Effects of rotational speed and fill level on particle mixing in a stirred tank with different impellers

The particle mixing was studied in a cylindrical stirred tank with elliptical dished bottom by experiments and simulations.The impeller types used were double helical ribbon(HR) + bottom HR,pitched blade ribbon + bottom HR,inner and outer HR + bottom HR,and pitched blade ribbon + Pfaudler + bottom HR labeled as impellers Ⅰ to Ⅳ,respectively.The quantitative correlations among the rotational speed,fill level and power consumption for impeller Ⅰ and impeller Ⅱ were obtained by experiments to validate the discrete element method(DEM) simulations.The particle mixing at different operating conditions was simulated via DEM simulations to calculate the mixing index using the Lacey method,which is a statistical method to provide a mathematical understanding of the mixing state in a binary mixture.The simulation results reveal that as the rotational speed increases,the final mixing index increases,and as the fill level increases,the final mixing index decreases.At the same operating conditions,impeller Ⅲ is the optimal combination,which provides the highest mixing index at the same revolutions.

Mass transfer in gas–liquid stirred reactor with various triple-impeller combinations

The gassed power demand and volumetric mass transfer coefficient(kLa) were investigated in a fully baffled,dished-base stirred vessel with a diameter of 0.30 m agitated by five triple-impeller combinations. Six types of impellers(six-half-elliptical-blade disk turbine(HEDT), four-wide-blade hydrofoil impeller(WH) pumping down(D) and pumping up(U), parabolic-blade disk turbine(PDT), and CBY narrow blade(N) and wide blade(W)) were used to form five combinations identified by PDT + 2CBYN, PDT + 2CBYW, PDT + 2WHD,HEDT + 2WHDand HEDT + 2WHU, respectively. The results show that the relative power demand of HEDT + 2WHUis higher than that of other four impeller combinations under all operating conditions. At low superficial gas velocity(uG), kLa differences among impeller combinations are not obvious. However,when uG is high, PDT + 2WHDshows the best mass transfer performance and HEDT + 2WHUshows the worst mass transfer performance under all operating conditions. At high uGand a given power input, the impeller combinations with high agitation speed and big projection cross-sectional area lead to relatively high values of kLa. Based on the experimental data, the regressed correlations of gassed power number with Froude number and gas flow number, and kLa with power consumption and superficial gas velocity are obtained for five different impeller combinations, which could be used as guidance for industrial design.

Torque and bending moment acting on a flexible shaft agitated by disk turbines in a gas–liquid stirred vessel

The torque and bending moment acting on a flexible overhung shaft in a gas–liquid stirred vessel agitated by a Rushton turbine and three different curved-blade disk turbines(half circular blades disk turbine, half elliptical blades disk turbine, and parabolic blades disk turbine) were experimentally measured by a customized moment sensor. The results show that the amplitude distribution of torque can be fitted by a symmetric bimodal distribution for disk turbines, and generally the distribution is more dispersive as the blade curvature or the gas flow rate increases. The amplitude distribution of shaft bending moment can be fitted by an asymmetric Weibull distribution for disk turbines. The relative shaft bending moment manifests a "rising-falling-rising" trend over the gas flow number, which is a corporate contribution of the unstable gas–liquid flow around the impeller, the gas cavities behind the blades, and the direct impact of gas on the impeller. And the "falling" stage is greater and lasts wider over the gas flow number for Rushton turbine than for the curved-blade disk turbines.

A review on single bubble gas–liquid mass transfer

It is common to empirically correlate volumetric mass transfer coefficient kLa for predicting gas–liquid mass transfer in industrial applications,and the investigation of single bubble mass transfer is crucial for a detailed understanding of mass transfer mechanism.In this work,experiments,models and simulations based on the experimental results were highlighted to elucidate the mass transfer between single bubbles and ambient liquid.The experimental setups,measurement methods,the mass transfer of single bubbles in the Newtonian and the nonNewtonian liquid,models derived from the concept of eddy diffusion,the extension of Whitman’s,Higbie’s and Danckwerts’models,or dimensionless numbers,and simulation methods on turbulence,gas–liquid partition methods and mass transfer source term determination are introduced and commented on.Although people have a great knowledge on mass transfer between single bubbles and ambient liquid in single conditions,it is still insufficient when facing complex liquid conditions or some phenomena such as turbulence,contamination or non-Newtonian behavior.Additional studies on single bubbles are required for experiments and models in various liquid conditions in future.

