Numerical simulation of two-phase flow with bubble break-up and coalescence coupled with population balance modeling

A computational fluid dynamic (CFD) model was developed with an improved source term based on previous work by Hagesaether et al. [1] for bubble break up and bubble coalescence to carry out numerical prediction of number density of different bubble class in turbulent dispersed flow. The numerical prediction was based on two fluid models, using the Eulerian–Eulerian approach where the liquid phase was treated as a continuum and the gas phase (bubbles) was considered as a dispersed phase. Bubble–bubble interactions, such as breakage due to turbulence and coalescence due to the combined effect of turbulence and laminar shear were considered. The result shows that the radial distributions of number densities of lower bubble classes are more than its higher counterpart. The result also shows that the Sauter mean diameter increases with the increase of height up to 1 m and then become steady. Simulated results are found to be in good agreement with the experimental data.     

Experimental Investigation and CFD Modeling of Hydrodynamic Parameters in a Pulsed Packed Column

In this work, a combination of computational fluid dynamics (CFD) and droplet population-balance model (DPBM) in the framework of Fluent was applied to simulate the drop-size distributions and flow fields in a pilot-plant liquid–liquid extraction pulsed packed column. The three-dimensional unsteady-state liquid–liquid flow was modeled using the Eulerian two-fluid equations in conjunction with the realizable k – ε turbulence model. The classes method (CM) was chosen for solving population-balance equations. Two models for breakage and coalescence, the models of Luo and Garthe, were used in the CFD code. The model was validated by comparing the simulated drop-size distributions and holdup with experimental measurements. After the validation of the model, the effects of the operating conditions (feed rates and pulsation) on the dispersed phase holdup and drop-size distributions were studied. The results of linked CFD-DPBM model and experiments revealed that the dispersed phase holdup was increased when the organic and aqueous flow rates increased and when the intensity of pulse was increased, the holdup increased. Increasing the dispersed and continuous feed rates caused the Sauter mean diameter of the drops decreased and when the intensity of pulse was increased, because of high droplets break up rate, the Sauter mean diameter decreased. Results of linked CFD-DPBM model show that the CFD-DPBM tool is able to predict hydrodynamic parameters in a pulsed packed column.     

Size adjustment of spherical temperature-sensitive hydrogel beads by liquid–liquid dispersion using a Kenics static mixer

Temperature-sensitive hydrogel beads were prepared by Kenics static mixer technology. The temperature-sensitive monomer N,N-diethylacrylamide and photo-crosslinkable pre-polymer ENT were used as model hydrogel materials. Drop dispersion of high viscosity polymer material in low viscosity hexadecane was made using the static mixer. Drops of a solution of the mixed materials were rapidly photo-crosslinked by UV irradiation after mixing in the static mixer, and spherical hydrogel beads with narrow, normal size distribution were thus prepared. The Kenics static mixer is a useful device for the preparation of spherical beads of temperature-sensitive hydrogels. The Sauter Mean Diameter of the hydrogel beads swollen in deionized water at 293 K was measured. The experimentally determined dimensionless swollen hydrogel bead diameter was well correlated with the Weber number, degree of swelling and viscosity ratio. The effects of gelation and ENT addition on the bead size were evaluated from the degree of swelling. The correlation equation can be used for size adjustment of temperature-sensitive spherical hydrogel beads.     

Numerical simulation of the gas–liquid flow in a laboratory scale bubble column: Influence of bubble size distribution and non-drag forces

In the present work, a computational model based on an Eulerian–Eulerian approach was used for the simulation of the transient two-phase flow in a rectangular partially aerated bubble column. Superficial gas velocities (U_G) ranging from 0.24 to 2.30 cm/s were used throughout both the experiments and the simulations. The calculated results were verified by comparing them with experimental data including measurements of gas hold-up, plume oscillation period (POP) and Sauter mean bubble diameter. The study shows the effect of mesh refinement, time-step and physical model selection, the latter regarding the role of bubble size distribution and non-drag forces, on the computational results. According to the results presented here, the representation of bubble populations using multiple size groups (MUSIG model) instead of a single group improves the prediction of the experimental parameters under study. Additionally, the results obtained after including the virtual mass force term do not differ considerably from those obtained including only the drag force. On the contrary, as a consequence of introducing the lift force term into the model, the gas hold-up is overestimated and a non-symmetric bubble plume oscillation appears, a fact that is not experimentally observed.     

