Rising behavior of single bubble in infinite stagnant non-Newtonian liquids

This work is an experimental study of the rising behavior of single air bubbles in infinite stagnant non-Newtonian liquids. Aqueous solutions of carboxymethyl cellulose (CMC) are selected to study the effect of rheological properties. The high speed photography is employed to record the bubble motion in CMC solutions. The bubble size, rising trajectory, bubble shape and velocities are determined by digital image processing technique. As expected, the rheological properties have great influence on the rising behavior of single bubble. In the less concentrated CMC solutions, the bubble rising process can be divided into three stages according to spatial evolution of bubble shape. The deformation changes the trajectories of rising bubbles and bubble hydrodynamics. As the solution concentration increases, the transitional stage gradually disappears. In the most concentrated CMC solution, the first continuous shape flattening stage is directly followed by a rising process with bubble shape basically constant, the rectilinear path and constant rising velocity. Dimensional analysis is performed to formulate a general dimensionless correlation for the deformation and motion of bubbles in infinite liquids by considering the rheological properties.     

Visualization of gas–liquid mass transfer and wake structure of rising bubbles using pH-sensitive PLIF

A planar laser-induced fluorescence (PLIF) technique for visualizing gas–liquid mass transfer and wake structure of rising gas bubbles is described. The method uses an aqueous solution of the pH-sensitive dye Naphthofluorescein and CO₂ as a tracer gas. It features a high spatial resolution and frame rates of up to 500 Hz, providing the ability to capture cinematographic image sequences. By steering the laser beam with a set of two programmable scanning mirrors, sequences of three-dimensional LIF images can be recorded. The technique is applied to freely rising bubbles with diameters between 0.5 and 5 mm, which perform rectilinear, oscillatory or irregular motions. The resulting PLIF image sequences reveal the evolution of characteristic patterns in the near and far wake of the bubbles and prove the potential of the technique to provide new and detailed insights into the spatio-temporal dynamics of mass transfer of rising gas bubbles. The image sequences further allow the estimation of bubble size and rise velocity. The analysis of bubble rise velocities in the Naphthofluorescein solution indicates that surfactant-contaminated conditions are encountered.     

A model of bubbles rising in a fluidized bed

A model for a single fully developed bubble moving in an unbounded fluidized bed is presented. The model allows bubble growth or shrinkage during the rise inside the bed, as well as dependence of the rise velocity upon specified bed parameters. Limiting cases of nearly spherical bubbles and of sufficiently large bubbles whose form resembles that of a spherical segment are considered in more detail. The form of bubbles rising in either fluidized beds or one-phase liquids, and its dependence on the effective “surface tension” acting on the bubble boundary are discussed.     

An experimental study of plane bubbles rising at inclination

The characteristics of bubbles rising in two-dimensional tanks is investigated. It is found that the influence of fluid properties, while negligible for vertically rising bubbles, measurably affects the inclined bubble rise velocity. The measured increase in the rise velocity at inclination relative to the vertical value is explained qualitatively. In addition, a comparison is made between the wave analogy correlation of Maneri & Mendelson and vertical rise velocity data. The comparisons show that the correlation predicts the three-dimensional effects of tank spacing when the data are reduced on an equivalent bubble radius basis.     

The transient buoyancy driven motion of bubbles across a two-dimensional quiescent domain

The transient buoyancy driven motion of two-dimensional bubbles across a domain bounded by two horizontal walls is studied by direct numerical simulations. The bubbles are initially released next to the lower wall and as they rise, they disperse. Eventually all the bubbles collect at the top wall. The goal of the study is to examine how a simple one-dimensional model for the averaged void fraction captures the unsteady bubble motion. By using void fraction dependent velocities, where the exact dependency is obtained from simulations of homogeneous bubbly flows, the overall dispersion of the bubbles is predicted. Significant differences remain, however. We suggest that bubble dispersion by the bubble induced liquid velocity must be included, and by using a simple model for the bubble dispersion we show improved agreement.     

