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.     

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.     

卧式搅拌磨搅拌叶轮形状对粉碎效果的影响

研究卧式搅拌磨的搅拌叶轮形状对磨矿效果的影响,设计3种搅拌叶轮,在不同搅拌速度的条件下,考察磨矿产品的粒度与能量新生能力。通过对比发现,3种叶轮中圆形孔叶轮的细磨效果最好,磨矿性能最优,是比较适合卧式搅拌磨机进行超细磨的搅拌叶轮形状;在能量输入基本一致的情况下,圆形孔叶轮在1~15μm粒级能量利用率最高,产率最大。     

DEM study of the effect of impeller design on mixing performance in a U-shape ribbon mixer

The mixing of powders in a U-shape mixer is significantly influenced by the mixer design, especially impellers, but the studies on the mixing processes are still insufficient. In this study, the effect of impeller designs on mixing performance in an industrial-scale U-shaped ribbon mixer is studied using DEM simulations. Three impeller designs are studied: 2-bladed impeller spiralling in the same direction (i.e., Design I) and the opposite direction (i.e., Design II), and 4-bladed impeller (i.e., Design III). Different particle mixing behaviours in three different impeller designs are studied in aspects of mixing status, particle path line, velocity distribution, and forces. The radial direction has the highest dispersion coefficient while the axial direction has the lowest dispersion coefficient. Most particles in the mixers are imposed a weak force. Design III shows the best mixing performance among the three with the front-by-back and top-by-bottom loading used. Design II shows a better mixing performance used than Design I and III with the side-by-side loading but takes a longer time to reach the stable status. This work evaluates the effect of different impeller designs on the mixing performance in an industrial-scale U-shaped ribbon mixer and provides an effective way to assist industrial design in an economical and safe manner.     

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。     

Flow of granular materials in a bladed mixer: Effect of particle properties and process parameters on impeller torque and power consumption

The torque and power needed to drive an impeller are important quantities that can indicate flow behavior and can be used to control processes, especially mixing and granulation in the pharmaceutical industry. In this study, experiments were conducted on monodisperse spherical glass beads flowing in a cylindrical bladed mixer agitated by an impeller. The impeller torque was measured using a rotating platform and a data recording device, and the power draw for the motor driving the impeller was measured using a power meter. The effect of various impeller blade designs and material properties on the torque and power were investigated as a function of the impeller blade rotation rate. It was found that the torque exerted on a granular bed and the power consumption were a strong function of the impeller blade configuration, the position of the blades in a deep granular bed, the fill height of the glass beads, and the size and friction coefficient of the particles. It was observed that the time-averaged torque and power consumption for different particle sizes qualitatively scaled with particle diameter. A scale-up relationship for a deep granular bed was developed: the time-averaged torque and average adjusted power consumption scaled with square of the material fill height.     

矿用对旋式轴流局部通风机噪声特性实验研究

对四种对旋式轴流局部通风机的噪声特性进行了实验研究,获得了风机噪声频谱曲线和A声级随工况变化曲线,详细分析了离散噪声的频谱特性,发现对旋风机Ⅰ级叶轮通过频率（BPF1）及两级叶片相互作用频率（BIF）对应噪声是对旋风机的主要离散噪声源。这为对旋式轴流通风机的降噪提供了有益参考。     

燃油系统旋涡泵压力脉动的控制研究

为了改善燃油泵噪声、振动、声振粗糙度(noise,vibration and harshness,NVH)性能,提高燃油泵声音品质,开展了燃油系统旋涡泵压力脉动的控制研究。采用计算流体动力学(Computational Fluid Dynamics,CFD)数值模拟方法和理论分析方法分析燃油系统微型旋涡泵的压力脉动特性,并采用随机叶片分布方法设计了2种非均布程度不同的非等距叶轮。基于CFD数值模拟结果和理论分析结果,提出一种改进的非等距叶轮设计方法。燃油泵噪声试验结果验证了该设计与控制方案的可行性。结果显示:相较于等距叶轮,随机非等距叶轮燃油泵的中高频段尖锐噪声消失,NVH性能提升;随机非等距叶轮能够显著分散叶频峰值,非均布程度的增加显著增大了随机非等距叶轮的叶频脉动幅值下降幅度。因此,采用随机叶片分布方法,有助于改善旋涡泵的压力脉动特性,对改善燃油泵的NVH性能具有重要的工程应用价值。     

