Study of periodically excited bubbly jets by PIV and double optical sensors

Interactions between large coherent structures and bubbles in two-phase flow can be systematically observed in a periodically excited bubbly jet. Controlled excitation at fixed frequency causes large eddy structures to develop at regular intervals. Thus, interactions between large vortices and bubbles can be studied with PIV and double optical sensors (DOS) using phase-averaging techniques. A number of results on the time and space dependence of velocities and void fractions are presented revealing physical interactions between the liquid flow field and bubble movement as well as feedbacks from bubble agglomeration on the development of flow structures. A clear indication of bubble trapping inside the vortex ring is the generation of a bubble ring that travels with the same velocity as the vortex ring. The DOS results indicate clustering of the bubbles in coherent vortex structures, with a periodic variation of void fraction during the excitation period.     

Experimental investigation of horizontal air–water bubbly-to-plug and bubbly-to-slug transition flows in a 3.81 cm ID pipe

The present study seeks to investigate horizontal bubbly-to-plug and bubbly-to-slug transition flows. The two-phase flow structures and transition mechanisms in these transition flows are studied based on experimental database established using the local four-sensor conductivity probe in a 3.81 cm inner diameter pipe. While slug flow needs to be distinguished from plug flow due to the presence of large number of small bubbles (and thus, large interfacial area concentration), both differences and similarities are observed in the evolution of interfacial structures in bubbly-to-plug and bubbly-to-slug transitions. The bubbly-to-plug transition is studied by decreasing the liquid flow rate at a fixed gas flow rate. It is found that as the liquid flow rate is lowered, bubbles pack near the top wall of the pipe due to the diminished role of turbulent mixing. As the flow rate is lowered further, bubbles begin to coalesce and form the large bubbles characteristic of plug flow. Bubble size increases while bubble velocity decreases as liquid flow rate decreases, and the profile of the bubble velocity changes its shape due to the changing interfacial structure. The bubbly-to-slug transition is investigated by increasing the gas flow rate at a fixed liquid flow rate. In this transition, gas phase becomes more uniformly distributed throughout the cross-section due to the formation of large bubbles and the increasing bubble-induced turbulence. The size of small bubbles decreases while bubble velocity increases as gas flow rate increases. The distributions of bubble size and bubble velocity become more symmetric in this transition. While differences are observed in these two transitions, similarities are also noticed. As bubbly-to-plug or bubbly-to-slug transition occurs, the formation of large elongated bubbles is observed not in the uppermost region of bubble layer, but in a lower region. At the beginning of transitions, relative differences in phase velocities near the top of the pipe cross-section to those near the pipe center become larger for both gas and liquid phases, because more densely packed bubbles introduce more resistance to both phases.     

绕水翼空化流动多尺度数值研究

空化的多尺度效应是一种涉及连续介质尺度、微尺度空化泡以及不同尺度间相互转化的复杂水动力学现象, 跨尺度模型的构建是解析该多尺度现象的关键. 本文基于欧拉-拉格朗日联合算法, 通过界面捕捉法求解欧拉体系下大尺度空穴演化, 通过拉格朗日体系下离散空泡模型求解亚网格尺度离散空泡的运动及生长溃灭. 同时, 通过判断空泡与网格尺度间的关系判定不同尺度空化泡的求解模型. 基于建立的多尺度算法对绕NACA66水翼空化流动进行模拟, 将数值结果与实验进行对比, 验证了数值计算方法的准确性. 研究结果表明, 离散空泡数量与空化发展阶段密切相关, 在附着型片状空穴生长阶段, 离散空泡数量波动较小, 离散空泡主要分布在气液交界面位置; 在回射流发展阶段, 离散空泡逐渐增加并分布在回射流扰动区; 在云状空穴溃灭阶段, 离散空泡数量增多且主要分布在气液掺混剧烈的空化云团溃灭区. 在各空化发展阶段, 离散空泡直径概率密度函数均符合伽玛分布. 空化湍流流场特性对拉格朗日空泡空间分布具有重要影响, 离散空泡主要分布在强湍脉动区、旋涡及回射流发展区域.      

