Simplified Calculation of Mixing and Suspending Processes in Agitated Vessels – Part I: Basis of The Model

Mixing processes with different stirring systems in agitated vessels are simulated by a multi‐region model. Because of discontinuities at the boundaries of different regions appearing for the already‐existing simple three‐region model, unrealistic values occur during the calculation of the concentration distribution at these locations. Therefore, the region model will be modified at first. The procedure is presented here for the example of a radial flow stirrer, considering the fluid velocity, the turbulence field, the particle diffusion, and the relative fluid‐to‐particle velocity. The modified model is discussed and validated. Thus, the behavior of single particles and particle swarms can be analyzed in the vessel considering different aspects.     

宽Re范围内气泡和液滴曳力系数的关联模型

流粒(气泡或液滴)的曳力系数CD和上升/终端速度因有助于准确预测反应器内相含率分布、液相速度分布、流粒停留时间和传质速率而具有重要意义。但现有用于估算流粒CD的关联式大多分段且只在低雷诺数Re区间内有效,并难以同时准确预测不同实验体系和操作条件下的实验结果。针对这些不足,基于实验测量和理论分析,本工作提出了一个能够在整个Re范围内合理描述实验观测到的流粒CD演变规律的新数学关联式,并利用单组实验数据和编写的求解多维无约束线性优化问题的计算机程序确定了模型参数,且将新流粒CD关联式与现有经验模型、实验结果或三维数值模拟结果进行了对比。结果表明,新流粒CD关联式展现出优异的预测能力,能对不同实验体系(空气?水、空气?甘油?水、空气?甘油、甲苯?水、正丁醇?水、正辛醇?水等)、不同操作条件(气泡：0.1相似文献   

垂直管道中塞状流的模拟

运用简化的硬球模型模拟垂直管道中的塞状流. 固相行为通过跟踪离散颗粒的运动轨迹处理,气相运动由局部平均的Navier–Stokes方程处理,气固两相间的耦合作用服从牛顿第三定律. 每个颗粒的运动过程被分解为颗粒间相互碰撞的过程及流体对其悬浮的过程. 该模型定性地模拟了垂直管道中的塞状流,即在细而长的管道中,颗粒形成沿管道运动的塞状物,且塞状物的运动速度独立于塞状物的长度,但随着气体速度的增加而增加.     

Coarse grained computational fluid dynamic simulation of sands and biomass fluidization with a hybrid drag

The bubbling fluidized bed reactor is widely used in fast pyrolysis of biomass. Discrete simulation of this reactor is challenging due to many sand particles and lack of accurate drag corrections accounting for the interaction of two different solid particles with different properties. In this research, the computational cost is reduced by using the coarse-grained computational fluid dynamic-discrete element method, where many sand particles are lumped into a larger numerical parcel. The Syamlal–O'Brien drag model is used for sand, while Ganser correction coupled with Gidaspow model is used for the nonspherical biomass particles. This hybrid approach shows superior behavior over other drag models using pressure drops as a benchmark. The predicted bed height and pressure fluctuating frequencies compare well with experiment. The mixing of biomass is close to perfect if the superficial velocity is larger than four times the minimum fluidization velocity.     

Mixing of viscoelastic fluids with helical-ribbon agitators. I — Mixing time and flow patterns

Batch mixing of viscous fluids with helical-ribbon agitators in 2.4 liter and 13 liter vessels has been studied for agitator speeds up to 200 RPM. Seven different agitators of different dimensions were employed in this work. Mixing times were measured using a decoloration technique and circulation times were determined by the tracer bead method. In addition, velocity profiles were obtained from streak photographs using selective illumination of the vessel and PVC powder as tracer particles. It was found that the mixing times of Newtonian fluids, which agreed with previously published data, were considerably (3 to 7 times) shorter than those of the viscoelastic fluids. The mixing time was strongly affected by the fluids' elasticity; increasing as the fluid elasticity increased. The velocity profiles were qualitatively similar for all the fluids but showed decreased axial circulation and increased circumferential flow as fluid elasticity increased. However, mixing is not only a function of the axial circulation (impeller pumping rate) but also is a function of the perturbations superimposed on the main flow. A simple, first approximation model based on the impeller geometry and flow patterns is proposed to correlate the circulation capacity and mixing time data for the various geometries studied.     

