Numerical simulation of solid-liquid suspension in a stirred tank with a dual punched rigid-flexible impeller

The hydrodynamics of solid-liquid suspension process in a stirred tank with a dual rigid impeller, a dual rigid-flexible impeller, and a dual punched rigid-flexible impeller were investigated using computational fluid dynamics (CFD) simulation. A classical Eulerian-Eulerian approach coupled with standard k-ε turbulence model was employed to simulate solid-liquid turbulent flow in the stirred tank. The multiple reference frame (MRF) approach was used to simulate impeller rotation. The effects of impeller type, impeller speed, flexible connection piece width/length of dual rigid-flexible impeller, aperture size/ratio of dual punched rigid-flexible impeller, particle diameter, and liquid viscosity on the homogeneity degree of solid-liquid system were investigated. Results showed that the homogeneity degree of solid-liquid system increased with an increase in impeller speed. A long and wide flexible connection piece was conductive to solid particles suspension process. Larger particle diameter resulted in less homogenous distribution of solid particles. An increase in liquid viscosity was beneficial to maintain solid particles in suspension state. The optimum aperture ratio and aperture diameter were 12% and 8 mm, respectively, for solid particles suspension process. It was found that dual punched rigid-flexible impeller was more efficient in terms of solid particles suspension quality compared with dual rigid impeller and dual rigid-flexible impeller under the same power consumption.     

Experimental and numerical investigations of particle suspension suppression mechanisms for a particle-suppression device in a stirred liquid bath

Particle suspension in a turbulent flow can seriously affect the performance of manufactured products in many industrial processes in which the motion of particles cannot be modeled using the numerical method because of the enormous number of particles. Therefore, in this study, a full-scale computational fluid dynamics (CFD) simulation and a 1/5 scaled-down water model experiment were employed to investigate the flow pattern and dynamic behavior of particles in a continuously stirred vessel system. Based on the understanding of the suspension mechanism of settling particles, a particle-suppression device was designed to realize the harmless movement and deposition of particles. The results showed that the flow guidance and division mechanisms of the particle-suppression device led to the inhibition of particle suspensions. In addition, the optimal parameter combination for the device from the water model experiment combined with the orthogonal experimental design, resulted in a 98.3% reduction in the concentration of suspended particles. The suspension of particles was effectively suppressed, which improves product quality and production efficiency. Reliable results can be achieved by combining CFD simulations and water model experiments.     

Numerical simulation of solid-liquid mixing characteristics in a stirred tank with fractal impellers

The hydrodynamics of solid-liquid mixing process in a stirred tank with four pitched-blade impellers, fractal 1 impellers, and fractal 2 impellers were investigated using computational fluid dynamics (CFD) simulation. An Eulerian-Eulerian approach, standard k-ε turbulence model, and multiple reference frames (MRF) technique were employed to simulate the solid-liquid two-phase flow, turbulent flow, and impeller rotation, respectively. The effects of impeller speed, impeller type, impeller spacing, impeller blade tilt angle, impeller blade shape, solid particle size and initial solid particle loading on the solid particle suspension quality were investigated. Results showed that the homogenous degree of solid-liquid system increased with the increase of impeller speed. The impeller spacing of T5/6 and T and impeller blade tilt angle of 60° and 45° were appropriate for the solid-liquid suspension process. Fractal shape impeller was more efficient than jagged shape impeller in solid-liquid mixing process. Larger particle diameter and higher initial solid particle loading resulted in less homogenous distribution of solid particles. It was found that fractal impeller could improve the solid particle suspension quality compared with four pitched-blade impeller under the same power consumption, increasingly so with the fractal iteration number of fractal impeller. Moreover, fractal impeller reduced the size of impeller trailing vortex and consumed less power consumption compared with four pitched-blade impeller at the same impeller speed, and the more the number of fractal iteration, the higher the impeller energy utilization rate of fractal impeller.     

