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.     

ON AVERAGED DIFFUSION EQUATIONS

Methods of obtaining averaged diffusion equations are considered in case of non-uniform profile of the velocity in a channel. With the flow of Couette as an example, the comparison of exact and approximate solutions (obtained by means of perturbation method) has been carried out. The peculiarities of function of residence time distribution of liquid in the flows with non-uniform velocity field are noted. It is shown that the distribution function moments values including the zero and first moments values would depend on the degree of the velocity profile irregularity, on efficiency of radial mixing in a system as well as on the averaging method. The averaged diffusion equations which have been found by means of perturbation method are the most general of proposed ones at present in the appropriate literature. The Taylor's model and Goldstein's hyperbolic equations are included in said averaged equations as particular cases. The table of the numerical values of first three moments of RTD-function necessary for determining of the model parameters is given. The problems of application of the obtained averaged equation for calculating real chemical apparatuses, e.g. reactors, are discussed.     

Improving the dynamic performance of continuous-flow mixing of pseudoplastic fluids possessing yield stress using Maxblend impeller

The strategic approach of this article is to characterize the continuous-flow mixing of pseudoplastic fluids possessing yield stress in a stirred reactor with the Maxblend impeller. Dynamic experiments were carried out through the frequency-modulated random binary input of a brine solution to determine the extent of non-ideal flows. Mixing quality was determined on the basis of the extent of channeling and fully mixed volume. The effects of important parameters such as impeller speed (25–500 rpm), absence of baffles, fluid rheology (0.5–1.5%), fluid flow rate (3.20–14.17 L min⁻¹), and the locations of inlet/outlet on the dynamic performance of the continuous-flow mixing vessel were explored. The performance of the Maxblend impeller was then compared to the performances of various types of impellers such as close-clearance (an anchor), axial-flow (a Lightnin A320), and radial-flow (a Scaba 6SRGT) impellers. It was found when the channeling approached zero and the fully mixed volume approached the total fluid volume in the vessel, the power drawn by the A320 impeller and the Scaba impeller were about 2.9 and 4.3 times greater than that of the Maxblend impeller. Thus, the Maxblend impeller was able to drastically improve the performance of continuous-flow mixing with huge power savings. The mixing quality was further improved by optimizing the impeller speed, decreasing the fluid flow rate, decreasing the fluid concentration, and using bottom inlet- top outlet configuration. The flow non-ideality of the mixing system increased in the absence of the baffles. Thus, better mixing quality and more energy savings can be achieved by employing the findings of this study.     

Turbulent mixing and residence time distribution in novel multifunctional heat exchangers–reactors

Multifunctional heat exchanger–reactors show significant promise in increasing the energy efficiency of industrial chemical processes. The performance of these systems is conditioned by flow properties and is strongly geometry dependent. Here CFD simulation and laser Doppler anemometry (LDA) measurements are used to investigate the redistributing effects of the longitudinal vorticity generated by rows of inclined trapezoidal tabs on turbulent mixing in static mixers. Studies are carried out on three different configurations: in the first, the tabs are aligned and inclined in the direction of flow (the reference geometry for a high-efficiency vortex (HEV) static mixer), in the second, a periodic 45° tangential rotation is applied to the tab arrays with respect to one another, and in the third the reference geometry is used in the direction opposite to the flow direction (reversed direction). The mixing efficiency, taken as the resultant of the momentum-transfer efficiency of the “mean” flow at different scales, is studied. Macro-mixing entails the dispersive capacity of the flow at the heat exchanger–reactor scale, and is generally measured by the residence time distribution (RTD). At the intermediate scale, meso-mixing is governed by the turbulent fluctuations; this process of turbulent mixing can be characterized by the turbulence kinetic energy (TKE). Micro-mixing is characterized by the local rate of turbulence energy dissipation and is related to the progress of fast chemical reactions and selectivity. It is shown here that the reversed-array arrangement (the third configuration) provides the best performance in micro- (50%) and meso-mixing (25%), but exhibits an approximately 40% increase in power consumption over the classical HEV (reference) geometry and somewhat pronounced bimodal behavior in the RTD.     