Interactions between two in-line drops rising in pure glycerin

The behaviors of time-dependent interaction between two buoyancy-driven in-line deformable drops rising in pure glycerin at Re b 1 were studied,where the diameter for the leading drops ranged from 9.51 mm to12.6 mm and for trailing drops from 12.7 mm to 15.8 mm.The situation while a larger drop chasing a smaller one was specifically considered which typically led to the smaller drop "coating" the larger one.Two approaches,the geometric feature approach and the energy change one,were used to judge the starting and ending times of the interaction between two drops.Based on a conical wake model,the drag coefficient of two approaching drops was calculated.Due to the approaching effect of the trailing drop,the leading drop was accelerated and the average drag coefficient was smaller than that for a free rising single drop.The frequency spectrums of the lateral oscillation of two drops during the interaction were obtained by using Fourier analysis.The oscillation frequency of the interactional drops was also different from that for a free rising single drop because of the wake effect produced by the leading drop.Due to a superposition of the drop shape oscillation and the drop internal circulation,the transverse oscillation frequencies of two drops have the same trend during the approaching process.

Gas dispersion and solid suspension in a three-phase stirred tank with triple impellers

The hydrodynamics is still not fully understood in the three-phase stirred tank equipped with multi-impeller due to the intensive interaction between phases.In this work,the solid critical suspension speed(NJSG),relative power demand(RPD)and overall gas holdup(ε_G)were measured in an air–water–glass beads stirred tank equipped with multi-impeller,which consists of a parabolic blade disk turbine below two down-pumping hydrofoils.Results show that either the NJSGor the specific power consumption increases when increasing the volumetric solid concentration or superficial gas velocity.RPD changes less than 10%when solid volumetric concentration ranges from 0 to 15%.ε_G decreases with the increase of solid concentration,and increases with the increase of both superficial gas velocity and the total specific power consumption.The quantitative correlations of NJSG,RPD andεGwere regressed as the function of superficial gas velocity,specific power consumption,Froude number and gas flow number,in order to provide the reference in the design of such three-phase stirred tank with similar multi-impellers.

具有双层桨结构的自吸式搅拌反应器的流体力学性能

在直径0.48 m的搅拌槽中以水-空气为介质,对具有双层桨结构的自吸式反应器的流体力学性能进行了实验研究,考察了自吸式桨浸没深度、底层桨结构和搅拌桨层间距对自吸式桨的临界吸气转速、吸气速率和气含率的影响。结果表明,临界吸气转速随自吸式桨浸没深度增加而增加,临界吸气转速几乎与下层桨的结构无关;吸气速率与气含率随浸没深度增加而减小,吸气速率与气含率受下层桨影响较大,层间距为自吸式桨直径(D)且采用上推式的四叶宽叶翼形轴流式桨作下层桨时,自吸式桨的吸气性能最佳。

具有黏结颗粒的搅拌槽功率特性

功耗是搅拌反应器设计和放大过程的重要参数。在圆柱形搅拌槽内通过实验研究了相对液体体积、转速和物料高度对功耗的影响,采用离散元方法(DEM),用Hertz-Mindlin with JKR模型模拟了不同相对液体体积颗粒的黏结力对功耗的影响。结果表明,随相对液体体积增大,功耗呈先增大后减小的变化趋势,在相对液体体积为0.0162时达到最大值。随转速增大,功耗增长变快,但随相对液体体积增大,转速对功耗的影响指数呈先减小后增大的趋势。不同物料高度的功耗最大值均为饱和颗粒的1.8倍,不同物料高度的单位质量功耗随相对液体体积的增长速率几乎一致。提出了新的间接测量颗粒间黏结力的方法,发现功耗与黏结力呈线性关系。

Discrete element method study of effects of the impeller configuration and operating conditions on particle mixing in a cylindrical mixer

We employed the discrete element method to study the effects of the impeller configuration(i.e.,blade diameter,inclination angle,and blade number),rotational speed,and fill level on the flow and mixing of particles in a cylindrical mixer equipped with flat and inclined blades.The coefficient of rolling friction,coefficient of static friction,and coefficient of restitution were experimentally determined before the simulation,and simulation results of the torque and surface particle distribution were validated in experiments,particularly when using a true Young's modulus in the discrete element method.The performance of the mixer was assessed using the Lacey mixing index.The input work per unit volume was used to represent the mixing efficiency.The circumferential velocity and axial diffusion coefficient of the particles were quantitatively analyzed to reveal the effect of particle flow on the mixing.It was found that the mixing performance and efficiency of a three-blade mixer are better than those of two-and four-blade mixers.For pitched blades,a three-fiat-blade mixer has better mixing performance than a three-45°-blade own-pumping or a three-45°-blade up-pumping mixer,but the mixing efficiency of the three-45°-blade up-pumping mixer is the best among these three mixers.As the rotational speed increases,the mixing performance improves but the mixing efficiency hardly changes.When the fill level is 0.4 times the cylinder diameter,the 160D two-flat-blade mixer has good mixing performance with high mixing efficiency.The circumferential velocity has the greatest effect on mixing performance for side-by-side initial loading.