3D Single Bubble Breakup Tracking in a Stirred Tank

A detailed understanding of turbulent fluid particle breakup mechanisms is essential for the accurate modeling of gas/liquid and liquid/liquid dispersions. The design of a fully automated setup for the three‐dimensional serial examination of the single bubble breakup process in a stirred tank, ensuring high repetition rates necessary for the additionally automated statistical analysis, is described. The implementation of a three‐dimensional automatic bubble breakup tracking tool is illustrated. At last, exemplary bubble breakup trajectories that show the benefits and limitations of the developed system and method are discussed.     

Three‐Dimensional Observation of Single Air Bubble Breakup in a Stirred Tank

A fully automated three‐dimensional observation of single bubble breakup trajectories in a stirred tank is demonstrated to gain unbiased and statistically relevant information about the breakup process. The mother bubble size is kept constant, independently of the stirring rate. The investigated parameter in this work is the power input. Three‐dimensional bubble breakup trajectories and heat maps for the initial breakup location probability for the bottom and side views are provided. The influence of the stirrer blade angle position, at the moment of bubble detachment from the capillary, on the breakup probability is analyzed. The breakup positions are linked to the current flow field, related to the stirrer blade angle, within the tank.     

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.     

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.     

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.     

Simulation of a Bubble Column by Computational Fluid Dynamics and Population Balance Equation Using the Cell Average Method

An axisymmetric computational fluid dynamics (CFD) simulation coupled with a population balance equation (PBE) has been applied in simulating the gas‐liquid flow in a bubble column with an in‐house code. The novel feature of this simulation is the application of the cell average method in a CFD‐PBE coupled model for the first time. The predicted results by this method are compared with those by the traditional fixed pivot method and experimental data. For both methods, the simulated results are in reasonable agreement with the reported experimentally measured values. However, the bubble size distributions determined by the cell average method are slightly better than those found by means of the fixed pivot method, i.e., the latter provides a smaller peak value and a wider bubble size distribution, and the probability density function of large bubbles is higher.     

Population balance modeling of bubble size distributions in a direct-contact evaporator using a sparger model

The study of bubble size distributions in direct-contact evaporators was addressed both theoretically and experimentally. Recently developed models for calculating bubble coalescence and breakage frequencies in isothermal bubble columns were adapted to the population balance equation using the bubble mass as the internal coordinate which was discretized using an expansion of the number density function by impulse functions. A sparger model was developed based on experimental data for a non-coalescing system and using bubble formation models for isothermal and non-isothermal conditions. Bubble size distributions in a direct-contact evaporator operating in the quasi-steady-state regime for four different gas superficial velocities, including the homogeneous and heterogeneous regimes, together with the sparger model, were used for estimating the three empirical parameters from the population balance model, which were observed to be functions of the gas superficial velocity. In all cases considered, the population balance model fitted the experimental data rather well and the regressed parameters exhibit the physically expected behavior with changes in the gas superficial velocity.     

Y型微通道内纳米颗粒稳定气泡的完全阻塞破裂动力学

研究了Y型微通道吸附型纳米颗粒稳定气泡的完全阻塞破裂的动力学,破裂过程可划分为挤压阶段和快速夹断阶段,两阶段内无量纲气泡最小颈部宽度与时间均呈幂率关系。气泡破裂过程的颈部动力学表明颗粒的存在并不影响两阶段转变的临界颈部宽度,但吸附在气泡表面的颗粒层会减弱挤压阶段中连续相对气泡颈部的挤压作用,以及快速夹断阶段角区中连续相液体回流对气泡的挤压作用,进而阻碍气泡颈部的形变,延长了气泡的破裂过程。纳米颗粒稳定的气泡的指前因子m及幂率指数α均小于常规气泡,但其差值随着毛细管数Ca和气泡长度l₀的增大而减小,颗粒对气泡破裂过程的影响逐渐减弱。此外,纳米颗粒稳定的气泡的头部曲率略小于常规气泡,颗粒对完全阻塞破裂过程气泡头部动力学的影响可以忽略。     

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.     

Large‐Scale Experiments on the Formation of Surface Vortices with and without Vortex Suppression

Experiments were carried out in a 50‐m³ cylindrical tank to determine the influence of strong momentum on the formation of large‐scale gas‐core vortices. Gas‐core lengths were measured for varying volume flow rates and submergence depths. The critical Froude numbers were also determined and the efficiency of different vortex suppressors on the gas‐core formation was investigated. The horizontal velocity field inside the vortex core region was additionally recorded using particle image velocimetry. The experimental results were used to verify numerical simulations and compared to vortex models and correlations from literature.     

Model based on population balance for the simulation of bubble columns using methods of the least-square type

A novel model is presented which uses mass and momentum equations based on population balances to describe the dispersed phase of bubble columns. A set of integro-differential non-linear equations constitutes the model, which can be solved directly using the least-squares methods. The implementation for these is presented.The model presents a degree of flexibility, as different density functions (number, mass and volume) and different internal coordinates (bubble diameter, volume and mass) can be used.A simplified 1D model of a bubble column is solved using the least-squares spectral element method. The results obtained for two different gas volume fluxes at the inlet are compared with experiments by several authors. The simulations show good agreement with the measured data.     

