CFD-PBE simulation of a bubble column in OpenFOAM

A general CFD-PBE (computational fluid dynamics-population balance equation) solver for gas–liquid poly-dispersed flows of both low and high gas volume fractions is developed in OpenFOAM (open-source field operation and manipulation) in this work. Implementation of this solver in OpenFOAM is illustrated in detail. The PBE is solved with the cell average technique. The coupling between pressure and velocity is dealt with the transient PIMPLE algorithm, which is a merged PISO-SIMPLE (pressure implicit split operator-semi-implicit method for pressure-linked equations) algorithm. Results show generally good agreement with the published experimental data, whereas the modeling precision could be improved further with more sophisticated closure models for interfacial forces, the models for the bubble-induced turbulence and those for bubble coalescence and breakage. The results also indicate that the PBE could be solved out the PIMPLE loop to save much computation time while still preserving the time information on variables. This is important for CFD-PBE modeling of many actual gas–liquid problems, which are commonly high-turbulent flows with intrinsic transient and 3D characteristics.     

气液鼓泡塔的CFD-PBM耦合模拟：离散法与QMOM方法的对比

采用CFD-PBM耦合方法,对高表观气速下的气?液鼓泡塔进行模拟,得到气含率、轴向液速及气泡尺寸。系统性对比求解群平衡方程(PBE)的不同方法：离散法(20 bins)和QMOM(包括四阶QMOM和六阶QMOM)。模拟结果与文献中的实验数据的对比结果表明,离散法和QMOM均能合理预测气含率、轴向液速、平均气泡大小和气泡尺寸分布。但QMOM比离散法节约2~3倍的计算成本。对于QMOM,使用四个矩能准确描述气相的演化。使用四阶QMOM和六阶QMOM得到的结果非常相似。利用QMOM的低阶矩可以快速有效地重构出单峰气泡尺寸分布。     

基于EMMS方法的鼓泡塔反应器CFD及群平衡模拟

能量最小多尺度（energy-minimization multi-scale,EMMS）方法已经被应用于气液体系中群平衡（population balance model,PBM）模型的改进。EMMS模型可计算气泡破碎聚并过程的能量,进而获得聚并速率的修正因子。应用这一模型对高气速鼓泡塔进行了模拟计算,并进一步对比了均一尺径模型、CFD-PBM模型以及CFD-PBM-EMMS模型的模拟结果与实验数据。结果表明,在高表观气速条件下,基于EMMS方法的群平衡模型可以更加准确地预测鼓泡塔中不同高度的气泡尺径分布和轴向液速,同时提高了对整体气含率和局部气含率的模拟准确性。在表观气速为0.16 m·s^-1和0.25 m·s^-1时,CFD-PBM-EMMS模型对气泡尺径分布的预测精度更高,同时整体气含率模拟的相对误差下降为5%和15%,局部气含率模拟平均相对误差下降为8%和17%。     

鼓泡床中的气泡尺寸分布

根据气泡聚并和破裂速率模型,提出一个描述鼓泡床中气泡尺寸分布的总体平衡(Population Balance)模型。该模型可预计鼓泡床中气泡尺寸分布随床高的变化。对空气-水体系的模拟结果与实测结果吻合较好。     

二维鼓泡床内气泡尺寸分布的实验与CFD模拟

在有机玻璃制成的二维鼓泡床(0.20m×0.02m×2.00m)内,采用摄像法对空气－自来水的气液两相体系的气泡尺寸分布进行了考察。以商业计算流体力学软件ANSYS CFX 10.0为平台,在双流体模型的基础上,采用k-ε湍流模型和GRACE曳力模型对气液鼓泡床内流体动力学行为进行了多相流CFD数值模拟。结果表明 MUSIG(Multiple Size Group)模型实现了对多气泡体系内气泡尺寸分布特性的考察,气泡尺寸分布的模拟结果与实验结果吻合得较好,从而说明了考虑了气泡聚并破碎的MUSIG模型能很好地反映出鼓泡床内气泡尺寸分布特性。     

CFD simulation of gas–liquid flow in a high-pressure bubble column with a modified population balance model

In this study, based on the Luo bubble coalescence model, a model correction factor C_e for pressures according to the literature experimental results was introduced in the bubble coalescence efficiency term. Then, a coupled modified population balance model (PBM) with computational fluid dynamics (CFD) was used to simulate a high-pressure bubble column. The simulation results with and without C_e were compared with the experimental data. The modified CFD-PBM coupled model was used to investigate its applicability to broader experimental conditions. These results showed that the modified CFD-PBM coupled model can predict the hydrodynamic behaviors under various operating conditions.     

