PREDICTION OF GAS-PHASE HOLDUP IN A BUBBLE COLUMN

Hydrodynamic properties of bubble columns play a significant role in many chemical and biochemical processes. Recent theoretical and experimental work conducted by Krishna et al. (1991, 1994), and Wilkinson et al. (1992) have been examined in conjunction with a bubble column and data for the air-water system operating at ambient conditions. The bubble column is 0.108 m in internal diameter, has a 1.70 m tall test section, and is equipped with a perforated plate distributor having 91 holes of 0.8 mm diameter. The data are taken for five values of the slumped water column height in range from 0.79 to 1.15 m, and for superficial air velocities up to about 0.4 m/s.

The data accord to the qualitative aspects of Krishna et al. model but lead to different values of the bubble swarm rise velocity, and superficial transition air velocity characterizing the transition from homogeneous bubbly flow regime to heterogeneous churn-turbulent flow regime. The quantitative reproduction by the model expressions of these recent works of the experimental data is poor. This may be partly attributed to the geometry of the column, diameter and distributor design.

The qualitative features of Krishna et al. model for the two regimes are confirmed by the present data. For quantitative predictions of gas-phase holdup, a new model is proposed in which the large bubble flow in the churn-turbulent regime is formulated following the drift-flux theory. The proposed theory and experimental data are in good agreement.     

Influence of the lift force in direct numerical simulation of upward/downward turbulent channel flow laden with surfactant contaminated microbubbles

In this work, we employ direct numerical simulation of turbulence one-way coupled to Lagrangian tracking to investigate microbubble distribution in upward and downward channel flow. We consider a closed channel flow at Re_τ=150 and a dispersion of microbubbles characterized by a diameter of . Bubbles are assumed contaminated by surfactants (i.e., no-slip condition at bubble surface) and are subject to drag, gravity, pressure gradient forces, Basset history force and aerodynamic lift.Our results confirm previous findings and show that microbubble dispersion in the wall region is dominated by the action of gravity combined with the lift force. Specifically, in upward flow, bubble rising velocity in the wall region generates a lift force which pushes bubbles to the wall. In downward flow, bubble rising velocity against the fluid generates a lift force which prevents microbubbles from reaching the viscous sublayer.In the wall region, we observe bubble preferential segregation in high-speed regions in the downflow case, and non-preferential distribution in the upflow case. This phenomenon is related to the effect of the lift force. Compared to experiments, the current lift force model produces larger consequences, this effect being overemphasized in the upflow case in which a large number of bubbles is segregated near the wall. In this case, the resulting bubble wall-peak of concentration outranges experimental results.These results, so deeply related to the lift force, underline the crucial role of current understanding of the fluid forces acting on bubbles and help to formulate questions about available force models, bubble-bubble interactions and two-way coupling which can be crucial for accurate predictions in the region very near the wall.     

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.     

Influence of the lift force on the stability of a bubble column

This work investigates the role of the lift force for the stability of a homogeneous bubble column. Instabilities caused by the lift force may be one important reason for the transition from homogeneous to heterogeneous bubble column. On rising bubbles the lift force acts in a lateral direction, when gradients of the liquid velocity are present. Non-uniform liquid velocity fields may be induced if the gas fraction is not equally distributed, e.g. caused by local disturbances. This feedback mechanism is studied in the paper. It was found, that a positive lift coefficient (small bubbles) stabilizes the flow, while a negative coefficient (large bubbles) leads to unstable gas fraction distributions, and thus it favours the appearance of a heterogeneous bubble column regime. The turbulent dispersion force has always a stabilizing action, i.e., it partially compensates the destabilization induced by a negative lift coefficient. A stability analysis for a mono-dispersed system nevertheless showed, that influence of the lift force is much larger, compared to the influence of the turbulent dispersion force, if only bubble induced turbulence is considered. Thus, the stability condition is practically the positive sign of the lift force coefficient. The extension of the analysis to two bubbles classes, from which one being small enough to have a positive lift coefficient, results in a minimum fraction of small bubbles needed for stability. Finally a generalized criterion for N bubble classes and for a continuous bubble size distribution is given.     