Design of impeller blades for efficient homogeneity of solid-liquid suspension in a stirred tank reactor

Computational fluid dynamics (CFD) was used to investigate the hydrodynamics of solid-liquid suspension process in a stirred tank with rigid impellers, rigid-flexible impellers and punched rigid-flexible impellers. The effects of impeller type, impeller speed, flexible connection piece length, impeller spacing, particle size, and aperture size/ratio on the mixing quality were investigated. Results showed that the degree of solid-liquid homogeneity increased with an increase in impeller speed. A long flexible connection piece was conductive to solid particles suspension process. The solid particles could not obtain enough momentum to suspend to the upper region of stirred tank with small impeller spacing. Larger particle size resulted in less homogenous distribution of solid particles. The optimum aperture ratio and aperture diameter of punched rigid-flexible impeller were 12% and 8 mm, respectively, for solid particles suspension process. It was found that punched rigid-flexible impeller was more efficient in suspending solid particles compared with rigid impeller and rigid-flexible impeller at the same power consumption. In addition, less impeller power was consumed by punched rigid-flexible impeller compared with rigid impeller and rigid-flexible impeller at the same impeller speed.     

Computational fluid dynamics study on the effect of stirring parameters on solid–liquid suspension in the slurry electrolysis square tank

As a sustainable hydrometallurgical technology, slurry electrolysis (SE) offers certain advantages in the treatment of complex ores and secondary electronic waste. It is therefore of considerable interest to understand the solid–liquid suspension in the stirred tank for overall process control. Here, a computational fluid dynamics (CFD) model based on the Eulerian-Eulerian framework combined with the kinetic theory of granular flow was employed to investigate the effects of varying the impeller speed (70–150 rpm), solids volume fraction (8–21 %), and particle specific gravity (2–6.7) on solid–liquid suspension behavior in a square tank equipped with electrodes and impeller. The results show that as the impeller rotating speed increases, turbulent kinetic energy is gradually transferred from the lower part of the electrodes to the region near the impeller shaft and between the membrane bags. The solids volume fraction was found to have little effect on the final liquid flow fields, but significantly increased the power consumption. The homogeneity and power consumption were quantified as functions of specific gravity, allowing the degree of homogeneity to be predicted under different operating conditions.     

气体涡轮流量传感器叶轮压力的数值模拟

在严格按照实际涡轮流量传感器几何结构的基础上,运用Solidworks三维建模,通过运用计算流体动力学的方法对内径为80mm的气体涡轮流量传感器进行了数值模拟,给出了流量计在不同流量下内部的压力场并特别给出叶轮表面的压力分布.从压力分布分析叶轮部分的受力情况,以此来讨论叶轮动受力.     

Numerical simulation of sedimentation in the presence of 2D compressible convection and reconstruction of the particle-radius distribution function

Numerical simulation of the sedimentation of a polydisperse suspension in a convectively unstable medium is presented. For the simulation of 2D compressible convection, the full system of hydrodynamic equations is solved by the explicit MacCormack scheme. Velocities and positions of suspension particles are calculated simultaneously with the solution of the equations. Initially, the particles are randomly distributed in the computational region. The total weight of sedimented matter is recorded during the numerical experiment. The results are compared with the sedimentation of the same suspension without convection. To reconstruct the particle-radius distribution function from the sedimentation curve, a new method is used. This method is based on the solution of the sedimentation integral equation by the Tikhonov regularization method and was recently developed by the author. To illustrate this technique, sedimentation of cement powder in air is simulated. The suspension contains 50000 particles. The particle radii are assumed to be log-normally distributed. Heat-driven convection is completely determined by the top and bottom boundary temperatures of the computational region and lateral boundary conditions. It is shown that convective motions of a medium with sedimented particles lead to the following effect: the fine disperse fraction of the suspension remains suspended much longer than without convection. Some particles will not sediment at all. The maximum radius of the particles of this fraction depends on the convection parameters (e.g. on convection cell size and convection velocities). These parameters, in their turn, depend only on the temperature difference of the top and bottom boundaries. The results of these calculations can be applied in geology and meteorology for studying dust sedimentation in air as well as in technology. Heat-driven convection can be used for separation of suspensions with the cut-off particle radius depending on temperature difference only.     

