A mapping tool using anisotropic unstructured meshes to study mixing in periodic flows

The objective of the present work is to describe a new mapping tool using anisotropic unstructured meshes to study mixing within a spatially periodic pipe flow. Instead of tracking the boundaries of elementary cell flow domains as it was done in the original mapping method established by Kruijt et al. (A.I.Ch.E. J. 47 (5) (2001a) 1005; Int. Polym. Process. 16 (2) (2001b) 151) and Galaktionov et al. (Comput. Fluids 30 (3) (2001) 271), the deformation of elementary triangles (only three nodal points) between the inlet and exit pipe cross-sections is followed. It is however necessary to adapt the initial mesh according to criteria which takes into account the spatial stretching and folding of fluid elements. The method developed is applied to the twisted curved pipes (TCP) three-dimensional (3D) flow. We show the evolution of concentration distributions along the TCP mixer for chaotic advection flow regimes. This method allows the emphasis of isolated unmixed regions (KAM islands). The flexibility of the method allows also the possibility of studying multiple stirring protocols, thus contributing to a better comprehension of the physical phenomena involved in chaotic mixing. The method developed is also applicable to 2D temporally periodic flows.     

On the performance of static mixers: A quantitative comparison

The performance of industrially relevant static mixers that work via chaotic advection in the Stokes regime for highly viscous fluids, flowing at low Reynolds numbers, like the Kenics, the Ross Low-Pressure Drop (LPD) and Low-Low-Pressure Drop (LLPD), the standard Sulzer SMX, and the recently developed new design series of the SMX, denoted as SMX(n) (n, N_p, N_x) = (n, 2n − 1, 3n), is compared using as criteria both energy consumption, measured in terms of the dimensionless pressure drop, and compactness, measured as the dimensionless length. Results are generally according to expectations: open mixers are most energy efficient, giving the lowest pressure drop, but this goes at the cost of length, while the most compact mixers require large pressure gradients to drive the flow. In compactness, the new series SMX(n), like the SMX(n = 3) (3, 5, 9) design, outperform all other devices with at least a factor 2. An interesting result is that in terms of energy efficiency the simple SMX (1, 1, 4, θ = 135°) outperforms the Kenics RL 180°, which was the standard in low pressure drop mixing, and gives results identical to the optimized Kenics RL 140°. This makes the versatile “X”-designs, based on crossing bars, superior in all respects.     

弹性棒对仿生学柔性反应器的流体混合强化

在柔性反应器底部放置竖直的弹性硅胶棒（弹性棒），通过弹性棒运动对周围流体产生扰动，强化流体混合。基于酸碱中和脱色法和图像分析方法，研究了柔性反应器的混合过程和混合时间；通过混合时间定量评估了弹性棒的强化效果；并分别研究了弹性棒的位置和高度及柔性反应器系统的最大挤压深度和频率对流体混合行为的影响。结果表明：弹性棒的放置能够使柔性反应器内隔离区结构改变，混合时间减少。弹性棒位置靠近挤压头一侧时，对流体混合强化最明显。在弹性棒高度低于柔性反应器内液面时，弹性棒高度增加，强化效果增加。超过液面之后，继续增加弹性棒高度，强化效果没有进一步增加。当弹性棒靠近挤压头、高度超过液面且最大挤压深度为2.5cm，与没有弹性棒时相比混合时间减少了57%。在其他实验条件不变的前提下，最大挤压深度增加，强化效果增加。     

Gas-assisted displacement of a viscoelastic fluid in capillary geometries

The effect of fluid viscoelasticity on the fraction of liquid deposited on the walls of capillary geometry and the pressure drop at the capillary static region are theoretically investigated using the Criminale-Ericksen-Filbey (CEF) constitutive equation to describe a non-Newtonian fluid displaced by the pressurized gas in a capillary. The singular perturbation method is used to determine the residual liquid film thickness of a viscoelastic fluid on the walls of a circular tube or a rectangular channel when displaced by another immiscible fluid. Inner and outer expansions are developed in terms of both a small parameter Ca^1/3 and a small parameter De/Ca^1/3. The method of matched asymptotic expansion is used to match the inner and outer solutions by means of a transition region between the advancing meniscus and the entrained film where the fluid rheology has its greatest effect. A detailed analysis indicates that the residual liquid film thickness of the viscoelastic fluid tends to decrease and the pressure drop across the bubble front tends to increase as the fluid becomes more viscoelastic. The theoretical results presented in this paper are in agreement with some of the experimental data and theoretical analyses available in the literature.     

