Novel phenomenological discrete bubble model of freely bubbling dense gas–solid fluidized beds: Application to two‐dimensional beds

A phenomenological discrete bubble model has been developed for freely bubbling dense gas–solid fluidized beds and validated for a pseudo‐two‐dimensional fluidized bed. In this model, bubbles are treated as distinct elements and their trajectories are tracked by integrating Newton's equation of motion. The effect of bubble–bubble interactions was taken into account via a modification of the bubble velocity. The emulsion phase velocity was obtained as a superposition of the motion induced by individual bubbles, taking into account bubble–bubble interaction. This novel model predicts the bubble size evolution and the pattern of emulsion phase circulation satisfactorily. Moreover, the effects of the superficial gas velocity, bubble–bubble interactions, initial bubble diameter, and the bed aspect ratio have been carefully investigated. The simulation results indicate that bubble–bubble interactions have profound influence on both the bubble and emulsion phase characteristics. Furthermore, this novel model may become a valuable tool in the design and optimization of fluidized‐bed reactors. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

A Novel Model for Predicting the Dense Phase Behavior of 3D Gas‐Solid Fluidized Beds

A novel phenomenological discrete bubble model was developed and tested for prediction of the hydrodynamic behavior of the dense phase of a 3D gas‐solid cylindrical fluidized bed. The mirror image technique was applied to take into account the effects of the bed wall. The simulation results were validated against experimental data reported in the literature that were obtained by positron emission particle tracking. The time‐averaged velocity profiles of particles predicted by the developed model were found to agree well with experimental data. The initial bubble diameter had no significant influence on the time‐averaged circulating pattern of solids in the bed. The model predictions clearly indicate that the developed model can fairly predict the hydrodynamic behavior of the dense phase of 3D gas‐solid cylindrical fluidized beds.     

Bubble formation in cocurrently upward flowing liquid

The effects of liquid velocity, nozzle diameter, gas chamber volume and gas flow rate on volumes, shapes and growth curves of bubbles formed at a nozzle submerged in a cocurrently upward flowing liquid in a bubble column were experimentally investigated. The bubble volume decreases with increasing liquid flow velocity. The effect of liquid flow velocity on the volume of bubble increases with an increase in the gas flow rate. To simulate bubble formation at a nozzle submerged in cocurrently upward flowing liquid, a revised non-spherical bubble formation model was proposed. Bubble volumes, bubble growth curves and shapes experimentally obtained in this study, as well as in previous experimental studies, are well predicted by the present model.     

黏性流体中单气泡的运动特性

采用高速CCD成像技术实验测定了单个气泡在水及不同黏度甘油水溶液中的形变特性及上升终速度.结果表明,随着液相黏度的增加,小气泡均能呈良好球形,而大气泡则由类似椭球形的不规则形状逐渐向球帽形转变;气泡的周期性振荡趋于平缓,气泡上升终速度降低.提出了计算气泡上升终速度的关联方程,其预测结果与实验值吻合良好.     

Evolution of the Population of Bubbles in 2D Fluidized Beds

The size of the bubbles in a solid‐gas 2D fluidized bed was estimated by image capture and digitalization using a CCD camera. It was confirmed that the size distribution for the bubbles in a slice of the bed was skewed, varying with the location of the slice. The results were analyzed using the Agarwal (1985) model, which is based on a population balance. For this model, four adjustable parameters are required, as well as the knowledge of bubble size just above the distributor. Experimental data were compared with values predicted by the model. The parameters that the model needs were obtained by three procedures: i) the constants supplied by Agarwal (1985) and Rowe and Everett (1972); ii) the parameters obtained from experimental data for a 1 cm wide slice bed; and iii) the parameters obtained by fitting the bubble diameter to all the bubbles in the bed. The second and third methods provided the best results.     

Heat Transfer to an Isolated Bubble Rising in a High‐Temperature Incipiently Fluidized Bed

Very few experimental data are available on the heat transfer between bubble and emulsion phases; no data are available at high temperatures. The effects of bed particle type and size, bubble size, and bed temperature on the heat transfer coefficient were examined in this experimental and modelling study. The heat transfer coefficient was found to increase to a maximum, and then decrease as the bubble mass increased in the bubble mass range investigated. Increase in bed temperature led to a significant decrease in the heat transfer coefficient. The simple mathematical model developed earlier was extended to include operation at high temperature.     