A numerical scheme for Euler–Lagrange simulation of bubbly flows in complex systems

An Eulerian–Lagrangian approach is developed for the simulation of turbulent bubbly flows in complex systems. The liquid phase is treated as a continuum and the Navier–Stokes equations are solved in an unstructured grid, finite volume framework for turbulent flows. The dynamics of the disperse phase is modeled in a Lagrangian frame and includes models for the motion of each individual bubble, bubble size variations due to the local pressure changes, and interactions among the bubbles and with boundaries. The bubble growth/collapse is modeled by the Rayleigh–Plesset (RP) equation. Three modeling approaches are considered: (a) one‐way coupling, where the influence of the bubble on the fluid flow is neglected, (b) two‐way coupling, where the momentum‐exchange between the fluid and the bubbles is modeled, and (c) volumetric coupling, where the volumetric displacement of the fluid by the bubble motion and the momentum‐exchange are modeled. A novel adaptive time‐stepping scheme based on stability‐analysis of the non‐linear bubble dynamics equations is developed. The numerical approach is verified for various single bubble test cases to show second‐order accuracy. Interactions of multiple bubbles with vortical flows are simulated to study the effectiveness of the volumetric coupling approach in predicting the flow features observed experimentally. Finally, the numerical approach is used to perform a large‐eddy simulation in two configurations: (i) flow over a cavity to predict small‐scale cavitation and inception and (ii) a rising dense bubble plume in a stationary water column. The results show good predictive capability of the numerical algorithm in capturing complex flow features. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Hydrodynamic and mass transfer characteristics of slug flow in a vertical pipe with and without dispersed small bubbles

In this work, we present a numerical study to investigate the hydrodynamic characteristics of slug flow and the mechanism of slug flow induced CO₂ corrosion with and without dispersed small bubbles. The simulations are performed using the coupled model put forward by the authors in previous paper, which can deal with the multiphase flow with the gas–liquid interfaces of different length scales. A quasi slug flow, where two hypotheses are imposed, is built to approximate real slug flow. In the region ahead of the Taylor bubble and the liquid film region, the presence of dispersed small bubbles has less impacts on velocity field, because there are no non-regular intensive disturbance forces or centrifugal forces breaking the balance of the liquid and the dispersed small bubbles. In the liquid slug region, the strong centrifugal forces generated by the recirculation below the Taylor bubble lead to the effect of heterogeneity, which makes the profile of the radial liquid velocity component sharper with higher volume fraction of dispersed small bubbles. The volume fraction has a maximum value in the range of r/R = 0.5–0.6. Meanwhile, it is usually higher than 0.35, which means that larger dispersed bubbles can be formed by coalescences in this region. These calculated results are in good agreement with experimental results. The wall shear stress and the mass transfer coefficient with dispersed small bubbles are higher than those without dispersed small bubbles due to enhanced fluctuations. For short Taylor bubble length, the average mass transfer coefficient is increased when the gas or liquid superficial velocity is increased. However, there may be an inflection point at low mixture superficial velocities. For the slug with dispersed small bubbles, the product scales still cannot be damaged directly despite higher wall shear stress. In fact, the alternate wall shear stress and the pressure fluctuations perpendicular to the pipe wall with high frequency are the main cause for breaking the product scales.     

