Effect of aspect ratio of elliptical stirred vessel on mixing time and flow field characteristics in the absence of baffles

Elliptical tanks were used as an alternative to circular tanks in order to improve mixing efficiency and reduce mixing time in unbaffled stirred tanks(USTs). Five different aspect ratios of elliptical vessels were designed to compare their mixing time and flow field. Computational fluid dynamics(CFD) simulations were performed using the k–ε model to calculate the mixing time and simulate turbulent flow field features, such as streamline shape, velocity distribution, vortex core region distribution, and turbulent kinetic energy(TKE) transfer. Visualization was also carried out to track the tinctorial evolution of the liquid phase. Results reveal that elliptical stirred tanks can significantly improve mixing performance in USTs. Specifically, the mixing time at an aspect ratio of 2.00 is only 45.3% of the one of a circular stirred tank. Furthermore, the secondary flow is strengthened and the vortex core region increases with the increase of aspect ratio. The axial velocity is more sensitive to the aspect ratio than the circumferential and radial velocity. Additionally, the TKE transfer in elliptical vessels is altered. These findings suggest that elliptical vessels offer a promising alternative to circular vessels for enhancing mixing performance in USTs.

A strategy for strengthening chaotic mixing of dual shaft eccentric mixers by changing non-Newtonian fluids kinetic energy distribution

Efficiently modulating the velocity distribution and flow pattern of non-Newtonian fluids is a critical challenge in the context of dual shaft eccentric mixers for process intensification,posing a significant barrier for the existing technologies.Accordingly,this work reports a convenient strategy that changes the kinetic energy to controllably regulate the flow patterns from radial flow to axial flow.Results showed that the desired velocity distribution and flow patterns could be effectively obtained by varying the number and structure of baffles to change kinetic energy,and a more uniform velocity distribution,which could not be reached normally in standard baffle dual shaft mixers,was easily obtained.Furthermore,a comparative analysis of velocity and shear rate distributions is employed to elucidate the mechanism behind the generation of flow patterns in various dual-shaft eccentric mixers.Importantly,there is little difference in the power number of the laminar flow at the same Reynolds number,meaning that the baffle type has no effect on the power consumption,while the power number of both unbaffle and U-shaped baffle mixing systems decreases compared with the standard baffle mixing system in the transition flow.Finally,at the same rotational condition,the dimensionless mixing time of the U-shaped baffle mixing system is 15.3%and 7.9%shorter than that of the standard baffle and the unbaffle mixing system,respectively,which shows the advantage of the U-shaped baffle in stirring rate.

Flow pattern visualization and nonlinear analysis of gas-liquid mixing process with top-blowing gas stirring

The evaluation of the mixing effect of gas-liquid two-phase flow during the top-blown gas agitation mixing is one of the difficulties in the testing field, especially in the process of using the model method to study the metallurgical top-blowing process. In order to evaluate the effect of gas-liquid two-phase flow mixing, a gas chromatography simulation based on capacitance tomography was used to visualize the flow pattern and analyze the mixed characteristics. A gas top-blown agitation test rig was set up, the gas phase was air-selected, and the liquid phase was selected from synthetic heat-conducting oil. The top-blown stirring test process was measured and imaged by electrical capacitance tomography (ECT) equipment from ECT Instruments Ltd (UK). The MATLAB program was used to identify the mixing areas of the images to obtain the distribution of gas-liquid two-phase. The flow pattern of the gas-liquid mixing region was obtained. The chaotic detection of the gas-liquid mixing process was performed by the three-state test method;the images were processed by the counting box dimension-corrosion method to obtain the mixing uniformity time of gas-liquid flow. Results show that it is feasible to use the capacitance tomography technique to visualize the gas-liquid two-phase distribution. The uniformity time quantification of the gas-liquid mixing process is also achieved.

Large Eddy Simulations of Mixing Time in a Stirred Tank

Large eddy simulations (LES) of mixing process in a stirred tank of 0.476m diameter with a 3-narrow blade hydrofoil CBY impeller were reported. The turbulent flow field and mixing time were calculated using LES with Sma-gorinsky-Lilly subgrid scale model. The impeller rotation was modeled using the sliding mesh technique. Better agree-ment of power demand and mixing time was obtained between the experimental and the LES prediction than that by the traditional Reynolds-averaged Navier-Stokes (RANS) approach. The curve of tracer response predicted by LES was in good agreement with the experimental. The results show that LES is a reliable tool to investigate the unsteady and quasi-periodic behavior of the turbulent flow in stirred tanks.