Experimental study of the hydraulic operation of an annular centrifugal contactor with various mixing vane geometries

The annular centrifugal contactor is a combination mixer/centrifuge that has been developed for solvent extraction processes for recycling used nuclear reactor fuel. The experimental observations presented were part of a simulation‐focused research effort aimed at providing a more complete understanding of the fluid flow within these contactors to enable further advancements in design and operation of future units and greater confidence for use of such contactors in a variety of other solvent extraction applications. Laser doppler velocimetry (LDV), particle image velocimetry (PIV), pressure measurements, and high‐speed video imaging for a range of flow rates and rotor speeds were performed to characterize the flow of water in the annular mixing region of the contactor using three different mixing vane geometries. It was found that the geometry of the mixing vanes has a significant impact on the annular liquid height and general flow in the contactor mixing zone. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

A unified interaction model for multiphase flows with the lattice Boltzmann method

The lattice Boltzmann method (LBM) has been increasingly adopted for modelling multiphase fluid simulations in engineering problems. Although relatively easy to implement, the ubiquitous Shan–Chen pseudopotential model suffers from limitations such as thermodynamic consistency and the formation of spurious currents. In the literature, the Zhang–Chen, Kupershtokh et al., the β-scheme, and the Yang–He alternative models seek to mitigate these effects. Here, through analytical manipulations, we call attention to a unified model from which these multiphase interaction forces can be recovered. Isothermal phase-transition simulations of single-component in stationary and oscillating droplet conditions, as well as spinodal decomposition calculations, validate the model numerically and reinforce that the multiphase forces are essentially equivalent. Parameters are selected based on the vapour densities at low temperatures in the Maxwell coexistence curve, where there is a narrow range of optimal values. We find that expressing the model parameters as functions of the reduced temperature further enhances the thermodynamic consistency without losing stability or increasing spurious velocities.     

Direct numerical simulation of particle collisions in two-phase flows with a meshless method

The element-free Galerkin (EFG) method was used to simulate particle motion in two-phase flows with a new node distribution arithmetic suitable for meshless methods. The control equations were discretized with the standard Galerkin method in space and a fractional step finite element scheme in time. Regular background cells were used for the quadrature. The forces of the fluid on the particles were obtained by integrating the stress and shear forces on the particle surfaces. Simulation of the movement of a particle in a channel showed the Karman vortex street forming behind the particle with increasing particle velocity. Simulation of the movement of two particles in a channel showed the well-known drafting, kissing and tumbling, which has been obtained experimentally. Multi-particle flows were simulated with the results showing that meshless methods are capable of dealing with real particle collisions, which makes meshless methods superior to all mesh-based methods. Moreover, the theoretical relation of interparticle collision rate derived using kinetic theory was compared with the present numerical results and it is found that the collision rate is much lower than the theoretical estimation based on kinetic theory.     

低温一次法炼胶工艺与传统法炼胶工艺在高结构炭黑配方中的应用

在胎面胶配方中采用高结构 N134炭黑进行大料对比实验,结果表明：一次法炼胶工艺较传统多段炼胶工艺的混炼胶流动性更好,利于后序半成品部件的加工;一次法生产的混炼胶物性及磨耗均优于传统多段混炼胶;同时,低温一次法减少了混炼段数,提高了生产效率;而且一次法也适用于多白炭黑配方胶料的混炼。因此,低温一次法炼胶工艺更能突出其必然优势     

A numerical study of stir mixing of liquids with particle method

The process of stir mixing of two viscous liquids is simulated using the moving particle semi-implicit (MPS) method. A mixing rate is defined within the particle method to characterize the level of mixing, as the number, position, period, and rotating speed of the stirring stick(s) and liquid viscosity are changed. The motions of liquid particles are tracked to reveal the flow field and mixing mechanisms. The variation of the mixing rate shows that the mixing rate is higher when the sticks are rotating monotonically at high speed, and an optimum position of the stick can be identified. The mixing rate does not enhance significantly when three or more sticks are employed, and the liquid viscosity has minor influences on the mixing rate. These results give useful qualitative suggestions on controlling the mixing rate during chemical reactions.     

