粉体混合过程及搅拌功率的DEM数值模拟和实验

采用数值模拟与功率测试相结合的方法,研究直叶桨式粉体混合机搅拌过程及搅拌功率、扭矩的变化规律。对粉体混合机内球形颗粒的混合过程进行离散单元法DEM数值模拟,研究直叶桨式粉体混合机内搅拌转速、搅拌桨直径、桨叶数目等特性参数对粉体混合时搅拌功率和扭矩的影响,并拟合得到功率计算公式。搭建粉体搅拌试验台,测试粉体搅拌功率并与模拟结果比较。结果表明,直叶桨式粉体混合机内功率消耗与搅拌桨转速、搅拌桨直径、桨叶数目等特性参数有密切关系。同时,扭矩值和功率值与搅拌桨转速、搅拌桨直径和桨叶数目都呈正相关。实验得到了与模拟类似的扭矩-转速关系以及功率-转速关系,模拟值与测试值具有较好的吻合性,验证了所推导公式的准确性。     

Discrete element simulation study of a Freeman powder rheometer

The powder rheometer is a commonly used device for assessing the bulk flow performance of pharmaceutical powders. Discrete element simulations were performed to determine the effects of particle properties such as size, shape, size distribution and friction on the force and torque on the impeller blade in a powder rheometer. DEM simulations are well suited for such a study as they can isolate the impact of each particle property on the bulk powder behavior. The results can then be used to guide the ‘particle engineering’ of pharmaceutical powders to meet specific performance targets. The operation of the FT4 Freeman powder rheometer system was simulated using the discrete element method (EDEM? from DEM Solutions). The effects of various particle properties (size, shape, friction, etc.) were examined using the force and torque on the impeller blade as the key performance indicators. The effect of particle size (mean, distribution) on the mixing torque/force was small and the use of a pre-conditioning step also had minimal impact. As the particle aspect ratio was increased from 1.0 (perfect spheres) to 2.0, both the torque and force values also increased (max increase of ～40%). Increasing the rolling friction of spherical particles produced similar results as the large aspect ratio particles. Increased particle–particle friction caused a larger increase in the measurements (max increase of ～60%) in comparison with increased particle–vessel and particle–impeller friction (max increase of ～20%). Experiments with glass beads were also performed and were used to validate the simulations.     

Effects of blade rake angle and gap on particle mixing in a cylindrical mixer

Performance optimization of a mixer is an issue of great significance in many industrial technologies dealing with particulate materials. By means of Discrete Element Method (DEM), this work examines how the mixing performance of a cylindrical mixer is affected by the two design parameters: blade rake angle and blade gap at the vessel bottom, extending our previous work on particulate mixing. The flow and mixing performance are quantified using the following: velocity fields in vertical cylindrical sections, Lacey’s mixing index, inter-particle forces in vertical cylindrical sections through the particle bed and the applied torque on the blade. Simulation results show that the mixing rate is the fastest for a blade of 90° rake angle, but inter-particle forces are large. Conversely, the inter-particle forces are small for a blade of 135° rake angle, but the mixing rate is slow. The simulation results also indicate that the force applied on particles, velocity field and mixing are interrelated in that order.     

Reduced IMRs in a mixing tank via agitation improvement

Mixing of Newtonian fluids in a stirred tank at low Reynolds numbers was investigated experimentally by means of a visual decolourization technique and shaft power measurements. The research was focused on the Isolated Mixing Regions (IMRs), which are “doughnut-shaped” structures in a stirred tank exhibiting little mixing with bulk of the fluids. The effect of Reynolds number on the IMRs was determined. The critical Reynolds numbers beyond which IMRs are destroyed were presented. The study was focused on agitation design which consumes less power input to destroy the IMRs. A pitch-bladed impeller with an alternating pitch was found more energy efficient than other test impellers in eliminating IMRs in both baffled and unbaffled configurations. It was also found that dramatic reduction in the power consumption could be achieved with installation of baffles to eliminate IMRs at typically low Reynolds numbers. The improved energy efficiency was thought related to generation of more chaotic mixing from the disturbance generated by the baffles, or impeller blade asymmetry such as alternating pitch. An energy parameter was introduced to account for the mixing time scale and the power required in regimes above the critical Reynolds number, in order to evaluate the energy efficiency when IMRs are non-existent.     