气液鼓泡床内的液体流速分布

引言 鼓泡床是一种重要的气液或气液固多相反应器.液体循环流动是鼓泡床的一个重要流体力学特征,从20世纪50年代人们就开始对此进行了比较系统的实验研究[1-6].这个特征对鼓泡床的流体返混行为、气含率、气液界面积以及传热传质系数都有很大影响,特别是液体返混行为可以由液体循环特性直接决定.如何准确地描述和预测鼓泡床中的液体流速沿径向的分布,关系到鼓泡床反应器的设计、放大和优化.因此,许多年来它一直是人们致力探讨的重要课题之一[7-8].     

基于相群平衡模型的浮选气泡聚并模拟

气泡尺寸分布直接影响气浮分离效率,而聚并是导致气浮池内气泡尺寸变化的主要因素。首先用实验方法测量气浮接触区气泡尺寸分布,然后用计算流体力学方法对气泡/水两相流动及气泡聚并进行模拟,最后通过对实验和数值模拟结果进行对比建立基于相群平衡模型的浮选气泡聚并行为的模拟方法,分别运用Luo、Free molecular和Turbulent聚并模型对气浮接触区气泡聚并行为进行模拟。结果表明:Turbulent聚并模型计算所得气泡尺寸分布与实验值最接近,适合模拟接触区气泡聚并;气泡平均直径随高度升高先变大后保持不变,气泡聚并主要发生在接触区中下部;气泡的加入增强了接触区流动混乱程度,上部产生对称涡流,中下部呈由边壁向中心的水平流动。     

Numerical simulations of gas-liquid mass transfer in bubble columns with a CFD-PBM coupled model

Gas-liquid mass transfer in a bubble column in both the homogeneous and heterogeneous flow regimes was studied by numerical simulations with a CFD-PBM (computation fluid dynamics-population balance model) coupled model and a gas-liquid mass transfer model. In the CFD-PBM coupled model, the gas-liquid interfacial area a is calculated from the gas holdup and bubble size distribution. In this work, multiple mechanisms for bubble coalescence, including coalescence due to turbulent eddies, different bubble rise velocities and bubble wake entrainment, and for bubble breakup due to eddy collision and instability of large bubbles were considered. Previous studies show that these considerations are crucial for proper predictions of both the homogenous and the heterogeneous flow regimes. Many parameters may affect the mass transfer coefficient, including the bubble size distribution, bubble slip velocity, turbulent energy dissipation rate and bubble coalescence and breakup. These complex factors were quantitatively counted in the CFD-PBM coupled model. For the mass transfer coefficient k_l, two typical models were compared, namely the eddy cell model in which k_l depends on the turbulent energy dissipation rate, and the slip penetration model in which k_l depends on the bubble size and bubble slip velocity. Reasonable predictions of k_la were obtained with both models in a wide range of superficial gas velocity, with only a slight modification of the model constants. The simulation results show that CFD-PBM coupled model is an efficient method for predicting the hydrodynamics, bubble size distribution, interfacial area and gas-liquid mass transfer rate in a bubble column.     

Frictional loss in multiplate bubble columns

Gas holdup and pressure loss were measured for various gas-liquid systems in a batch, multistage bubble column. Experimental results show that the use of screen plates (α = 0.64) considerably increases the gas holdup but introduces a significant pressure loss for the two-phase mixture. The pressure loss was found to be independent of physical properties of the mixture, and predictable either from the modified separated flow model (Chen et al., 1986) or from the kinetic energy loss based on the liquid circulation velocity.     