Three‐dimensional numerical simulation of coalescence and interactions of multiple horizontal bubbles rising in shear‐thinning fluids

The dynamics of multiple horizontal bubbles rising from different orifice arrangements in shear‐thinning fluids was simulated numerically by three‐dimensional Volume of Fluid method. The effects of bubble size, rheological properties of shear‐thinning fluids, and orifice structure arrangements on multiple bubbles interaction and coalescence were analyzed, and the mechanisms of bubble coalescence and breakup were fully discussed and elucidated. The variation of bubble rising velocity during coalescence process and freely rising processes for different orifice arrangements was also deeply investigated. The critical initial horizontal intervals for coalescence of multiple horizontal bubbles with various orifice arrangements were attained by simulation, which could serve as the critical criterion of bubble coalescence or noncoalescence. Furthermore, the critical bubble interval was predicted based on the film drainage model, the prediction accords well with the simulation result and is quite conducive for the design and optimization of perforated gas–liquid contact equipment. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3528–3546, 2015     

A novel approach for modeling bubbling gas–solid fluidized beds

A phenomenological discrete bubble model is proposed to help in the design and dynamic diagnosis of bubbling fluidized beds. An activation region mechanism is presented for bubble formation, making it possible to model large beds in a timely manner. The bubbles are modeled as spherical‐cap discrete elements that rise through the emulsion phase that is considered as a continuum. The model accounts for the simultaneous interaction of neighboring bubbles by including the trailing effects due to the wake acceleration force. The coalescence process is not irreversible and therefore, the coalescing bubble pair is free to interact with other rising bubbles originating the splitting phenomena. To validate the model, the simulated dynamics are compared with both experimental and literature data. Time, frequency, and state space analysis are complementarily used with a multiresolution approach based on the empirical method of decomposition to explore the different dynamic scales appearing in both the simulated time series and those obtained from experimental runs. It is concluded that the bubble dynamics interactions play the main role as the driver of the resulting bed dynamics, matching the main features of measured bubble dynamics. Exploding bubble phenomena have been identified by establishing a direct relation between the bubble generation, interaction and eruption, and the measured signals. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Bubble Motion Pattern and Rise Velocity in Two‐dimensional Horizontal and Vertical Vibro‐fluidized Beds

The motion pattern of a bubble was examined and the bubble rise velocity was measured in horizontally and vertically sinusoidal vibro‐fluidized beds. Experimental results showed that the motion pattern of a bubble depends on the vibration direction. Compared with the case of no vibration, it seems that the flow pattern of bubbles is not affected significantly by vertical vibrations, while bubbles rise in the form of a tower for horizontal vibrations. For vertical vibrations, all the local average bubble rise velocities were larger than those in the case of no vibration, but they were hardly influenced by horizontal vibrations at the lower bed height and were larger than those in the case of no vibration at the higher bed height.     

Local hydrodynamics modeling of a gas–liquid–solid three-phase bubble column

A three-dimensional (3D) transient model was developed to simulate the local hydrodynamics of a gas–liquid–solid three-phase bubble column using the computational fluid dynamic method, where the multiple size group model was adopted to determine the size distribution of the gas bubbles. Model simulation results, such as the local time-averaged gas holdups and axial liquid velocities, were validated by experimental measurements under varied operating conditions, e.g., superficial gas velocities and initial solid loadings at different locations in the three-phase bubble column. Furthermore, the local transient hydrodynamic characteristics, such as gas holdups, liquid velocities, and solid holdups, as well as gas bubble size distribution were predicted reasonably by the developed model for the dynamic behaviors of the three-phase bubble column. © 2007 American Institute of Chemical Engineers AIChE J, 2007     

A Simplified Correlation for Bubble Volume Estimation

In order to propose a simplified correlation to predict the detached bubble volume without considering the gas velocity, an experimental work has been performed to measure the detached bubble volume through a micro‐hole submerged in liquid. Several micro‐holes with diameters of 60, 90, 126, 220, 580, and 1200 µm are respectively used for bubble formation, while liquid in a test chamber is continuously drained at a constant rate of 0.006 ml/s. The predicted results by the present simplified correlation agree well with the measured values. Predictions of the detached bubble volume from previously published correlations using a model to compute the gas velocity are also compared with experimental data.     

Heat transfer between an isolated bubble and the dense phase in a fluidized bed

Heat transfer between the bubble and dense phases of a bubbling fluidized bed plays a very important role in the system performance, especially for applications involving solids drying and gas‐phase combustion. However, very few experimental data are available on this subject in the literature. An experimental and modelling investigation on the heat transfer behaviour of isolated bubbles injected into an incipiently fluidized bed is reported in this paper. A new single‐thermocouple technique was developed to measure the heat transfer coefficient. The effects of bed particle type and size, and bubble size on the heat transfer coefficient were examined. The heat transfer coefficient was found to exhibit a maximum as the bubble size increased in the bubble size range investigated. The bed particle size had a comparatively small effect on the heat transfer coefficient. A simple mathematical model was developed which provides good agreement with experimental data.     