Experimental and numerical study of mixing behavior inside droplets in microchannels

For the practical applications of droplet‐based microfluidics, we have paid special attention to the complex hydrodynamics and mixing performance inside microdroplets and the profound process intensification when forcing the droplets to move in winding channels. In this work, experimental studies using micro laser induced fluorescence (μ‐LIF) technique and three‐dimensional simulation based on a multiphase, multicomponents lattice Boltzmann model approach were adopted. The simulation results clearly revealed that the mixing inside the droplet is due to the convection in symmetric vortices in the two hemispheres of the droplet and the diffusion between them. They also showed the fluids inside the droplet could be reoriented due to the winding effect. Three designs of winding channels were studied, where interesting results showed the similar effect of process intensification by breaking up the flow symmetry. The revealed flow mechanism and the mixing performance inside the droplet in droplet‐based microfluidics should be helpful for microdevice design and optimization. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1801–1813, 2013     

环流反应器的流动、混合与传递特性

由于环流反应器内存在定向循环,与鼓泡塔反应器相比,其混合性能大幅提升,已广泛应用于许多工业过程,如发酵、反应器结晶等工业过程,近年来成为国内外学者研究的热点。针对环流反应器内操作条件下的流动形态、流体力学（包括相含率分布、循环液速、混合时间以及离集指数等）及传质/传热特性,总结了其最新研究进展,分析了相含率尤其是固含率变化对反应器中关键参数如循环液速和化学反应速率的影响,展望了从机理上研究相互耦合的多相流动、传质/传热和化学反应规律,为进一步推动其工业应用提供参考。     

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     

一种计算搅拌槽混合时间的新方法

基于对混合时间定义的思考,提出了一种新的定义方法,在湍流流场数值计算的基础上通过求解示踪剂的浓度输运方程,研究了单层涡轮桨搅拌槽内的混合过程。结果表明：搅拌转速和搅拌桨安装位置都影响混合时间的大小,而进料位置对混合时间的影响不大。对于不同的搅拌转速而言,随搅拌转速的增大,相同体积分数对应的混合时间逐渐减小。当搅拌桨安装在槽中间位置时所对应的混合时间最小。利用适宜的尺寸和安装位置的导流筒可有效降低混合时间。     

RGB颜色模型应用于评价顶吹混匀时间的方法

针对评价顶吹宏观混匀时间的方法进行了气体顶吹搅拌水动力学实验研究,利用基于混合过程中示踪粒子的分布随时间演化规律的RGB颜色模型来确定搅拌容器内的宏观混匀时间。通过定义像素阈值分离每一像素,构建混匀像素比M值作为确定混匀时间的指标,观察M值的变化规律,利用3σ方法确定混匀时间。针对喷枪插入深度及流量,用量纲为1强度单位表述为0.5和1的实验工况一,当阈值分数X=90%时,测定混匀时间为13.30s。分析结果发现,RGB颜色模型能够基于混合过程中示踪粒子的分布情况确定混匀时间,且与贝蒂数法和电导率法测定的混匀时间偏差不超过10%。为解决在视觉上评价多相流混合效果等工程问题提供了一种新的思路,为提高ISA炉使用寿命、强化ISA炉冶炼生产以及优化ISA炉工艺过程提供了一定的实验依据。     

Approximate mapping method for prediction of chaotic mixing in spatial-periodic microchannel

The use of approximate Poincaré maps for prediction of chaotic mixing in spatial-periodic channel is investigated in this article. The maps are constructed based on the corresponding distribution of discrete tracers on two successive Poincaré sections. Three methods are analysed including the triangular weighted interpolation, Shepard's method and weighted-least-square polynomial fitting (WLS-PF). Their application to a three-dimensional (3D) chaotic micromixer is demonstrated. Relevant results show that all the schemes can provide reliable predictions of the mixing quality within a limited number of mixer units. Among the three, the WLS-PF is less influenced by the grid-sizes. The mapping approach provides an alternative way to examine the performance of the spatial-periodic chaotic micromixer. It will greatly reduce the enormous efforts involved in 3D computational fluid dynamics (CFD) analysis.     

