Numerical investigation of closures for interface forces acting on single air-bubbles in water using Volume of Fluid and Front Tracking models

Closures for the drag and virtual mass forces acting on a single air bubble rising in initially quiescent pure water have been numerically investigated using direct numerical simulation techniques. A 3D Front Tracking model was used and the results were compared with simulation results obtained with a 2D Volume of Fluid model to assess the influence of the third dimension. In the simulations realistic values were taken for the physical properties, i.e., a density ratio of 800. The computed time-averaged terminal rise velocity and mean aspect ratio for individual air bubbles ranging in equivalent diameter from 1 to 10 mm rising in pure water compare well with available experimental data.     

Effect of bed characteristics on local liquid spreading in a trickle bed

Trickle bed reactors are important to several chemical process applications. While the available computational fluid dynamics models can predict overall liquid volume fraction, the prediction of spatial liquid distribution continues to be a challenging task. In the present work, Eulerian multifluid simulations were performed to investigate the effects of particle size, gas and liquid flow rates, and bed structure on local liquid spreading, and the predictions were validated using measured liquid spreading. It was found that the capillary pressure force caused liquid to spread in the lateral direction and that the interphase interaction forces pushed it in the downward direction and the relative magnitudes of these forces governed the local liquid distribution. While the use of existing capillary pressure force model led to satisfactory prediction of the observed trends of dynamic and steady state local liquid spreading, the modified capillary pressure force led to quantitatively correct predictions of local liquid spreading. © 2016 American Institute of Chemical Engineers AIChE J, 63: 347–357, 2017     

Simulation of drop formation in a single hole in solvent extraction using the volume-of-fluid method

Computational fluid dynamics (CFD) simulations were performed to investigate drop formation in single holes in solvent extraction. The effects of various operating and design parameters were investigated in order to optimize the drop formation. The obtained results show that CFD simulations can give useful information about drop formation in sieve plates. The numerical results indicated different drop formation periods. These periods were different for the straight and conical holes. Furthermore, it was shown that the shape of the hole has considerable effect on the size of the drops formed. The simulation results were verified by comparison with experimental observations obtained using high-speed video technology. The numerical results for the drop sizes, shapes and formation times were found to be consistent with images of experimental drops across a wide range of solvent volumetric flow rates.     

Numerical simulation of bubble columns flows: effect of different breakup and coalescence closures

Two-dimensional axisymmetric Eulerian/Eulerian simulations of two-phase (gas/liquid) transient flow were performed using a multiphase flow algorithm based on the finite-volume method. These numerical simulations cover laboratory scale bubble columns of different diameters, operated over a range of superficial gas velocities ranging from the bubbly to the churn turbulent regime. The bubble population balance equation (BPBE) is implemented in the two-fluid model that accounts for the drag force and employs the modified k-ε turbulence model in the liquid phase. Several available bubble breakup and coalescence closures are tested. Quantitative agreements between the experimental data and simulations are obtained for the time-averaged axial liquid velocity profiles, as well as for the kinetic energy profiles, only when model predicted breakup rate is increased by a factor of ten to match the coalescence rate. The calculated time-averaged gas holdup profiles deviate in shape from the measured ones and suggest that full three-dimensional simulation is needed. Implementation of BPBE leads to better agreement with data, especially in the churn-turbulent flow regime, compared to the simulation based on an estimated constant mean bubble diameter. Differences in the predicted interfacial area density, with and without BPBE implementation, are significant. The choice of bubble breakup and coalescence closure does not have a significant impact on the simulated results as long as the magnitude of breakup is increased tenfold.     

Effects of cross-flow velocity, capillary pressure and oil viscosity on oil-in-water drop formation from a capillary

The formation of oil drops from a single capillary with a diameter of 200 μm into a cross-flowing continuous water phase has been studied experimentally with the particle image velocimetry (PIV) technique and numerically with the computational fluid dynamics (CFD) software Fluent. The drop formation time and the volume of the detached drop were used as validation parameters and the results from the two methods corresponded well, with a difference of less than 5% for the drop formation time and 10% for the drop volume. The cross-flow velocity has a major impact on drop size, which decreases as the cross-flow increases. An increase in cross-flow, oil viscosity and capillary pressure displace the position of necking and drop detachment away from the capillary opening, which will have a decreasing effect on the final size of the drop.     

Numerical simulation of reacting plane mixing layer by particle method

This paper proposes a two-dimensional particle method for a plane mixing layer with a single-step and irreversible chemical reaction. The vorticity and concentration fields are discretized into the vortex and concentration elements, respectively, and the behavior of the elements is calculated with the Lagrangian method. The reaction is estimated through the calculation for the time rate of change in the strength for concentration element. The method is applied to simulate the reactive plane mixing layer. The simulation demonstrates that the mixing and reaction phenomena caused by the large-scale eddies are successfully captured. It is also confirmed that the effects of the Damköhler number and stoichiometric ratio on the reaction are favorably analyzed by the method.     

