DEM investigation of mixing indices in a ribbon mixer

Mixing index is an important parameter to understand and assess the mixing state in various mixers including ribbon mixers,the typical food processing devices.M...     

Numerical simulation of tetrahedral particle mixing and motion in rotating drums

A regular tetrahedron is the simplest three-dimensional structure and has the largest non-sphericity. Mixing of tetrahedral particles in a thin drum mixer was studied by the soft-sphere-imbedded pseudo-hard particle model and compared with that of spherical particles. The two particle types were simulated with different rotation speeds and drum filling levels. The Lacey mixing index and Shannon information entropy were used to explore the effects of sphericity on the mixing and motion of particles. Moreover, the probability density functions and mean values and variances of motion velocities, including translational and rotational, were computed to quantify the differences between the motion features of tetrahedra and spheres. We found that the flow regime depended on the particle shape in addition to the rotation speed and filling level of the drum. The mixing of tetrahedral particles was better than that of spherical particles in the rolling and cascading regimes at a high filling level, whereas it may be poorer when the filling level was low. The Shannon information entropy is better than the Lacey mixing index to evaluate mixing because it can reflect the real change of flow regime from the cataracting to the centrifugal regime, whereas the mixing index cannot.     

Discrete element method study of parameter optimization and particle mixing behaviour in a soil mixer

Soil mixing is an emerging research in the field of construction resource recovery. In this study, the mixing behaviour of soil particles in a mixer is numerically simulated by the discrete element method (DEM). A four-factor, three-level orthogonal experiment is designed to optimize the mixer design by selecting the fly-cutter speed, spindle speed, number of blades and fly-cutter diameter, using Lacey mixing index and power consumption as evaluation indicators. Then, the impact of soil cohesion and type on the mixing behaviour is investigated. The results show that the optimal parameter combination of this experiment is 280 rpm fly-cutter speed, 40 rpm spindle speed, 4 blades and 250 mm fly-cutter diameter. This optimal combination reaches a comparatively uniform state mix in 5.9 s with an average power consumption of 704.11 W. In addition, the wear and tear of the mixer increases as soil cohesion increases, while the mixing quality of materials declines, resulting in a “shaft hugging” phenomenon. The mixing efficiency varies greatly among different soil types, but the radial and tangential velocities have a similar law. This work can provide some guidance for the optimization design of a mixer and study of soil mixing.     

Two-fluid mixing in a microchannel

A numerical study of the mixing of two fluids (pure water and a solution of glycerol in water) in a microchannel was carried out. By varying the glycerol content of the glycerol/water solution, the variation in mixing behavior with changes in the difference in the properties of the two fluids (e.g., viscosity, density and diffusivity) was investigated. The mixing phenomena were tested for three micromixers: a squarewave mixer, a three-dimensional serpentine mixer and a staggered herringbone mixer. The governing equations of continuity, momentum and solute mass fraction were solved numerically. To evaluate mixing performance, a criterion index of mixing uniformity was proposed. In the systems considered, the Reynolds number based on averaged properties was Re=1 and 10. For low Reynolds number (Re=1), the mixing performance varied inversely with mass fraction of glycerol due to the dominance of molecular diffusion. The mixing performance deteriorated due to a significant reduction in the residence time of the fluid inside the mixers.     

On the vorticity characteristics of lobe-forced mixer at different configurations

Lobe-forced mixer is one typical example of the passive flow controllers owing to its corrugated trailing edge. Besides the spanwise Kelvin–Helmholtz vortex shedding, streamwise vortices are also generated within its mixing layer. The geometrical configuration of the lobe significantly affects these two types of vortices, which in turn affects the mixing performance of the mixer. In the present investigation, characteristics of mixers with five different configurations were examined and evaluated for two velocity ratios (r = 1, 0.4). The mixers have only one lobe in order to eliminate any possible interactions between neighboring vortices generated by the adjacent lobes. Hot-wire anemometer was used to examine the Kelvin–Helmholtz vortices via the spectrum analysis while laser Doppler anemometer was employed to examine the streamwise vortices. It was found that there were two main frequencies for the Kelvin–Helmholtz vortices in the wake of the mixer; and the Strouhal numbers approached their respective maximum values at high Reynolds number. The rectangular mixer had similar mixing performance with the semicircular one; and both of them were better than the triangular mixer. The scalloping modification enhanced mixing by generating additional streamwise vortices while the scarfing modification could not improve the mixing performance.     

Assessing mixing characteristics of particle-mixing and granulation devices

The mixing of particulates such as powders is an important process in many industries including pharmaceuticals, plastics, household products (such as detergents) and food processing. The quality of products depends on the degree of mixing of their constituent materials which in turn depends on both geometric design and operating conditions. Unfortunately, due to lack of understanding of the interaction between mixer geometry and the granular material, limited progress has been made in optimizing mixer design. The discrete element method (DEM) is a computational technique that allows particle systems to be simulated and mixing to be predicted. Simulation is an effective way of acquiring information on the performance of different mixers that is difficult and/or expensive to obtain using traditional experimental approaches. Here we demonstrate how DEM can be used to unravel flow dynamics and assess mixing in several different types of devices. These devices used for mixing and/or granulation of particulates, are classified broadly as gravity controlled, bladed and high shear. We also explore the role of particle shape in mixing performance and use DEM to test whether Froude number scaling is suitable for predicting scale performance of rotating mixers.     

