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.

Modeling and optimization of industrial Fischer–Tropsch synthesis with the slurry bubble column reactor and iron-based catalyst

To optimize industrial Fischer-Tropsch （IT） synthesis with the slurry bubble column reactor （SBCR） and iron- based catalyst, a comprehensive process model for IT synthesis that includes a detailed SBCR model, gas liquid separation model, simplified CO2 removal model and tail gas cycle model was developed. An effective iteration algorithm was proposed to solve this process model, and the model was validated by industrial demonstration experiments data （SBCR with 5.8 m diameter and 30 m height）, with a maximum relative error 〈 10% for predicting the SBCR performances. Subsequently, the proposed model was adopted to optimize the industrial SBCR performances simultaneously considering process and reactor parameters variations. The results show that C5＋yield increases as catalyst loading increases within 10-70 ton and syngas H2/CO value decreases within 1.3-1.6, but it doesn＇t increase obviously when the catalyst loading exceeds 45 ton （about 15 wt% concentration）. Higher catalyst loading will result in higher difficulty for wax/catalyst separation and higher catalyst cost. There- fore, the catalyst loading （45 ton） is recommended for the industrial demonstration SBCR operation at syngas H2/ CO = 1.3, and the C5 ＋ yield is about 402 ton＂ per day, which has an about 16% increase than the industrial dem- onstration run result.

A model for predicting bubble rise velocity in a pulsed gas solid fluidized bed

Bed stability, and especially the bed density distribution, is affected by the behavior of bubbles in a gas solid fluidized bed. Bubble rise velocity in a pulsed gas-solid fluidized bed was studied using photographic and computational fluid dynamics methods. The variation in bubble rise velocity was investigated as a function of the periodic pulsed air flow. A predictive model of bubble rise velocity was derived: ub=ψ(Ut+Up-Umf)+kp(gdb)(1/2). The software of Origin was used to fit the empirical coefficients to give ψ = 0.4807 and kp = 0.1305. Experimental verification of the simulations shows that the regular change in bubble rise velocity is accurately described by the model. The correlation coefficient was 0.9905 for the simulations and 0.9706 for the experiments.

A numerical model for cloud cavitation based on bubble cluster

The cavitation cloud of different internal structures results in different collapse pressures owing to the interaction among bubbles. The internal structure of cloud cavitation is required to accurately predict collapse pressure. A cavitation model was developed through dimensional analysis and direct numerical simulation of collapse of bubble cluster. Bubble number density was included in proposed model to characterize the internal structure of bubble cloud. Implemented on flows over a projectile, the proposed model predicts a higher collapse pressure compared with Singhal model. Results indicate that the collapse pressure of detached cavitation cloud is affected by bubble number density.

Very Large Eddy Simulation of Cavitation from Inception to Sheet/Cloud Regimes by A Multiscale Model

The cavitating flow in different regimes has the intricate flow structure with multiple time and space scales.The present work develops a multiscale model by coupling the volume of fluid(VOF)method and a discrete bubble model(DBM),to simulate the cavitating flow in a convergent-divergent test section.The Schnerr-Sauer cavitation model is used to calculate the mass transfer rate to obtain the macroscale phase structure,and the simplified Rayleigh-Plesset equation is applied to simulate the growing and collapsing of discrete bubbles.An algorithm for bridging between the macroscale cavities and microscale bubbles is also developed to achieve the multiscale simulation.For the flow field,the very large eddy simulation(VLES)approach is applied.Conditions from inception to sheet/cloud cavitation regimes are taken into account and simulations are conducted.Compared with the experimental observations,it is shown that the cavitation inception,bubble clouds formation and glass cavity generation are all well represented,indicating that the proposed VOF-DBM model is a promising approach to accurately and comprehensively reveal the multiscale phase field induced by cavitation.