Numerical simulations of bubble formation on submerged orifices: Period-1 and period-2 bubbling regimes

The process of bubble formation is involved in several gas-liquid reactors and process equipment. It is therefore important to understand the dynamics of bubble formation and to develop computational models for the accurate prediction of the bubble formation dynamics in different bubbling regimes. This work reports the numerical investigations of bubble formation on submerged orifices under constant inflow conditions. Numerical simulations of bubble formation at high gas flow rates, where the bubble formation is dominated by inertial forces, were carried out using the combined level set and volume-of-fluid (CLSVOF) method and the predictions were experimentally validated. Effects of gas flow rate and orifice diameter on the bubbling regimes and in particular, on the transition from period-1 to period-2 bubbling regime (with pairing or coalescence at the orifice) were investigated. Using the simulation data on the transition of bubble formation regimes, the bubble formation regime map constructed using Froude and Bond numbers is presented.     

有机硅单体合成的气固流化床的三维数值模拟

为了探索有机硅单体合成气固流化床内硅粉颗粒的流化特性,作者利用计算流体力学CFD软件,采用双欧拉气固两相流模型及SIMPLE算法,模拟了三维的气固流化床内硅粉颗粒的流化特性;分析了气泡生成、长大和破裂的过程,及不同床层高度的固体颗粒运动速度矢量图,不同床层高度处横截面颗粒体积分数变化。结果表明:三维模拟能直观的表现颗粒在流化床中的流化状态,为工业生产及应用提供了有效的依据。     

搅拌槽内固液两相流的数值模拟及功率计算

使用计算流体动力学的方法对搅拌槽中的流场进行模拟,得到搅拌槽中液体的流动状况和体积分数分布。对流场分布规律、固体颗粒体积分数特点加以分析,进而利用模拟出的数据计算搅拌轴的功率,为搅拌器的设计提供参考。     

Numerical modeling of particle fluidization behavior in a rotating fluidized bed

In this study, numerical modeling of particle fluidization behaviors in a rotating fluidized bed (RFB) was conducted. The proposed numerical model was based on a DEM (Discrete Element Method)-CFD (Computational Fluid Dynamics) coupling model. Fluid motion was calculated two-dimensionally by solving the local averaged basic equations. Particle motion was calculated two-dimensionally by the DEM. Calculation of fluid motion by the CFD and particle motion by the DEM were simultaneously conducted in the present model. Geldart group B particles (diameter and particle density were 0.5 mm and 918 kg/m³, respectively) were used for both calculation and experiment. First of all, visualization of particle fluidization behaviors in a RFB was conducted. The calculated particle fluidization behaviors by our proposed numerical model, such as the formation, growth and eruption of bubble and particle circulation, showed good agreement with the actual fluidization behaviors, which were observed by a high-speed video camera. The estimated results of the minimum fluidization velocity (U_mf) and the bed pressure drop at fluidization condition (ΔP_f) by our proposed model and other available analytical models in literatures were also compared with the experimental results. It was found that our proposed model based on the DEM-CFD coupling model could predict the U_mf and ΔP_f with a high accuracy because our model precisely considered the local downward gravitational effect, while the other analytical models overpredicted the ΔP_f due to ignoring the gravitational effect.     

微裂缝内液固两相流动特性研究

应用欧拉-拉格朗日模型,对微裂缝中液-固两相流动过程进行数值模拟。在数学模型中,液相采用连续相模型,颗粒当做离散分散在连续相中,并考虑了相间耦合作用。对于物理模型,建立了二维直微裂缝模型,研究裂缝的液相粘度、液相速度和颗粒密度等因素对裂缝中两相流动的影响。模拟得到了微通道内颗粒瞬时分布状态、颗粒运动轨迹、颗粒停留时间、颗粒轴向速度分布、液相轴向速度分布等参数的变化规律,定性的揭示了储层裂缝内液固两相流动过程。     

搅拌釜内流场三维数值模拟及功率预测

大型搅拌釜,尤其是涉及传热或两相介质搅拌的容器,其搅拌效果和功率往往难以预测。针对大型搅拌釜的搅拌器设计、流场结构模拟和功率预测等问题,采用CFD数值模拟技术,对搅拌釜内部的三维流场进行了数值计算。分析了搅拌釜内的流动结构,计算了不同曝气量时的搅拌功率,获得了详细的流场信息和各项特性参数。     

Spontaneous spreading of emulsions on solid surfaces: Morphology and dynamics

The spontaneous spreading of emulsions of water dispersed in silicone oil onto glass surfaces is examined using differential interference contrast (DIC) microscopy. Spreading occurs via a precursor film from which the emulsion droplets are excluded. The radius of the interline of the bulk drop is found to vary as (time)^1/10, as is commonly observed for the spontaneous spreading of pure liquids. The spreading rate constant decreases linearly with the volume percent of the dispersed phase, but drops suddenly to zero at approximately 73% dispersed phase. The width and spreading rate of the precursor film also is found to decrease with dispersed phase concentration. A fingering type of instability is evident at the leading edge of the precursor film, yet has little effect on the spreading rate of either the precursor film or the droplet interline. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 1817–1825, 2001     

Computational fluid dynamics model of viscous droplet breakup

A computational fluid dynamics (CFD) model is being developed to help guide the design of equipment to enhance viscous droplet breakup. The first generation model was able to show qualitative agreement with experimental results. This 2D model follows a single droplet (with a specified initial diameter) flowing past a series of cylinders using a volume of fluid (VOF) method to track the interface. The model is able to predict droplet breakup and provide insights into the physics of the breakup process. Three different breakup mechanisms are hypothesized that help explain experimental observations, including a minimum in breakup efficacy (ability to create smaller droplets) versus velocity data. Important parameters include the system rheology, velocity, cylinder size versus droplet size, and cylinder layout.     

