Numerical Study of Solid-Liquid Two-Phase Flow in Stirred Tanks with Rushton Impeller (Ⅰ) Formulation and Simulation of Flow Field

Three-dimensional solid-liquid flow is mathematically formulated by means of the "two-fluid" approach and the two-phase k-ε-Ap turbulence model. The turbulent fluctuation correlations appearing in the Reynolds time averaged governing equations are fully incorporated. The solid-liquid flow field and solid concentration distribution in baffled stirred tanks with a standard Rushton impeller are numerically simulated using an improved "inner-outer" iterative procedure. The flow pattern is identified via the velocity vector plots and a recirculation loop with higher solid concentration is observed in the central vicinity beneath the impeller. Comparison of     

搅拌槽内液-固两相体系的数值研究(Ⅱ)临界搅拌转速的预测

The critical impeller speed, NJS, for complete suspension of solid particles in the agitated solid-liquid two-phase system in baffled stirred tanks with a standard Rushton impeller is predicted using the computational procedure proposed in Part Ⅰ. Three different numerical criteria are tested for determining the critical solid suspension. The predicted NJS is compared with those obtained from several empirical correlations. It is suggested the most reasonable criterion for determining the complete suspension of solid particles is the positive sign of simulated axial velocity of solid phase at the location where the solid particles are most difficult to be suspended.     

低比转速高速复合离心叶轮的流动模拟和试验研究

Based on the Navier-Stokes equations and the Spalart-Allmaras turbulence model, three-dimensional turbulent flow in four low-specific-speed centrifugal impellers are simulated numerically and analyzed. The relative velocity distribution, pressure distribution and static pressure rise at the design point are obtained for the regular impeller with only long blades and three complex impellers with long, mid or short blades. It is found that the back flow region between long-blade pressure side and mid-blade suction side is diminished and is pushed to pressure side of short blades near the outlet of impeller at suction side by the introduction of mid, short blades, and the size of back flow becomes smaller in a multi-blade complex impeller. And the pressure rises uniformly from inlet to outlet in all the impellers. The simulated results show that the complex impeller with long, mid and short blades can improve the velocity distribution and reduce the back flow in the impeller channel. The experimental results show that the back flow in the impeller has an important influence on the performance of pump and a more-blade complex impeller with long, mid and short blades can effectively solve low flow rate instability of the low-specific-speed centrifugal pump.     

用各向异性代数应力模型数值模拟搅拌槽中的三维全流场

In accordance to the anisotropic feature of turbulent flow, an anisotropic algebraic stress model is adopted to predict the turbulent flow field and turbulent characteristics generated by a Rushton disc turbine with the improved inner-outer iterative procedure. The predicted turbulent flow is compared with experimental data and the simulation by the standard κ-ε turbulence model. The anisotropic algebraic stress model is found to give better prediction than the standard κ-ε turbulence model. The predicted turbulent flow field is in accordance to experimental data and the trend of the turbulence intensity can be effectively reflected in the simulation. The distribution of turbulent shear rate in the stirred tanks was simulated with the established numerical procedure.     

Numerical optimization for blades of Intermig impeller in solid–liquid stirred tank

The multiphase flow in the solid-liquid tank stirred with a new structure of Intermig impeller was analyzed by computational fluid dynamics(CFD).The Eulerian multiphase model and standard k-ε turbulence model were adopted to simulate the fluid flow,turbulent kinetic energy distribution,mixing performance and power consumption in a stirred tank.The simulation results were also verified by the water model experiments,and good agreement was achieved.The solid-liquid mixing performances of Intermig impeller with different blade structures were compared in detail.The results show that the improved Intermig impeller not only enhances the solid mixing and suspension,but also saves more than 20% power compared with the standard one.The inner blades have relatively little influence on power and the best angle of inner blades is 45°,while the outer blades affect greatly the power consumption and the optimized value is 45°.     

Numerical Study of Solid-Liquid Two-Phase Flow in StirredTanks with Rushton Impeller(Ⅱ) Prediction of Critical Impeller Speed

The critical impeller speed, NJS, for complete suspension of solid particles in the agitated solid-liquid two-phase system in baffled stirred tanks with a standard Rushton impeller is predicted using the computational procedure proposed in Part I. Three different numerical criteria are tested for determining the critical solid suspension. The predicted NJS is compared with those obtained from several empirical correlations. It is suggested the most reasonable criterion for determining the complete suspension of solid particles is the positive sign of simulated axial velocity of solid phase at the location where the solid particles are most difficult to be suspended.     