一种跨音速伺服气动弹性分析方法

基于CFD技术,运用系统辨识方法,建立了基于模态坐标的跨音速气动力降阶模型(ROM)。耦合气动状态方程、结构状态方程和伺服状态方程,建立了一个适合跨音速伺服气动弹性分析的数学模型。算例首先通过对比基于ROM技术的分析结果和直接仿真结果,以证明该模型的正确性和精度。在保证精度的同时,其计算效率比直接耦合CFD技术的仿真方法高1个～2个数量级。算例还研究了传感器安放位置和结构陷幅滤波器对该导弹伺服气动弹性特性的影响,结果显示结构陷幅滤波器的引入可以显著地降低开环气动弹性系统和控制系统的耦合。     

Computational and experimental studies on bed dynamics of a gas–solid fluidized bed using Geldart-A particle: A comparison

The bed dynamics of a two-dimensional gas–solid fluidized bed is studied experimentally and computationally using Geldart-A particles. Commercial software ANSYS FLUENT 13 is used for computational studies. Unsteady behavior of gas–solid fluidized bed is simulated by using the Eulerian–Eulerian model coupled with the kinetic theory of granular flow. The two-equation standard k?? model is used to describe the turbulent quantities. The simulation predictions are compared with experimentally observed data on volume fraction, bed pressure drop and bed expansion ratio. The results of simulations are found to be in close agreement with the experimental observations, implying that computational fluid dynamics (CFD) can be used for the design of an efficient bench-scale catalytic fluidized bed reactor.     

机械搅拌自吸式浮选机气-液-固三相流场的数值研究简

 为了研究机械搅拌自吸式浮选机内叶轮转速对浮选动力学环境所产生的影响,采用Mixture多相流模型、k-ε湍流模型和雷诺时均方程,对有效容积为20 m³机械搅拌自吸式浮选机内部气-液-固三相流流场进行数值模拟,分析了3种粒度、3种转速所组成的9组模型的三相流体在浮选槽内的速度以及湍流强度的分布规律.数值模拟结果表明：浮选机叶轮转速在147～196 r/min区间时,液面的湍流强度保持稳定,且该范围内浮选机性能较优.试验结果与模拟预测结果比较吻合,验证了所得结论.     

Numerical simulation of a centrifugal slurry pump handling solid-liquid mixture: Effect of solids on flow field and performance

The effect of solids on a centrifugal slurry pump performance is a major concern to the design of slurry transportation system. In the present study, the multiphase modeling of centrifugal slurry pump is performed using two models, Mixture and Eulerian-Eulerian multiphase. Sliding mesh approach is employed for unsteady simulation of the pump. The accuracy of the simulations is ascertained by comparing the performance characteristics of the pump obtained numerically and experimentally. Experimental results are obtained by measurements in a pilot plant test rig with three different mean size sand particulate slurries. The Eulerian-Eulerian multiphase model predicted the effect of the solids on pump performance close to the experimental results as compared to Mixture model. The obtained accuracy with Eulerian-Eulerian model for predicting the effect of solids on head and efficiency is around ±2% and ±3%, respectively. The predicted results using Eulerian-Eulerian model confirm that the head and efficiency of the pump decrease with the increase in particle size and concentration. The particles of high specific gravity show less reduction in head and efficiency of the pump. Further, the effect of variation in particle size and concentration on the flow field in the impeller and casing has also been analyzed at best efficiency point operation. Non-homogeneous suspension of particles inside the blade channels and casing passages is examined. The particulate concentration is observed higher near the impeller back shroud, pressure side of the blades, and non-suction side of the casing as compared to other locations.     

Zweiphasenströmung in Kreiselpumpen für den hydraulischen Feststofftransport

A mathematical model of the trajectories of fluid and particles is developed based on the two dimensional equations of motion in plane flow for the impeller and the casing. The set of differential equations for plane flow is solved numerically using a 4th order Runge–Kutta method using the velocity profile of the fluid and the velocity components of the particles at the inlet of the impeller as initial conditions. The strong effect of the particle density ?_S and of the particle diameter d_S on the particle trajectory is analysed. Based on the solution of the equations of motion of both phases in the impeller and in the casing the velocity ratio of particles and fluid is calculated.     