A mechanistic model to determine the critical flow velocity required to initiate the movement of spherical bed particles in inclined channels

This study presents a mechanistic model that predicts the critical velocity, which is required to initiate the movement of solid bed particles. The model is developed by considering fluid flow over a stationary bed of solid particles of uniform thickness, which is resting on an inclined pipe wall. Sets of sand bed critical velocity tests were performed to verify the predictions of the model. An flow loop with recirculation facilities was constructed to measure the critical velocities of the sand beds. The tests were carried out by observing the movement of the bed particles in a transparent pipe while regulating the flowrate of the fluid. Water and aqueous solutions of PolyAnoinic Cellulose were used as a test fluid. The critical velocities of four sand beds with different particle size ranges were measured. The model was used to predict the critical velocities of the beds. The model predictions and experimentally measured data show satisfactory agreement. The results also indicated that the critical velocity is influenced by the properties of the fluid, flow parameters, and particle size.     

Estimation of Concentration of Particles in Polymerizing Fluid during Centrifugal Casting of Functionally Graded Polymer Composites

The concentration of uniformly distributed particles in a fluid changes with time in the direction of gravitational or centrifugal force to form a concentration gradient. The change in the concentration is an outcome of velocity variation of particles in a fluid. A modified equation for terminal velocity, v _m of particles in polymerizing-fluid under centrifugal force is proposed to estimate the changes in the volume fraction of particles in the graded composites. The proposed equation introduces the effect of cure kinetics of polymer and its effect on particle movement in the model that was based on the modified Stoke’s law, considering the parameters related to particle hindrance, centrifugal force, particle dimensions, viscosity variation etc. The model predictions of concentration changes at the different locations of samples were compared with calcium carbonate filled polysulphide-modified-epoxy graded composites prepared by centrifugal casting.. The effect of particle size, delayed curing rate of matrix were explored. The simulated results are in good agreement with those of experiments.     

Computational investigation of the mechanisms of particle separation and “fish‐hook” phenomenon in hydrocyclones

The motion of solid particles and the “fish‐hook” phenomenon in an industrial classifying hydrocyclone of body diameter 355 mm is studied by a computational fluid dynamics model. In the model, the turbulent flow of gas and liquid is modeled using the Reynolds Stress Model, and the interface between the liquid and air core is modeled using the volume of fluid multiphase model. The outcomes are then applied in the simulation of particle flow described by the stochastic Lagrangian model. The results are analyzed in terms of velocity and force field in the cyclone. It is shown that the pressure gradient force plays an important role in particle separation, and it balances the centrifugal force on particles in the radial direction in hydrocyclones. As particle size decreases, the effect of drag force whose direction varies increases sharply. As a result, particles have an apparent fluctuating velocity. Some particles pass the locus of zero vertical velocity (LZVV) and join the upward flow and have a certain moving orbit. The moving orbit of particles in the upward flow becomes wider as their size decreases. When the size is below a critical value, the moving orbit is even beyond the LZVV. Some fine particles would recircuit between the downward and upward flows, resulting in a relatively high separation efficiency and the “fish‐hook” effect. Numerical experiments were also extended to study the effects of cyclone size and liquid viscosity. The results suggest that the mechanisms identified are valid, although they are quantitatively different. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

单螺杆混沌挤出过程周期性行为数值模拟

建立了混沌单螺杆挤出机计量段物理和数学模型。定义了更合理的边界条件,采用Carreau本构方程,采用有限体积方法对聚合物熔体在螺槽内流动的周期性效应进行了数值模拟分析。得到了不同位置的速度分布细节以及流体示踪粒子的行为轨迹。发现螺槽内速度分布表现出周期性和对称性的变化,揭示了同宿点及椭圆点存在及位置不变性,为进一步分析流体质点在相空间的动力学行为奠定了基础。     

颗粒移动床内不稳定运动的计算颗粒动力学模拟

采用考虑滚动摩擦的三方程离散单元法（DEM）模型对侧开孔的移动床中的颗粒流动进行了数值研究。结果表明，计算颗粒动力学(CGD)方法可对复杂颗粒系统内颗粒的运动行为进行准确的预测，包括时均速度场和脉动速度场。讨论了模型中颗粒摩擦参数的重要影响，并对颗粒流动表现出的间歇现象进行了分析。颗粒流动与流体流动有相似之处，都存在随机的脉动，但颗粒流的随机脉动机理与流体中的湍流机理有很大不同，颗粒流动会表现出很强的不连续性。     

