Experimental characterization and multi-scale modeling of mixing in static mixers. Part 2. Effect of viscosity and scale-up

Static micro-mixers are used in precipitation processes to avoid mixing limitations. The mixing performance of these mixers, which are used in this study to mix two streams of different viscosity, is characterized using competitive-parallel chemical reactions and computational fluid dynamics (CFD). This work is an extension of a previous paper where mixing of fluids with equal viscosity has been studied [Lindenberg, C., Schöll, J., Vicum, L., Brozio, J., Mazzotti, M., 2008. Experimental characterization and multi-scale modeling of mixing in static mixers. Chemical Engineering Science 63, 4135-4149]. It is found that the mixing performance in terms of reaction yield and mixing time decreases slightly with increasing viscosity ratio in a two jet vortex mixer (Roughton mixer). In the Y-mixer the trend is the same at low flow rates, but it is the opposite at large flow rates due to a symmetry breaking phenomenon. The Roughton mixer is scaled-up using the CFD model and a linear relationship between scale-up factor and mixing time is observed. Finally, it is shown that mixing times can be described satisfactorily as a function of velocity, jet diameter and viscosity.     

Comparative analysis of different static mixers performance by CFD technique: An innovative mixer

The flow and mixing behavior of two miscible liquids has been studied in an innovative static mixer by using CFD,with Reynolds numbers ranging from 20 to 160. The performance of the new mixer is compared with those of Kenics, SMX, and Komax static mixers. The pressure drop ratio(Z-factor), coefficient of variation(CoV), and extensional efficiency(α) features have been used to evaluate power consumption, distributive mixing, and dispersive mixing performances, respectively, in all mixers. The model is firstly validated based on experimental data measured for the pressure drop ratio and the coefficient of variation. CFD results are consistent with measured data and those obtained by available correlations in the literature. The new mixer shows a superior mixing performance compared to the other mixers.     

黏度变化范围大的组合桨的数值模拟与应用

利用计算流体力学的方法研究了ZBK+BKS组合桨和螺带桨(LD)的流场和混合性质。对比研究了组合桨的流型、功率消耗、混合时间及混合能。结果表明:ZBK+BKS组合桨在过渡流区域,BKS起主要的流体混合作用,形成很好的整体轴向混合,而在层流区ZBK与BKS同等重要并且ZBK加强了轴向混合。ZBK+BKS组合桨的混合时间在过渡流区域要小于螺带桨,而层流区相差很小,并且二者的混合能相差较小。所以ZBK+BKS组合桨能够适用于黏度变化较大的混合过程。     

Numerical investigation of blade shape in static mixing

The mixing performance of the KMX and SMX static mixers have been compared using 3D high-resolution computational fluid dynamics (CFD) simulations. Although these mixers have a similar design composed of layers of blades, their blade shape is different: curved for the KMX and flat for the SMX. The flow of a Newtonian fluid in steady laminar regime has been considered as the benchmark of the study. The simulation was first validated by assessing the pressure drop vs. the number of mixer elements and the results were found to be in good agreement with experimental data. To evaluate the mixing quality, cross-section stream function, extensional efficiency, mean shear rate, residence time, intensity of segregation, stretching, and Lyapunov exponent have been selected. Analysis of the flow pattern and mixing parameters shows differences between the mixers and it appears that the curved blade is more efficient than the flat blade design at the expense of a slightly higher pressure drop. In practice, the KMX mixer should provide a higher mixing rate at high viscosity ratio than the SMX mixer. © 2004 American Institute of Chemical Engineers AIChE J, 51: 44–58, 2005     

数值模拟静态混合器结构对PS/CO_2熔体温度的影响

利用专用CFD软件Polyflow对SMX型和Kenics型静态混合器中PS/CO_2发泡溶液进行数值模拟计算,分析比较不同板厚在不同元件个数条件下两种静态混合器消耗的压力损失,以及不同CO_2浓度对静态混合器压力损失的影响;并引入"离散系数"分析比较两种静态混合器出口温度均匀性的变化.数值模拟的结果表明:SMX型静态混合器冷却效果优于Kenics型静态混合器,并且SMX型静态混合器出口温度均匀性高于Kenics型静态混合器.     