Scale-up and flow behavior of cohesive granular material in a four-bladed mixer: effect of system and particle size

Flow of cohesive granular materials with different moisture contents was examined in a four-bladed mixer via the discrete element method (DEM). Firstly, the mixer diameter (D) was increased while keeping the particle diameter (d) constant. It was observed that when the mixer diameter to the particle diameter ratio (D/d) was larger than a certain critical size (D/d ≥ 75), granular flow behaviors and mixing kinetics followed simple scaling relations. For D/d ≥ 75, flow patterns and mixing kinetics were found to be independent of system size, and velocities of particles scaled linearly with the tip speed of the impeller blades and particle diffusivities scaled with the tip speed of the blades and mixer diameter. These results suggest that past a certain system size the flow and mixing of cohesive particles in large-scale units can be predicted from smaller systems. Secondly, system size was kept constant and particle diameter was changed and it was observed that by keeping the Bond number constant (by changing the level of cohesion) the flow behavior and mixing patterns did not change, showing that larger particles can be used to simulate flow of smaller cohesive particles in a bladed mixer by matching the Bond numbers.     

Solid-Liquid Interface Motion of 4He in an Acoustic Field

When acoustic waves were applied to the solid-liquid interface of ⁴He perpendicularly, from the solid side, the solid was megted at high temperatures and grown at low temperatures. This means that the direction of the force on the interface was inverted at an inversion temperature, T _i. We attributed this effect to the acoustic radiation pressure, which induced crystallization and megting [Phys. Rev. Lett. 90, 075301, (2003)]. Temperature dependence of the interface motion by acoustic waves was investigated in several surface orientations. Anisotropy of T _i was found and T _i was lower on a vicinal surface than on a rough surface.     

新型超音速压气机内气固两相流场CFD模拟分析

为预测和预防压气机叶轮磨损，基于多相流理论对超音速压气机内的三维气固两相流场进行数值模拟。在分析中将压气机内的流场按可压缩气体处理，同时考虑温度对颗粒运动轨迹的影响。模拟结果表明，叶片出口端部前缘，温度达到最大，颗粒的运动速度也达到最大值。由此判明叶轮磨损最严重处位于叶片端部。     

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.     

Numerical study of particle mixing in a tilted three-dimensional tumbler and a new particle-size mixing index

A new mixing index is proposed, which is an improved Lacey index based on coordination number fraction. The differences and similarities among many mixing indices are compared, including the new mixing index, the information entropy based on coordination number fraction, the Lacey index based on local concentration, and the information entropy based on local concentration. The first two indices are microscopic since the coordination number fraction is on particle-scale, whereas the latter two are mesoscopic as the local concentration is mesoscopic scale. The newly proposed mixing evaluation indices does not include inauthentic temporal oscillations. Moreover, using mixing index, the mixing characteristics of particles in a tilted tumbler are studied by discrete element method (DEM). The tumbler’s angle of tilt α = 0°, 10°, 20°, 30°, 40°, 50°, 60° and 70°, at five rotating velocities ω = 0.175, 0.35, 0.5, 0.6, 0.7 and 1.4 rad/s corresponding to Froude number F_r = 0.0025, 0.001, 0.002, 0.003, 0.004, 0.016 respectively are simulated. It is found that both increasing the tilt angle and the rotating speed have negative effects on the particle mixing within the scope of this study.     