Perturbed turbulent stirred tank flows with amplitude and mode-shape variations

Stirred tank (STR) flows at low and moderate Reynolds numbers show poor mixing behavior due to formation of segregated zones inside which both magnitude and fluctuation level of velocity components show lower values compared to the active fluid regime (i.e., impeller jet stream, circulation loops). Active perturbation of the STR flow using a time-dependent impeller rotational speed can potentially enhance mixing by breaking up these segregated unmixed zones and enhancing the turbulence level throughout the tank volume. In the present study, the effect of different perturbation cycles on an unbaffled turbulent stirred tank flow at a moderate Reynolds number (rotational speed N=3 rps) is studied using a large-eddy simulation (LES) technique coupled with immersed boundary method (IBM). The perturbation frequency (f) is chosen to correspond to a dominant macro-instability in the flow (f/N=0.022). Two different perturbation amplitudes (20% and 66%) and two perturbation shapes (square-wave and sine-wave) are investigated, and changes in the mean flow field, turbulence level and impeller jet spreading are examined. Large-scale periodic velocity fluctuations due to perturbations are noticed to produce large strain rates favoring higher turbulence levels inside the tank. Production of turbulent kinetic energy due to both the mean and periodic component of the velocity field is presented. Fluctuations in power consumption due to perturbation are also calculated, and shown to correlate with the perturbation amplitude.     

Study on the flow characteristics and mixing performance of multi-blade combined agitator

Developing an agitator suitable for wide viscosity range is of great significance to the energy saving and efficiency improvement by the intensification of fluid flow and mixing process. The power characteristics, flow field distribution, turbulence characteristics and mixing performance of multi-blade combined (MBC) agitator under laminar to turbulent flow state were studied experimentally and numerically at the level of large eddy simulation. The predicted power curve is consistent with the experimental results. Tangential flow is the main flow in laminar flow. With the increase of Reynolds number (Re), axial and radial flows in the vessel gradually increase. When Re reaches 486, the velocity field distribution is basically the same as that in the turbulent flow. At the same energy consumption level, MBC agitator is superior to the commercial Maxblend agitator in mixing high viscosity fluid. The intensification of axial and radial flows is due to the dispersed arrangement of the blades, enabling the MBC agitator to achieve larger axial and radial flows from the transitional flow to the turbulence state. Moreover, the turbulent kinetic energy is evenly distributed and the mixing process is significantly accelerated.     

多叶片组合式搅拌桨釜内流动特性和混合性能研究

开发可适用于较宽黏度范围的搅拌桨,强化釜内的流体流动和混合过程对于搅拌釜的节能增效具有重要的意义。实验与数值模拟相结合,在大涡模拟层面研究了多叶片组合式搅拌桨（MBC桨）从层流到湍流状态下,釜内的功率特性、流场分布、湍流特性和混合性能。结果表明：预测的功率曲线与实验结果一致;层流状态下釜内以切向流动为主,随着Reynolds数（Re）的增大,釜内轴向和径向流动逐渐增强,当Re达到486时,速度场分布与湍流状态下基本一致;在相同的能耗水平下,MBC桨对高黏度流体的混合性能优于商业Maxblend桨。桨叶的分散组合布置,强化了釜内的轴向和径向流动,使得MBC搅拌桨在从过渡流到湍流状态下均可实现较大的轴径向流动,湍动能分布较为均匀,混合过程显著加快。     

Mixing induced by buoyancy‐driven flows in porous media

A theoretical model for fluid mixing in steady and transient buoyancy‐driven flows induced by laminar natural convection in porous layers is presented. This problem follows a highly nonlinear dynamics and its accurate modeling poses numerical challenges. Based on the Taylor dispersion theory, a one‐dimensional analytical model is developed for steady and transient velocity fields. To investigate steady‐state mixing, a unicellular steady velocity field is established by maintaining a thermal gradient across a porous layer of finite thickness. A passive tracer is then introduced into the flow field and the mixing process is studied. In the case of transient flows, as the convective flow grows and decays with time the behavior of the dispersion coefficient is characterized by a four‐parameter Weibull function. The simple analytical model developed here can recover scaling relations that have been reported in the literature to characterize the mixing process in steady and transient buoyancy‐driven flows. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1378–1389, 2013     

Numerical characterisation of folding flow microchannel mixers

Micromixers have been considered in numerous recent studies with the aim of mixing different liquid streams for the common circumstance of non-inertial flow, i.e., in the Stokes flow regime. Under such conditions, the diffusion of momentum is dominant but the diffusion of species remains weak because the Schmidt number of liquids is large. Most mixers that have potential for application in the Stokes regime make use of a folding flow pattern that approximates the baker's transformation. In the work presented here, the general scaling of mixers of this type is developed from the exact equation for species transport and computations are made for a specimen mixer geometry to test the effectiveness of the resulting scaling. The scaling relation developed is found to give an excellent representation of the actual mixing characteristics of the specimen mixer over the entire range of Péclet number of practical interest. Finite volume computations are employed to solve the governing equations up to around Pe=10³. At higher Péclet numbers, where finite volume numerical solution becomes inaccurate with affordable mesh sizes, the species equation is solved using a Monte Carlo method instead. Finally, the scaling relation is used to develop the design relations needed to determine the number of mixing elements, the pressure drop incurred and the Péclet number of operation to achieve a given mixture uniformity within a specified mixing time.     