静态混合器中液液分散的实验及CFD模拟

在SK型静态混合器上进行甲苯-水两相混合实验,采用截面直接拍摄法获得分散混合性能指标Sauter平均直径（SMD）。利用Box-Behnken响应面分析设计实验,在Design Expert 7.0平台上拟合实验数据,获得SMD的多项式形式的表达式。建立了与实验相同的静态混合器物理模型,使用Mixture多相流模型、k-ε湍流模型进行了CFD模拟研究,获得了浓度场云图及分布混合指标不均匀系数。模拟所得压降与实验值的相对误差在15%以内,表明模拟结果与实验结果吻合较好。结果表明,静态混合器中液液分散过程是分散混合和分布混合共同作用的结果,两种混合经过6～8个混合单元后共同达到充分发展。充分发展后的SMD受表观流速、分散相分率和静态混合器直径三因素影响,且表观流速的影响最为显著;充分发展后的不均匀系数均达0.05以下,表明静态混合器自身具有较好的分布混合性能。     

Application of extended quadrature method of moments for simulation of bubbly flow and mass transfer in gas‐liquid stirred tanks

In the present paper, two gas‐liquid stirred tanks, one agitated by a radial impeller and another by an axial impeller, are modelled using the open‐source computational fluid dynamic (CFD) package OpenFOAM (open source field operation and manipulation). The combined effect of the bubble break‐up and coalescence in the tank is considered by a population balance model (PBM) called extended quadrature method of moments (EQMOM). The three‐dimensional simulation is made using a multiple reference frame (MRF), a well‐established method for the modelling of mixers. Dispersed gas and bubble dynamics in the turbulent flow are modelled using the Eulerian‐Eulerian approach (E‐E) with mixture k‐epsilon turbulent model and the modified Tomiyama drag coefficient for the momentum exchange. The model is developed to predict the spatial distribution of gas phase fraction, Sauter mean bubble diameter (), number density function (NDF), dissolved oxygen (DO) evolution, and flow structure. The numerical results are compared with experimental data and a fair agreement is achieved. The results of the axial impeller are discussed based on four impeller rotational speeds with different volumetric mass transfer coefficients.     

Kenics型静态混合器和GK型静态混合器流场的数值模拟及比较

采用计算流体动力学(CFD)的方法,分别计算了Kenics型静态混合器和GK型静态混合器内的流场。数值模拟的结果表明,Kenics型静态混合器内流场的湍动强度大于GK型静态混合器的,导致了Kenics型静态混合器的流体阻力和传热系数大于GK型静态混合器的。GK型静态混合器的压力降大约只是Kenics型静态混合器压力降的0.554~0.579倍,但两者的传热膜系数相差不大。GK型静态混合器具有较强的综合性能。     

数值模拟静态混合器结构对PS/CO_2熔体温度的影响

利用专用CFD软件Polyflow对SMX型和Kenics型静态混合器中PS/CO_2发泡溶液进行数值模拟计算,分析比较不同板厚在不同元件个数条件下两种静态混合器消耗的压力损失,以及不同CO_2浓度对静态混合器压力损失的影响;并引入"离散系数"分析比较两种静态混合器出口温度均匀性的变化.数值模拟的结果表明:SMX型静态混合器冷却效果优于Kenics型静态混合器,并且SMX型静态混合器出口温度均匀性高于Kenics型静态混合器.     

