increases due to the increased Marangoni stress and a wake vortex would arise behind the surfactant-laden bubble, which opposes the surfactant accumulation at bubble bottom. We then simulate the rise of two coaxial bubbles and study the surfactant roles on bubble coalescence for varying Ga and radius ratios of leading to trailing bubbles. It is found that the presence of surfactants delays bubble coalescence when Ga or radius ratio is relatively low, but promotes coalescence when Ga or radius ratio is high.