Robust numerical analysis of the dynamic bubble formation process in a viscous liquid

The dynamics of bubble formation from a submerged nozzle in a highly viscous liquid with relatively fast inflow gas velocity is studied numerically. The numerical simulations are carried out using a sharp interface coupled level set/volume-of-fluid (CLSVOF) method and the governing equations are solved through a hydrodynamic scheme with formal second-order accuracy. Numerical results agree well with experimental results and it is shown that the sharp interface CLSVOF method enables one to reproduce the bubble formation process for a wide range of inflow gas velocities. From numerical results, one can improve their understanding of the mechanisms regarding the dynamics of bubble formation. For example, it is found that for some sets of parameters that the bubble formation process reaches steady state after several bubbles are released from the nozzle. At steady state, bubbles uniformly rise freely in the viscous liquid. It is observed that the fluid flow around a formed bubble has a significant role in determining the overall dynamic process of bubble formation; e.g. the effect of the fluid flow from the preceding bubble can be seen on newly formed bubbles.     

A computational study of the effect of initial bubble conditions on the motion of a gas bubble rising in viscous liquids

In order to examine the influence of initial bubble conditions on bubble rise motion, two-dimensional direct numerical simulations of the motion of a gas bubble rising in viscous liquids were carried out by a coupled level set/volume-of-fluid (CLSVOF) method. For dimensionless groups predicting a “spherical-cap bubble shape” (high Eötvös and low Morton numbers), we have found computationally that solutions depend on initial bubble conditions. Specifically, for spherical-cap bubble areas, we could obtain computational results of toroidal bubbles or spherical-cap bubbles depending on initial bubble conditions. On the other hand, we showed for low Eo and high M conditions that initial bubble conditions did not affect the final state of bubble rise motion.     

均匀电场中气泡上升特性的实验研究

电场中的气泡对于强化传热有显著的作用, 对于电场中气泡动力学特性的研究对增强换热器效率, 提高能源利用率有重要意义. 为了获得外加电场作用下气泡的动力学特性, 设计与搭建了可视化实验平台. 采用50 kV高压直流电源构建均匀电场, 高清摄像机拍摄实验图像. 引入电场强度、气泡体积与溶液介电常数作为变量, 探究其对于气泡动力学特性的影响. 观测了竖直与水平均匀电场中气泡的上升过程, 分析了不同变量下气泡变形状况与上升速度的变化. 引入气泡长宽比L/D用于表示气泡拉伸变形程度, 截取单个气泡上升过程分时段图像展示形态变化过程. 研究结果表明, 气泡沿电场方向伸长, 且电场强度越大, 变形越明显; 竖直电场中气泡伸长导致上升速度增大, 而水平电场中气泡上升速度减小. 气泡尺寸增大, 浮升力作用增强, 气泡上升速度增大. 溶液介电常数增加, 电场力作用明显增加, 气泡变形更加明显.      

Ellipsoidal model of the rise of a Taylor bubble in a round tube

The rise velocity of long gas bubbles (Taylor bubbles) in round tubes is modeled by an ovary ellipsoidal cap bubble rising in an irrotational flow of a viscous liquid. The analysis leads to an expression for the rise velocity which depends on the aspect ratio of the model ellipsoid and the Reynolds and Eötvös numbers. The aspect ratio of the best ellipsoid is selected to give the same rise velocity as the Taylor bubble at given values of the Eötvös and Reynolds numbers. The analysis leads to a prediction of the shape of the ovary ellipsoid which rises with same velocity as the Taylor bubble.     

Numerical and experimental study on the motion characteristics of single bubble in a complex channel

This paper is an extended study from previous work. In this study, the focus is paid to the dynamics of bubble rising and deformation in a complex channel, while the previous work is in straight channel. For this purpose, a three-dimensional lattice Boltzmann method (LBM) is employed to simulate the dynamics behaviour of a bubble rising in a complex channel consisting of three half-round throats. To validate the numerical method, a visual experiment was carried out by means of a high-speed digital camera and computer image processing technology. The behaviour of the rising bubble through glycerine solution in a complex channel was recorded. Some physical parameters such as rising velocities, trajectory and shapes of the bubble were calculated and processed based on the experimental data. In the same conditions, the trajectory, shapes and rising velocities of the bubble were simulated during its rising process by the proposed LBM. The numerical results are in good agreement with the experimental results. It demonstrates that LBM used in this work is feasible for simulating two-phase flow in such a complex channel.     