Pressure drop and mixing behaviour of non‐Newtonian fluids in a static mixing unit

Static or motionless mixers have received wide application in chemical and allied industries due to their low cost and high efficiency. The pressure drop and mixing behaviour of such mixers have been widely studied. However, the available information for non‐Newtonian fluids is scanty. The results of pressure drop and mixing studies conducted with a locally made motionless mixer (MALAVIYA mixer) and four non‐Newtonian fluids—aq. CMC, PVA, and PEG solutions are reported in this article. The new mixer causes less pressure drop compared to some of the commercial mixers. Mixing behaviour of the unit is more closer to plug flow and a two‐parameter model correlates the dispersion data.     

Agitation of Herschel–Bulkley fluids with the Scaba–anchor coaxial mixers

The design of the coaxial mixers depends on many interrelated parameters including the geometry and dimensions of the mixing vessel, the location and type of the impellers, speed ratio, impeller diameter, rotation mode, and fluid rheology. No study has been reported in the literature regarding the mixing performance of the coaxial mixers in the agitation of yield-pseudoplastic fluids. Thus, the main objective of this study was to evaluate the performance of a Scaba–anchor coaxial mixer (a novel configuration) in the mixing of xanthan gum solutions (yield-pseudoplastic fluids). The Herschel–Bulkley model was used to describe the rheological behavior of the xanthan gum solutions. To develop new correlations for the generalized Reynolds and power numbers of the coaxial mixers employed in the agitation of this class of non-Newtonian fluids, we utilized numerous experimental and computational fluid dynamics (CFD) data. The new correlations were tested successfully at different operating conditions (e.g. speed ratio, fluid rheology, and operation mode).     

Characterization of the Mixing Quality in Micromixers

The laminar flow patterns and mixing performance of two different micromixers have been investigated and quantified using CFD. The micromixer geometries consist of a channel with either diagonal or asymmetric herringbone grooves on the channel floor. The numerical results show that a single helical flow is produced for the diagonal mixer, whereas the herringbone mixer creates a double helical flow, composed of an alternating large and small vortex. Particle tracking of a tracer shows that very little convective mixing occurs in the diagonal mixer. However, in the herringbone mixer, very good mixing occurs. Quantitative analysis methods that are traditionally used for characterizing macro‐scale static mixers have been employed. Calculation of the variance of tracer dispersion and the stretching has shown to be well adapted for quantifying the mixing in the micromixers. However, methods based on the deformation rate appear to be less suitable. The results are in excellent agreement with previous experimental findings.     

无序环流混合器的流体力学特性和颗粒混合特性

在内径为Φ286 mm的无序环流混合器装置中,研究了无序环流混合器的流体力学特性和颗粒混合特性。以催化裂化(FCC)平衡剂为颗粒相,在中心区表观气速为0.3~0.5 m/s,边壁区表观气速为0.1 m/s,系统循环强度为0.25~1.00 kg/s的操作条件下,采用PV-6D型颗粒速度密度测量仪测量了混合器内床层各截面密度,并给出不同操作条件下的截面不均匀指数(RNI);采用热颗粒示踪技术给出了混合器内各测量截面的无因次温度分布,并引入混合指数用来定量描述不同操作条件下的颗粒混合程度,同时对比了传统环流混合器与无序环流混合器的混合能力。结果表明,无序环流混合器内部床层密度呈现中心低,边壁高的分布模式。随着循环强度的增加,RNI先减小后增大,随着表观气速的增加,RNI增大。预混合区混合指数为0.7~0.9,在高循环量,低中心区表观气速条件下(G_s为1.00 kg/s,u_(gd)为0.3 m/s),下料管进料影响区的截面混合指数低于其他操作条件。另外,无序环流混合器混合能力优于传统环流混合器。     

A SIMULATION OF A MOTIONLESS MIXER

Continuous laminar mixing in segmented twisted-tape motionless mixers is considered. A solution to the steady isothermal creeping flow of a Newtonian fluid in a twisted-tape mixer has been obtained via two-dimensional numerical procedures. The developed flow within a section of the mixer has been solved in a helical coordinate system by an iterative scheme. The resulting solution is rigorously correct in the absence of entrance and exit flows at the junction between sections. An algorithm is presented for the modelling of these junction flows via two-dimensional procedures. Simulated cross-sectional mixing patterns have been generated for comparison with experimental results

The performance of twisted-tape mixers is simulated for various designs, beginning with the particular geometry of the Kcnics Static Mixer, and for different operating conditions Results suggest that the rate of mixing as a function of the total twist per section is optimized with respect to pressure drop when sections contain 80 degrees of twist. The capability for rational improvement in other design and operating parameters is illustrated. The mechanisms of laminar mixing are discussed and quantified; of primary importance is the tendency for interfacial area to assume an orientation within each section which is favorable to mixing in subsequent sections.     