Optimization of mixing time in a ladle with dual plugs

Based on the two-phase fluid （Eulerian-Eulerian） model, a mathematical model about the gas-liquid flow and mixing behavior was developed to investigate the effect of the offset of dual plugs, the included angle of dual plugs with a center point, and gas flow rate on the mixing time in a ladle with dual plugs. Numerical results indicate that two types of recirculation zones exist in the ladle. One is the middle recirculation between gas and liquid plumes, and the other is the sidewall recirculation between plumes and the ladle sidewall. The correction shows that the mixing time is in proportion to -0.2676 power of gas flow rate. There is a unique optimum offset of dual plugs with a particular included angle, in turn, a unique optimum included angle of dual plugs exits with a particular offset.

CFD Simulation of Local and Global Mixing Time in an Agitated Tank

The Issue of mixing efficiency in agitated tanks has drawn serious concern in many industrial processes. The turbulence model is very critical to predicting mixing process in agitated tanks. On the basis of computational fluid dynamics（CFD） software package Fluent 6.2, the mixing characteristics in a tank agitated by dual six-blade-Rushton-turbines（6-DT） are predicted using the detached eddy simulation（DES） method. A sliding mesh（SM） approach is adopted to solve the rotation of the impeller. The simulated flow patterns and liquid velocities in the agitated tank are verified by experimental data in the literature. The simulation results indicate that the DES method can obtain more flow details than Reynolds-averaged Navier-Stokes（RANS） model. Local and global mixing time in the agitated tank is predicted by solving a tracer concentration scalar transport equation. The simulated results show that feeding points have great influence on mixing process and mixing time. Mixing efficiency is the highest for the feeding point at location of midway of the two impellers. Two methods are used to determine global mixing time and get close result. Dimensionless global mixing time remains unchanged with increasing of impeller speed. Parallel, merging and diverging flow pattern form in the agitated tank, respectively, by changing the impeller spacing and clearance of lower impeller from the bottom of the tank. The global mixing time is the shortest for the merging flow, followed by diverging flow, and the longest for parallel flow. The research presents helpful references for design, optimization and scale-up of agitated tanks with multi-impeller.

Theoretical analysis of fluid mixing time in liquid-continuous impinging streams reactor

The mixing time of impact zone in liquid-continuous impinging streams reactor(LISR) is theoretically calculated by empirical model and modern micromixing model of the fluid mixing process, and the variation laws of macromixing time and micromixing time are quantitatively discussed. The results show that under a continuous and stable operating condition, as the paddle speed increases, the macromixing time and micromixing time calculated by the two models both decrease, even in a linkage equilibrium state. Simultaneously, as the paddle speed increases, the results figured by the two models tend to be consistent. It indicates that two models both are more suitable for calculation of mixing time in high paddle speed. Compared with the existing experimental results of this type of reactor, the mixing time computed in the speed of 1500 r/min is closer to it. These conclusions can provide an important reference for systematically studying the strengthening mechanism of LISR under continuous mixing conditions.

Flow zone distribution and mixing time in a Peirce-Smith copper converter

Peirce-Smith copper converting involves complex multiphase flow and mixing.In this work,the flow zone distribution and mixing time in a Peirce-Smith copper converter were investigated in a 1:5 scaled cold model.Flow field distribution,including dead,splashing,and strong-loop zones,were measured,and a dimensionless equation was established to determine the correlation of the effects of stirring and mixing energy with an error of<5%.Four positions in the bath,namely,injection,splashing,strong-loop,and dead zones,were selected to add a hollow salt powder tracer and measure the mixing time.Injecting a quartz flux through tuyeres or into the backflow point of the splashing wave through a chute was recommended instead of adding it through a crane hopper from the top of the furnace to improve the slag-making reaction.