Discrete particle simulation of gas fluidization of ellipsoidal particles

Fluidization is widely used in industries and has been extensively studied, either experimentally or theoretically, in the past decades. In recent years, a coupled simulation approach of discrete element method (DEM) and computational fluid dynamics (CFD) has been successfully developed to study the gas–solid flow and heat transfer in fluidization at a particle scale. However, to date, such studies mainly deal with spherical particles. The effect of particle shape on fluidization is recognized but not properly quantified. In this paper, the CFD–DEM approach is extended to consider the fluidization of ellipsoidal particles. In the simulation, particles used are either oblate or prolate, with aspect ratios varying from very flat (aspect ratio=0.25) to elongated (aspect ratio=3.5), representing cylinder-type and disk-type shaped particles, respectively. The commonly used correlations to determine the fluid drag force acting on a non-spherical particle are compared first. Then the model is verified in terms of solid flow patterns. The effect of aspect ratio on the flow pattern, the relationship between pressure drop and gas superficial velocity, and microscopic parameters such as coordination number, particle orientation and force structure are investigated. It is shown that particle shape affects bed permeability and the minimum fluidization velocity significantly. The coordination number generally increases with aspect ratio deviating from 1.0. The analysis of particle orientations shows that the bed structures for ellipsoids are not random as that for spheres. Oblate particles prefer facing upward or downward while prolate particles prefer horizontal orientation. Spheres have the largest particle–particle contact force and fluid drag force under the comparable conditions. With aspect ratio deviating from 1.0, particle–particle interaction and fluid drag become relatively weak. The proposed model shows a promising method in examining the effect of particle shape on different flow behaviour in gas fluidization.     

Fluidization of spherical versus elongated particles: Experimental investigation using magnetic particle tracking

In biomass processing fluidized beds are used to process granular materials where particles typically possess elongated shapes. However, for simplicity, in computer simulations particles are often considered spherical, even though elongated particles experience more complex particle– particle interactions as well as different hydrodynamic forces. The exact effect of these more complex interactions in dense fluidized suspensions is still not well understood. In this study we use the magnetic particle tracking technique to compare the fluidization behavior of spherical particles to that of elongated particles. We found a considerable difference between fluidization behavior of spherical versus elongated particles in the time-averaged particle velocity field as well as in the time-averaged particle rotational velocity profile. Moreover, we studied the effect of fluid velocity and the particle's aspect ratio on the particle's preferred orientation in different parts of the bed, which provides new insight in the fluidization behavior of elongated particles.     

Hydrodynamics in a gravity settling vessel: CFD modelling with LDA validation

Vertical gravity settling vessels, usually referred to as primary separation vessels (PSV), are used in separating bitumen aggregates from slurry containing sand and fine clays. The hydrodynamics in the PSV influences the separation efficiency of recovered bitumen through the overall mean flow and turbulent interaction. In order to deepen our understanding of the hydrodynamic conditions in such vessels, this paper presents a combined study of the flow field using Laser Doppler Anemometry (LDA) to measure the velocity field, and computational fluid dynamics (CFD) simulations to validate the CFD model. The investigation shows that the flow geometry has a significant influence on the overall flow pattern in such vessels. It also demonstrates that the CFD simulation is a reliable tool in capturing the complex mean flow pattern observed in experiments. Use of different turbulent models such as the standard k‐ε model and Reynolds stress model has very little effect on the mean flow field.     

Numerical Simulation of a Spouted Bed Using Computational Fluid Dynamics (CFD)

In this article, computational fluid dynamics (CFD) technology is used to model a spouted bed(SB). The multifluid Eulerian-Eulerian approach based on kinetic theory of granular flows and Gidaspow's drag model for the interaction between gas and particles are applied in the modeling. The effects of the SB properties—that is, cone angle, particle size, cylinder diameter, and static bed height of particles—on its dynamics performance are investigated. The simulated results—that is, flow pattern of particles, fountain height, voidage, and particle velocity of the spout zone—are presented. It is shown that periodic fluctuation of spouting appears in an SB with conical angle of 30° and inlet velocity at 16.6 m/s. When the SB cylinder diameter becomes 0.52 m, periodic fluctuation appears, too. The stable spouting of the SB with a 90° cone angle could be obtained at an inlet air velocity of 24.3 m/s. The fountain height of particles decreased with an increase in particle size and the static bed height of particles. It is kept at about 0.19 m when different SB cylinder diameters in the range of 0.36 to 0.48 m are used. In the spouting region, the voidage decreased with static particle height in bed, but the particle velocity increased. For a certain particle size, the voidage decreased with an increase in particle height, but the velocity of the particles increased. It was also found that the cylinder diameter did not affect the volume fraction of particles except for the cylinder diameter 0.52 m and the change in particle velocity was minimal in the spout zone. With the different static bed height of particles used, the voidage and particle velocity did not change much at the same level of spout zone.     