Performance comparison of micromixers

The present paper proposes a detailed comparison of mixing efficiency of different mixers that have been characterized by the Villermaux/Dushman test reaction. Considering simple relations of mixing in laminar flow, it is shown how to obtain the theoretical mixing time and how to relate it with operating parameters as the Reynolds number of the flow and the specific power dissipation per mass unit of fluid. The comparison of the experimental and of the theoretical mixing times indicates that only a few percents of the total mechanical power transmitted to the fluid is effective for mixing.     

Characterization of mixing in an optimized designed T-T mixer with cylindrical elements

Passive micromixers are preferred over active mixers for many microfluidic applications due to their relative ease in integration into complex systems and operational flexibility. They also incur very low cost of manufacturing. However, the degree of mixing is comparatively low in passive mixers than active mixers due to the absence of disturbance in the flow by external forces and the inherent laminar nature of microchannel flows. Various designs of complex channel structures and three-dimensional geometries have been investigated in the past to obtain an efficient mixing in passive mixers. But the studies on mixing enhancement with simple planar geometries of passive mixers have been few and limited. The present work aims to investigate the possibility of mixing enhancement by employing simple planar type designs, such as T-mixer and T-T mixer with cylindrical elements placed in the mixing channel. The mixing performance has been evaluated in the Reynolds number range of 6 to 700. Numerical results have shown that T-T mixer with cylindrical elements performed significantly well and obtained very good mixing quality over basic T-mixer for the entire range of Reynolds number (6 to 700). The device has also shown better mixing as compared to basic T-T mixer and T-mixer with cylindrical elements. A larger pair of vortices formed in the stagnation area due to the presence of a cylindrical element in the junction. Cylindrical elements downstream caused significant enhancement in mixing due to splitting and recombining action. The size of the cylindrical element in the T-T mixer has been optimized to obtain better mixing performance of the device. Remarkable improvement in mixing quality by T-T mixer with cylindrical elements has been obtained at the expense of small rise in pressure drop as compared to other passive designs considered in this study. Therefore, the current design of T-T mixer with cylindrical elements can act as an effective and simple passive mixing device for various micromixing applications.     

Statische Mischer und ihre Anwendung

Static mixers and their applications . Static mixers are generally made up of similar, fixed mixing units installed at right angles to each other in series along a tube or a channel. The energy of mixing is extracted from the flow. Twelve different units are presented. The mixing effect in static mixers under conditions of laminar flow is accomplished either by specially designed feed systems, by cutting and twisting, by displacement and distortion, or by separation and expansion. Depending upon the mixer, very different lengths are required to achieve the same degree of homogeneity. Compared with an empty tube, the pressure drop in static mixers is some 7-to 200-fold greater for laminar flow and 100- to 600-fold greater for turbulent flow. Static mixers are employed in all areas of chemical engineering for homogenization, for reduction of the resisdence-time spectrum, and for heat exchange. Since maintenance and wear are negligible, since incorporation frequently requires no extra space, and since they can be used over wide ranges of viscosity, static mixers are being increasingly employed in continuous processes.     

立式捏合机捏合间隙影响CFD分析

本文利用计算流体力学(CFD)方法研究捏合间隙对立式捏合机混合性能的影响。首先,根据立式捏合机搅拌桨叶运动特点以及被混物料的流变特性,进行立式捏合机混合流场数值模拟。其次,确定立式捏合机混合性能宏观评价指标。最后,分析了捏合间隙的变化对混合性能评价指标的影响。分析结果表明：间隙越小,立式捏合机的混合性能越好;当空心桨叶两侧的捏合间隙大小相等时,立式捏合机的功耗最小。     

Relation between hydrodynamics and drop size distributions in pump–mix mixer

In the present work, experiments have been carried out to measure the drop size distributions in a pump–mix mixer over a wide range of geometry and operating conditions. The effects of impeller type, (single and multiple impellers), impeller speed, location, phase flow rates, and interfacial tension have been investigated. Computational fluid dynamics model has been developed to predict the hydrodynamic characteristics of pump–mix mixers. Population balance modeling has been carried out to predict the drop size distributions. The hydrodynamic characteristics predicted through CFD simulations have been related to the drop size distributions. The role of convection and energy dissipation in influencing the drop size distributions has been elucidated.     