Multicompartment hydrodynamic model for slurry bubble columns

A core-annulus multicompartment two-dimensional two-bubble class model accounting for slurry recirculation and coupled with catalyst transport was developed as a part and parcel of the analysis of the behavior of slurry bubble column reactors at high gas throughputs corresponding to the churn turbulent flow regime. The model analyzed the contributions of bubble-induced turbulence closures, bubble coalescence and breakup phenomena, and catalyst axial distribution as the resultant of sedimentation, advection via liquid-solid slip, per-compartment axial dispersion and core-annulus lateral exchange of catalyst by bubble-induced turbulence. The model was also used to analyze the effects of catalyst loading, gas density and superficial velocity, and column diameter and vessel aspect ratio on the hydrodynamics of slurry bubble column reactors, namely, the per-compartment phase holdups and interstitial velocities, pressure gradient, bubble coalescence and break-up rates, and loci of velocity inversion for the gas and slurry profiles.     

鼓泡塔中气泡尺寸分布和局部气含率研究

在内径为0.38 m的鼓泡塔中采用双电导探针法对不同通气速率下的气泡尺寸分布和局部气含率进行了实验研究,分析了气泡尺寸的概率密度分布。结果表明:气泡尺寸随轴向高度的增加而增大,随径向距离增加而减小;鼓泡塔中气液流动可分为过渡流域和充分发展流域,在过渡流域气含率随轴向高度增加而增大,在充分发展流域气含率趋于均值,径向局部气含率分布呈抛物线型下降。高气速下气泡尺寸概率密度分布比低气速下宽,且随轴向高度的增加分布变宽。     

Experimental investigation of local bubble properties: Comparison to the sectional quadrature method of moments

In recent years, population balance models coupled to computational fluid dynamics have been used as a tool to model bubbly flows. In this work, we established a setup to measure the local size distribution, the velocity and orientation of bubbles in different zones of a bubble column. As a population balance model, we used the sectional quadrature method of moments for the first time in OpenFOAM to simulate the local change in the bubble size distribution and compared its results to the quadrature method of moments as well as to the experimental results. A satisfactory agreement between local experimental values of three investigated flow rates and simulations were found and enables the characterization of heterogeneous bubbly regimes as found in industrial reactive bubble columns.     

双气泡间的聚并时间测量及其影响因素

聚并时间是研究气泡聚并行为过程中的一个重要参数。在消除气泡生长速度对聚并时间影响的条件下,利用自行开发的光学测试技术对双气泡间的聚并时间进行了精确的测量。考察了气泡尺寸、靠近速度、有机溶质的扩散、电解质和表面活性剂的加入对气泡聚并行为的影响。实验结果表明,双气泡间的聚并时间随着气泡直径的增加、气泡老化时间的延长、靠近速度的减小和有机溶质浓度的增大而增加。     

Bubble size distribution in bubble columns

The bubble size distributions are measured for the air-water system as a function of air velocity at room temperature in two bubble columns. High speed cinephotography and fiber optic probe techniques are used to measure the bubble size. Our limited measurements suggest that the bubble size may be independent of gas velocity in the range 3.6 to 9.2 cm/s and may be dependent on column diameter with smaller bubbles for narrower columns. The bubble size appears to be smaller at the column wall than at distances away from the wall.     

Characteristic mixing length in bubble columns

Liquid-phase mixing in bubble columns is discussed on the basis of the mixing length theory. A characteristic mixing length defined as a lumped hydrodynamic parameter is estimated. The results indicate that the characteristic mixing length assumed previously by one of the authors is reasonable.     

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.     

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。     

Theoretical prediction of flow regime transition in bubble columns by the population balance model

Theoretical prediction of flow regime transition in bubble columns was studied based on the bubble size distribution by the population balance model (PBM). Models for bubble coalescence and breakup due to different mechanisms, including coalescence due to turbulent eddies, coalescence due to different bubble rise velocities, coalescence due to bubble wake entrainment, breakup due to eddy collision and breakup due to large bubble instability, were proposed. Simulation results showed that at relatively low superficial gas velocities, bubble coalescence and breakup were relatively weak and the bubble size was small and had a narrow distribution; with an increase in the superficial gas velocity, large bubbles began to form due to bubble coalescence, resulting in a much wider bubble size distribution. The regime transition was predicted to occur when the volume fraction of small bubbles sharply decreased. The predicted transition superficial gas velocity was about 4 cm/s for the air-water system, in accordance with the values obtained from experimental approaches.