Numerical simulation of dielectric bubbles coalescence under the effects of uniform magnetic field

In this research, the co-axial coalescence of a pair of gas bubbles rising in a viscous liquid column under the effects of an external uniform magnetic field is simulated numerically. Considered fluids are dielectric, and applied magnetic field is uniform. Effects of different strengths of magnetic field on the interaction of in-line rising bubbles and coalescence between them were investigated. For numerical modeling of the problem, a computer code was developed to solve the governing equations which are continuity, Navier–Stokes equation, magnetic field equation and level set and reinitialization of level set equations. The finite volume method is used for the discretization of the continuity and momentum equations using SIMPLE scheme where the finite difference method is used to discretization of the magnetic field equations. Also a level set method is used to capture the interface of two phases. The results are compared with available numerical and experimental results in the case of no-magnetic field effect which show a good agreement. It is found that uniform magnetic field accelerates the coalescence of the bubbles in dielectric fluids and enhances the rise velocity of the coalesced bubble.     

CFD study on rise and deformation characteristics of buoyancy-driven spheroid bubbles in stagnant Carreau model non-Newtonian fluids

The bubbles are almost ubiquitous in many chemical and processing industries; and many of the polymeric solutions obey non-Newtonian rheological characteristics. Therefore, in this work the rise and deformation characteristics of spheroid bubbles in Carreau model non-Newtonian fluids are numerically investigated using a level set method. To demonstrate the validity of the moving bubble interface, the present simulations are compared with existing numerical and experimental results available in the literature; and for these comparisons, the computational geometries are considered same as reported in corresponding literatures. The present bubble deformation characteristics are satisfactorily agreeing with their literature counterparts. After establishing the validity of the numerical solution procedure, the same method is applied to obtain the deformation characteristics of an air bubble in Carreau model non-Newtonian fluids. Further, the results in terms of the volume fraction images, streamlines, and viscosity profiles around the deforming bubbles are presented as function of the bubble rise time.     

电场作用下气泡上升行为特性的数值计算研究

利用电场控制气泡形态及运动,强化气液相间传热传质是电流体动力学的重要研究内容之一. 然而目前多数研究集中在非电场下的气泡动力学上,对于电场下的气泡行为特性及电场的作用机制仍需开展深入研究. 本研究对电场作用下单个气泡在流体中上升过程的动力学行为进行了数值模拟研究. 在建立二维模型的基础上求解电场方程与Navier-Stokes方程,并采用水平集方法捕捉了上升气泡的位置及形状. 模拟结果的准确性与有效性通过与前人实验和数值结果进行对比得到了验证. 通过改变雷诺数、邦德数和电邦德数等不同参数研究了电场下液体黏度、表面张力和电场力对气泡运动变形的影响. 计算结果表明,电场对气泡的动态特性有显著影响. 非电场情况下液体黏度和表面张力较大时气泡基本维持球状,反之气泡发生变形并逐步达到稳定状态. 此外,电场作用使气泡在初始上升阶段发生剧烈形变,随着不断上升,气泡形变程度不断减小,且气泡的上升速度和长径比均出现振荡. 垂直电场使气泡的上升速度有较大的提高,且随着电邦德数的增大,难以达到相对稳定的状态.      

An advanced LIF-PLV system for analysing the hydrodynamics in a laboratory bubble column at higher void fractions