毛细管内气液Taylor流动的气泡及阻力特性

采用相对坐标系方法,研究毛细管(d 2mm)内充分发展垂直上升气液Taylor流动,分析两种工作介质下Taylor气泡的形状、上升速度、液膜厚度以及压降特性。结果表明:随着两相表观速度(V_tp)增大,Taylor气泡长度增大,气泡尾部曲率半径增大。气泡长度及内部回流区随着气泡体积分数(ξ_g)增大而增大,量纲1液膜厚度与气泡上升速度与毛细数(Ca)正相关,模拟结果与经验公式吻合较好。摩擦阻力因子(f_c)随V_tp与ξ_g的增大而降低,N₂/乙二醇为工质的Taylor流动f_c低于单相情况,而N₂/水为工质的Taylor流动f_c高于单相情况。Kreutzer等的流型依赖公式以及Lockhart等的分离模型可较好预测本文的两相压降,模拟结果与预测值的误差在±10%以内,常规通道所推荐C 5仍然适用于本文毛细管情况。     

基于径向力平衡的鼓泡塔二维流体力学模型

提出了一种鼓泡塔二维轴对称流体力学模型,模型中将气泡所受的升力以及湍动扩散力作为形成塔内气含率稳定分布的主要机制.采用Fluent 6.3流体力学软件求解模型,能得到稳定的二维流场,气含率与液速分布与实验值吻合良好,模型能准确反映表观气速(0.12～0.62 m·s^-1)以及塔径(ø200 mm、ø500 mm、ø800 mm)对流型的影响.利用该模型对更大直径鼓泡塔的流动参数进行了预测,结果与文献给出的经验关联式相符.     

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。     

HYDRODYNAMIC CHROMATOGRAPHY: THREE DIMENSIONAL LAMINAR DISPERSION IN RECTANGULAR CONDUITS WITH TRANSVERSE FLOW

Experimental observations^1,9 indicate much poorer separations than are predicted by two dimensional theory. The purpose of this work is to explain these differences and suggest ways in which system performance can be improved.

The large effect of span-wise variation in axial velocity caused by side walls on hydrodynamic separations carried out in rectangular conduits with transverse flow is studied theoretically. As the aspect ratio increases, the steady stale retentivity (convection coefficient) approaches an asymptotic value obtained by neglecting side wall effects. However, the dispersion coefficient does not reduce to that for a flow with no side walls. Indeed, the asymptotic steady state dispersion coefficient is at least six times larger than that obtained by two dimensional theory which neglects side wall effects. As the transverse Peclet number increases, the effect of side walls on the dispersion coefficient becomes much larger.

The present three dimensional theoretical predictions, in contrast to two dimensional ones, are in good agreement with the experimental data of Caldwell, et al.⁹ and Kesner, et al.¹ on electrical field flow fractionation. The results indicate that side wall effects may be of major importance in hydrodynamic chromatography even when the aspect ratio is 70 or more.

The adverse effect of side walls may be avoided by having the membranes enclose thin annular regions rather than rectangular conduits. This should improve performance significantly.     

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。     

INTERPRETATION OF MICROMIXING EFFECTS ON FAST CONSECUTIVE-COMPETING REACTIONS IN SEMI-BATCH STIRRED TANKS BY A SIMPLE INTERACTION MODEL

A model is proposed for interpreting micromixing experiments in a semi-batch reactor. In these experiments, a fast consecutive-competing reaction system is used A + B → R, R + B → S, B being added either dropwise or as a pulse into an excess of A. A segregation index X_s = 2n_s/n_B0 is measured after completion of the reaction for various locations of the injection point. The macroscopic flow pattern is assumed to be known, essentially characterized by the recirculation time t_c. Micromixing then takes place within the cloud via a mechanism of interaction with the mean environment (IEM model, micromixing time t_m). Experimental results published by Barthole et al. (precipitation of barium sulphate) and Bourne et al. (diazo coupling) are successfully interpreted by this model. The influence of stirring speed, injection volume, concentration of species and mode of injection (pulse or dropwise) are especially well accounted for. This model provides a simple method for predicting the influence of mixing on selectivity in semi-batch reactors.     

Void fraction measurement and calculation model of vertical upward co-current air–water slug flow

The focus of this paper is on the measurement and calculation model of void fraction for the vertical upward co-current air–water slug flow in a circular tube of 15 mm inner diameter. High-speed photography and optical probes were utilized, with water superficial velocity ranging from 0.089 to 0.65 m·s^-1 and gas superficial velocity ranging from 0.049 to 0.65 m·s^-1. A new void fraction model based on the local parameters was proposed, disposing the slug flow as a combination of Taylor bubbles and liquid slugs. In the Taylor bubble region, correction factors of liquid film thickness C_δ and nose shape C_Z^* were proposed to calculate α_TB. In the liquid slug region, the radial void fraction distribution profiles were obtained to calculate α_LS, by employing the image processing technique based on supervised machine learning. Results showed that the void fraction proportion in Taylor bubbles occupied crucial contribution to the overall void fraction. Multiple types of void fraction predictive correlations were assessed using the present data. The performance of the Schmidt model was optimal, while some models for slug flow performed not outstanding. Additionally, a predictive correlation was correlated between the central local void fraction and the cross-sectional averaged void fraction, as a straightforward form of the void fraction calculation model. The predictive correlation showed a good agreement with the present experimental data, as well as the data of Olerni et al., indicating that the new model was effective and applicable under the slug flow conditions.     