New approach to the formulation of hydrogel beads by emulsification/thermal gelation using a static mixer

A new approach in the formulation of hydrogel beads by emulsification/in situ thermal gelation using static mixer technology is described. κ-Carrageenan was selected as the model hydrogel. The emulsion generated by a Sulzer SMX6 static mixer consisted of warm κ-carrageenan sol (1.5% w/w in water or ) as the dispersed phase, and ambient temperature sunflower seed oil as the continuous phase. Dispersion followed by in situ gelation of κ-carrageenan droplets was possible within a short residence time (1-) in the static mixer, under defined operational conditions, known as the feasibility region. This region was defined as the zone of operation conditions necessary to obtain discrete gel beads, within a defined range of κ-carrageenan solution injection temperature, volume fraction and total flowrate. The temperature boundaries of the feasibility region were determined by the κ-carrageenan gelation temperature and solution viscosity. The resulting beads had a Sauter mean diameter ranging from 350 to , which decreased with the increase of κ-carrageenan injection temperature, total flowrate and/or the number of static mixer elements. Theoretical values of maximal bead diameter and Sauter mean diameter were calculated on the base of critical Weber number, which was demonstrated through good agreement with the experimental values. It was demonstrated that an existing model for the prediction of gel bead diameter in a SMX static mixer is applicable for the new procedure described in this study.     

Bubble size modeling approach for the simulation of bubble columns

The constant bubble size modeling approach (CBSM) and variable bubble size modeling approach (VBSM) are frequently employed in Eulerian–Eulerian simulation of bubble columns. However, the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved. This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns. The distribution of bubble sizes is represented by a series of discrete points, and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics (CFD)–population balance model (PBM) simulations, whereas the influence of bubble coalescence and breakup is neglected. The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling. Furthermore, the convergence issues caused by solving population balance equations are addressed.     

快速流化床颗粒团絮特征的MP-PIC数值模拟

为了研究快速流化床颗粒的团絮特征,建立了基于多相质点网格法的快速流化床气固多相流三维数理模型,气相场采用大涡湍流模型,通过求解牛顿运动方程得到颗粒相运动信息,气固间相互作用力采用Gidaspow曳力模型,固体间作用力通过计算颗粒应力梯度得到。基于该模型,对三维快速流化床上升管（H=3 m、d=0.1 m）气固流动开展了数值模拟,并与实验进行了校正,研究了在气速工况U_g=5.28 m·s^-1下的颗粒（ρ_p=2650 kg·m^-3、d_p=250 mm）团絮性质,实现了对上升管内颗粒团絮的基本类型（条形团絮、马鞍形团絮、U形团絮）的成功预测,并揭示了不同类型团絮在上升管内形成、发展、聚并直至破碎的演化规律。结果表明,上升管径向颗粒团絮的平均颗粒浓度分布呈现中间低两边高的环核结构,颗粒团絮速度的分布与其相反;随着轴向高度的增加,颗粒团絮的颗粒浓度逐渐降低而速度逐渐增加,但达到一定高度后变化减缓。     

Investigation of residence time distribution in Kenics static mixers

Experimental investigations of residence time distributions (RTDS) of fluids in tubes filled with Kenics static mixers were carried out. Two Newtonian and two non-Newtonian fluids described by the rheological model of Ostwald and de Waele were used in the measurements. Tubes of different lengths containing 4–30 Kenics elements were employed. The fluid flow was laminar, the Reynolds number ranging from 0.72 to 442.5. The results of measurements obtained in the form of RTD function F were correlated using a log—normal distribution. The distribution parameters were presented as a function of the number of Kenics elements and the Reynolds number. The experimental and model curves were in good agreement.     

A general correlation for pressure drop in a Kenics static mixer

A new pressure drop correlation in a Kenics static mixer has been developed. Pressure drop data were generated from computational fluid dynamics (CFD) calculations, avoiding the experimental limitations in obtaining comprehensive data enough for developing a reliable pressure drop correlation. Dimensional analysis reveals that the pressure drop characteristic of the Kenics static mixer can be described by three dimensionless groups, i.e., the friction factor, Reynolds number (Re), and aspect ratio of a mixing element (AR). A systematic graphical analysis led to a single master curve governing the pressure drop behavior of the Kenics static mixer, which had never been achieved before. We derived a pressure drop correlation fitting well with the obtained master curve in a general form into which the AR effect on the pressure drop is directly incorporated. Unlike the already existing correlations available in the literature, the correlation proposed in this study can cover the whole range of Re from laminar to turbulence. The reliability of the proposed correlation was validated by the comparison with various pressure drop data reported in the literature.     