The effect of internal impellers on mixing in an electrochemical reactor with rotating rings electrodes

An electrochemical reactor with rotating electrodes has been used to to remove pollutants from aqueous media. Poor mixing and passivation of electrodes surface have been identified as the major drawbacks for the operation of this type of reactors because they adversely affect the critical reactions that take place in the liquid bulk. In this work, three different reactor configurations are proposed and their performance on reactor mixing time and process costs is evaluated. CFD simulations, based on previously validated models, were used to observe mixing inside the electrochemical reactors. Three different arrays were used for the rotating rings electrodes: (a) without impellers, (b) with four internal vertical fins and (c) with a pitched blade central impeller. Power consumption, torque, and parameters such as turbulent intensity, mixing time, among others, were evaluated for all configurations. The reactor with no impellers showed two separated zones of recirculation, reducing the reactor mixing and performance. The reactor with pitched blade impeller, showed no significant improvement due to its low central impeller pumping capacity at low rotational speeds (150 rpm). The array with 4 vertical fins operated at 130 rpm presented the highest flow/power ratio, and the lowest mixing time.     

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.     

Effect of blade angle and particle size on powder mixing performance in a rectangular box

This study focuses on the understanding of flow over a single blade and its impact on powder mixing. The Discrete or Distinct Element Method (DEM) is used and the flow of a single blade through a bed of a binary particle mixture is studied. Mixing performance with respect to a blade-rake angle and particle size is investigated using the Modified Generalized Mean Mixing Index (MGMMI) and the maximum mean instantaneous velocities. A wide range of angles and different loading scenarios of the binary particle mixture were studied. Velocity profiles for all these cases were computed, as well as the forces on particles and the blade. The results showed an inverse relation between the interparticle force and blade-rake angle. Systems with a higher number of larger particles experienced a higher interparticle force. Similar results were obtained for the blade force. The results for mixing efficiency showed that if the smaller particles are placed at the top this leads to a higher mixing performance. The mixing performance was highest for blade-rake angles that offered a maximal surface area or maximal resistance to the flow of particles, which occurred for blade-rake angles from 70° to 90°.     

Chaotic mixing performance enhanced by rigid-flexible impeller with long-short blades in stirred tank

The presence of a mixing isolation regions in a stirred reactor is a major obstacle to enhancing fluid mixing. Breaking the symmetrical flow field structure in the stirred tank and destroying the mixing isolation area can improve the fluid mixing efficiency. The Matlab software was used to calculate the maximum Lyapunov exponent (LLE) and multi-scale entropy (MSE). The effects of different blade types, flexible blade length, flexible blade number, blade height from bottom and rotation speed on fluid mixing were compared. The results show that the rigid-flexible impeller with long-short blades (RF-LSB) can enhance the flow field structure more unstable and asymmetric with deformation and random vibration of flexible pieces, destroy the symmetry flow in the process of fluid mixing, induce the asymmetric flow field, and make more fluid into the chaotic state. When at 90 r/min and three pieces of flexible, the LLE of the RF-LSB is larger than that of rigid impeller and rigid-flexible impeller RF-LSB with increase of 20.22% and 7.98% respectively. The mixing time (θ_m) of the three systems [RF-LSB (three pieces), rigid impeller, rigid-flexible impeller] has an exponential relationship with the power consumption per unit volume (P_v). When P_v is constant, θ_m of the RF-LSB system is the smallest. Results showed that the RF-LSB (three pieces) is superior to rigid impeller and rigid-flexible impeller, which is more conducive to fluid chaotic mixing.     

长短叶片复合型刚柔桨强化搅拌槽内流体混沌混合行为

搅拌反应器中混合隔离区的存在是强化流体混合的主要障碍。打破搅拌槽中的对称性流场结构,破坏混合隔离区,可以提高流体混合效率。采用Matlab软件编程计算最大Lyapunov指数（LLE）和多尺度熵（MSE）,比较了不同桨叶类型、柔性片长度、柔性片数量和桨叶离底高度以及转速对流体混合的影响。结果表明,长短叶片复合型刚柔桨（RF-LSB）桨叶通过刚柔耦合错位连接,柔性片的形变与随机振动对流体的非稳态扰动,使流场结构不稳定性和不对称性增强,强化了流体混合效果。当柔性片数量为3,搅拌转速为90 r/min时,RF-LSB体系比刚性桨和刚柔桨体系的LLE值分别提高了20.22%和7.98%;三种体系[RF-LSB（柔性片数量为3）、刚性桨和刚柔桨体系]的混合时间（θ_m）与单位体积功耗（P_v）呈指数型关系,当P_v相同时,RF-LSB（柔性片数量为3）的θ_m最小,表明RF-LSB（柔性片数量为3）更有利于流体混沌混合。     

