Numerical study of bubbly upflows in a vertical channel using the Euler–Lagrange two-way model

Bubbly flows exist extensively in industrial processes, so it is very meaningful to study hydrodynamic characteristics of them to improve efficiency of bubbly flow equipments. This paper introduces a numerical method of the Euler–Lagrange two-way model for the air–water bubbly flows in detail. The flow field is simulated by using direct numerical simulations (DNS) in Euler frame of reference, while the bubble dynamics are fully analyzed by integration of Newtonian equations of motion taking into account interphase interaction forces including drag force, lift force, wall lift force, pressure gradient force, virtual mass force, gravity force, buoyant force, and inertia force in Lagrange frame of reference. The coupling between phases is considered by regarding the interphase interaction forces as a momentum source term of the continuous phase. Bubbles distribution and turbulent statistics of the liquid phase are comprehensively analyzed. The results show that an overwhelming majority of bubbles cluster near the walls, and turbulent structures of the liquid phase are modified to some certain by addition of bubbles, namely, the mean streamwise velocity become increased at the core of the channel, the wall-normal and spanwise turbulent intensities and Reynolds stress are reduced. Redistribution of turbulent energy from the streamwise velocity components to wall-normal and spanwise velocity components is also suppressed due to the addition of bubbles.     

A Comparison of the Mixing Characteristics in Single‐ and Two‐Phase Grid‐Generated Turbulent Flow Systems

The mixing process is studied in grid‐generated turbulent flow for single‐ and bubbly two‐phase flow systems. Concentration and mixing characteristics in the liquid phase are measured with the aid of a PLIF/PLIF arrangement. A nearly isotropic turbulent flow field is generated at the center of the vertical pipe by using a honeycomb, three grids and a contraction. In two‐phase flow experiments, air bubbles were injected into the flow from a rectangular grid, with mesh size M = 6 mm, which is placed midway between two circular grids each with a mesh size of M = 2 mm. For single‐phase flow, the normalized mean concentration cross‐stream profiles have rather similar Gaussian shapes, and the cross‐stream profiles of the normalized root‐mean‐square (RMS) values of concentration were found to be quite similar. Cross‐stream profiles of the mean concentration, for bubbly two‐phase flow, were also found to be quite similar, but they did not have the Gaussian shape of the profiles for single‐phase flow. Almost self‐similar behavior was also found for the RMS values of the concentration in two‐phase systems. The turbulent diffusion coefficient in the liquid phase was also calculated. At the center of the plume, the flow was found to have a periodic coherent structure, probably of vortex shedding character. Observations showed that the period of oscillation is higher in the case of two‐phase flow than in single‐phase flow.     

运用单元系综平均方法研究"层流"泡状流压力场

在考虑真实流体粘度、忽略气泡尾迹区影响的前提下,通过对真实流体绕球形气泡的流场进行研究,运用单元系综平均方法推导出液相界面平均压力与液相平均压力差pli-pl的表达式,反映了液体粘度对该压力差的影响. 由于湍流泡状流相对雷诺数较大,无法忽略尾迹区对其气泡周围压力场的影响,因此该表达式只适用于"层流"泡状流.     

底吹气连铸中间包内气液两相流的数值模拟

以宝钢集团梅山钢厂1台连铸中间包为原型,进行底吹气中间包水模型研究. 实测结果表明,底吹气在中间包内形成"鼓泡流"形式的流动结构;"鼓泡流"的形成一方面能够破坏中间包内"层流"形式的短路流动,增强混合,另一方面能在中间包内形成"气幕挡墙",有利于夹杂物去除. 针对中间包内气-液两相"鼓泡流"特征,建立了底吹气中间包内气-液两相欧拉多流体模型,模型中考虑了气泡的存在对湍流增强的影响,考虑了相间滑移、气泡浮力及湍流分散力. 采用所建立的模型对底吹气中间包内气液两相流动和混合特性进行了模拟和分析,结果与水模型实测结果一致.     

Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows

Closure laws are needed for the qualification of CFD codes for two-phase flows. In case of bubbly and slug flow, forces acting on the bubbles usually model the momentum transfer between the phases. Several models for such forces can be found in Literature. They show, that these forces depend on the liquid flow field as well as on the size and the shape of the bubbles. A validation of consistent sets of bubble force models for poly-disperse flows is given, basing on a detailed experimental database for vertical pipe flows, which contains data on the radial distribution of bubbles of different size as well as local bubble size distributions. A one-dimensional (1D) solver provides velocity profiles and bubble distributions in radial direction. It considers a large number of bubble size classes and is used for the comparison with the experiments. The simplified model was checked against the results of full 3D simulations done by the commercial code CFX-5.7 for simplified monodisperse cases. The effects of the number of bubbles classes as well as the effect of the lateral extension of the bubbles were analyzed. For the validation of bubble force models measured bubble size distributions were taken as an input for the calculation. On basis of the assumption of an equilibrium of the lateral bubble forces, radial volume fraction profiles were calculated separately for each bubble class. In the result of the validation of different models for the bubble forces, a set of Tomiyama lift and wall force, deformation force and Favre averaged turbulent dispersion force was found to provide the best agreement with the experimental data. Some discrepancies remain at high liquid superficial velocities.     

稀疏两相射流中颗粒碰撞的数值研究

为了研究稀疏气固两相流动中颗粒间的碰撞行为及其对颗粒扩散的影响,对三维两相湍流射流进行了直接数值模拟。其中对流场控制方程的求解采用有限容积法和分步投影算法,对颗粒的跟踪采用拉格朗日方法,对颗粒间的碰撞采用硬球模型模拟。结果发现,在流场中局部浓度较高的区域颗粒碰撞频繁发生;受局部富集效应和湍流输运作用两方面的影响,颗粒的平均碰撞次数并不是随着Stokes数的增加呈现简单的线性增加,而是在Stokes数为0.1附近存在一个极值;考虑颗粒间的碰撞作用以后,颗粒的分布更加均匀,沿横向和展向的扩散也都有所增加。     

Multi-fluid simulation of turbulent bubbly pipe flows

Radial distributions of void fraction α_G, bubble aspect ratio E, phasic velocities V_G and V_L and turbulent kinetic energy k in bubbly pipe flows are measured using an image processing method and a laser Doppler velocimetry. Multi-fluid simulations are conducted to examine applicability of state-of-the-art closure relations to the turbulent bubbly pipe flows. The experimental results indicate that aspect ratio of bubbles in the near wall region takes a higher value than that of free rising bubbles due to the presence of wall, and that the change in the aspect ratio induces decrease in relative velocity between bubbles and liquid in the near wall region. Drag coefficient C_D of a bubble in a bubbly pipe flow tends to increase with magnitude of shear flow, and the effect of shear flow on C_D is estimated by the correlation proposed by Legendre and Magnaudet (1998). Comparison between the simulated and the measured results indicate that the effects of bubble shape and shear flow on drag force acting on bubbles should be taken into account for accurate predictions of bubbly pipe flows. The turbulence models proposed by Lopez de Bertodano et al. (1994) and by Hosokawa and Tomiyama (2004a) give good predictions for turbulence modification caused by bubbles.     

Flow regime identification of two-phase liquid-liquid upflow through vertical pipe

The present work has attempted to identify the flow patterns during liquid-liquid two phase flow through a vertical pipe. Dyed kerosene and water have been selected as the test fluids. The measurements have been made for phase velocities varying from 0.05 to 1.5 m/s for both the liquids. The conductivity probe technique has been adopted and three different probe designs have been used to identify the patterns under different flow conditions. A parallel wire type probe traversing the entire cross-section along a diametral plane has indicated the existence of bubbly flow at low phase flow rates and dispersed bubbly flow at high velocities of water. Apart from the visual appearance of the signals, different statistical analysis namely the probability density function and wavelet analysis have been performed for a better appraisal of the flow situation. The information in the PDFs have been quantified by means of the statistical moments. The existence of the core-annular flow at high kerosene and low water velocities has been confirmed from measurements using a different probe design. The intermediate region between the bubbly and annular flow patterns is characterized by a random distribution of the two liquids with continually changing interface between them. This has been named as the churn turbulent flow pattern. The information thus obtained has been represented in the form of a flow pattern map.     