Particle shape effects on particle size measurement for crushed waste glass

Recently, narrow particle size distributions, as measured by sieve analysis, of crushed waste glass were used as a replacement for Portland cement in concrete. Their chemical reactivity was successfully studied as a function of this measure of particle size. Differences between sieve analysis and laser diffraction measures of particle size prompted this current re-analysis. Extremely careful sieving was used to divide the crushed waste glass particles into 0–25 μm, 25–38 μm, and 63–75 μm sieve size ranges, but laser diffraction did not agree with these particle size cutoffs. We use these same materials to try and understand the discrepancies between particle size as measured by laser diffraction and sieve analysis by using X-ray computed tomography followed by spherical harmonic analysis to measure the three-dimensional particle shape and size, as well as the length (L), width (W), and thickness (T) of each particle. We show how laser diffraction and X-ray CT results, along with sieve analyses, can be quantitatively related for these crushed waste glass particles in the approximate size ranges considered. In contrast to previous speculation, the particle width W does not have to correspond closely to the sieve opening – the correspondence depends on overall particle shape. In addition, we demonstrate how many particles are needed to analyze in order to achieve stable averages and distributions of the L/W, W/T, and L/T aspect ratios, which approximately define particle shape. These results have implications for how particle size is measured and interpreted in the cement and concrete and other industries.     

Effect of impeller on sinking and floating behavior of suspending particle materials in stirred tank: A computational fluid dynamics and factorial design study

The present study focuses upon the effect of the impeller on sinking and floating behavior of suspending particles in stirred tank reactor, employing computational fluid dynamics (CFD) simulation where factorial design is used to investigate the main and interaction effects of design parameters on the particle distribution performance of four typical impeller designs. Factorial design results show the effect of diameter and width of the impeller and off-bottom clearance on sinking particles is different from that of floating particles and regression equations for sinking particles and floating particles are achieved separately. Meanwhile, optimal equations which quantitatively reveal the effect of impeller factors on suspension quality and energy input is established for impeller improvement. Besides the development of computational models, the combination of CFD simulation with factorial design method provides a useful approach to gain insight into the suspension behavior of sinking and floating particles, also it guides to optimize the impeller design.     

Mixing assessment of non-cohesive particles in a paddle mixer through experiments and discrete element method (DEM)

In this study the mixing kinetics and flow patterns of non-cohesive, monodisperse, spherical particles in a horizontal paddle blender were investigated using experiments, statistical analysis and discrete element method (DEM). EDEM 2.7 commercial software was used as the DEM solver. The experiment and simulation results were found to be in a good agreement. The calibrated DEM model was then utilized to examine the effects of the impeller rotational speed, vessel fill level and particle loading arrangement on the overall mixing quality quantified by the relative standard deviation (RSD) mixing index. The simulation results revealed as the impeller rotational speed was increased from 10?RPM to 40?RPM, generally a better degree of mixing was reached for all particle loading arrangements and vessel fill levels. As the impeller rotational speed was increased further from 40?RPM to 70?RPM the mixing quality was affected, for a vessel fill level of 60% and irrespective of the particle loading arrangement. Increasing the vessel fill level from 40% to 60% enhanced the mixing performance when impeller rotational speed of 40?RPM and 70?RPM were used. However, the mixing quality was independent of vessel fill level for almost all simulation cases when 10?RPM was applied, regardless of the particle loading arrangement. Furthermore, it was concluded that the particle loading arrangement did not have a considerable effect on the mixing index. ANOVA showed that impeller rotational speed had the strongest influence on the mixing quality, followed by the quadratic effect of impeller rotational speed, and lastly the vessel fill level. The granular temperature data indicated that increasing the impeller rotational speed from 10?RPM to 70?RPM resulted in higher granular temperature values. By evaluating the diffusivity coefficient and Peclet number, it was concluded that the dominant mixing mechanism in the current mixing system was diffusion.     