错位刚柔桨强化搅拌槽内流体混合实验及数值模拟

为消除搅拌反应器中混合隔离区,对标准刚性桨（R-RT）、错位刚性桨（PR-RT）和错位刚柔桨（PRF-RT）三种桨叶体系的流体混沌特性参数、流场结构以及流体运动速度进行了探讨。采用Matlab软件编程计算最大Lyapunov指数（LLE）和多尺度熵（MSE）,通过计算流体力学研究了三种桨叶体系流场结构和流体运动速度的差异。实验及计算结果表明,错位刚柔桨通过柔性桨叶的随机扰动破坏了隔离区介稳态流场边界,较大程度地消除了混合隔离区。PRF-RT的LLE相比于R-RT和PR-RT分别提高了13.29%和7.25%,MSE也较PR-RT和R-RT大;PRF-RT增强了流场不稳定性,形成了不对称性流场结构,减少了隔离区分布范围;PRF-RT强化桨叶能量耗散,提高了搅拌槽底部、顶部液面以及搅拌槽壁区域流体运动速度,减小了流体混合时间。     

新型大双叶片搅拌器功率与混合特性的数值模拟

针对过程工业体系特性复杂多变的特点,开发了新型大双叶片宽适应性搅拌器,并建立了描述其流动、混合过程的综合数学模型,模拟分析了搅拌釜内的功率特性、流场特性和混合特性。模拟结果表明:新型大双叶片搅拌器所形成流场中存在着上部叶片区域循环流、下部叶片区域循环流以及纵贯全釜的整体循环流;随体系黏度增加,新型大双叶片搅拌器所产生流场的轴向速度、径向速度和切向速度均波动趋缓,且仍保持良好的功率与混合特性,对流态和黏度具有宽适应性;对新型大双叶片搅拌器而言,近液面加料方式不利于整体混合,适宜的加料点应在上下叶片之间,以缩短混合时间;在消耗相同单位体积功率的前提下,新型大双叶片搅拌器较同尺寸规格的FZ搅拌器的混合效率更高,具有高效节能的竞争优势。模拟结果对改进和优化新型大双叶片搅拌器的结构与运行具有参考价值。     

反向旋转卧式双轴捏合反应器混合特性的数值模拟

以差速反向旋转卧式双轴捏合反应器为研究对象,选用高黏牛顿流体糖浆为模拟物料,通过三维有限元数值模拟方法研究了高黏糖浆在捏合反应器中的流动过程,获取了流速和剪切速率的空间分布,进一步结合粒子示踪技术探究了分布混合过程与混合效率,并且考察了搅拌结构对流动与混合过程的影响规律。研究表明,捏合反应器中几乎不存在流动死区,桨叶末端和重叠区域的流速和剪切速率较高,且高流速和高剪切区域均随着捏合杆数目和捏合杆长度的增加而增大。捏合杆可以推动物料在圆周方向上的运动,在重叠区域存在周期性交互作用,进而可以强化分布混合过程。拉伸率随着混合时间以指数形式增加,且随着捏合杆数目和捏合杆长度的增加而增加。时均混合效率大于零,随着捏合杆数目的增大而增大,随着捏合杆长度的增加呈现先增大后减小的趋势。     

Experiment and numerical simulation of chaotic mixing performance enhanced by perturbed rigid-flexible impeller in stirred tank

To eliminate the isolated mixing regions in the stirred tank, factors associated with chaotic mixing performance were studied, including flow field structure and fluid velocity of rigid RT impeller (R-RT), perturbed rigid RT impeller (PR-RT) and perturbed rigid-flexible RT impeller (PRF-RT). The maximum Lyapunov exponent (LLE) and multi-scale entropy (MSE) were calculated by using Matlab software programming, and the differences in flow field structure and fluid velocity of the three blade systems were studied through computational fluid mechanics. The experimental and computational results showed that perturbed rigid-flexible RT impeller could destroy the boundary of the mesostatic flow field in the isolated mixing regions and the symmetry flow in the process of fluid mixing through the random disturbance of the flexible blade, eliminating the isolated mixing regions. At 90 r/min, the LLE of the perturbed rigid-flexible RT impeller is larger than that of rigid RT impeller and perturbed rigid RT impeller. The LLE of the rigid-flexible RT impeller compared with the rigid RT impeller and perturbed rigid RT impeller increases 13.29% and 7.25% respectively and the MSE of the perturbed rigid-flexible RT impeller is also larger than that of rigid RT impeller and perturbed rigid RT impeller. The perturbed rigid-flexible RT impeller enhances the flow field instability, forms an asymmetric flow field structure, and reduces the distribution range of isolated mixing regions. The perturbed rigid-flexible RT impeller enhances the energy dissipation of the blade, improves the fluid velocity at the bottom and top of the tank and the wall of the tank, and reduces the mixing time.     