SURFACE TENSION-DRIVEN CONVECTION IN A CYLINDRICAL GEOMETRY

Three aspects of surface tension-driven natural convection in a bounded cylindrical geometry are investigated. First, the linear stability of the steady subcritical and supercritical convective solutions near the critical point is examined using a perturbation analysis and the theory of differential operators. Second, the effect of small surface tension gradients on free surface flows in deep fluid layers is studied. It is shown that surface tension effects produce subcritical convective solutions for this buoyancy-dominated flow. Finally, solutions are obtained for finite amplitude surface tension-driven flows in a cylindrical container.     

SURFACE TENSION-DRIVEN CONVECTION IN A CYLINDRICAL GEOMETRY

Three aspects of surface tension-driven natural convection in a bounded cylindrical geometry are investigated. First, the linear stability of the steady subcritical and supercritical convective solutions near the critical point is examined using a perturbation analysis and the theory of differential operators. Second, the effect of small surface tension gradients on free surface flows in deep fluid layers is studied. It is shown that surface tension effects produce subcritical convective solutions for this buoyancy-dominated flow. Finally, solutions are obtained for finite amplitude surface tension-driven flows in a cylindrical container.     

Comparative efficiency of shear,elongation and turbulent droplet breakup mechanisms: Review and application

The study of phase dispersion of two immiscible fluids in different flows requires identifying the relevant breakup mechanisms. We propose here a detailed investigation of droplet breakup in a multifunctional exchanger-reactor of the vortex generator type in which transfer intensification is due to longitudinal vortical structures. We compare the efficiency of the mean gradients and turbulent mechanisms in droplet breakup in this industrial reactor. This efficiency is essentially characterized by the resulting distribution of droplet diameters. Then, the roles of the mean flow and the turbulent field, intensity, energy spectrum, and turbulence scales are examined in relation to the liquid/liquid dispersion in order to explore the governing mechanisms of drop breakup. In the complex flow considered here – nonhomogeneous and anisotropic turbulence at moderate Reynolds numbers (<15,000) – with weak turbulence intensity (about 10%), it can be demonstrated that turbulent breakup mechanisms largely dominate mean flow effects; elongation and shear effects are shown to have minor effects on the breakup mechanisms. Moreover, the global characteristic scales of the flow are not the relevant parameters in predicting the final size of the emulsion, but instead the Kolmogorov microscale, implying that the residence time in the reactor is not a limiting factor. Hence, the local dissipation rate governs the performance of the actual multifunctional reactor. This study provides some insight in the design and scaling-up of multiphase reactors.     

振动强化锥面磨盘拉伸流动及混合性能模拟

基于拉伸流动原理设计的锥面磨盘可改变流道内熔体流动类型,增大拉伸流场作用。而叠加适当振动参数的振动力场可以进一步增强锥面磨盘流场的拉伸作用、提高拉伸速率,减小分离尺度并使其变化趋稳、增大混合指数并提高混合效率,从而使混合物料粒径减小、粒度均匀,获得良好的混合分散效果,为混合加工设备设计及聚合物混合性能的提高提供了新的参考依据。     

The mixing criterion in crystallization by cooling

In processes where mass flows have to be mixed, and the formation of new phases has to be prevented, it is essential for the composition and enthalpy (J/kg) to be so adjusted to each other that, whatever the mixing ratio, the ultimate mixture will consist of one single phase under physical equilibrium conditions (temperature and pressure).The requirements imposed on the composition and enthalpy will be called the mixing criterion.The mixing criterion plays an important role in technical crystallization processes involving mixing — frequently under adiabatic conditions — of liquid flows differing in temperature and/or concentration.For a binary system and a ternary one, both containing one component that can be crystallized, the authors determined the conditions under which supersaturation and its consequences (scaling and undesired nucleation) can be avoided during adiabatic mixing of the feed and the mother liquor in a draft-tube baffled (D.T.B.)-crystallizer.The correctness of the theory is confirmed by the results of runs conducted with a ternary system in a 100 l. experimental crystallizer; compliance with the mixing criterion proved to prevent scaling, and to increase the average crystal size by a factor of 3·5.     