3D numerical investigation of effects of density and surface tension on mixing time in bottom-blown gas-stirred ladles

In molten phase metallurgical processes,mixing via gas injection has a vital role in obtaining a homogeneous product.The efficiency of mixing depends on operational variables such as gas flow rate and slag height as well as physical properties of the molten phases.A numerical simulation is conducted to study the above parameters in the flow behavior of a bottom-blown bath.The molten metal and the slag are modeled by water and oil,respectively.The numerical results,particularly the mixing time,are validated against experimental data.The results show that mixing time increases as the slag height increases and decreases as the density of the slag material increases.The mixing time decreases with an increase in the density of the primary phase;however,it increases as the surface tension between air and water increases.A case with properties close to a real molten metal is also modeled.The performance of the system is influenced by the momentum rather than the dissipative forces.Thus,the effect of the density of the molten phase on the mixing process is more pronounced compared to the effect of the surface tension between the air and the molten phase.

Effect of Melt Mixing Time in Internal Mixer on Mechanical Properties and Crystallization Behavior of Glycidyl Methacrylate Grafted Poly (Lactic Acid)

Glycidyl methacrylate (GMA) was grafted onto poly (lactic acid) (PLA) by melt mixing in internal mixer using dicumyl peroxide (DCP) as an initiator. The results from proton nuclear magnetic resonance (1H-NMR) and Fourier transform infrared (FTIR) spectroscopy indicated that the grafting reaction of GMA onto PLA took place successfully. The impact strength of PLA-g-GMA was significantly higher than that of pure PLA. The crystallinity of PLA, obtained from differential scanning calorimetry (DSC), decreased after grafting. In order to obtain the optimal mixing conditions, the mixing time was varied into 7, 10 and 14 min. The optimum mixing time of 10 min was found to give the optimum mechanical properties of glycidyl methacrylate grafted poly (lactic acid) (PLA-g- GMA). However, the mixing time played no important role in impact behavior of PLA-g-GMA. In addition, the highest crystallinity was obtained with the PLA-g-GMA prepared with the mixing time of 7 min.

ERT Imaging of Gas-Liquid Mixing in Agitated Vessel

An investigation using Electrical Resistance Tomography （ERT） was carried out in order to characterize gas-liquid mixing in an agitated vessel. The experimental work was carried out in a 400 mm diameter agitated vessel that was fitted with four planes, 16 stainless steel electrodes. Agitation was carried out using the Lightnin Labmaster and Rushton turbine while conductivity data acquisition was carried out using the ITS P2000 ERT system. A Mathlab code was developed to construct a surface plot for gas hold-up from the ERT data. Various gas dispersion conditions such as flooded, loaded and fully dispersed were successfully characterized using the ERT technique.

THE MIXING OF GAS-LIQUID FLOW WITH VAPOR AND GAS-SOLID FLOW

In the industrial production, the mixing of gas-liquid flow with vapor and gas-solid flow is a very common problem. In the process of the mixing, solid particle-clusters will form, and will have steady radii when the effect of the gathering of particles is balanced withthat of the breaking of particle-clusters. Then, the population distribution function of size of particles per unit length per unit volume is introduced, and its governingequation is derived on the analogy of the molecular kinetic theory. Finally, when the gas flow is very slow, the expression of steady average radius of particle-clusters is obtained.

A Method in Mixed Frequency-time domain for Fatigue Life Estimation of Steel Girders of Cable-stayed Bridges Due to Buffeting

发展了斜拉桥钢主梁抖振疲劳寿命的混合时－频域方法．在本方法中，首先建立了桥面处的风速风向概率密度函数，导出的应力谱因其包括背景分量而不再是窄带谱．据应力谱模拟出了疲劳应力的时间历程，并用雨流计数法统计了其幅值特性．基于修正的Ｍｉｎｅｒ定理导出了考虑风速风向作用的桥梁主梁抖振疲劳寿命的估算公式，并用此分析了杨浦大桥钢主梁的抖振疲劳寿命．结果表明，风向对抖振疲劳寿命有很大影响；杨浦大桥主梁的疲劳寿命远大于设计寿命．

CFD simulation of flow and mixing characteristics in a stirred tank agitated by improved disc turbines

To reduce the power consumption and improve the mixing performance in stirred tanks,two improved disc turbines namely swept-back parabolic disc turbine(SPDT)and staggered fan-shaped parabolic disc turbine(SFPDT)are developed.After validation of computational fluid dynamics(CFD)model with experimental results,CFD simulations are carried out to study the flow pattern,mean velocity,power consumption,pumping capacity and mixing efficiency of the improved and traditional impellers in a dished-bottom tank under turbulent flow conditions,The results indicate that compared with the commonly used parabolic disc turbine(PDT),the power number of proposed SPDT and SFPDT impellers is reduced by 43%and 12%,and the pumping efficiency is increased by 68%and 13%,respectively.Furthermore,under the same power consumption(0-700 W·m^(-3)),the mixing performance of both SPDT and SFPDT is also superior to that of Rushton turbine and PDT.