双组分颗粒鼓泡流化床内气泡形状参数

在二维双组分鼓泡床实验装置上,采用高速摄像技术,对床内气泡的形状特性进行了研究,考察了不同形状气泡在床内的轴径向分布,探索了颗粒组成和操作气速对气泡形状的影响。结果表明:不同形状的气泡在鼓泡床内呈正态分布,球形度较好的气泡主要分布于床层底部和壁面附近,而细长的气泡则主要集中于床层中心区域。随着气体速率的增加,气泡的球形度和宽纵比降低,气泡形状趋于细长和不规则;随着重组分增加,气泡的球形度增大而宽纵比减小。双组分颗粒鼓泡流化床内气泡球形度的概率密度较单组分的分布更宽,而宽纵比的概率密度分布与添加的颗粒密度有关。     

Bubble characteristics of a scaled‐down three‐phase fluidized bed

Experiments were carried out in a 0.29 m diameter column to provide information on bubble characteristics relevant to an industrial three‐phase fluidized bed reactor. Using a specially built electrical conductivity probe, together with a series of computer programs to gather and filter the data, local bubble properties (rise velocities, pierced chord lengths, frequencies, and direction of travel) were measured. The data are compared to existing correlations. Since the operating conditions were within the dispersed bubble regime, uniform bubbling was anticipated. However, the actual system indicated considerable non‐uniformity, with individual bubbles, large swarms of bubbles and particles traveling at all angles. As a result, it is shown that bubble rise velocities are not necessarily a good measure of the bubble properties and must be vectorized to provide a good means of estimating gas hold‐up.     

筛板上液体横向流动时气泡的形成特性

An apparatus,desinged to simulate bubbling of a sieve tray operated in froth regime,was employed. Bubble contact angles in and above the incipient weeping regimer for an air-water-plexiglas system were investigated. The influence of both liquid cross-flow and gas up-flow upon bubble contact angles was examined. A model considering the influence of liquid cross-flow was developed to predict bubble size from a sieve hole in froth operation regime.The comparison shows that the bubble sizes predicted by the present model are consistent with our experimental values and the available published experimental data.     

流化床中气泡的汇合长大和床层膨胀

根据文中提出的沿单位床层高度气泡平均直径的长大与气泡在水平面内的平均分开程度成比例的简化模型和已有的大量实验数据,获得了气泡沿床高长大的计算方程 本文还根据两相邻生成的初始气泡的垂直中心距与初始气泡直径成正比的简化模型及已有的实验数据,提出了初始气泡直径D_B_0的计算方程 基于上述获得的方程式以及假定鼓泡流化床的床层膨胀纯因气泡存在所造成,本文还导得了自由鼓泡流化床膨胀高度的计算式     

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。     

Bubble coverage and bubble resistance using cells with horizontal electrode

The resistivity ratio due to gas bubbles underneath horizontal anodes in electrolytic cells was measured and compared with that in an air–water model of identical geometry. It was found that at equal current density or equivalent gas generation rate, the difference in the bubble resistivity ratio between these two situations can be up to 20%. Consequently, the results obtained from an air–water model cannot be directly applied to an electrolytic cell. Results also showed that within the range of experimental conditions covered, the bubble resistivity ratios obtained for a given anode–cathode distance in both cells are linearly related to the bubble coverage ratio, based on bubbles greater than a certain size as limited by the measurement method.     

大孔径高气速单孔气泡形成

在内径为190mm的鼓泡塔内,研究了空气-去离子水系统在大孔径高气速条件下的单孔气泡形成。考察了五个不同的孔径,分别为4、8、10、15及21mm,孔口气速范围为0.8~154.8m·s^-1。以CCD摄像记录气泡的形状及尺寸,根据气泡长径比的变化,得到气泡初始形态转变时的临界孔口气速：当孔口气速低于20m·s^-1时,孔口气泡近似于球形,长径比小于1.1;当孔口气速大于50m·s^-1时,气泡呈现椭球形,长径比大于1.5。并对气泡尺寸与孔径及孔口气速进行关联,所得关联式对孔径大于3mm、孔口气速在10~80m·s^-1范围内所形成的气泡尺寸预测效果较好。     

The Effect of Bed Temperature on Mass Transfer between the Bubble and Emulsion Phases in a Fluidized Bed

The rate of interphase mass transfer between the bubble and emulsion phases of a bubbling fluidized bed is of primary importance in all models for fluidized bed reactors. Many experimental studies have been reported, however, all these investigations have been carried out in fluidized beds operated at room temperature. In this work, the effect of the bed temperature on the interphase mass transfer is reported. Single bubbles containing argon – used as a tracer – were injected into an incipiently fluidized bed maintained at the required temperature. The change in argon concentration in the bubble was measured using a suction probe connected to a mass spectrometer. The effects of bed particle type and size, bubble size, and bed temperature on the mass transfer coefficient were examined experimentally. The interphase mass transfer coefficient was found to decrease with the increase in bed temperature and bubble size, and increase slightly with increase in particle size. Experimental data obtained in this study were compared with some frequently used correlations for estimation of the mass transfer coefficient.