INVISCID LIQUID CIRCULATION IN BUBBLE COLUMNS

For circulation in axi-symmetric (cylindrical) bubble columns, the recently developed mathematical model^25,26 has been used along with the criterion of minimum circulation strength to determine the height of each circulation cell in a tall column. This is then used to derive a theoretical expression, first of its kind, for gas hold-up inside a bubble column. The predictions of this equation as well as the equation derived here for axial liquid velocity at column axis have been compared with available data and the comparison is found to be excellent for both the variables. An explicit relation is derived for the average liquid circulation velocity. The model is also used to derive an expression for liquid axial dispersion coefficient which compares almost exactly with Deckwer et al.'s⁴ correlation.

For circulation in two-dimensional bubble columns a new mathematical model is developed. The predictions of bubble envelope shape and bubble envelope area compare well with published data. The predictions of number of circulation cells in the horizontal direction also compare well with published data.     

EFFECTS OF PARTICLE CHARACTERISTICS ON THE PERFORMANCE OF A FAST FLUIDIZED BED REACTOR

A heterogeneous model for the fast fluidized bed reactor which carries out a gas-solid non catalytic reaction is presented. The hydrodynamics of the fast fluidized bed is characterized by the model of Kwauk et al. (1985) which assumes the existence of two phases; a dense phase and a dilute pneumatic transport phase. For a given solid flowrate, the length of the reactor occupied by each phase depends on gas velocity, particle diameter and density and average voidage within the reactor. The gas-solid reaction is assumed to follow the shrinking core model. The solids are assumed to be completely backmixed in the dense phase and move in plug How in the dilute pneumatic transport phase. The gas phase is assumed to be in plug flow in both phases

For given gas and solid flowrates, the transition from the dense phase flow to the fast fluidized bed (containing two regions) as functions of particle size and density is determined using the model of Kwauk et al. (1985). The numerical solution of the governing mass balance equations show that for given solid and gas flowrates, (and average voidage) the gas phase conversion shows an unusual behavior with respect to particle diameter and density. Such behavior is resulted from the effects of particle diameter and density on the reactor volume occupied by each phase and the effect of particle diameter on the apparent reaction rate. The numerical results show that a fast fluidized bed gives the best conversion at large particle density and for the particle diameter which results the fast fluidized bed to be operated near the pure dense phase flow.     

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.     

LONG-RANGE MAGNETIC FORCES IN TWO-DIMENSIONAL HYDRODYNAMICS OF MAGNETIC FLUID PATTERN FORMATION

Phenomena associated with long-range forces of interparticle interaction have received great attention since the stable colloids of ferromagnetics were first prepared. One of these-surface instability of magnetic fluid in a vertical field-was first observed by Cowley and Rosensweig (Cowley, Rosensweig, 1967) and is a remarkable demonstration of the properties of liquid magnetics. The studies here have displayed a lot of interesting characteristics of these phenomena such as subcritical character of bifurcation at the origin of hexagonal pattern of a magnetic fluid (Gailitis, 1969), a possible change of hexagonal pattern into the square one (Gailitis, 1977; Kuznetsov el al., 1976), subcritical bifurcation of a uni-dimensional pattern (Zaitsev et al., 1969; Bacri et ai., 1984).

The development of a concept of the hydrodynamical stability control by the field has demonstrated the stabilizing effect of a magnetic field at both the Rayleigh-Taylor instability (Rosensweig, 1979a) and the Saffman-Taylor instability of displacement front (Rosensweig et al, 1977; Zahn et al, 1980) and others. Using this basis, Rosensweig was able to put forward an alluring idea of possible application of magnetic forces to stabilize ftuidized beds (Rosensweig, 1979b, 1979c). It is the significant contribution of Rosensweig's works into further investigations of the hydrodynamic instability control by a magnetic field, which should be given a special mention. These developments have lead to new insights and will add a new dimension to the study of magnetic fluids.

We shall consider a comparatively new type of two-dimensional hydrodynamical instability revealing an intricate pattern of selforganization of a magnetic fluid due to long-range magnetic forces.     