Modulation of homogeneous turbulence seeded with finite size bubbles or particles

The dynamics of homogeneous, isotropic turbulence seeded with finite sized particles or bubbles is investigated in a series of numerical simulations, using the force-coupling method for the particle phase and low wavenumber forcing of the flow to sustain the turbulence. Results are given on the modulation of the turbulence due to massless bubbles, neutrally buoyant particles and inertial particles of specific density 1.4 at volumetric concentrations of 6%. Buoyancy forces due to gravity are excluded to emphasize finite size and inertial effects for the bubbles or particles and their interactions with the turbulence. Besides observing the classical entrapment of bubbles and the expulsion of inertial particles by vortex structures, we analyze the Lagrangian statistics for the velocity and acceleration of the dispersed phase. The turbulent fluctuations are damped at mid-range wavenumbers by the bubbles or particles while the small-scale kinetic energy is significantly enhanced. Unexpectedly, the modulation of turbulence depends only slightly on the dispersion characteristics (bubble entrapment in vortices or inertial sweeping of the solid particles) but is closely related to the stresslet component (finite size effect) of the flow disturbances. The pivoting wavenumber characterizing the transition from damped to enhanced energy content is shown to vary with the size of the bubbles or particles. The spectrum for the energy transfer by the particle phase is examined and the possibility of representing this, at large scales, through an additional effective viscosity is discussed.     

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.     

Turbulence measurements in the bubbly flow region of hydraulic jumps

A hydraulic jump is characterized by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air–water flow measurements were performed in a large-size facility using two types of phase-detection intrusive probes: i.e. single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent integral time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of Chanson [H. Chanson, Bubbly flow structure in hydraulic jump, Eur. J. Mech. B/Fluids 26 (3) (2007) 367–384], providing the turbulent scales of the eddy structures advecting the air bubbles in the developing shear layer. The length scale L_xz is an integral air–water turbulence length scale which characterized the transverse size of the large vortical structures advecting the air bubbles. The experimental data showed that the dimensionless integral turbulent length scale L_xz/d₁ was closely related to the inflow depth: i.e. L_xz/d₁ = 0.2–0.8, with L_xz increasing towards the free-surface.     

An experimental study on the effect of air bubble injection on the flow induced rotational hub

Modification of shear stress due to air bubbles injection in a rotary device was investigated experimentally. Air bubbles inject to the water flow crosses the neighbor of the hub which can rotate just by water flow shear stresses, in this device. Increasing air void fraction leads to decrease of shear stresses exerted on the hub surface until in high void fractions, the hub motion stopped as observed. Amount of skin friction decrease has been estimated by counting central hub rotations. Wall shear stress was decreased by bubble injection in all range of tested Reynolds number, changing from 50,378 to 71,238, and also by increasing air void fraction from zero to 3.06%. Skin friction reduction more than 85% was achieved in this study as maximum measured volume of air fraction injected to fluid flow while bubbles are distinct and they do not make a gas layer. Significant skin friction reduction obtained in this special case indicate that using small amount of bubble injection causes large amount of skin friction reduction in some rotary parts in the liquid phases like as water.     

Experiments on transport of hydrophobic particles and gas bubbles in porous media

Adhesion of hydrophobic colloids (clay minerals) on the surface of bubbles of air and the transport of the composite units formed by bubbles and mineral particles were observed in a glass micro model.When a clay mineral suspension flowed in a porous medium that contained bubbles of air trapped in small pores, particles accumulated preferentially on the upstream portion of the bubbles, and quasi-stable bubble-mineral particle units were formed. With an increase in the flow velocity, the particles moved along the interface between the bubble and the liquid and accumulated on the downstream portion of the bubbles. A large stress could mobilize the units which, occasionally, accumulated in larger voids.The mechanism suggested is adhesion of the particles on the surface of the bubble due to compression of their diffuse electrical double layer. The adsorbed particles can be moved by shear stresses which act in the region of water molecules between the well-organized layers of water on the surfaces of the bubble and the clay particles. A large enough shear stress causes the bubbles to become more streamlined, allowing them to move in the channel system. If in contact, the common lamina of the bubbles can withdraw and rupture.Bubbles transport from 20 to 50 times more particles than can be transported by average suspension.     

Prediction of bubble concentration profiles in vertical turbulent two-phase flow

In vertical bubbly flow, the bubbles are not distributed evenly across the flow section. Several investigators have observed a wall-skewed bubble concentration profile in a vertical upward flow. This paper presents an analysis that predicts this type of bubble distribution by incorporating into the equation of motion a lateral force due to the relative velocity of the two phases and the eddy diffusivity of the liquid. Comparison of analysis and experiment shows good agreement.     