搅拌釡中层流流场的模拟

Stirred tanks are used extensively in process industry and one of the most commonly used impellers in stirred tanks is the R.ushton disk turbine. Surprisingly few data are available regarding flow and mixing in stirred-tank reactors with Rushton turbine in the laminar regime, in particular the laminar flow in baffled tanks.In this paper, the laminar flow field in a baffled tank stirred by a standard R.ushton turbine is simulated with the improved inner-outer iterative method. The non-inertial coordinate system is used for the impeller region, which is in turn used as the boundary conditions for iteration. It is found that the simulation results are in good agreement with previous experiments. In addition, the flow number and impeller power number calculated from the simulated flow field are in satisfactory agreement with experimental data. This numerical method allows prediction of flow structure requiring no experimental data as the boundary conditions and has the potential of being used to scale-up and design of related process equipment.     

SOLID-LIQUID SUSPENSION SYSTEM IN AGITATED TANK WITH DRAFT TUBE

Solid-liquid suspension in an agitated tank with a draft tube was investigated witha newly developed infrared turbidimeter for measuring solid concentration.The diameter of theflared inlet transition tube and the distance from the inlet to the tank bottom are two importantparameters for draft tube design The NAX-4 impeller,developed in this study,is characterized byits high flow efficiency and low power consumption.Some modifications are made to the Bald′smodel by considering the effects of solid concentration and fluid viscosity on the critical speed forcomplete off-bottom suspension.The modified equation fits the experimental data satisfactority andcan be used in scale-up design     

Solid concentration and velocity distributions in an annulus turbulent fluidized bed

Solid concentration and particle velocity distributions in the transition section of a?200 mm turbulent fluidized bed (TFB) and a?200 mm annulus turbulent fluidized bed (A-TFB) with a?50 mm central standpipe were mea-sured using a PV6D optical probe. It is concluded that in turbulent regime, the axial distribution of solid concen-tration in A-TFB was similar to that in TFB, but the former had a shorter transition section. The axial solid concentration distribution, probability density, and power spectral distributions revealed that the standpipe hin-dered the turbulence of gas–solid two-phase flow at a low superficial gas velocity. Consequently, the bottom flow of A-TFB approached the bubbling fluidization pattern. By contrast, the standpipe facilitated the turbulence at a high superficial gas velocity, thus making the bottom flow of A-TFB approach the fast fluidization pattern. Both the particle velocity and solid concentration distribution presented a unimodal distribution in A-TFB and TFB. However, the standpipe at a high gas velocity and in the transition or dilute phase section significantly affected the radial distribution of flow parameters, presenting a bimodal distribution with particle concentration higher near the internal and external wal s and in downward flow. Conversely, particle concentration in the middle an-nulus area was lower, and particles flowed upward. This result indicated that the standpipe destroyed the core-annular structure of TFB in the transition and dilute phase sections at a high gas velocity and also improved the particle distribution of TFB. In conclusion, the standpipe improved the fluidization quality and flow homogeneity at high gas velocity and in the transition or dilute phase section, but caused opposite phenomena at low gas ve-locity and in the dense-phase section.     

T-形分叉槽道纤维悬浮湍流场的数值模拟

The concentration and orientation of fiber in a turbulent T-shaped branching channel flow are investigated numerically. The Reynolds averaged Navier-Stokes equations together with the Reynolds stress turbulent model are solved for the mean flow field and the turbulent kinetic energy. The fluctuating velocities of the fluid are assumed as a random variable with Gaussian distribution whose variance is related to the turbulent kinetic energy. The slender-body theory is used to simulate the fiber motion based on the known mean and fluctuating velocities of the fluid. The results show that at low Reynolds number, fiber concentration is high in the flow separation regions, and fiber orientation throughout the channel is widely distributed with a slight preference of aligning along the horizontal axis. With increasing of Re, the high concentration region disappears, and fiber orientation becomes ho- mogeneous without any preferred direction. At high Reynolds number, fiber concentration increases gradually along the flow direction. The differences in the distribution of concentration and orientation between different fiber aspect ratio are evident only at low Re. Both Re and fiber aspect ratio have small effect on the variance of orientation angle.     