Theoretical estimation of sonochemical yield in bubble cluster in acoustic field

In order to learn more about the physical phenomena occurring in cloud cavitation,the nonlinear dynamics of a spherical cluster of cavitation bubbles and cavitation bubbles in cluster in an acoustic field excited by a square pressure wave are numerically investigated by considering viscosity,surface tension,and the weak compressibility of the liquid.The theoretical prediction of the yield of oxidants produced inside bubbles during the strong collapse stage of cavitation bubbles is also investigated.The effects of acoustic frequency,acoustic pressure amplitude,and the number of bubbles in cluster on bubble temperature and the quantity of oxidants produced inside bubbles are analyzed.The results show that the change of acoustic frequency,acoustic pressure amplitude,and the number of bubbles in cluster have an effect not only on temperature and the quantity of oxidants inside the bubble,but also on the degradation types of pollutants,which provides a guidance in improving the sonochemical degradation of organic pollutants.

Numerical simulation and experimental verification of bubble size distribution in an air dense medium fluidized bed

Bubble size distribution is the basic apparent performance and obvious characteristics in the air dense medium fluidized bed (ADMFB). The approaches of numerical simulation and experimental verification were combined to conduct the further research on the bubble generation and movement behavior. The results show that ADMFB could display favorable expanded characteristics after steady fluidization. With different particle size distributions of magnetite powder as medium solids, we selected an appropriate prediction model for the mean bubble diameter in ADMFB. The comparison results indicate that the mean bubble diameters along the bed heights are 35 mm < D b < 66 mm and 40 mm < D b < 69 mm with the magnetite powder of 0.3 mm+0.15mm and 0.15mm+0.074mm, respectively. The prediction model provides good agreements with the experimental and simulation data. Based on the optimal operating gas velocity distribution, the mixture of magnetite powder and <1mm fine coal as medium solids were utilized to carry out the separation experiment on 6-50mm raw coal. The results show that an optimal separation density d P of 1.73g/cm 3 with a probable error E of 0.07g/cm 3 and a recovery efficiency of 99.97% is achieved, which indicates good separation performance by applying ADMFB.

Electrode Potential Explaining the Growth of Anodic Oxides

The formation mechanism of porous anodic oxides remains unclear till now.The classical field-assisted dissolution(FAD)theory cannot explain the relationship between the current curve and FAD reaction,and the influence of the electrode potential on anodization is rarely reported.The electrode potential theory,oxygen bubble model and the ionic current and electronic current theories were introduced to explain the growth of porous anodic oxides of three metals(Ti,Zr and Fe).Taking the anodization of Ti in aqueous solution containing 0.5wt% NH_(4)F as an example,the electrode potential was calculated,and the morphology of porous anodic oxides was investigated at low voltages.Results show that the growth of porous anodic oxides is determined by the ratio of the ionic current to the electronic current.During the anodization,metals are classified into two groups:one is easy to form the compact oxide layer,and the other is easy to induce oxygen releasing,thus forming oxygen bubbles.The electrolyte is also classified into two groups correspondingly:compact oxide layer-assisted electrolyte and releasing oxygen-assisted electrolyte.

A new drag model for TFM simulation of gas-solid bubbling fluidized beds with Geldart-B particles

In this work, a new drag model for TFM simulation in gas-solid bubbling fluidized beds was proposed, and a set of equations was derived to determine the meso-scale structural parameters to calculate the drag characteristics of Geldart-B particles under low gas velocities. In the new model, the meso-scale structure was characterized while accounting for the bubble and meso-scale structure effects on the drag coefficient. The Fluent software, incorporating the new drag model, was used to simulate the fluidization behavior. Experiments were performed in a Plexiglas cylindrical fluidized bed consisting of quartz sand as the solid phase and ambient air as the gas phase. Comparisons based on the solids hold-up inside the fluidized bed at different superficial gas velocities, were made between the 2D Cartesian simulations, and the experimental data, showing that the results of the new drag model reached much better agreement with exoerimental data than those of the Gidasoow dra~ model did.