The minimum in-line coalescence height of bubbles in non-Newtonian fluid

The minimum in-line coalescence height of bubbles generated from a submerged nozzle was investigated experimentally in shear thinning non-Newtonian fluid at lower Reynolds number (2∼60). Carboxymethyl cellulose sodium (CMC) aqueous solution and carbon dioxide were used as the liquid phase and the gas phase, respectively. The process of the formation, movement and in-line coalescence of bubbles was visualized and recorded by a high-speed digital camera. The influences of bubble size, bubble generation frequency and liquid property on the minimum in-line coalescence height of bubbles were investigated by changing nozzle diameter, gas flow rate and the mass concentration of CMC aqueous solutions. For a given liquid, the generating frequency and size of bubbles increased but the minimum coalescence height of in-line bubbles decreased when the nozzle diameter and gas flow rate were increased. When the nozzle diameter and gas flow rate were fixed, the shear-thinning effect of CMC aqueous solution became stronger with increasing CMC mass concentration, which led to the increase in both the terminal rise velocity and average acceleration of the trailing bubble, consequently, the minimum in-line coalescence height of bubbles decreased. An empirical correlation for estimating the minimum in-line bubble coalescence height was proposed, the calculating values accords well with experimental data with a mean relative deviation only 7.6%.     

Prediction of mono-disperse gas–liquid turbulent flow in a vertical pipe

A two-fluid model in the Eulerian–Eulerian framework has been implemented for the prediction of gas volume fraction, mean phasic velocities, and the liquid phase turbulence properties for gas–liquid upward flow in a vertical pipe. The governing two-fluid transport equations are discretized using the finite volume method and a low Reynolds number $k-\varepsilon$ model is used to predict the turbulence field for the continuous liquid phase. In the present analysis, a fully developed one-dimensional flow is considered where the gas volume fraction profile is predicted using the radial force balance for the bubble phase. The current study investigates: (1) the turbulence modulation terms which represent the effect of bubbles on the liquid phase turbulence in the k–ε transport equations; (2) the role of the bubble induced turbulent viscosity compared to turbulence generated by shear; and (3) the effect of bubble size on the radial forces which results in either a center-peak or a wall-peak in the gas volume fraction profiles. The results obtained from the current simulation are generally in good agreement with the experimental data, and somewhat improved over the predictions of some previous numerical studies.     

Transition of plug to slug flow and associated fluid dynamics

Transition of plug to slug flow is associated with bubble detachment from elongated bubble tail or bubble entrainment inside the liquid slug. The mechanism responsible for this transition was earlier identified by Ruder and Hanratty (1990) and Fagundes Netto et al. (1999) based on the shape of the hydraulic jump observed at elongated bubble tail region. The transition mechanism reported by Ruder and Hanratty (1990) and Fagundes Netto et al. (1999) was only based on their flow visualization study. Plug to slug transition and associated dynamics of bubble detachment from the elongated bubble is analysed in the present paper using flow visualization and local velocity measurements. Experiments are reported for 13 different inlet flow conditions of air and water phases. Images of plug/slug flow structures are captured at a rate of 4000 FPS using FASTCAM Photron camera and the local values of axial liquid velocity are measured using LDV system synchronised with a 3D automated traverse system. LDV measurement of local liquid velocity in the liquid slug and liquid film establishes the reason for detachment of bubbles from the slug bubble tail.     

A turbulence model for inclined, bubbly flows

A new turbulence model for the flow of a two phase (liquid-liquid) flow in an inclined pipe is presented. An eddy viscosity is used to model the effects of shear induced turbulence and bubble induced turbulence. The cross-pipe momentum transport arising from the buoyant rise of bubbles across the axial flow is also modelled. Numerical simulations have been carried out in both one and two dimensions. One and two dimensional numerical simulations are presented.On leave from the University of Leeds, Leeds LS2 9JT, U.K.     

