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.     

槽道湍流内气泡瞬态受力数值研究

为了深入理解气泡在湍流场内的运动机制,使用欧拉-拉格朗日单向耦合数值方法,详细分析了气泡在低雷诺数槽道湍流场内的瞬态受力情况;其中液相湍流速度场采用直接数值模拟方法求解,气泡的瞬态受力由牛顿运动方程计算;计算时,考虑了相间阻力、剪切升力、压力梯度力、虚拟质量力、重力对气泡运动的影响。目前的计算结果表明:气泡所受的瞬态作用力分量同时取决于重力作用方向、液相流向以及气泡所处的法向位置;不同方向上、不同位置处影响气泡运动的主要作用力分量是不同的;相比较而言,与重力方向垂直的剪切升力分量在近壁面区域为影响气泡运动的主要作用力,压力梯度力的法向分量在近壁面区域之外为影响气泡运动的主要作用力,相间阻力分量在整个槽道区域内均为影响气泡运动的主要作用力,除了竖直槽道近壁面处之外、虚拟质量力也均为影响气泡运动的主要作用力。     

Bubble‐separation dynamics in a planar cyclone: Experiments and CFD simulations

A planar cyclone is designed for visualizing bubbles in the cross‐section of a degassing hydrocyclone. The pressure distribution is studied through a series of experiments and Reynolds stress model simulations. The velocity distribution of the planar cyclone mostly exhibits the quasi‐forced vortex zone and boundary layer zone. The bubble dynamics are simulated using both Euler‐Euler and Euler‐Lagrange approaches, and the output is compared with the imaging results. The Euler‐Euler simulation provides more accurate predictions of the bubble trajectory. The histograms of residence time and traveling distance given by the Euler‐Lagrange approach exhibit a reasonably regular pattern. With higher values of the inlet Reynolds number, stronger forces acting on the bubbles lead to a decreased but more uniform residence time. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2689–2701, 2018     

Experimental Study and CFD Simulation of Hydrodynamic Behaviours in an External Loop Airlift Slurry Reactor

The local hydrodynamic behaviours in an external loop airlift slurry reactor, including the gas holdup, bubble rise velocity, bubble size, were measured with a fibre optic probe. The liquid circulation velocity was measured with an ultrasound Doppler velocimetry. Two‐dimensional simulations were carried out in the framework of Two‐Fluid formulation coupled with a k‐? turbulence model. The lateral forces and interphase turbulence were taken into account and good agreement between the experimental and simulation results was obtained. The simulations show that the lateral forces and interphase turbulence have noticeable influence and should be included in the CFD model.     

CFD simulation and experimental measurement of gas holdup and liquid interstitial velocity in internal loop airlift reactor

This paper documents experiments and CFD simulations of the hydrodynamics of our two-phase (water, air) laboratory internal loop airlift reactor (40 l). The experiments and simulations were aimed at obtaining global flow characteristics (gas holdup and liquid interstitial velocity in the riser and in the downcomer) in our particular airlift configurations. The experiments and simulations were done for three different riser tubes with variable length and diameter. Gas (air) superficial velocities in riser were in range from 1 to 7.5 cm/s. Up to three circulation regimes were experimentally observed (no bubbles in downcomer, bubbles in downcomer but not circulating, and finally the circulating regime). The primary goal was to test our CFD simulation setup using only standard closures for interphase forces and turbulence, and assuming constant bubble size is able to capture global characteristics of the flow for our experimental airlift configurations for the three circulation regimes, and if the simulation setup could be later used for obtaining the global characteristic for modified geometries of our original airlift design or for different fluids. The CFD simulations were done in commercial code Fluent 6.3 using algebraic slip mixture multiphase model. The secondary goal was to test the sensitivity of the simulation results to different closures for the drag coefficient and the resulting bubble slip velocity and also for the turbulence. In addition to the simulations done in Fluent, simulation results using different code (CFX 12.1) and different model (full Euler–Euler) are also presented in this paper. The experimental measurements of liquid interstitial velocity in the riser and in the downcomer were done by evaluating the response to the injection of a sulphuric acid solution measured with pH probes. The gas holdup in the riser and downcomer was measured with the U-tube manometer. The results showed that the simulation setup works quite well when there are no bubbles present in the downcomer, and that the sensitivity to the drag closure is rather low in this case. The agreement was getting worse with the increase of gas holdup in the downcomer. The use of different multiphase model in the different code (CFX) gave almost the same results as the Fluent simulations.     