A Dynamical Systems Approach to Mixing in Circulating Flows

Circulating flows are found in a variety of mixing equipment such as stirred tanks and airlift loop vessels. This paper presents a different route towards modeling the mixing in circulating flows. This route is based on an innovative use of Poincaré maps and suspended flows, concepts which are found in dynamical systems theory. The mixing model is developed for an arbitrary recirculating flow and uses a circulation time distribution function that is incorporated into the transport equations for an inert tracer injected into the flow system. Two cases are used to study the application of the mixing model in this work. The first case addresses the question of whether the mixing model can be used to study airlift vessels differing in scale and the second case highlights the application of the model to a standard stirred tank. In the first case, model predictions have been compared with experimental data obtained from two geometrically similar airlift systems of different volumes and good agreement is observed. A single parameter correlation for the mixing time is also proposed. In the second case, computational fluid dynamics was used to obtain the flow field of a standard stirred tank fitted with a six bladed Rushton turbine. From the flow field, the distribution of the circulation times is extracted and used to determine the tracer concentration profile in the stirred tank. Good agreement between the model predictions and published experimental data is observed thus indicating that the mixing model shows promise as a technique for studying the mixing in stirred tanks.     

Investigation of alternating-flow mixing in microchannels

A number of different approaches to mixing liquids in microscale systems can be found in the literature. In the case of miscible liquids it is desirable to produce mixtures with residual non-uniformity in composition that is below some specified level. Yet very little quantitative information is available concerning the conditions required to produce a given level of mixture uniformity. A theoretical approach to this problem is described. Computational fluid dynamics and simple scaling are used to develop a quantitative understanding of the alternating flow method of mixing using pressure driven flow. In this approach, external flow control is used to produce alternating injection into a single microchannel of two or more solutions to be mixed. The resulting streamwise slugs of solution then mix by the stretching of the slugs into thin striations resulting from shear strain. The most challenging condition for mixing is where the Reynolds number is approaching zero and inertia effects are negligible, a common situation in microchannel flows, particularly where relatively high-viscosity liquids, for example ionic liquids, are involved. The scaling theory demonstrates that an initial time period of rapid mixing of fluid outside the core of the flow, scaling as Pe^-2/3, is followed by a far slower process of mixing in the core region, scaling as Pe^-1/2. An approximate correlation for the deviation from the perfectly mixed state as a function of time is found. This correlation applies over the range of Peclet number, slug length and solution mixture ratio that are of interest. The mixture uniformity produced is shown to be limited by the initial uniformity of each solution over the channel section resulting from the injection process.     

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。     

Chaotic mixing in a single‐screw extruder with a moving internal baffle

A geometry in which the mixing of a single‐screw extruder was enhanced by a reciprocating baffle is proposed in this article. The effect of the baffle's amplitude on the mixing kinematics of the screw channel was investigated. A model with the baffle lower than the screw channel and the corresponding mathematical model were developed. The periodic flow and mixing performance of Newtonian fluid in such an extruder were numerically simulated. The finite volume method was used, and the flow domain was meshed by staggered grids with the periodic boundary conditions of the barrier motion being imposed by the mesh supposition technique. Fluid particle tracking was performed by a fourth‐order Runge–Kutta scheme. Distributive mixing was visualized by the evolution of passive tracers initially located at different positions. The growth of the interface stretch of tracers with time and the cumulative residence time distribution were also obtained. Poincaré sections were applied to reveal the geometrical scale of chaotic mixing patterns and the regions with embedded regular laminar flows. For comparison, the mixing performance in a conventional single extruder with fixed baffle was also investigated. POLYM. ENG. SCI., 54:198–207, 2014. © 2013 Society of Plastics Engineers     

Mixing studies of non-Newtonian fluids in an anchor agitated vessel

The success of any mixing operation involving liquid–liquid, gas–liquid and gas–liquid–solid systems depends mainly on the geometry of the vessel and impeller, operating conditions and properties of the system. Transformation of laboratory results to commercial scale unit is very difficult due to the complexity of flow phenomena and the scale up is being done by adopting a conservative approach which is based on the geometric, kinematic and dynamic similarities. This approach does not take into account the non-ideal flow behavior of the fluid and the design of commercial unit will be more rational if this information is included in the design of the unit.     

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.