On the prediction of the phase distribution of bubbly flow in a horizontal pipe

Horizontal bubbly flow is widely encountered in various industrial systems because of its ability to provide large interfacial areas for heat and mass transfer. Nonetheless, this particular flow orientation has received less attention when compared to vertical bubbly flow. Owing to the strong influence due to buoyancy, the migration of dispersed bubbles towards the top wall of the horizontal pipe generally causes a highly asymmetrical internal phase distributions, which are not experienced in vertical bubbly flow. In this study, the internal phase distribution of air-water bubbly flow in a long horizontal pipe with an inner diameter of 50.3 mm has been predicted using the population balance model based on direct quadrature method of moments (DQMOM) and multiple-size group (MUSIG) model. The predicted local radial distributions of gas void fraction, liquid velocity and interfacial area concentration have been validated against the experimental data of Kocamustafaogullari and Huang (1994). In general, satisfactory agreements between predicted and measured results were achieved. The numerical results indicated that the gas void fraction and interfacial area concentration have a unique internal structure with a prevailing maximum peak near the top wall of the pipe due to buoyancy effect.     

Deduction and Validation of an Eulerian-Eulerian Model for Turbulent Dilute Two-Phase Flows by Means of the Phase Indicator Function---Disperse Elements* Probability Density Function

A statistical formalism overcoming some conceptualand practical difficulties arising in existing two-phase flow (2PHF)mathematical modelling has been applied to propose a model for dilute2PHF turbulent flows. Phase interaction terms with a clear physical meaning enterthe equations andthe formalism provides some guidelines for the avoidance of closure assumptions orthe rational approximation of these terms. Continuous phase averaged continuity,momentum, turbulent kinetic energy and turbulencedissipation rate equations have been rigorously andsystematically obtained in a single step.These equations display a structure similar to that forsingle-phase flows. It is also assumed thatdispersed phase dynamics is well described by a probability densityfunction (pdf) equation and Eulerian continuity,momentum and fluctuating kinetic energy equations for the dispersedphase are deduced. Anextension of the standard k- turbulencemodel for the continuous phase is used. A gradient transport model is adopted forthe dispersedphase fluctuating fluxes of momentum and kinetic energy at the non-colliding, largeinertia limit. This model is thenused to predict the behaviour of three axisymmetric turbulent jets of air laden withsolid particlesvarying in size and concentration. Qualitative and quantitative numericalpredictions comparereasonably well with the three different sets of experimental results, studying theinfluence ofparticle size, loading ratio and flow confinement velocity.     

绝热层流泡状流运动的双流体模型

绝热层流泡状流是泡状流研究中的一个基础范例 .目前描述绝热层流泡状流常采用的双流体模型由于相间作用考虑欠缺而适用性差 .本文结合理论和实验研究结果导出了描述壁面“排斥”作用的表达式 ,并建立了一个封闭的双流体模型 .模型预测值和实验值的比较表明 ,由于相间作用的合理考虑 ,扩大了该模型的适用范围     

Comparison of Eulerian QBMM and classical Eulerian–Eulerian method for the simulation of polydisperse bubbly flows

The spatial gas distribution of poly-disperse bubbly flows depends greatly on the bubble size. To reflect the resulting polycelerity, more than two momentum balance equations (typically for the gas and liquid phases) have to be considered, as done in the multifluid approach. The inhomogeneous multiple-size group model follows this approach, also combined with a population balance model. As an alternative, in a previous work, an Eulerian quadrature-based moments method (E-QBMM) was implemented in OpenFOAM; however, only the drag force was included. In this work, different nondrag forces (lift, wall lubrication, and turbulent dispersion) are added to enable more complex test cases to be simulated. Simulation results obtained using E-QBMM are compared with the classical E–E method and validated against experimental data for different test cases. The results show that there is good agreement between E-QBMM and E–E methods for mono-disperse cases, but E-QBMM can better simulate the separation and segregation of small and large bubbles.     