CFD analysis of two‐phase turbulent flow in internal airlift reactors

The hydrodynamic performance of three internal airlift reactor configurations was studied by the Eulerian–Eulerian k–ε model for a two‐phase turbulent flow. Comparative evaluation of different drag and lift force coefficient models in terms of liquid velocity in the riser and downcomer and gas holdup in the riser was highlighted. Drag correlations as a function of Eötvös number performed better results in comparison to the drag expressions related to Reynolds number. However, the drag correlation as a function of both Reynolds and Eötvös numbers fitted well with experimental results for the riser gas holdup and downcomer liquid velocity in configurations I and II. Positive lift coefficients increase the liquid velocity and decrease the riser gas holdup, while opposite results were obtained for negative values. By studying the effects of bubble size and their shape, the smaller bubbles provide a lower liquid velocity and a gas holdup. The effects of bubble‐induced turbulence and other non‐drag closure models such as turbulent dispersion and added mass forces were analysed. The gas velocity and gas holdup distributions, liquid velocity in the riser and downcomer, vectors of velocity magnitude and streamlines for liquid phase, the dynamics of gas holdup distribution and turbulent viscosity at different superficial gas velocities for different reactor configurations were computed. The effects of various geometrical parameters such as the draft tube clearance and the ratio of the riser to the downcomer cross‐sectional area on liquid velocities in the riser and the downcomer, the gas velocity and the gas holdup were explored. © 2011 Canadian Society for Chemical Engineering     

Development of a CFD Model of Bubble Column Bioreactors: Part Two – Comparison of Experimental Data and CFD Predictions

The application of computational fluid dynamics (CFD) as a tool to simulate bubble column bioreactors is investigated. A three‐dimensional model utilizing the Euler‐Euler approach is evaluated. The role of various terms, i.e., lift, drag, bubble‐induced turbulence, and volume fraction correction terms for drag, is determined. Good agreement between experimental data and simulation results was obtained by means of a single‐bubble size model provided that bubble‐induced turbulence and the reduction in drag due to the presence of other bubbles were taken into account.     

鼓泡塔反应器气液两相流CFD数值模拟

对圆柱形鼓泡塔反应器内的气液两相流动进行了三维瞬态数值模拟,模拟的表观气速范围为0.02～0.30 m•s^-1; 模拟采用了双流体模型,并耦合了气泡界面密度单方程模型预测气泡尺寸,该模型考虑了气泡聚并与破碎对气泡尺寸的影响。液相湍流采用考虑气相影响的修正k-ε模型,两相间的动量传输仅考虑曳力作用。模拟获得了轴向气/液相速度分布、气含率分布、湍流动能分布以及气泡表面面积密度等,对部分模拟结果与实验值进行了定量比较,结果表明模拟结果与实验结果吻合较好。     

Numerical studies of the effects of fines on fluidization

Euler‐Lagrange simulations of fluidized beds of Geldart Group A particles containing different levels of fines are performed in periodic domains with various domain‐averaged solid volume fractions. Bubble‐like voids readily form when no fines are added. Introducing fines does not reduce bubble sizes if van der Waals force between particles is not accounted for. In contrast, the addition of van der Waals force produces significant changes. With no fines, bubbles are found to be suppressed at sufficiently high solid volume fractions, corresponding to the expanded bed regime for Group A particles. With the addition of fines, bubbles can be suppressed at lower solid volume fractions. With more fines added, bubbles can be suppressed at even lower solid volume fractions. When bubbles are suppressed, the system is found to be in a stable solid‐like regime. In this regime, forces on each particle are balanced, and the particle velocity fluctuations are dampened. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2271–2281, 2016     