Effects of embedded streamwise vorticity on turbulent mixing

This work concerns the characterization of turbulent flow underlying mixing in the presence of streamwise vorticity. An experimental test section made of a cylindrical tube equipped with seven rows of streamwise vortex generators was designed and constructed for this study. Each row is composed of four vortex generators fixed symmetrically on the tube wall. This new type of mixer, called a high-efficiency vortex (HEV) mixer, generates coherent structures in the form of longitudinal counter-rotating vortices. The resulting flow enhances radial mass transfer and thus facilitates particle dispersion and mixing. The energy cost of this mixer used as an emulsifier has been evaluated as up to a thousand times less than that of other static mixers for a given interface area generation (Lemenand et al. [1] and [2]).The aim of this work is to study experimentally and numerically the turbulence structure and mixing properties of the flow composed of streamwise vortices superimposed on a turbulent flow, in particular the more energetic structures present in the base flow. Experiments were carried out in the test section in a flow loop by measuring instantaneous velocities by laser Doppler anemometry. Numerical simulations of the velocity distribution and turbulence field inside the flow were conducted for various turbulence models using a computational fluid dynamic CFD package. Attention is focused on the evolution and distribution of turbulent kinetic energy dissipation as the underlying mechanism for turbulent mixing. Mean and turbulent quantities are compared with experimental results.Both laboratory experiments and numerical simulations show a vortex zone behind each tab that could explain the efficiency of the HEV mixer. This study provides a basis for understanding the physical mechanisms in the mixing and homogenizing of the flow and therefore the efficiency of the mixer.     

Effects of geometry and flow rate on secondary flow and the mixing process in static mixers—a numerical study

A method based on computational fluid dynamics (CFD) for the characterization of static mixers using the Z factor, helicity and the rate of striation thinning is presented. These measures were found to be well-suited for the characterization of static mixers as they reflect the pressure drop, the formation of secondary flow, i.e. vortices, and their effect on the mixing process. Two commercial static mixers, the Kenics KM and Lightnin Series 45, have been characterized. In the mixers investigated, secondary flow is formed in the flow at the element intersections and due to the curvature of the mixer elements. The intensity of the vortices is higher in the Lightnin than the Kenics mixer due to edges in the middle of the Lightnin mixer elements. The formation of vortices affects the Z factor by an increase in the power requirement, and the rate of striation thinning by an increase in the stretching of the striations. The formation of vortices was observed at a Reynolds number of 10 in both mixers with aspect ratios of 1.5. However, the intensity of the vortices was greater in the Lightnin than the Kenics mixer, which was observed in not only the magnitude of the helicity, but also the Z factor, rate of striation thinning and the distribution of striation thickness.The distribution in striation thickness is shifted towards thin striations as the flow rate is increased from below to above the Reynolds numbers of which vortices were first observed, but some striations still pass the mixer elements almost unaffected, which can be seen in the skewness of the distribution of the striation thickness, which shifts from being negative to positive.     

Investigations of mixing in a fluid Jet agitated tank

Mixing can be achieved in a variety of ways including mechanical agitation, agitation by a fluid jet impingement or by static mixers. This article is concerned with mixing by a fluid jet impingement. Jet mixing can be described as a fast-moving stream of liquid being injected into a slow-moving or stationary liquid. In this study, computational fluid dynamics (CFD) is used to investigate the performance of a jet mixer. The degree of mixing has been evaluated by monitoring mixing of a hot volume of fluid in the larger tank until criteria for 95% mixing are met at a number of monitoring points. A wide range of jet injection rates has been investigated. Good agreement was shown between numerical and published experimental results. Moreover, the need to monitor mixing at more than one point, and especially at points in zones with little liquid motion, is shown to be necessary. Numerical results provided detailed plots of velocity and temperature fields and clearly showed the locations of zones with very low velocities, which require the longest time to become well mixed.     

An Analysis of Mixing in a Typical Experimental Set‐up to Measure Nnucleation Rates of Precipitation Processes

Mixing in a typical experimental setup to measure nucleation rates in precipitation processes was assessed. To determine these rates as a function of the driving force for concomitant polymorphs, it is necessary to perform these experiments at constant supersaturation. Therefore, the mixing time must be shorter than the time for the first nuclei to appear. For fast precipitation processes complete mixing has to be achieved within milliseconds. The mixing performance of a wide angle Y‐mixer was studied to see whether this is possible. An analysis of characteristic mixing times as a function of the average energy dissipation rate showed that turbulent dispersion of the feed streams determined the rate of the mixing process. The characteristic time for turbulent dispersion was of the same order as an arbitrarily set residence time in the Y‐mixer. However, CFD simulations of the flow showed large variation in the spatial distribution of the dissipation rate and revealed unsatisfying macromixing.