Near-wake flow characteristics of two side-by-side circular cylinders close to a wall

Flow characteristics in the near wake of two identical side-by-side circular cylinders located close to a fully developed turbulent boundary layer are investigated experimentally using the particle image velocimetry (PIV) and the pressure sensor. The Reynolds number based on the cylinder diameter (D) is 1,696, the boundary layer thickness is 6.6 D, the cylinder center-to-center spacing (T) is varied from T/D = 1 to 1.906, and the gap spacing between the lower cylinder and the wall (G) is varied from G/D = 0 to 1.811. To study the effects of changing the gap ratios of T/D and G/D on the wake flow, various wake characteristics such as averaged streamlines, Reynolds stress and vorticity contours as well as other key flow features including the length scales and the Strouhal number are investigated for different ratios of T/D and G/D. According to these wake characteristics, five basic flow patterns have been identified.     

Druckverlauf und Gasdruckschwingung im Schaufelkanal von Seitenkanalverdichtern

The pressure in the impeller, in the side channel and in the breaker of a side channel compressor with the polytropic compression and with the polytropic expansion of the breaker mass flow was investigated experimentally, and the occurring shock waves were detected during the expansion of the gas in the breaker. Thereby different pressure flows occur at the four measuring points in blade channel on the blade pressure and suction side of the related radius from r _i /r ₂=0.80 and r _i /r ₂=0.95, which give an indication of the blade channel flow. In addition to the periodic increase in pressure and the gas expansion in the breaker, the superimposed pressure oscillation in the side channel is caused by the blade rotation frequency. This superimposed pressure oscillation can be decomposed by Fourier transformation in the two pressure oscillation components. These phenomena are the reason for the more accurate investigation of the pressure flow in the blade channel during the polytropic compression and expansion of the breaker mass flow. The gradient of the effective values of the gas pressure oscillation in the blade channel leads not only to the operating characteristics of the side channel compressor ??p=f(?,n), but also to the breaker curve characteristic ??p _U =f(?,n).     

Stage-wise characterization of the high shear granulation process by impeller torque changing rate

Fine cornstarch powders are wet granulated in a lab-scale high shear granulator. The torque required for maintaining the impeller passing through the bed with a constant rotating speed is monitored during the continuous binder addition granulation process. A new method is proposed to identify 6 stages during the granulation process based on the fraction of the positive impeller torque changing rate in a characteristic period of time. The morphologies and the behavior of the bed are found intrinsically different in the identified 6 stages. The influence of the impeller blade inclined angle on the impeller torque in each stage is initially reported. The impeller with planner 45° blades requires higher torques in Stages I and II due to the overall powder bed mass loading. The impeller with steeper 60° blades requires higher torques in Stages III and IV due to the higher collision frequencies between the blade and granules. The suitable granulation liquid binder to solid powder mass ratio can be readily identified in Stages II and III, and its range is found to increase with the increasing of the impeller rotational speed and is independent to the blade inclined angle.     

Macro-instability: a chaotic flow component in stirred tanks

Chaotic features of the macro-instability (MI) of flow patterns in stirred tanks are studied in this paper. Datasets obtained by measuring the axial component of the fluid velocity and the tangential force affecting the baffles are used. Two geometrically identical, flat-bottomed cylindrical mixing tanks (diameter of 0.3m) stirred with either pitched blade turbine impellers or Rushton turbine impeller are used in the experiments, and water and aqueous glycerol solutions are used as the working liquids. First, the presence of the MI component in the data is examined by spectral analysis. Then, the MI components are identified in the data using the proper orthogonal decomposition (POD) technique. The attractors of the macro-instability are reconstructed using either the POD eigenmodes or a method of delays and finally the attractor invariants are evaluated. The dependence of the correlation dimension and maximum Lyapunov exponent on the vessel operational conditions is determined together with their distribution within the tank. No significant spatial variability of the correlation dimension value is observed. Its value is strongly influenced by impeller speed and by the vessel-impeller geometry. More profound spatial distribution is displayed by the maximum Lyapunov exponent taking distinctly positive values. These two invariants, therefore, can be used to locate distinctive regions with qualitatively different MI dynamics within the stirred tank.