幂律流体在Kenics型静态混合器中流动特性分析

为了探究Kenics型静态混合器内扭旋叶片剪切作用对幂律流体流动的影响,利用旋转流变仪测量了浓度为0.5wt%, 0.7wt%, 0.9wt%的羧甲基纤维素(CMC)水溶液的流变参数,采用数值模拟与实验研究了扭旋叶片作用下幂律流体流动阻力和剪切稀化特性。对流场研究表明,扭旋叶片诱导产生了内流涡旋、绕流涡旋和近壁面涡旋,有效强化了静态混合器内流体流动的剪切作用。受多个纵向涡旋分布的影响,扭旋叶片局域流场中周向45°位置速度最高,周向30°位置涡量与剪切应力最高而黏度最低。径向0.4倍半径位置速度最高,0.7倍半径位置黏度最高。静态混合器有效提高了流体的二次流流动速度和剪切应力,降低了幂律流体的黏度和流动阻力系数。     

Liquid phase residence time distribution for gas–liquid flow in Kenics static mixer

The residence time distribution (RTD) of the liquid phase for co-current gas–liquid upflow in a Kenics static mixer (KSM) with air/water and air/non-Newtonian fluid systems was investigated. The effect of liquid and gas superficial velocities on liquid holdup and Peclet number was studied. Experiments were conducted in three KSMs of diameter 2.54 cm with 16 elements and 5.08 cm diameter with 8 and 16 elements, respectively, of constant L_e/D_e = 1.5 for different liquid and gas velocities. A correlation was developed for Peclet number, in terms of generalized liquid Reynolds number, gas Froude number and liquid Galileo number, where as for liquid holdup, a correlation was developed as a function of gas Reynolds number. The axial dispersion model was found to be in good agreement with the experimental data.     

Lightnin静态混合器内气泡分散流体动力学特性实验研究

以Lightnin静态混合器（LSM）内水-空气气液两相体系为研究对象,在连续相水表观速度U_L=0.071~0.127 m/s和离散相空气表观速度U_G=0.007~0.042 m/s的条件下,研究内径100 mm的LSM内气液两相湍流流动阻力与气泡分散水动力学行为。使用分辨率为1920×1080的高速相机Revealer-2F04M采集混合器内不同轴向窗口的气泡群演化过程。结果表明：当U_L<0.085 m/s和U_G=0.025~0.042 m/s时,LSM内的流型为泡状流。随着气泡群流经混合元件数的增加,气泡群的Sauter平均直径d₃₂逐渐减小。当液体表观速度U_L≤0.085 m/s时,Sauter平均直径d₃₂随气体表观速度的增加先减小后增大;U_G =0.028 m/s时d₃₂达到局部最小值,53%的气泡直径d_B/D₀在0.02~0.05范围内。Sauter平均直径、内径与无量纲停留时间τ之间的关系满足d₃₂/D₀=0.031τ^-0.14We^-0.41。平均气含率α的增大显著增加了单位体积内气泡数量密度,加剧气泡与元件表面碰撞频率,增大旋涡二次流强度,导致摩擦系数显著降低;采用Lockhart-Martinelli方法对实验数据回归,得到气液两相流压降预测常数C的关联式：C=5.26×10⁵U_G^-0.91/Re^0.74。     

CFD simulation of gas and solids mixing in FCC strippers

The gas and solid mixing in fluid catalytic cracking strippers with and without internals were investigated using computational fluid dynamics simulations. The Eulerian–Eulerian two‐fluid model coupled with the modified Gidaspow drag model was used to simulate the gas‐solid flow behavior. The grid independency study and the comparison of 2D and 3D simulations were carried out first. The residence time distribution model and axial dispersion model were utilized to obtain the parameters indicating the back‐mixing degree, such as mean residence time, dimensionless variance and Peclet number of gas and solids. Moreover, the influence of bubble size and gas/solid flow distribution on the mass transfer between the bubble and emulsion phase were also analyzed. The results show that the baffles in the V‐baffle stripper can efficiently enhance the gas and solids mixing, reduce the back‐mixing degree of gas and solids, strengthen the mass transfer between the bubble and emulsion phase, and hence improve the stripping efficiency. © 2011 American Institute of Chemical Engineers AIChE J, 2012