A numerical study of mixing in a microchannel with circular mixing chambers

The mixing of fluids in a microchannel is numerically investigated using three-dimensional Navier–Stokes equations. The microchannel has circular mixing chambers that are designed to create a self-circulating flow that operates at low Reynolds numbers. The investigations have been performed on a design that comprises of four circular mixing chambers that are joined together with constriction channels. The study has been carried out in two parts. Firstly, the mixing and the flow field are analyzed for a wide range (1–250) of the Reynolds number. Secondly, the effects of two design parameters, namely, the ratio, w/d, of the width of the constriction channel to the diameter of the circular chamber, and the angle, θ, between the outer walls of the chamber and the connection channel, on the mixing and the flow field have been evaluated. The mixing has been evaluated using a parameter, called mixing index, which is based on the variance of the mass fraction. The mixing index at the end of the device increases rapidly with the Reynolds number. The presence of a flow recirculation zone in the circular chamber is found to be effective in enhancing mixing, especially for larger Reynolds numbers. The mixing performance improves with an increase in θ, and with a decrease in w/d. The characteristics of the pressure drop have also been investigated as a function of the Reynolds number and geometric parameters. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Single and two-phase flows in a horizontal pipe with a Kenics static mixer: Effect of pressure drop on mixing

Single and two-phase flows pressure drops through a Kenics static mixer were investigated, for liquid and gas Reynolds numbers ranging from 8110 < Re_L < 18 940 to 1730 < Re_G < 8680, respectively. New friction factor correlations were established for single and two-phase flows, showing better agreement than those available in the literature. Dissipated energy and characteristic time constants were estimated from experimental data. For instance, a dissipated energy with a maximum value of 510 W/kg was calculated in two-phase flow with the drift-flux model. The dispersed phase reduced the characteristic mixing times and its influence was more important than the continuous phase for all the characteristic mixing time investigated. Furthermore, the macroscopic characteristic mixing time was shown to be the governing mixing process for almost all gas and liquid flow rates explored.     

Estimation of mixing volumes in buoyant miscible displacement flows along near‐horizontal pipes

We present a methodological framework for estimating the degree of mixing between successive miscible fluids pumped along a near‐horizontal pipe. Either or both of the fluids can be non‐Newtonian, of Herschel–Bulkley type. Overall it is considered that the objective is to minimise mixing. In laminar regimes our estimates are based on front velocity of the leading displacement front. In turbulent regimes the spreading mechanism is dispersion. In addition to the estimates of mixing volumes/lengths, we also predict a minimal flow rate necessary in order to achieve a successful displacement of the residual fluid. © 2013 Canadian Society for Chemical Engineering     

Analysis of the advection–diffusion mixing by the mapping method formalism in 3D open‐flow devices

This article extends the analysis of laminar mixing driven by a chaotic flow in the presence of diffusion to three‐dimensional open‐flow devices by means of the mapping‐matrix method. The extended formulation of the mapping matrix recently proposed by Gorodetskyi et al. (2012) allows inclusion of the molecular diffusion in the mixing process. This provides an efficient numerical tool for understanding the interplay between a chaotic advective field and diffusion, especially for high Péclet numbers. As a prototypical open‐flow device we consider the partitioned‐pipe mixer. Results deriving from the application of the extended mapping method are compared with Galerkin simulations, and a close agreement is found. Short‐term properties in the evolution of the concentration and the effect of axial diffusion are also addressed. © 2013 American Institute of Chemical Engineers AIChE J, 60: 387–407, 2014