基于流固耦合的重载飞艇副气囊形态分析与试验研究

为了研究非饱和副气囊在重载飞艇升降和巡航过程的形态变化,建立了缩尺比例氦气囊模型。基于向量式有限元(vector form of intrinsic finite element,VFIFE)对副气囊膜结构进行结构动力学分析,并考虑几何大变形和边界非线性;基于有限元法对氦气域和空气域进行流体动力学分析,分别采用自编MATLAB程序和ANSYS软件流体模块独立求解控制方程之后,通过映射网格在CSD(computational structural dynamics)/CFD(computational fluid dynamics)之间进行数据传递并迭代,以实现双向流固耦合。开展了氦气囊的缩尺比例模型试验,对囊体在泄气过程中得到的位移测量值与数值模拟结果进行对比。结果表明,氦气囊在不同充盈度下的形态变化与双向流固耦合数值分析结果一致,证明了该研究提出的数值模拟方法可有效用于副气囊随氦气充盈度变化导致的非稳定形态变化规律的研究。     

Numerical investigation of gas-particle hydrodynamics in a vortex chamber fluidized bed

Gas-particle hydrodynamic behaviour inside a vortex chamber fluidized bed is studied numerically with respect to different design and operating conditions. A three-dimensional computational fluid dynamics (CFD) model of a cylindrical vortex chamber is developed. Simulations are carried out with particles and without particles. In order to understand the gas-particle flow behavior velocity distribution, particle volume fraction distribution, radial pressure distribution and axial pressure distribution inside the vortex chamber are analyzed in detail. Particles of different diameters are used and its effect on the gas-particle flow behaviour is studied. Design parameters like the number of gas inlet slots and slot width are varied and their impact on the hydrodynamics of the vortex chamber is investigated. The numerical model is validated by comparing the numerical results with experimental results reported in literature.     

漂浮式光伏电站方阵环境载荷计算方法研究

针对我国建成的全球首个单体容量达到40 MW的漂浮式光伏电站方阵进行了环境载荷数值预报研究,在与风洞模型试验结果对比验证的基础上,基于计算流体力学（computational fluid dynamics,CFD）方法对该大规模方阵的整体风载荷和流载荷进行了数值研究。CFD计算的数值考察验证了采用简化浮体模型进行研究的可行性,单体模型的计算结果与风洞试验结果吻合良好;对方阵进行实尺度建模及3D简略计算,得到了整体风载荷在不同风向角下的变化规律;通过对最大载荷风向的北风条件下的载荷分布规律的分析,提出了2.5D计算的策略,得到了数值验证;根据计算结果设计并实施了18行×11列单元模块的缩尺方阵风洞试验,试验结果和CFD计算结果吻合良好,据此构建了完整的数值计算方法;对2.5D进行高精度计算,确定了针对3D简略计算的修正系数,得到较为准确的整体风载荷结果。流载荷计算方法与风载荷相同。采取势流计算方法开展了波浪载荷数值分析研究,得到了在单位波幅规则波作用下漂浮方阵波浪载荷随行和列的变化规律;根据此规律获得了整体漂浮方阵的波浪载荷,并据此计算了50年一遇的极端条件下漂浮方阵所受的波浪载荷。该研究为漂浮式光伏电站的风、流、波浪等环境载荷的数值预报提供了方法,为漂浮方阵的锚泊计算及水上光伏电站的系统设计提供了技术支持。     

Development of a reduced-order model for large-scale Eulerian–Lagrangian simulations

Multiphase flows with solid particles are commonly encountered in various industries. The CFD–DEM method is extensively used to simulate their dynamical behavior. However, the application of the CFD–DEM method to simulate industrial-scale powder processes unavoidably leads to huge computational costs. With the aim of overcoming this issue, we propose a nonintrusive reduced-order model for Eulerian–Lagrangian simulations (ROM-EL) to efficiently reproduce gas–solid flow in fluidized beds. In the model, a Lanczos based proper orthogonal decomposition (LPOD) is newly employed to efficiently generate a set of POD bases. After the numerical snapshots are projected onto the reduced space spanned by the POD bases, a series of multidimensional functions of POD coefficients are constructed using a surrogate interpolation method. To demonstrate the effectiveness of this model, validation studies are performed based on the simulations of a fluidized bed. The macroscopic properties, such as the particle distribution, bed height, pressure drop, and distribution of bubble size, are shown to agree well in the CFD–DEM model and ROM-EL. Further, our proposed ROM-EL reduces the computational cost by several orders of magnitude compared with the CFD–DEM simulation. Accordingly, the ROM-EL could significantly contribute to the progress of modeling and simulation for industrial granular flows.     