CFD simulations of gas-liquid-solid stirred reactor: Prediction of critical impeller speed for solid suspension

In this work, simulations have been performed for three phase stirred dispersions using computational fluid dynamics model (CFD). The effects of tank diameter, impeller diameter, impeller design, impeller location, impeller speed, particle size, solid loading and superficial gas velocity have been investigated over a wide range. The Eulerian multi-fluid model has been employed along with the standard k-ε turbulence model to simulate the gas-liquid, solid-liquid and gas-liquid-solid flows in a stirred tank. A multiple reference frame (MRF) approach was used to model the impeller rotation and for this purpose a commercial CFD code, FLUENT 6.2. Prior to the simulation of three phase dispersions, simulations were performed for the two extreme cases of gas-liquid and solid-liquid dispersions and the predictions have been compared with the experimental velocity and hold-up profiles. The three phase CFD predictions have been compared with the experimental data of Chapman et al. [1983. Particle-gas-liquid mixing in stirred vessels, part III: three phase mixing. Chemical Engineering Research and Design 60, 167-181], Rewatkar et al. [1991. Critical impeller speed for solid suspension in mechanical agitated three-phase reactors. 1. Experimental part. Industrial and Engineering Chemistry Research 30, 1770-1784] and Zhu and Wu [2002. Critical impeller speed for suspending solids in aerated agitation tanks. The Canadian Journal of Chemical Engineering 80, 1-6] to understand the distribution of solids over a wide range of solid loading (0.34-15 wt%), for different impeller designs (Rushton turbine (RT), pitched blade down and upflow turbines (PBT45)), solid particle sizes (120-) and for various superficial gas velocities (0-10 mm/s). It has been observed that the CFD model could well predict the critical impeller speed over these design and operating conditions.     

基于颗粒动力学理论的搅拌器中固液流动的数值模拟

在欧拉双流体模型基础上引入颗粒动力学理论(KTGF)，对带挡板圆盘涡桨式搅拌器内的固液两相流动进行数值模拟。结果表明，搅拌器底部颗粒温度分布与固相浓度分布趋势吻合，转速低于600 r/min时，槽底会形成明显的颗粒沉积，转速从600 r/min增至1500 r/min，堆积区向轴中心收缩，基于颗粒动力学理论可以合理解释挡板及叶轮转速对固相浓度分布的影响。随叶轮转速增大，搅拌器内固液两相湍流运动加剧，颗粒温度、湍动能及轴向速度增加，颗粒分布更均匀，但达到完全悬浮状态后颗粒温度趋于稳定。搅拌器底部和挡板处颗粒堆积导致了局部颗粒浓度增加及颗粒平均自由行程减少，颗粒温度反而降低；同时挡板布置使搅拌器内形成了双循环回路，加强了流体的湍流程度，增强了湍动能，但导致颗粒在挡板处积聚，不利于固相在挡板处均匀分布。     

CFD simulation of liquid-phase mixing in solid-liquid stirred reactor

A comprehensive CFD model was developed to gain an insight into solid suspension and its implications on the liquid-phase mixing process in a solid-liquid stirred reactor. The turbulent solid-liquid flow in a stirred reactor was simulated using a two-fluid model with the standard k-ε turbulence model with mixture properties. The multiple reference frames (MRFs) approach was used to simulate impeller rotation in a fully baffled reactor. The computational model with necessary sub-models was mapped on to a commercial solver FLUENT 6.2 (of Fluent Inc., USA). The predicted solid concentration distribution was compared with the experimental data of Yamazaki et al. [1986. Concentration profiles of solids suspended in a stirred tank. Powder Technology 48, 205-216]. The computational model was then further extended to simulate and understand the implications of the suspension quality on liquid-phase mixing process. The computational model and the predicted results discussed here will be useful for understanding the liquid-phase mixing process in stirred slurry reactors in various stages of solid suspension.     