A probabilistic model for correcting the directional sensitivity of optical probe measurements

A probabilistic model is introduced for correcting the directional sensitivity of the optical probe technique routinely used to determine gas holdup and bubble dynamics in gas‐liquid systems. Measurements from optical probes oriented at various angles were collected from the tapered end of optical probes in regions where approximately unidirectional and bubbly flow conditions were observed. Based on logical assumptions, constitutive equations for a probabilistic model were formulated, and contributions to the overall local gas phase holdup from bubbles traveling in two opposite directions were quantified. The results demonstrate a novel and useful way to interpret optical probe measurements. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3516–3527, 2015     

Liquid holdup in concentric annuli during cocurrent gas‐liquid upflow

In the recent paper, an in‐depth investigation of liquid holdup during air‐water upflow through concentric annuli has been reported. The liquid holdup has been determined experimentally for the bubbly, slug and churn flow regimes. The drift flux model has been adopted for the theoretical estimation of holdup in the bubbly, dispersed bubbly and slug flow regimes. The pronounced effect of flow regime on this parameter as observed from experiments has been incorporated in the model by adopting different values of U₀, n and C₀. The asymmetry of the Taylor bubbles has been incorporated in the slug flow regime. The theoretical predictions exhibit a good agreement with the experimental data of the present work and that available in literature (Caetano et al., 1989b). The Hughmark's correlation is observed to correlate the churn flow data of the present work reasonably well.     

Eulerian–Lagrangian simulation of bubble coalescence in bubbly flow using the spring-dashpot model

The Eulerian–Lagrangian simulation of bubbly flow has the advantage of tracking the motion of bubbles in continuous fluid, and hence the position and velocity of each bubble could be accurately acquired. Previous simulation usually used the hard-sphere model for bubble–bubble interactions, assuming that bubbles are rigid spheres and the collisions between bubbles are instantaneous. The bubble contact time during collision processes is not directly taken into account in the collision model. However, the contact time is physically a prerequisite for bubbles to coalesce, and should be long enough for liquid film drainage. In this work we applied the spring-dashpot model to model the bubble collisions and the bubble contact time, and then integrated the spring-dashpot model with the film drainage model for coalescence and a bubble breakage model. The bubble contact time is therefore accurately recorded during the collisions. We investigated the performance of the spring-dashpot model and the effect of the normal stiffness coefficient on bubble coalescence in the simulation.The results indicate that the spring-dashpot model together with the bubble coalescence and breakage model could reasonably reproduce the two-phase flow field, bubble coalescence and bubble size distribution. The influence of normal stiffness coefficient on simulation is also discussed.     

蛇形管内汽液泡状流与传热的数值模拟

建立了含有相变过程的汽液泡状流VOF数值模型,通过同实验进行流型对比,验证了模型的有效性。模拟研究了蛇形管内汽液泡状流传热过程,结果表明：二次流导致冷热流体混合;在单汽泡流动时,弯管壁面上温度场在汽泡经过后具有良好的恢复能力;在汽泡串流动时,二次流将弯管下半部温度较高的流体带入上半部,有效提升上半部壁温,从而造成上壁面温度在汽泡经过前后出现较大的变化。     