CFD Simulation of Mixing in a Stirred Tank with Multiple Hydrofoil Impellers

The mixing process in a stirred tank of 0.476 m diameter with single, dual and triple 3-narrow blade hydrofoil CBY impellers was numerically simulated by using computational fluid dynamics (CFD) package FLU-ENT6.1. The multi-reference frame (MRF) and standard k-ε turbulent model were used in the simulation. The shaft power and the mixing time predicted by CFD were in good agreement with the experiment. The effects of tracer feeding and detecting positions on mixing time were investigated. The results are of importance to the optimum design of industrial stirred tank/reactors.

Mixed time discontinuous space-time finite element method for convection diffusion equations

A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.

Numerical Simulation of Macroscopic Mixing in a Rushton Impeller Stirred Tank

The macroscopic mixing in a stirred tank with different tracer injection locations, impeller speeds and impeller positions is simulated numerically by solving the transport equation of the tracer based on the whole flow field in the baffled tank with a Rushton disk turbine numerically resolved using the improved inner-outer iterative procedure. Predicted mixing time is compared well with the literature correlations. The predicted residence time distribution of the stirred tank is very close to the present experimental results. The effect of the installation of a draft tube on the mixing time and residence time distributions is addressed.

ANALYSIS AND IMPROVEMENT OF LEAD TIME FOR JOB SHOP UNDER MIXED PRODUCTION SYSTEM

Firstly an overview of the potential impact on work-in-process （WIP） and lead time is provided when transfer lot sizes are undifferentiated from processing lot sizes. Simple performance examples are compared to those from a shop with one-piece transfer lots. Next, a mathematical programming model for minimizing lead time in the mixed-model job shop is presented, in which one-piece transfer lots are used. Key factors affecting lead time are found by analyzing the sum of the longest setup time of individual items among the shared processes （SLST） and the longest processing time of individual items among processes （LPT）. And lead time can be minimized by cutting down the SLST and LPT. Reduction of the SLST is described as a traveling salesman problem （TSP）, and the minimum of the SLST is solved through job shop scheduling. Removing the bottleneck and leveling the production line optimize the LPT. If the number of items produced is small, the routings are relatively short, and items and facilities are changed infrequently, the optimal schedule will remain valid. Finally a brief example serves to illustrate the method.

A DISCRETE TIME TWO-LEVEL MIXED SERVICE PARALLEL POLLING MODEL

We present a discrete time single-server two-level mixed service polling systems with two queue types, one center queue and N normal queues. Two-level means the center queue will be successive served after each normal queue. In the first level, server visits between the center queue and the normal queue. In the second level, normal queues are polled by a cyclic order. Mixed service means the service discipline are exhaustive for center queue, and parallel 1-limited for normal queues. We propose an imbedded Markov chain framework to drive the closed-form expressions for the mean cycle time, mean queue length, and mean waiting time. Numerical examples demonstrate that theoretical and simulation results are identical the new system efficiently differentiates priorities.

Mixed sensitivity H_∞ control for LTI systems with varying time delays

Designing a robust controller for a system with timevarying delays poses a major challenge. In this paper, we propose a method based on mixed sensitivity H∞ for the control of linear time invariant（LTI） systems with varying time delays. The time delay is assumed bounded and the upper bound is known. In the technique we propose, the delay affecting the plant to be controlled is treated as an unmodeled uncertainty（in form of multiplicative uncertainty）. That uncertainty is approximated and then an H∞based controller, for the plant represented by the multiplicative uncertainty and the nominal model, is calculated. The obtained H∞controller is used to control the LTI systems with varying time delays. Simulation examples are given to illustrate the effectiveness of the proposed method.