Bubble columns are widely used in the chemical industry and biotechnology. Flow and turbulence in such an apparatus are induced by the bubble rise, and the bubble behaviour is strongly affected by swarm effects (i.e. the interaction between bubbles). For analysing the bubble swarm behaviour and simultaneously evaluating the flow structure and bubble-induced turbulence, a bubble column of 140 mm diameter and a height of 650 mm or 1,400 mm (initial water level) were considered. The bubble column was aerated with relatively fine bubbles having a mean size between about 0.5 and 4.0 mm. The gas hold-up was varied in the range between 0.5 and 19%. A two-phase pulsed-light velocimetry (PLV) system was developed to evaluate instantaneous flow fields of both rising bubbles and the continuous phase. The measurement of the liquid velocities in the bubble swarm was achieved by adding fluorescing seed particles. Images of bubbles and fluorescing tracer particles were acquired by two CCD cameras. Hence, the images from tracers and bubbles were easily separated by optical interference filters with a bandwidth corresponding to the emitting wavelength of the fluorescing tracer particles and the wavelength of the applied Nd-YAG pulsed laser, respectively. To improve the phase separation of the system, the CCD cameras were additionally placed in a non-perpendicular arrangement with respect to the light sheet. The acquired images were evaluated with the minimum-quadratic-difference algorithm. The potential of this technique for the analysis of bubbly flows with higher void fraction was explored. In order to obtain averaged velocity maps of bubble and fluid within the entire column, about 1,000 image pairs were recorded and evaluated for each phase. In addition, turbulence intensities of the fluid were deduced from the measurements. The turbulence properties were used to characterise bubble-induced turbulence for various bubble mean diameters and gas hold-ups. Moreover, the determination of the average bubble slip velocity within the bubble swarm was possible.     

Interaction between Taylor bubbles rising in stagnant non-Newtonian fluids

The interaction between Taylor bubbles rising in stagnant non-Newtonian solutions was studied. Aqueous solutions of carboxymethylcellulose (CMC) and polyacrylamide (PAA) polymers were used to study the effect of different rheological properties: shear viscosity and viscoelasticity. The solutions studied covered a range of Reynolds numbers between 10 and 714, and Deborah numbers up to 14. The study was performed with pairs of Taylor bubbles rising in a vertical column (0.032 m internal diameter) filled with stagnant liquid. The velocities of the leading and trailing bubbles were measured by sets of laser diodes/photocells placed along the column. The velocity of the trailing bubble was analysed together with the liquid velocity profile in the wake of a single rising bubble (Particle Image Velocimetry data obtained from the literature). For the less concentrated CMC solutions, with moderate shear viscosity and low viscoelasticity, the interaction between Taylor bubbles was similar to that found in Newtonian fluids. For the most concentrated CMC solution, which has high shear viscosity and moderate viscoelasticity, a negative wake forms behind the Taylor bubbles, inhibiting coalescence since the bubbles maintain a minimum distance of about 1D between them. For the PAA solutions, with moderate shear viscosity but higher viscoelasticity than the CMC solutions, longer wake lengths are seen, which are responsible for trailing bubble acceleration at greater distances from the leading bubble. Also in the PAA solutions, the long time needed for the fluid to recover its initial shear viscosity after the passage of the first bubble makes the fluid less resistant to the trailing bubble flow. Hence, the trailing bubble can travel at a higher velocity than the leading bubble, even at distances above 90D.     

Experimental and numerical investigation a bubble-driven laminar flow in a axisymmetric vessel

Measurements have been obtained, by laser-Doppler anemometry (LDA), of the axisymetric, recirculating liquid flow caused by a column of air bubbles ($\text{5–6}\text{1}\text{2}\text{mm dia.}$) rising through caster oil in a cylindrical enclosure (100 mm dia.). The liquid velocities correspond to creeping flow. Axial and radial liquid velocity profiles are reported at eight axial stations and, close to within the bubble column, as a function of time. The maximum liquid velocity found outside the bubble column is about 0.5 of that of the bubbles and a very rapid radical decay from this value is noted. The temporal variation of the velocity field, due to the passage of the air bubbles, is undetectable at radial locations greater than about $\text{1}\text{1}\text{2}$ bubble radii from the centreline.The variation of bubble velocity with axial distance was aise measured by LDA for liquid height to enclosure diámeter ratios of 0.98 and 2.78. The maximum bubble velocities were about 0.1–0.2 higher than the Strokes law terminal velocity. The increase is due to the convection of the bubble column by the liquid flow. The maximum bubble velocity is established within approximately three bubble diameters of the air inlet.The motion of the liquid has been calculated by the numerical solution of the steady form of the equations of motion, with the inner boundary of the area of integration lying 1.3 bubble radii from the centerline. The boundary conditions at this surface are assumed to be steady and are taken from measurements of the time-averaged velocity components. The assumption of steady flow at this boundary is supported by experimental observation and results in calculations which are generally in close agreement with the measurements. Discrepancies are confined to the immediate vicinity of the bubble column near to the top and bottom of the enclosure. These are ascribed to a combination of small asymmetries in the experiment and inadequate numerical resolution in these regions.     