不同形状混合器中二元颗粒的分聚与混合研究

采用实验、模拟及理论的分析方法, 研究了在圆形混合器、椭圆形混合器、正方形混合器中, 不同转速和填充率条件下, 容器形状对二元颗粒体系分聚与混合的影响. 实验中通过改变转速与填充率, 可获得不同的颗粒分聚与混合图样, 对示踪颗粒运动轨迹的分析发现, 在圆形混合器中, 随着混合器转速的增大, 颗粒在径向的随机性减少;在正方形混合器中, 随着混合器转速的增大, 颗粒在径向的随机性增大.模拟结果发现颗粒流动分为两个区域, 在表面的快速流动和在整体的旋转运动. 通过理论分析发现颗粒分聚在圆形混合器中最明显, 在正方形混合器中最弱, 椭圆形混合器介于二者之间.      

Assessing mixing characteristics of particle-mixing and granulation devices

The mixing of particulates such as powders is an important process in many industries including pharmaceuticals, plastics, household products （such as detergents） and food processing. The quality of products depends on the degree of mixing of their constituent materials which in turn depends on both geometric design and operating conditions. Unfortunately, due to lack of understanding of the interaction between mixer geometry and the granular material, limited progress has been made in optimizing mixer design. The discrete element method （DEM） is a computational technique that allows particle systems to be simulated and mixing to be predicted. Simulation is an effective way of acquiring information on the performance of different mixers that is difficult and/or expensive to obtain using traditional experimental approaches. Here we demonstrate how DEM can be used to unravel flow dynamics and assess mixing in several different types of devices. These devices used for mixing and/or granulation of particulates, are classified broadly as gravity controlled, bladed and high shear. We also explore the role of particle shape in mixing performance and use DEM to test whether Froude number scaling is suitable for predicting scale performance of rotating mixers.     

Using the discrete element method to assess the mixing of polydisperse solid particles in a rotary drum

Despite the wide applications of powder and solid mixing in industry, knowledge on the mixing of polydisperse solid particles in rotary drum blenders is lacking. This study investigates the mixing of monodisperse, bidisperse, tridisperse, and polydisperse solid particles in a rotary drum using the discrete element method. To validate the model developed in this study, experimental and simulation results were compared. The validated model was then employed to investigate the effects of the drum rotational speed, particle size, and initial loading method on the mixing quality. The degree of mixing of polydisperse particles was smaller than that for monodisperse particles owing to the segregation phenomenon. The mixing index increased from an initial value to a maximum and decreased slightly before reaching a plateau for bidisperse, tridisperse, and polydisperse particles as a direct result of the segregation of particles of different sizes. Final mixing indices were higher for polydisperse particles than for tridisperse and bidisperse particles. Additionally, segregation was weakened by introducing additional particles of intermediate size. The best mixing of bidisperse and tridisperse particles was achieved for top–bottom smaller-to-larger initial loading, while that of polydisperse systems was achieved using top–bottom smaller-to-larger and top–bottom larger-to-smaller initial loading methods.     

Comparison between three static mixers for emulsification in turbulent flow

This paper deals with comparing performances of three different static mixers in terms of pressure drop generated by both single-phase flow and liquid–liquid flow in turbulent flow regime and in terms of emulsification performances. The three motionless mixers compared are the well-known SMX™ and SMV™ and the new version of the SMX called SMXPlus™. This experimental study aims at highlighting the influence of the dispersed phase concentration and some of the geometrical parameters such as number of elements and design of the motionless mixer on droplets size distributions characteristics. Finally, experimental results are correlated in terms of Sauter mean diameter as a function of hydrodynamic dimensionless numbers.     

Chaotic mixing and mixing efficiency in a short time

Several studies of the chaotic motion of fluid particles by two-dimensional time-periodic flows or three-dimensional steady flows, called Lagrangian chaos, are first introduced. Secondly, some of the studies on efficient mixing caused by Lagrangian chaos, called chaotic mixing, are reviewed with discussion of several indices for the estimation of mixing efficiency. Finally, several indices to estimate the efficiency of mixing in a short time, such as those related to transport matrices, stable and unstable manifolds of hyperbolic periodic points of Poincaré maps, and lines of separation, are explained by showing examples of mixing by two-dimensional time-periodic flows between eccentric rotating cylinders and mixing by three-dimensional steady flows in a model of static mixers.     

Numerical study of influence of different parameters on mixing in a coaxial jet mixer using LES

We present a comparative numerical study about the overall mixing process in a coaxial jet mixer. The two-stream mixing problem was investigated in non-reacting single phase gas and liquid mixtures using Large-Eddy Simulations with wall functions and subgrid scale models from eddy viscosity concepts. The influence of different parameters like Reynolds number, Schmidt number, Prandtl number, density ratio and flow rate ratio on the overall mixing process was investigated. Additionally two methods of control of mixing are shown to have a significant effect on the overall mixing in a coaxial jet mixer.     