用FPIV方法研究固-液方形搅拌槽内液相湍流

采用粒子图像测速和分析技术,研究了固-液方槽体系中液相湍流特性. 测得固体颗粒浓度从0增加到0.9%(j)时,液相在桨叶区和近壁区的湍流流场分布. 结果表明,随固体颗粒浓度增加到0.9%(j),液相轴向平均速度<ν>持续减小,在桨叶区其衰减幅度Dv*与固体颗粒浓度Cv的关系为Dv*μCv0.776,近壁区为Dv*μCv1.474. 桨叶区湍流动能分布较复杂,与单相相比,固体颗粒浓度从0增加到0.5%(j)时,湍流动能增强;固体颗粒浓度从0.5%增加到0.9%(j)时,湍流动能减小. 在整个测量区域,随固体颗粒浓度增加,平均湍流动能呈减小趋势,拟合平均湍流动能 与固体颗粒浓度的关系为 μCv-0.073,平均湍流动能耗散率呈增长趋势,拟合平均湍流动能耗散速率 与固体颗粒浓度的关系为 μCv1.113.     

含细长颗粒的洗涤冷却室内的多相分布特性

采用改进的直接取样法,在按几何尺寸缩小的工业气化炉洗涤冷却室冷模装置内,同时测量不同操作条件下的轴径向局部固含率和气含率,对细长颗粒在洗涤冷却室内的多相分布特性进行研究。结果表明：以下降管出口截面为界,洗涤冷却室可分为上部气液固混合区和下部固液流动区,其中上部区域由下降管出口区、破泡板作用区和气垫层区组成,下部区域由气相湍动作用区、回流区和二次流动区组成;在颗粒阻碍效应减速沉降和团聚效应加速沉降的共同作用下,轴向固含率呈现波动分布;环隙气速、固相体积分数和长径比的增加均会增强床层的湍动,促进气体的径向扩散;操作条件的改变使颗粒的漂移速度发生改变,径向固含率分布出现波动;在气相扰动和回流作用下,二次流动区呈现环状流动,流体和颗粒的"壁面效应"使该区域的固含率呈现中心高边壁低的特点。     

Study on the solid–liquid suspension behavior in a tank stirred by the long-short blades impeller

We investigated the solid-liquid suspension characteristics in the tank with a liquid height/tank diameter ratio of 1.5 stirred by a novel long-short blades (LSB) impeller by the Euler granular flow model coupled with the standard k-ε turbulence model. After validation of the local solid holdup by experiments, numerical predictions have been successfully used to explain the influences of impeller rotating speed, particle density, particle size, liquid viscosity and initial solid loading on the solid suspension behavior, i.e. smaller particles with lower density are more likely to be suspended evenly in the liquid with higher liquid viscosity. At a low impeller rotating speed (N), increase in N leads to an obvious improvement in the solid distribution homogeneity. Moreover, the proposed LSB impeller has obvious advantages in the uniform distribution of the solid particles compared with single Rushton turbine (RT), dual RT impellers or CBY hydrofoil impeller under the same power consumption.     

The Flow Simulation and Experimental Study of Low-Specific-Speed High-Speed Complex Centrifugal Impellers

1 INTRODUCTION Low-specific-speed high-speed centrifugal pumps are widely used in petrochemical, aerospace and chemical industries to deliver low flow rate and high-head liquids, but there exist many problems to be solved, such as low efficiency due to disc loss and low flow rate instability due to positive slope of head-capacity characteristic curve. Through the ex- perimental study on the low-specific-speed high-speed centrifugal pumps, it is found that complex impeller with long, mid an…     

NUMERICAL SIMULATION OF LAMINAR SOLID-LIQUID TWO-PHASE FLOW IN STIRRED TANKS

Laminar flow of solid-liquid suspension has been rarely reported in the literature. In this article, the laminar solid-liquid two-phase flow in a lab-scale stirred tank is measured with digital particle image velocimetry (DPIV) and numerically simulated with the improved inner-outer iterative method. The simulation results show good agreement with the present data. In the range of low solid volume concentration under investigation, solid particles have minor impact on two-phase flow, and the simulated flow fields of both phases are similar to the counterpart of single-phase laminar liquid flow. The comparison of simulation with experiments of single-phase laminar flow shows reasonable agreement. These observations suggest that the numerical method employed in the present study is reliable for analysis of stirred tanks. The influence of impeller off-bottom clearance on velocities is found significant: the lower the impeller, the smaller the radial and axial velocities, and the higher the solid concentration.