CFD simulation of solid–liquid stirred tanks

Solid liquid stirred tanks are commonly used in the minerals industry for operations like concentration, leaching, adsorption, effluent treatment, etc. Computational Fluid Dynamics (CFD) is increasingly being used to predict the hydrodynamics and performance of these systems. Accounting for the solid–liquid interaction is critical for accurate predictions of these systems. Therefore, a careful selection of models for turbulence and drag is required. In this study, the effect of drag model was studied. The Eulerian–Eulerian multiphase model is used to simulate the solid suspension in stirred tanks. Multiple reference frame (MRF) approach is used to simulate the impeller rotation in a fully baffled tank. Simulations are conducted using commercial CFD solver ANSYS Fluent 12.1. The CFD simulations are conducted for concentration 1% and 7% v/v and the impeller speeds above the “just suspension speed”. It is observed that high turbulence can increase the drag coefficient as high as forty times when compared with a still fluid. The drag force was modified to account for the increase in drag at high turbulent intensities. The modified drag is a function of particle diameter to Kolmogorov length scale ratio, which, on a volume averaged basis, was found to be around 13 in the cases simulated. The modified drag law was found to be useful to simulate the low solids holdup in stirred tanks. The predictions in terms of velocity profiles and the solids distribution are found to be in reasonable agreement with the literature experimental data. Turbulent kinetic energy, homogeneity and cloud height in the stirred tanks are studied and discussed in the paper. The presence of solids resulted in dampening of turbulence and the maximum deviation was observed in the impeller plane. The cloud height and homogeneity were found to increase with an increase in impeller speed. The work provides an insight into the solid liquid flow in stirred tanks.     

两种二元离心叶轮型线优化方法比较

以二元离心风机叶轮叶片型线为研究对象,对7—40和bb24风机叶轮运用等减速和等当量扩张角规律,分别对其进行叶片型线的重新设计,并运用CFD数值模拟叶轮内部复杂三维流动。结果表明,在设计工况下,无论是等减速规律还是等当量扩张角规律对于2个不同的风机叶轮都取得了较好的效果,尤其是应用等减速规律改进的叶轮,改进效果更加明显,叶轮性能显著提高。     

Numerical analysis of flow field and particle motion in a dynamic cyclonic selector

Computational Fluid Dynamics is employed to investigate the flow field and the fate of particles in a dynamic cyclonic classifier which is used to separate fine particles of dried sludge, produced as waste by pulp and paper-making processes. The cyclonic classifier is equipped with a rotating impeller, which improves the tangential flow, and a circular baffle, which distributes the inlet stream of gas and particles. Unsteady Reynolds-averaged Navier-Stokes equations are solved for the continuous phase, addressing the impeller motion though the Sliding Mesh approach, whereas Lagrangian tracking is employed for the particles. Surprisingly, the removal efficiency is found to be non monotonic with particle size, instead presenting a fish-hook shape. This is partly imputed to the presence of the circular baffle that promotes, in the bottom region of the cyclone, the formation of a nearly toroidal recirculation zone which entrains small particles, subsequently separated at the bottom. Moreover, too high inlet velocities were found to hamper the action of impeller rotation with a resulting detrimental effect on removal efficiency.     

Investigation of optimum design for nanoparticle dispersion in centrifugal bead mill using DEM-CFD simulation

A bead mill is commonly used to produce nanomaterials. The design of the bead mill rotor is an important factor in efficient nanomaterial production to avoid re-agglomeration. We investigated the effect of bead-mill rotor shape on the dispersion state using experimental tests and the discrete-element method (DEM) coupled with computational fluid dynamics (CFD) simulations. Experimental results using TiO₂ in the bead mill showed that the high rotor rotation speed caused TiO₂ particles re-agglomeration, and a sharp particle-size distribution was obtained by dispersion with a mill with a wide gap between the rotor and the chamber. To evaluate the dispersion performance, bead collisions were analyzed using the DEM-CFD simulation. The simulation results indicated that an increase in bead-collision energy lead to damage of the TiO₂ primary particles and re-agglomeration at a high rotation speed. A uniform dispersion was achieved when the frequency of high-energy collision between the particle and wall decreased and a small standard deviation of the collision energy frequency was obtained by the mill with a wide gap. These simulation results correlate with the experimental results. Therefore, this study shows that the DEM-CFD simulation could contribute to an appropriate rotor design for uniform dispersion.