Particle attrition mechanism with a sonic gas jet injected into a fluidized bed

High velocity gas jets in fluidized beds provide substantial particle attrition: they are used industrially to control the particle size in fluid bed cokers and to grind products such as toner, pharmaceutical or pigment powders. One method to control the size of the particles in the bed is to use an attrition nozzle, which injects high velocity gas and grinds the particles together. An important aspect of particle attrition is the understanding and modeling of the particle breakage mechanisms. The objective of this study is to develop a model to describe particle attrition when a sonic velocity gas jet is injected into a fluidized bed, and to verify the results using experimental data. The model predicts the particle size distribution of ground particles, the particle breakage frequency, and the proportion of original particles in the bed which were not ground. It was found that the particle breakage frequency can be used to predict the attrition results in different bed sizes. A correlation was also developed, which uses the attrition nozzle operating conditions such as gas density and equivalent speed of sound to predict the mass of particles broken per unit time.     

三维喷动床内异径干湿颗粒混合特性数值模拟

基于计算流体力学-离散单元法,建立了三维喷动床内气固两相流数学模型,采用Fortran语言编制了并行数值模拟程序。对三维喷动床内两种不同直径的干颗粒及湿颗粒的混合特性进行了数值模拟,并从颗粒角度分析了双组分颗粒的运动机制。利用Lacey混合指数对床内整体以及特定区域的混合程度进行了定量分析,并研究了液桥体积、颗粒密度比以及表观气速对异径颗粒混合的影响。结果表明：在单孔射流喷动床内,干湿两种颗粒流动方式相似,湿颗粒无明显的聚团现象;液桥力对小直径的颗粒影响较大,使不同直径湿颗粒速度差减小;环隙区内颗粒的混合是影响整床颗粒混合的关键因素;液桥体积对颗粒混合的影响较大,对颗粒密度比以及表观气速的影响有限。     

Numerical calculation of particle collection by a row of cylinders in a viscous fluid

A method for calculating the collection efficiency of particles by a row of cylinders in a viscous fluid is presented. The Navier-Stokes equation is solved by the finite element method to determine the carrier gas velocity field. Then, the particle equation of motion is also solved by the finite element method to find the particle velocity of impact. Finally, the collection efficiency is obtained by integration of the intercepted particles on the cylinder surface. Results of this model are compared with other theoretical models as well as with some experimental data.     

Hydrodynamic modeling of the entrainment of Geldart A group particles in gas-solid fluidized bed: The effect of column diameter

A multi-fluid Eulerian computational fluid dynamics (CFD) model is used to simulate the entrainment of fluid catalytic cracking (FCC) particles in gas-solid fluidized beds. Entrainment of Geldart A group particles was studied because of their wide range of industrial use. The model was based on the kinetic theory of granular flow. The CFD model was used to investigate the effect of column diameter on the entrainment flux of particles in a binary mixture. Two different sizes of particles were used because many engineering applications deal with binary mixture of particles in fluidized beds. Various column diameters, including 38 mm, 76 mm, 114 mm, 152 mm, and 190 mm, were investigated. The entrainment flux of particles was increased with decreasing column diameter. The effect of column diameter was not significant for column diameters larger than 114 mm. Furthermore, increasing the superficial gas velocity increased the entrainment flux of particles. Model predictions were also compared with experimental findings.     

Quantitative experimental study of shear stresses and mixing in progressive flow regimes within annular-flow bioreactors

Annular-flow bioreactors are normally operated under laminar Couette flow conditions in order to minimise shear-induced damage to cells. In this study, we computed the fluid shear stresses in model annular vessels over a range of laminar flow regimes, from Couette flow to Taylor-vortex flow, and at two geometric scales, using a shear rate model for freely suspended particles, together with experimental Laser Doppler Anemometry data for a 2-D velocity field. The shear stresses were greatest in the boundary layers adjacent to each wall in each case, with values typically 6 times higher than the mean stresses in the annular space; their respective magnitudes were significantly lower in the larger of the two vessels studied, however. Cell viability studies were also performed in which mammalian cells were cultured under dynamic conditions in a functional bioreactor having the same dimensions as the smaller vessel. The results of these studies demonstrated that a significantly greater number of cells remained in suspension in Taylor-vortex flows than in Couette flow, but at the expense of cell viability at higher Taylor numbers. Taken together, these findings suggest that the benefits of enhanced convective mass transport afforded by Taylor-Couette flows could be realised without risk of appreciable shear induced damage of cells and tissues in larger vessels operating under dynamically similar flow conditions.     

Terminal velocity of non-spherical particles falling through a Carreau model liquid

A procedure has been proposed for the estimation of the terminal falling velocity of non-spherical particles moving in a Carreau model fluid in the transition flow region. The procedure is based on a modification of the relationship formerly developed for the fall of spherical particles including the particle dynamic shape factor. The suitability of the proposed procedure has been confirmed by good agreement between experimental and calculated terminal falling velocity data. In the experiments, the terminal falling velocity of short cylinders and rectangular prisms in polymer solutions of different measure of shear thinning and elasticity has been measured.