A solids mixing rate correlation for small scale fluidized beds

A new first degree solids mixing rate is proposed to evaluate the mixing of solids in small scale fluidized beds. Particle mixing experiments were carried out in a 2D fluidized bed with a cross-section of 0.02 m × 0.2 m and a height of 1 m. White and black particles with average diameters of 850 and 450 μm were used in our experiments. Image processing was used to measure the concentration of the tracers at different times. The effects of four representative operating parameters (superficial gas velocity, ratio of tracer particles to bed particles, tracer particle position, and particle size) on mixing are discussed with reference to the mixing index. We found that the Lacey index depends on the concentration of the tracers. The position of the tracers affects the initial mixing rate but not the final degree of mixing. However, the new mixing rate equation does not depend on the initial configuration of the particles because this situation is considered to be the initial condition. Using the data obtained in this work and that found in literature, an empirical correlation is proposed to evaluate the mixing rate constant as a function of dimensionless numbers (Archimedes, Reynolds, and Froude) in small scale fluidized beds. This correlation allows for an estimation of the mixing rate under different operating conditions and for the detection of the end point and/or the time of mixing.     

The evolution of the brabender farinograph

The importance of the consistency of wheat flour dough in baking is defined. This is normally determined with the aid of a recording dough mixer.Such a mixer was first patented byHogarth, a Scottish miller in 1889 but proved inadequate. About 40 years laterHankóczy a Hungarian cereal chemist initiated the line of recording dough mixers which are used today.His andBrabender's work are reviewed which led from a factory mixer fitted with an ammeter, via the early torque recording laboratory instruments to the modern Farinograph. The basic unit is described in some detail.Slides of the various attachments are shown which allow application to grinding and high speed mixing both on a batch and continuous basis.The use of the system for the testing of cereal products, fats, rubber, filler and plastics is described.The theoretical significance of the results obtained is briefly discussed. The lecture is illustrated by 14 slides.Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968. — Original paper unpublished.     

Topology optimization of microfluidic mixers

This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering the layout of flow/non‐flow regions subject to a constraint on the pressure drop between inlet and outlet. For a square cross‐sectioned pipe the mixing is increased by 70% compared with a straight pipe at the cost of a 2.5 fold increase in pressure drop. Another example where only the bottom profile of the channel is a design domain results in intricate herring bone patterns that confirm findings from the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

Lattice‐Boltzmann and finite element simulations of fluid flow in a SMRX Static Mixer Reactor

A detailed comparison between the finite element method (FEM) and the lattice‐Boltzmann method (LBM) is presented. As a realistic test case, three‐dimensional fluid flow simulations in an SMRX static mixer were performed. The SMRX static mixer is a piece of equipment with excellent mixing performance and it is used as a highly efficient chemical reactor for viscous systems like polymers. The complex geometry of this mixer makes such three‐dimensional simulations non‐trivial. An excellent agreement between the results of the two simulation methods was found. Furthermore, the numerical results for the pressure drop as a function of the flow rate were close to experimental measurements. Results show that the relatively simple LBM is a good alternative to traditional methods. Copyright © 1999 John Wiley & Sons, Ltd.     

采用重要抽样法的结构动力可靠度计算

首次对比分析了结构动力可靠度计算的三种重要抽样法,并对部分方法进行了补充修正.单元失效域法补充了依据随机教决定抽样区间的产生方法,根据单元失效域的条件概率和权重系数给出重要抽样密度函教.方差放大系数法直接通过激励过程的特性给出重要抽样密度函数的具体表达式.功率谱法的重要抽样密度函数仅为激励幅值的函数,根据结构反应的功率谱密度增大激励幅值的方差,建议幅值样本值的联合概率密度函数可表示为幅值样本值分量的概率密度函数的连乘形式.结果表明:对于线性体系三种方法的计算效率均比Monte-Carlo法有显著提高,而单元失效域法的计算效率又比另两种方法高.     

光纤陀螺零漂数据滤波方法的研究

在对光纤陀螺零偏稳定性数据建立时间序列模型（ARMA模型）的基础上,采用卡尔曼滤波算法对光纤陀螺的漂移数据进行了处理,并采用Allan方差法和最小二乘法对滤波后的数据进行了处理,拟合,最后求出滤波后数据中各噪声的误差系数。     

用双视场电子散斑干涉实现检测表面的变尺度同时测量

结构或材料中所含的微小缺陷对其宏观力学性能具有重要的影响，探讨这些微小缺陷引起的微变形及其在结构整体变形中所占的份额，对于有效地评估结构和材料的整体性能及局部演化过程都具有重要的理论和工程价值，本文应用双视场电子散斑干涉技术，实现了对被测对象表面的全场变形和局部微观场变形的同时实时检测，给出了宏观及局部位移场分布，并结合有限元数值分析与实验结果进行了比较。