鼓泡塔中非牛顿流体体系的传质研究

本文在直径0.10 m、高1.05 m的鼓泡塔中,以羧甲基纤维素钠作为模拟介质,采用单孔喷嘴布气、孔径d_o=0.01 m,测定了该类反应器的比相界面积和容积传质系数,提出了比相界面积和传质系数的关联式。     

Studies on the Hydrodynamics of Chaotic Bubbling in a Gas‐Liquid Bubble Column with a Single Nozzle

In this work, the chaotic bubbling mechanism in a gas‐liquid bubble column with a single nozzle was investigated. The signal for the analysis was the time series of pressure fluctuations measured from a pressure transducer probe placed in the bubble column close to the nozzle. In order to study the bubbling process, statistical analysis, qualitative and quantitative nonlinear analyses were carried out for the pressure fluctuations. Power spectra used as standard statistical measures provided preliminary evidence that bubbling in the middle values of gas flow rates may be chaotic in nature. Phase plots provided a qualitative means of analyzing the fine geometry structure of the attractor reconstructed from the bubbling time signal. Positive finite estimates of the Kolmogorov entropy provided a quantitative evidence of behavior consistent with chaos. Besides previous diagnostic tools, the local nonlinear short‐term prediction was also used as a supplement method. It was found that the bubbling process exhibits a deterministic chaotic behavior in a certain range of the gas flow rate. When increasing the gas flow rate, the sequence of periodic bubbling, primary and advanced chaotic bubbling, and jetting or random bubbling were successively observed. However, no clear period doubling sequence leading to chaotic behavior was observed. The sharp loss of the ability to predict the pressure signal successfully with the nonlinear prediction method provides the strongest evidence of the presence of the chaotic bubbling. The variations of the nonlinear invariants, such as the Kolmogorov entropy and the correlation dimension together with the plot of the correlation integral with the operation conditions, might be developed as potential and effective quantitative tools for flow regime identification of the bubbling process.     

AI-Based Supervision for a Stirred Extraction Column Assisted with Population Balance-Based Simulation

Solvent extraction as environmental benign separation technique can be modeled in physical detail by population balance of the droplet size distribution. However, much information on the droplet generation and coalescence is necessary for representative results. In this contribution, we present a comparison of AI-evaluated experimental and simulated data on the behavior of a stirred solvent extraction column with an inner diameter of 32 mm. Lab experiments were performed using the standard test system with n-butyl acetate, acetone, and deionized water. A digital camera is placed in front of the middle section as well as the head of the column. Droplet size evaluation is performed using a retrained neural net (Mask R-CNN). The stirred DN32 extraction column is modeled and simulated using a 1D CFD population balance software. The simulation allows for behavior analysis, trends comparison, and validation of the hydrodynamics and mass transfer performances.     

Parameter effects on dry fine pulverization of alumina particles in a fluidized bed opposed jet mill

The paper presents the experimental results on dry fine pulverization of alumina particles in a fluidized bed opposed jet mill. The effect of operating parameters (i.e., feed load, inlet air pressure and the distance between nozzle outlet and jet meeting point) on the grinding results was investigated in detail. The breakage behaviors of alumina particles with respect to the effects of different parameters were discussed via the selection and breakage functions calculated by the first Kapur function method. In addition, the product size distributions could be simulated by a proposed model.     

Bubble size distribution modeling in stirred gas–liquid reactors with QMOM augmented by a new correction algorithm

Local gas hold‐up and bubbles size distributions have been modeled and validated against experimental data in a stirred gas–liquid reactor, considering two different spargers. An Eulerian multifluid approach coupled with a population balance model (PBM) has been employed to describe the evolution of the bubble size distribution due to break‐up and coalescence. The PBM has been solved by resorting to the quadrature method of moments, implemented through user defined functions in the commercial computational fluid dynamics code Fluent v. 6.2. To overcome divergence issues caused by moments corruption, due to numerical problems, a correction scheme for the moments has been implemented; simulation results prove that it plays a crucial role for the stability and the accuracy of the overall approach. Very good agreements between experimental data and simulations predictions are obtained, for a unique set of break‐up and coalescence kinetic constants, in a wide range of operating conditions. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Fines removal in a continuous plug flow crystallizer by optimal spatial temperature profiles with controlled dissolution

This work presents a systematic study for obtaining the optimal temperature profile in a continuous plug flow crystallizer (PFC). The proposed PFC consists of multiple segments where the temperature of each segment can be controlled individually. An optimization problem is formulated for a target crystal size distribution (without fines) with the temperature of the segments as decision variables. The results indicate that for the crystallization kinetics considered, dissolution steps are necessary for the reduction of fines due to nucleation. A systematic study on the form of growth and dissolution kinetics suggested that the key factor that determines whether the dissolution steps will be successful in reducing fines, without compromising the final size of the crystals from seed, is the size dependence of the growth and dissolution kinetics. Best fines removal is achieved when the larger crystals grow faster than the smaller ones and the smaller crystals dissolve faster than the larger ones. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4582–4594, 2013     

Starch foam material performance prediction based on a radial basis function artificial neural network trained by bare‐bones particle swarm optimization with an adaptive disturbance factor

A novel model based on a radial basis artificial neural network and bare‐bones particle swarm optimization tuned with adaptive disturbance factor for predicting the performances of starch‐based foam materials was established. The ethylene–vinyl acetate/starch mass ratio, glycerin content, and NaHCO₃ content were used as the input variables, whereas the tensile strength and rebound rate were taken as the output variables of the model. The prediction results show that model predictions were in great accordance with the experimental values. The root mean square error of prediction and the correlation coefficients were 0.0256 and 0.9873; this indicated the good performance of the model. The model predicted that the tensile strength of the starch‐based foam materials would decrease slowly with increasing glycerin content and showed a V‐shaped variation with increasing NaHCO₃ content. The rebound rate increased with increasing glycerin content and presented an inverted V‐shaped variation with increasing NaHCO₃ content. The predicted results were consistent with the experimental results. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 44252.