穿流式刚-柔组合搅拌桨强化混合澄清槽内油-水两相混沌混合

运用LabView和Matlab软件分别采集和处理穿流式刚-柔组合搅拌桨扰动澄清槽中油-水两相流体内部的压力脉动信号,得出的最大Lyapunov指数（LLE）和多尺度熵（MSE）,反映流体内部的混沌程度;同时采用流场可视化技术观测流体混合状态。结果表明,相比于刚性组合桨,穿流式刚-柔组合搅拌桨通过穿流孔与柔性部分的共同作用改变流场的结构和能量耗散方式,使流体的混沌程度和混合状态都优于刚性组合桨。当转速为88 r·min^-1时,流体的混沌混合都达到最佳状态,各实验条件下的LLE均大于零,表明流场混合体系已进入混沌状态,且穿流式刚-柔组合搅拌桨体系的MSE明显高于刚性组合桨体系,说明穿流式刚-柔组合搅拌桨的混合效果优于刚性组合桨。另外,柔性片上穿流孔的数目和柔性桨叶的厚度对流场的混沌特性也有明显的影响。     

Characterization of continuous convective powder mixing processes

The Process Analytical Technology (PAT) initiative has encouraged the development of new technology to improve upon the current manufacturing paradigm. As a result substantial attention has recently focused on continuous processing due to the ability to control disturbances online, avoiding the loss of processing materials and enabling effective process scale-up. In this paper, a pharmaceutical formulation is blended using a continuous flow “high shear” mixer utilizing different operating and design parameters. The mixing efficiency is characterized by extracting samples at the discharge of the blender, and analyzing them using Near Infrared Spectroscopy to determine compositional distribution. Operational conditions such as the inclination angle of the mixer and impeller rotation rate were investigated and showed to affect the mean residence time. The effects of mixer angle, agitation speed, number of blades, blade angle, number of passes through the mixer on the mixing performance of a powder continuous convective mixer are also examined and shown to affect mixing performance whereas the cohesive properties of the material did not significantly affect the mixing operation.     

多层刚柔组合桨诱发流场界面失稳强化非牛顿流体混沌混合行为

传统多层刚性桨用于假塑性非牛顿流体混合搅拌死区较大,流场界面稳定,混合效率低。提出多层刚柔组合桨诱发流场界面失稳强化非牛顿流体混沌混合的方法。实验以羧甲基纤维素钠为非牛顿流体体系,通过扭矩传感器测量功率特性,酸碱中和脱色法测定混合时间,并利用Matlab 软件编程计算最大Lyapunov 指数,分析了非牛顿流体混合过程中的混沌特性及其混合性能。结果表明,组合方式为RF-（PBTD+PBTD+DT）、桨叶排列方式θ=60°、柔性片长度安装比例r=0.8、1.2时,混沌程度较高,混合性能较好。多层刚柔组合桨可以产生多股螺旋流,并在层间柔性片扰动频率差下实现流场界面失稳,搅拌死区减小,在较低转速下使体系进入混沌状态（多层刚柔组合桨体系N>88 r/min时LLE>0,多层刚性桨体系N>125 r/min时LLE>0）;在相同转速下,多层刚柔组合桨混合速率、单位体积功率高于多层刚性桨,而单位体积混合能大致相同。     

单层钢丝柔性桨强化搅拌槽中流体混沌混合行为

实验运用扭矩传感器测量搅拌功率特性,Matlab软件编程计算最大Lyapunov指数（LE_max）,流场可视化技术观测流体混合状态。研究了桨叶类型、桨叶离底距离、柔性钢丝长度、柔性钢丝直径对混合效率数（C_e）、LE_max的影响。结果表明：单层钢丝柔性桨通过刚-柔-流耦合作用,改变流场结构和能量耗散方式,提高了流体混沌混合程度,实现了流体的高效节能混合;当转速为120 r·min⁻¹时,与传统刚性桨相比,单层钢丝柔性桨使流体C_e减小了87.4%,LE_max增大了53.2%,与单层钢丝刚性桨相比,单层钢丝柔性桨使流体C_e减小了43.8%,LE_max增大了10.8%。另外,当搅拌转速相同时,柔性钢丝越长,越有利于流体混沌混合,但其功耗也会随之明显增加;当柔性钢丝直径为0.8 mm,桨叶离底距离为0.25T（T为搅拌槽内径）时,各个转速对应的C_e小于其他情况、LE_max大于其他情况,流体达到相对最佳混沌混合状态。     