Shock structure in bubbly liquids: comparison of direct numerical simulations and model equations

Shock wave structure in a bubbly mixture composed of a cluster of gas bubbles in a quiescent liquid with initial void fractions around 10% inside a 3D rectangular domain excited by a sudden increase in the pressure at one boundary is investigated using the front tracking/finite volume method. The effects of bubble/bubble interactions and bubble deformations are, therefore, investigated for further modeling. The liquid is taken to be incompressible while the bubbles are assumed to be compressible. The gas pressure inside the bubbles is taken uniform and is assumed to vary isothermally. Results obtained for the pressure distribution at different locations along the direction of propagation show the characteristics of one-dimensional unsteady shock propagation evolving towards steady-state. The steady-state shock structures obtained by the present direct numerical simulations, which show a transition from A-type to C-type steady-state shock structures, are compared with those obtained by the classical Rayleigh–Plesset equation and by a modified Rayleigh–Plesset equation accounting for bubble/bubble interactions in the mean-field theory.      

Bubble formation in co-fed gas–liquid flows in a rotor-stator spinning disc reactor

The gas–liquid flow in a rotor-stator spinning disc reactor, with co-feeding of gas and liquid, is studied for high gas volumetric throughflow rates and high gas/liquid volumetric flow ratios. High speed imaging and spectral analysis of pressure drop signals are employed to analyse the flow. Two mechanisms of bubble formation are observed, one due to gas overpressure leading to large irregular bubbles, and one due to liquid turbulent vortices leading to small, well-defined bubbles. The two mechanisms lead to three distinct gas dispersion regimes, distinguished by their characteristic oscillations in pressure drop. At low rotational Reynolds numbers (Re_ω < 0.4 · 10⁶), in the gas spillover regime, the gas is dispersed as large bubbles only. Above this critical Re_ω, small bubbles are sheared off as well, thus forming a heterogeneous dispersion. At sufficiently high Re_ω, depending on the gas flow rate, the gas is homogeneously dispersed as small bubbles. The maximum gas flow that can be dispersed as small bubbles is linearly proportional to the local energy dissipation rate. The understanding of the bubble formation mechanisms and pressure signature allows prediction and detection of the prevailing hydrodynamic regime in scaled up spinning disc reactors and for different reaction fluids.     

Momentum and heat transfer in two-phase bubble flow—I. Theory

A theory is proposed which describes the transfer process of momentum and heat in a two-phase bubble flow in channels. The eddy diffusivity to express the turbulent structure of the liquid phase is subdivided into the two components, one for the inherent wall turbulence independent of bubble agitation and the other for the additional turbulence caused by bubbles. On the basis of the theory, the velocity profile and the frictional pressure gradient for a given flow can be predicted when its void fraction profile is known. Furthermore, when a uniform heat flux is added to the system, its temperature distribution and heat transfer coefficient can be determined. A method for the numerical calculation of these parameters is also presented.     

A visualized study of interfacial behavior of air–water two-phase flow in a rectangular Venturi channel

A visualized investigation was carried out on the effect of the diverging angle on the bubble motion and interfacial behavior in a Venturi-type bubble generator.It was found two or three large vortexes formed in the diverging section,resulting in strong reentrant jet flow in the front of the bubbles or slugs rushing out of the throat.The jet flow in return bumps into the ongoing bubbles or slugs,leading to strong interaction between the gas and liquid phases.The diverging angle has significant influence on the reentrant flow process and the performance of the bubble generator as well.Increasing the diverging angle results in the reentrant flow moving further forward to the upstream and intensifies the interaction between the two phases.As a consequence,the breakup or collapse of bubbles becomes more violent,whereby finer bubbles are generated.As such,the reentrant flow strongly links to the performance of the Venturi channel taken as a bubble generator,and that a moderate increase in the diverging angle can improve its performance without additional increase in flow resistance like that by increasing liquid flow rate.