A parametric study of droplet deformation through a microfluidic contraction: Low viscosity Newtonian droplets

Numerical simulations are conducted to investigate how a droplet of Newtonian liquid, entrained in a higher viscosity Newtonian liquid, behaves when passing through an axisymmetric microfluidic contraction. Simulations are performed using a transient Volume of Fluid finite volume algorithm, and cover ranges of Reynolds and Weber numbers relevant to microfluidic flows. Results are presented for a droplet to surrounding fluid viscosity ratio of 0.001. In contrast to behaviour at higher viscosity ratios obtained previously by the authors, shear and interfacial tension driven instabilities often develop along the droplet surface, leading to complex shape development, and in some instances, droplet breakup.     

Numerical simulation of gas-particle flow with a second-order moment method in bubbling fluidized beds

Flow behavior of gas and particles is performed by means of gas-solid two-fluid model with the second-order moment model of particles in the bubbling fluidized bed. The distributions of velocity and moments of particles are predicted in the bubbling fluidized beds. Predictions are compared with experimental data measured by Jung et al. (2005) in a bubbling fluidized bed and Patil et al. (2005) experiments in a bubbling fluidized bed with a jet. The simulated second-order moment in the vertical direction is on average 1.5-2.3 times larger than that in the lateral direction in the bubbling fluidized bed (Jung et al., 2005). For a bubbling fluidized bed with a jet, the ratio of normal second-order moment in the vertical direction to in the lateral direction is in the range of 0.5-2.5 (Patil et al., 2005). The bubblelike Reynolds normal stresses per unit bulk density used by Gidaspow et al. (2002) are computed from the simulated hydrodynamic velocities. The simulated bubblelike Reynolds normal stresses in the vertical direction is on average 4.5-6.0 times larger than that in the lateral direction in the bubbling fluidized bed (Jung et al., 2005). The predictions are in agreement with experimental second-order moments measured by Jung et al. (2005) and porosity measured by Patil et al. (2005).     

Numerical simulation on flow, combustion and heat transfer of ethylene cracking furnaces

With the study object of an 100kt/a SL-II ethylene cracking furnace, this paper used Computational Fluid Dynamics (CFD) method to carry out coupled simulation studies on the flow, combustion, radiative heat transfer and thermal cracking reaction processes in the cracking furnace. The standard k–ε two-equation model was applied to turbulence simulation. The finite-rate/eddy-dissipation model was used for modeling of non-premixed combustion of the bottom burners and premixed combustion of the sidewall burners. The Discrete Ordinates (DO) model was applied to the simulation of radiative heat transfer of furnace. The simulation results show the detailed information about velocity, temperature and concentration fields in the furnace and heat flux distribution on the reactor tubes skin. This work will provide a theoretical basis for the optimization of the geometrical structure and operational parameters of the cracking furnace.     

The influence of inclined plates on expansion behaviour of solid suspensions in a liquid fluidised bed — A computational fluid dynamics study

A significant increase in the particle sedimentation rate can be achieved by introducing inclined plates into conventional fluidised beds. In turn, high suspension densities are possible at fluidisation velocities in excess of the particle terminal velocity. The installation of the inclined plates, however, alters the dynamic characteristics of the fluidised bed, in particular, impacting upon the expansion behaviour of the suspension. In the present work a Computational Fluid Dynamics (CFD) approach was employed to investigate the influence of inclined plates on the expansion behaviour of solids suspensions in liquid fluidised beds. The model is based on the solution of the Eulerian multiphase equations for up to two different particle sizes with a continuous phase of water. The momentum equations treat hindered settling behaviour via the inclusion of a volume fraction dependent drag law. The computational model was validated against our experimental data and compared with the predictions of a kinematic model developed in one of our earlier works. In general the predictions made by both the CFD and the kinematic models were found to be in good agreement with the experimental results.     

Model of inertial spreading and imbibition of a liquid drop on a capillary plate

We outline a low‐order Lagrangian model for the inertial dynamics of spreading and imbibition of a spherical liquid cap on a plane featuring independent cylindrical capillaries without gravity. The analysis predicts the relative roles of radial and axial kinetic energy, reveals the critical Laplace number beyond which the drop oscillates, and attributes the exponent of the initial power‐law for contact patch radius vs. time to the form of capillary potential energy just after the liquid sphere touches the plate. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5474–5481, 2017