Drag force and clustering in bubble swarms

In this article, results of detailed numerical simulations are reported meant to provide a closure relation for the drag force acting on bubbles rising in a dense swarm. The formation of clusters of bubbles in a periodic domain and the effect thereof on the rise velocity and effective drag coefficient on the bubbles are studied. Using smaller bubble sizes than presented in our earlier work, we are also able to refine our correlation for the drag coefficient acting on bubbles rising in a swarm, such that it is applicable for a large range of bubble sizes. The simulations are performed with an advanced Front‐Tracking model in which Lagrangian marker points are used to track the gas–liquid interface, while accounting for surface tension and substantial interface deformation. Simulations were performed using periodic domains to simulate rising air bubbles in water from 1.0 mm up to 6.0 mm in diameter. The effect of liquid phase viscosity was also studied to extend the range of validity of the drag correlation. For the 1.0 and 1.5 mm cases, strong horizontal clustering effects are observed. Especially, at high gas fractions, the bubbles tend to form rigid horizontal arrays, which have been shown to strongly increase the drag force acting on the bubbles in the cluster. For viscous liquids, the tendency to form horizontal clusters is lower, and even vertical clustering is observed. The bubble slip velocity was compared with the experimental results of Zenit et al., which agree very well taking into account the differences between simulations and experiments. Based on our simulations, a new drag correlation was proposed, taking into account Eötvös numbers ranging from 0.13 to 4.9, and Morton numbers in the range 3.8 ≤ ? log Mo < 6.6, and gas hold‐ups up to 40% (30% for Eo < 0.3). At lower values for ?log Mo, the Reynolds number drops to the order of unity, and the correlation overpredicts the drag coefficient, which defines the range of applicability of the currently proposed drag correlation. The correlation itself describes a linear increase of the normalized drag coefficient as a function of the gas hold‐up. The strength of linear increase is stronger at lower Eötvös numbers. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1791–1800, 2013     

CFD-PBM simulation of the column flotation unit of FCMC: Importance of gas–liquid interphase forces models

The cyclonic micro-bubble flotation column (FCMC) is an efficient flotation device for the separation of fine minerals, but its mechanisms are rarely studied using computational fluid dynamics (CFD). This paper reports the air–water two-phase computational fluid dynamics-population balance model (CFD-PBM) simulations for the column flotation unit of an FCMC. The shear stress transport (SST) k-ω model with curvature correction (CC) is used to simulate turbulence effects. Then, the interphase forces models considering bubble size distribution are selected according to the experimental data in a bubble column, which is in analogy to the column flotation unit of the FCMC. Finally, the optimal combination of interphase forces models (i.e., the Ishii–Zuber drag force model, the Hosokawa–Frank wall lubrication force model, and the Lopez de Bertodano turbulent dispersion force model) is applied to simulate an FCMC with a superficial gas velocity of 0.0144 m/s. The results show that the CFD-PBM simulation can achieve a relative error of 9.09% for gas volume fraction and −5.45% for bubble rising velocity, indicating the reliability of the selected combination of interphase forces models.     

Role of free surface on gas‐induced liquid mixing in a shallow vessel

The present work is carried out to understand the effect of free surface on liquid velocity distribution, dynamics and liquid phase mixing in a shallow basic oxygen furnace (BOF). Three‐dimensional/transient Euler–Lagrange (EL) without/with volume‐of‐fluid (VOF) simulations of dispersed gas–liquid flow in a scaled‐down model of the BOF were performed. For lower H/D ratios, EL simulations performed with no‐slip and free‐slip boundary conditions led to oscillatory plume behavior and higher liquid velocity regions which in turn led to lower mixing time. In contrast, EL + VOF simulations led to reduced meandering motion of bubble plumes and lower liquid velocities resulting in higher mixing times. Interestingly, the mixing time predicted using EL + VOF approach was found to be in a good agreement with the measurements. The results presented in this work show that free surface has a significant effect on dynamics of gas–liquid flow and liquid phase mixing for shallow vessels with H/D ≤ 0.5. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3582–3598, 2017     