Numerical study of single bubble motion in liquid metal exposed to a longitudinal magnetic field

The paper presents numerical simulations modeling the ascent of an argon bubble in liquid metal with and without an external magnetic field. The governing equations for the fluid and the electric potential are discretized on a uniform Cartesian grid and the bubble is represented with a highly efficient immersed boundary method. The simulations performed were conducted matching experiments under the same conditions so that sound validation is possible. The three-dimensional trajectory of the bubble is analyzed quantitatively and related to the flow structures in the wake. Indeed, the substantial impact of the magnetic field in the bubble trajectory results from its influence on the wake. Quantitative data describing the selective damping of vortex structures are provided and discussed. As a result of applying a longitudinal field, the time-averaged bubble rise velocity increases for large bubbles, it reaches a maximum and then decreases when further increasing the magnetic interaction parameter. For small bubbles, the time-averaged bubble rise velocity decreases when increasing the magnetic field. The bubble Strouhal number as a dimensionless frequency is reduced with the application of a magnetic field for all bubbles considered and the zig–zag trajectory of the bubble becomes more rectilinear.     

Degassing of water-solved gases in thin pipings during fast pressure drops

 A one-dimensional model is presented, which describes the transient two-phase flow in thin pipes during fast pressure drops and degassing by use of Eulerian and Lagrangian systems. The reduction in dimension is obtained by introduction of a geometry model for bubbly and slug flow regimes. The complete model includes the transient two-phase flow, bubble formation and bubble growth. The flow model predicts rising velocities of bubbles and plugs in arbitrary inclined highly accurate pipes. The mass transfer (diffusion) of the dissolved phase is calculated by the bubble growth model. The quality of the model was examined by simulation of experimental series, whereby water was depressurised from the saturation pressure of the dissolved gas mixture (air), by variation of saturation pressure, pressure gradient and pipe geometry. The results of numerical simulation fit the experimental data well. Received on 17 January 2000     

The effect of viscoelasticity on a rising gas bubble

This paper investigates the role of viscoelasticity on the dynamics of rising gas bubbles. The dynamics of bubbles rising in a viscoelastic liquid are characterised by three phenomena: the trailing edge cusp, negative wake, and the rise velocity jump discontinuity. There is much debate in the literature over the cause of the jump discontinuity, which is observed once the bubble exceeds a certain critical volume. In this paper, the employment of some choice modelling assumptions allows insights into the mechanisms of the jump discontinuity which cannot be ascertained experimentally. The ambient fluid is assumed incompressible and the flow irrotational, with viscoelastic effects included through the stress balance on the bubble surface. The governing equations are solved using the boundary element method. Some Newtonian predictions are discussed before investigating the role of viscoelasticity. The model predicts the trademark cusp at the trailing end of a rising bubble to a high resolution. However, the irrotational assumption precludes the prediction of the negative wake. The corresponding absence of the jump discontinuity supports the hypothesis that the negative wake is primarily responsible for the jump discontinuity, as mooted in previous studies.     

Hydrodynamic interaction between a pair of bubbles ascending in shear-thinning inelastic fluids

The interaction of two bubbles rising in shear-thinning inelastic fluids was studied. The experimental results were complemented by numerical simulations conducted with the arbitrary Lagrangian–Eulerian technique. Different initial alignments of the bubble pair were considered. Similarities and differences with the Newtonian fluids were found. The most noticeable difference is the so-called drafting–kissing–tumbling (DKT) process: for the case of bubbles rising in thinning fluids, the tumbling phase does not occur and the pair tends to form a stable doublet. The DKT process is also influenced by the amount of inertia and deformability of the individual bubbles and the initial angle between them. The experimental and numerical results suggest that the thinning wake formed behind the bubbles plays an important role in the speed of the pair and the formation of clusters in thinning fluids.