Chaotic mixing behavior of non-Newtonian fluid intensified by multilayer rigid-flexible impeller induced flow field interface instability

The traditional multilayer rigid impeller has large dead zone for the mixing of pseudoplastic non-Newtonian fluid, stable flow field interface and low mixing efficiency. A method for enhancing the chaotic mixing of non-Newtonian fluid by multilayer rigid-flexible impeller induced flow field interface instability was proposed. In the experiment, sodium carboxymethylcellulose was used as the non-Newtonian fluid system. The power characteristics were measured by the torque sensor. The mixing time was determined by the acid-base neutralization and decolorization method. The largest Lyapunov exponents were calculated by using Matlab software programming. The chaotic characteristics and mixing performance in the mixing process are analyzed. The results show that when the combination mode was RF-(PBTD+PBTD+DT), the impeller arrangement mode θ=60°, and the flexible sheet length installation ratio r=0.8, 1.2, the degree of chaos was higher and the mixing performance was better. Multilayer rigid-flexible impeller can generate multiple spiral flows, and realize the flow field interface instability under the disturbance frequency difference of the flexible sheet between the layers, the stirring dead zone was reduced, and the system enters a chaotic state at a lower speed (when the multilayer rigid-flexible impeller system N>88 r/min, LLE>0; when the multilayer rigid impeller system N>125 r/min, LLE>0). At the same speed, the mixing rate and power per unit volume of the multilayer rigid-flexible combined impeller are higher than that of the multilayer rigid impeller, but the mixing energy per unit volume is approximately the same.     

Experimental and computational fluid dynamic (CFD) studies on mixing characteristics of a modified helical ribbon impeller

Experimental and computational fluid dynamic (CFD) modeling studies have been performed on mixing characteristics of a new modified helical ribbon impeller in a viscous medium. A novel arrangement for the multiple reference frame (MRF) technique was proposed and the modeling results were compared with those of conventional MRF selecting method. Calculations were performed to study the effects of several parameters: axial flow number, axial circulation time, impeller clearance, and power consumption. The higher performance of the modified impeller has been proven in terms of axial flow number and axial circulation time. The results showed that significant improvement in mixing performance can be obtained at a higher impeller clearance with the modified impeller employed. In addition, the power consumption by the new impeller has been compared with that of the classic one. The CFD-predicted flow patterns generated by the impellers were used to explain the higher performance of the modified impeller. In addition, the results reveal that the CFD-predicted particle volume fractions at various axial distances from the tank bottom are reasonably in agreement with the experimental observations.     

刚柔组合桨强化粉煤灰酸浸搅拌槽内固液混沌混合

传统粉煤灰提铝工艺中酸浸搅拌槽均采用刚性搅拌桨。因刚性桨卷吸能力有限，导致固体颗粒易沉槽、流体混沌混合效率低。提出刚柔组合桨强化酸浸搅拌槽中固液混沌混合行为。实验基于固含率为30%的粉煤灰-自来水体系，研究了刚柔组合酸浸搅拌槽内混沌混合特性及能量耗散规律。采用扭矩传感器采集扭矩时间序列信号，借助Matlab软件编译计算混合过程中最大Lyapunov指数和多尺度熵等混沌特性参数，以单位体积功耗表征搅拌反应器的功率特性。实验考察了搅拌桨安装离底高度、柔性片长度、柔性片宽度等因素对酸浸槽内粉煤灰混沌混合的影响，对比了刚性桨与刚柔组合桨体系的能耗差异。研究结果表明：刚柔组合桨通过柔性片的作用，能增大搅拌桨的卷吸力，进而减少固体颗粒沉槽现象，促进全槽混沌混合；在最优化条件（120 r/min，搅拌桨安装离底高度为T/4，柔性片长度为1.2H ₁、柔性片宽度为D/8）下，体系最大Lyapunov指数达到最大值0.0645，各尺度下的MSE均比其他条件更大，表明刚柔组合桨能够通过柔性片的多体运动，强化体系混沌混合，均化体系能量分布；刚性桨与刚柔组合桨的单位体积功耗随着转速的增加呈现指数规律增长。