CFD Simulations of a Bubble Column Operating in the Homogeneous and Heterogeneous Flow Regimes

Bubble columns are operated either in the homogeneous or heterogeneous flow regime. In the homogeneous flow regime, the bubbles are nearly uniform in size and shape. In the heterogeneous flow regime, a distribution of bubble sizes exists. In this paper, a CFD model is developed to describe the hydrodynamics of bubble columns operating in either of the two flow regimes. The heterogeneous flow regime is assumed to consist of two bubble classes: “small” and “large” bubbles. For the air‐water system, appropriate drag relations are suggested for these two bubble classes. Interactions between both bubble populations and the liquid are taken into account in terms of momentum exchange, or drag‐, coefficients, which differ for the “small” and “large” bubbles. Direct interactions between the large and small bubble phases are ignored. The turbulence in the liquid phase is described using the k‐ϵ model. For a 0.1 m diameter column operating with the air‐water system, CFD simulations have been carried out for superficial gas velocities, U, in the range 0.006–0.08 m/s, spanning both regimes. These simulations reveal some of the characteristic features of homogeneous and heterogeneous flow regimes, and of regime transition.     

Numerical and experimental investigation of the lift force on single bubbles

In recent years CFD has proven itself as a valuable tool for gaining insight in flow phenomena in general and complex multiphase flows arising in process equipment in particular. However for (dispersed) multiphase flows, the reliability of the outcome of these computations depends in a sensitive way on the correctness of the representation of the phase interactions (for instance due to drag and lift forces) which leads to the well-known and difficult closure problem. In this paper we report results of direct numerical simulations supplemented with dedicated experiments to obtain quantitative data for the representation of the lift force. This force is known to be responsible for the segregation of small and large (deformed) bubbles in bubbly flows through pipes and bubble columns.Both numerical simulations using an improved front tracking (FT) model and experiments under well-defined conditions have been performed for air bubbles rising through water/glycerine mixtures, where the bubble diameter, liquid viscosity and linear shear rate were varied. The numerical simulations show a good agreement with the correlation presented by Legendre and Magnaudet (1998) for spherical bubbles at sufficiently high Reynolds numbers. For large deformed bubbles a good agreement with the correlation by Tomiyama et al. (2002) was found over a wide range of liquid viscosities, although the computed lift force was always slightly lower. Therefore a new correlation has been proposed, which combines a fit of the numerical data for deformed bubbles with the correlation by Legendre and Magnaudet (1998) for small bubbles. Finally, it was shown that the shear rate has no significant influence on the drag and lift coefficient.An experimental set-up (similar to the one used by Tomiyama) was constructed using a running belt submerged in a liquid, consisting of a glycerine–water mixture of varying viscosity. PIV measurements have been used to calibrate the linear shear field and to obtain the flow profile around the bubbles. Contrary to the numerical simulations, the experimental data show a very strong influence of the shear rate on the lift force coefficient. This may be attributed to the rigid behaviour of the contaminated bubble surface, which changes the shear stress at the bubble interface.     

竖直上升气液泡状流数学模型封闭的研究

竖直上升管气液两相流广泛应用于相变传热、核反应堆等工业过程。本文以竖直上升气液两相流为研究对象,运用欧拉双流体模型,针对表观液速为0.45m/s、表观气速分别为0.015m/s和0.1m/s的泡状流数值模拟过程中的升力、壁面润滑力、湍流扩散力、气泡诱导湍流（BIT）等封闭模型,开展数值模拟比较研究。模拟发现：①低气速泡状流中,升力和壁面润滑力的同时加入能够改善壁面附近的气含率,气泡在这两个力作用下在径向上达到一个相对平衡,得到与实验气含率类似的壁面峰,模拟的液相速度较合理;低气速时,BIT的影响可以忽略。②高气速泡状流中,BIT对气-液两相流的模拟结果影响比较明显,湍动耗散源项的加入能使液速分布的模拟结果得到改善,Troshko模型相对Sato模型更能反映气泡诱导湍流对液相湍流的作用。③高气速时升力的引入使气含率产生壁面峰,加入湍流扩散力能使峰值略微降低,但仍没有解决高气速时引入升力出现的气含率壁面峰问题,说明在径向上湍流扩散力还不足以抵抗升力。     