Numerical investigation of the time-resolved bubble cluster dynamics by using the interface capturing method of multiphase flow approach

The present paper proposes a multiphase flow approach for capturing the time-resolved collapse course of bubble clusters in various geometrical configurations.The simulation method is first verified by computing the dynamic behavior of an isolated vapor bubble placed in a uniform ambient pressure.The comparison between the numerical result and the theoretical solution indicates that the method can accurately capture the bubble shape,the characteristic time and the extremely high pressure induced by the collapse.Then the simulation method is applied to investigate the behavior of two kinds of bubble clusters in hexagonal and cubic geometrical configurations.The predicted collapsing sequence and the shape characteristics of the bubbles are generally in agreement with the experimental results.The bubbles transform and break from the outer layer toward the inner layers.In each layer,the bubbles on the corner first change into a pea shape and cave before collapsing,then the bubbles on the sides begin to shrink.It is also found that,in comparison with the case of an isolated single bubble,the central bubble in the cluster always contracts more slowly at the early stage and collapses more violently at the final stage.

A comparative assessment of empirical and lattice Boltzmann method-based drag models for simulation of gas-solid flow hydrodynamics in a bubbling fluidized bed

In simulations of fluidized beds using computational fluid dynamics （CFD）, the description of gas-solid flow hydrodynamics relies on a drag model to account for the momentum transfer between gas and solid phases. Although several studies of drag models have been published, there have been few investigations of the application of lattice Boltzmann method （LBM）-based drag models to bubbling fluidized bed simu- lations. In the present study, a comprehensive comparison of empirical and LBM-based drag models was carried out to assess the performance of these models during simulations of gas-solid flow hydrodynam- ics in a bubbling fluidized bed. A CFD model using the MFIX code based on the Eulerian-Eulerian approach and the kinetic theory of granular flow was used to simulate a 2D bubbling fluidized bed with Geldart B particles. The simulation results were validated by comparison with experimental data. Statistical anal- ysis of the results shows that LBM-based drag models can reliably model gas-solid flow hydrodynamics in a bubbling fluidized bed.

CFD-DEM simulation of Small-Scale Challenge Problem 1 with EMMS bubble-based structure-dependent drag coefficient

In this study,the energy minimization multi-scale(EMMS)/Bubbling model is coupled with the computational fluid dynamics/discrete element method(CFD-DEM)model via a structure-dependent drag coefficient to simulate the National Energy Technology Laboratory(NETL)small-scale challenge problem using the open-source multiphase flow code MFIX.The numerical predictions are compared against particle velocity measurements obtained from high-speed particle image velocimetry(HSPIV)and differential pressure measurements.The drag-reduction effect of the EMMS bubble-based drag coefficient is observed to significantly improve predictions of the horizontal particle velocity and granular temperature when compared to several other drag coefficients tested;however,the vertical particle velocity and pressure fluctuation characteristic predictions are degraded.The drag-reduction effect is characterized by a reduction in the sizes of slugs or voids,as identified through spectral decomposition of the pressure fluctuations.Overall,this study shows great promise in employing drag coefficients,developed via multi-scale approaches(such as the EMMS paradigm),in CFD-DEM models.

适用于二维及三维瑞利-泰勒湍流混合的统一气泡融合模型

瑞利-泰勒(RT)湍流混合阶段的气泡统计直径d和高度h随时间的演化规律对许多自然现象和工程应用都至关重要.对于由多模短波扰动演化而来的RT问题,大量数值模拟和最新实验(R.V.Morgan et al.,2020)均表明,气泡统计直径d和高度h具有普适性的增长规律.但是,到目前为止,先前研究者仍然没有给出能够同时准确预测这两个特征量的自洽模型.在本文中,基于半约束思想和浮阻力模型,我们建立了一个能够同时适用于二维(2D)及三维(3D)流动的统一气泡融合模型.新模型表明:(1)气泡平均直径d呈自相似增长,相应的自相似结构参数β≡d/h≈(1+A)/2和(1+A)/4,其中阿特伍德数A是密度比的函数;(2)气泡高度h与时间呈二次增长关系,其中二次增长系数α≡h/(Agt^(2))≈0.05(2D)和0.025(3D),其中g为加速度,t为时间.结果表明,新模型的预测结果与先前的实验和数值模拟结果一致,对理解RT湍流混合具有重要意义.