Interfacial area density in bubbly flow

The interfacial area per unit volume is one of the key parameters in bubbly flow. Momentum, mass and energy transfer occur through the interface between the phases. The functionality of two phase reactors with bubbly flow depends mainly on these three transfer processes. Thus, the design process of a reactor requires the prediction of interfacial area density. In the present work a simple equation for the interfacial area density is derived from the population balance, taking into account the events of coalescence and bubble break-up for each bubble fraction. The system of partial integro-differential equations is simplified. Since the integrals in these equations complicate a numerical treatment. This reduces the balance to one single partial differential equation. An approximate analytical solution is given. If the resulting equation is applied to large gas fluxes, the instability of the coalescence process causes large bubbles and gas plugs to develop. From the instability the volume fraction of the large bubbles and gas plugs may be predicted. Additives may hinder the coalescence process. Experiments show that coalescence hindrance changes the coalescence kernel only by a factor. Calculations are done for bubble columns and vertical pipe flow.     

Experimental investigation of cocurrent two-phase flow in a vertical rectangular channel

New time averaged data of two-phase flow in bubbly and slug regimes are presented. A modified dual spherical tipped optical fiber probe is used to measure local void fractions, gas velocity and bubble sizes. Hot film anemometry was used to measure the local mean liquid velocity axially. The void fraction, gas and liquid velocities values were presented as averages over the long and short dimensions respectively. Also core values of these variables are presented along the smaller dimension of 12.7 mm, near the plane of symmetry of the longer dimension, to show the most general trend of the different bubbly and slug flow runs. Bubble sizes obtained experimentally were compared with predictive models applied to circular geometries and were found to have a reasonable agreement. It was also interesting to find that local void fractions measured using hot film anemometers were comparable to those found by optical fiber probes. Frequencies of interfacial passage of bubbles and slugs are presented which show rather flat profiles across the channel. It is hoped that these data can be further used in predictive two-phase two-fluid models in the future. Lastly of interest is the fact that slip values near the boundaries were shown to be less than 1.0 for some cases in bubbly flow similar to those observed in circular geometries.     

Numerical studies on effects of bubbles regular array on the liquid‐phase turbulence

It is well known that additive drag‐reducing methods have broadly developing prospects, so studies on mechanisms of additive drag reduction are very necessary. We hypothesised that the main reason for bubbles induced drag reduction is the modification on liquid‐phase turbulence structure by the addition of bubbles, and therefore such modification is the focus of our investigation. In this paper, effects of bubbles on liquid‐phase turbulence under the circumstance of regular bubble array were investigated by using Euler–Lagrange two‐way numerical simulations. The liquid‐phase velocity field was solved by using direct numerical simulations (DNS) in Euler frame of reference, and the bubble motion was tracked by using Newtonian motion equations that took into account interaction forces including drag force, shear lift force, gravity force, buoyant force, and inertia force in Lagrange frame of reference. The coupling between the phases was realised by regarding the interphase forces as momentum source terms of the continuous phase. Similarities and differences for effects of bubbles and surfactants on liquid turbulent flows were also analysed. The study indicated that addition of bubbles enhances the mean streamwise velocity, greatly reduces the Reynolds stress, and shows anisotropic suppression to the velocity fluctuations. The interphase force has a great influence on budget of energy balance. It is a gain term near the wall and is a loss term in a wide range of the channel core.     

鼓泡塔内气液两相湍流实验研究

介绍了研究鼓泡塔气液两相流的实验装置、实验方法。液相用激光多普勒测速技术(LDV)测量,气相用粒子示踪测速技术(PIV)测量。实验表明,轴向液相速度的径向分布呈塔中心峰值、壁面附近倒流形式,且与气相表观速度大小有关,当液相表观速度一定时,随气相表观速度增大而愈加陡峭,返混也剧烈。当表观液速与表观气速之比小于19．6时,返混区总是存在,且返混区大小与高度有关：当表观液遣与表观气速之比大于19．6时,返混消失,含气率分布由塔中心峰值转向壁面峰值。径向液相速度既与气相表现速度有关又与位置高度有关,在塔底部呈现负值,这意味着向塔轴心方向流动。随着塔高增加。流动方向逐渐转变为向塔壁方向,且又有明显的峰值。