Effect of interfacial forces and turbulence models on predicting flow pattern inside the bubble column

The numerical approaches have been used in many studies to predict the flow pattern inside the bubble column reactors because of the difficulties that are still found in designing and scaling-up the bubble columns. This review makes an effort to show suitable interfacial forces i.e., drag force, lift force, turbulent dispersion models and virtual mass and turbulence models such as standard k–ɛ model, Reynolds Stress Model, Large Eddy Simulation to predict flow pattern inside the bubble column using Eulerian–Eulerian. The effect of various interfacial forces and turbulence models on gas–liquid velocity and gas hold-up in bubble column is critically reviewed.     

Euler–Lagrange modeling of a gas–liquid stirred reactor with consideration of bubble breakage and coalescence

Simulations of a gas–liquid stirred reactor including bubble breakage and coalescence were performed. The filtered conservation equations for the liquid phase were discretized using a lattice‐Boltzmann scheme. A Lagrangian approach with a bubble parcel concept was used for the dispersed gas phase. Bubble breakage and coalescence were modeled as stochastic events. Additional assumptions for bubble breakup modeling in an Euler–Lagrange framework were proposed. The action of the reactor components on the liquid flow field was described using an immersed boundary condition. The predicted number‐based mean diameter and long‐term averaged liquid velocity components agree qualitatively and quantitatively well with experimental data for a laboratory‐scale gas–liquid stirred reactor with dilute dispersion. Effects of the presence of bubbles, as well as the increase in the gas flow rate, on the hydrodynamics were numerically studied. The modeling technique offers an alternative engineering tool to gain detailed insights into complex industrial‐scale gas–liquid stirred reactors. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

附加惯性力作用下竖直矩形流道内过冷流动沸腾的数值模拟

摇摆条件下附加惯性力的作用会对两相流动的压降及汽泡受力产生影响。考虑相变能量和质量输运,采用流体体积(VOF)多相流模型对附加惯性力条件下竖直矩形流道内过冷流动沸腾进行了数值模拟。汽液界面位置通过分段线性插值(PLIC)的方法获得。模拟结果获得了孤立汽泡周围压力、速度、温度分布以及二次流动现象,分析了汽泡聚合过程汽泡形态及内部速度矢量的演变过程,模拟结果与文献中结论吻合良好。附加惯性力作用使得流动压降比静止条件下要大,过冷流动沸腾压降由于汽相产生会在单相流动的基础上产生波动,且热通量越大,压降波动幅度越大。摇摆产生的附加惯性力相对汽泡所受的其他力而言可以忽略不计,而摇摆导致的流量波动会改变汽泡受力大小,进而影响沸腾换热。     

Hydrodynamic Model for Horizontal Two‐phase Flow Through Porous Media

A unidirectional, two‐fluid model based on the volume‐average mass and momentum balance equations was developed for the prediction of two‐phase pressure drop and external liquid hold‐up in horizontally positioned packed beds experiencing stratified, annular and dispersed bubble flow regimes. The so‐called slit model drag force closures were used for the stratified and annular flow regimes. In the case of dispersed bubble flow regime, the liquid‐solid interaction force was formulated on the basis of the Kozeny‐Carman equation by taking into account the presence of bubbles in reducing the available volume for the flowing liquid. The gas‐liquid interaction force was evaluated by using the respective solutions of drag coefficient for an isolated bubble in viscous and turbulent flows. The proposed drag force expressions for the different flow patterns occurring in the bed associated with the two‐fluid model resulted in a predictive method requiring no adjustable parameter to describe the hydrodynamics for horizontal two‐phase flow in packed beds.