加热上升管内过冷流动沸腾数值模拟

采用计算流体动力学（CFD）程序CFX4.4对加热上升管内过冷流动沸腾工况下气水两相流动局部两相流参数（空泡份额和汽泡尺寸）进行了数值模拟。对数值差分方法、相关模型（界面力和气泡诱导的紊流）和汽泡尺寸进行了敏感性分析。空泡份额分布计算结果与实验结果比较表明,在低空泡份额工况下,两者符合较好,在高空泡份额工况下两者存在一定偏差,并且气相速度和汽泡尺寸的计算结果不理想。计算结果与实验结果之间的差异说明程序模型对于加热上升管内过冷流动沸腾模拟并不完善,建立更为合理的汽泡尺寸模型,考虑汽泡的合并和撕裂是必要的。     

Experimental and numerical investigations of scale-up effects on the hydrodynamics of slurry bubble columns

Experiments and simulations were conducted for bubble columns with diameter of 0.2 m(180 mm i.d.), 0.5 m(476 mm i.d.) and 0.8 m(760 mm i.d.) at high superficial gas velocities(0.12–0.62 m·s-1) and high solid concentrations(0–30 vol%). Radial profiles of time-averaged gas holdup, axial liquid velocity, and turbulent kinetic energy were measured by using in-house developed conductivity probes and Pavlov tubes. Effects of column diameter, superficial gas velocity, and solid concentration were investigated in a wide range of operating conditions. Experimental results indicated that the average gas holdup remarkably increases with superficial gas velocity, and the radial profiles of investigated flow properties become steeper at high superficial gas velocities. The axial liquid velocities significantly increase with the growth of the column size, whereas the gas holdup was slightly affected. The presence of solid in bubble columns would inhibit the breakage of bubbles, which results in an increase in bubble rise velocity and a decrease in gas holdup, but time-averaged axial liquid velocities remain almost the same as that of the hollow column. Furthermore, a 2-D axisymmetric k–ε model was used to simulate heterogeneous bubbly flow using commercial code FLUENT 6.2. The lateral lift force and the turbulent diffusion force were introduced for the determination of gas holdup profiles and the effects of solid concentration were considered as the variation of average bubble diameter in the model. Results predicted by the CFD simulation showed good agreement with experimental data.     

Simulation of oscillatory baffled column: CFD and population balance

In the present work, an attempt has been made to combine population balance and a CFD approach for simulating the flow in oscillatory baffled column (OBC). Three-dimensional Euler-Euler two-fluid simulations are carried out for the experimental data of Oliveira and Ni [2001. Gas hold-up and bubble diameter in a gassed oscillatory baffled column. Chemical Engineering Science 56, 6143-6148]. The experimental data include the average hold-up profile and bubble size distribution in the OBC. All the non-drag forces (turbulent dispersion force, lift force) and the drag force are incorporated in the model. The coalescence and breakage effects of the gas bubbles are modeled according to the coalescence by the random collision driven by turbulence and wake entrainment while for bubble breakage by the impact of turbulent eddies. Predicted liquid velocity and averaged gas hold-up are compared with the experimental data. The profile of the mean bubble diameter in the column and its variation with the superficial gas velocity is studied. Bubble size distribution obtained by the model is compared with the experimental data.     

THE EFFECT OF BUOYANCY ON PHASE DISTRIBUTION IN DISPERSED TURBULENT TWO-PHASE FLOWS

Advanced generation three-dimensional (3-D) two-fluid models and computational multiphase fluid dynamic (CMFD) solvers give good predictions of dispersed flows on earth (i.e., at 1 g), where the lift, wall, and turbulent dispersion forces determine the lateral void fraction distribution. However, for microgravity (μ-g) conditions these buoyancy-related forces become quite small and two-fluid model predictions are generally inadequate. This implies that some of the physics lost during ensemble averaging was not included back into the two-fluid model with the closure laws that were used.

Recent modeling advances that include the effect of the phasic velocity fluctuations on the phase distribution are presented. The resultant two-fluid model was evaluated and compared with various data sets for steady, fully developed turbulent conditions using a novel one-dimensional (1-D) CMFD solver that is numerically very efficient. It was found that with the addition of these new physical mechanisms to the closure laws, one is able to achieve good predictions of both the gas/liquid and solid/liquid dispersed phase distribution over a wide range of particle/bubble buoyancies and gravity levels.     

影响FCC再生立管输送催化剂影响因素的分析

再生立管是FCC装置再生器和提升管反应器之间再生催化剂循环的输送管,其操作复杂性在于立管内催化剂的流态受多种因素影响。本文中在1.0Mt/a FCC装置上,通过测量立管改造前后不同操作条件时的轴向压力分布,考察再生立管输送催化剂的影响因素。生产运行结果表明,影响立管操作的主要因素包括催化剂密度和平均粒径、立管几何结构、滑阀安装位置、松动风性质和流量等;选用低密度催化剂和高黏度流化介质可以减小气泡尺寸,维持反应温度稳定;松动风流量应根据立管推动力、滑阀压降和反应温度及时调整,避免填充流。另外,立管结构和滑阀的安装位置对立管推动力影响较大,分析结果可供立管设计和装置改造参考。