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.

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.

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.

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.

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.

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.

A Novel Criterion of Mixing Time in Gas-Stirred Ladle Systems

A novel criterion of mixing time in gas-stirred ladle systems was proposed in this paper. The essential difference between the previous criterion and the present one is that the former is based on the concentration itself while the latter is based on the variation rate of the concentration, which reflects the mixing efficiency directly. Experiment was carried out in an acrylic glass vessel with bottom blowing, and the tracer concentration was monitored by electrical conductivity probes. The mixing time obtained through the new criterion is approximately 20% less than that obtained through the 95% criterion, and the deviations of mixing times calculated from the new criterion are smaller than that from the previous one under the same conditions.

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.

Impingement and mixing dynamics of micro-droplets on a solid surface

The hydrodynamics and mixing during the nonaxisymmetry impingement of a micro-droplet and a sessile droplet of the same fluid are investigated by many-body dissipative particle dynamics(MDPD) simulation.In this work,the range of the impingement angle(θ_(i)) between the impinging droplet and the sessile droplet is 0°-60° and the contact angle is set as 45° or 124°.The droplets impingement and mixing behavior is analyzed based on the droplet internal flow field,the concentration distribution and the time scale of the decay of the kinetic energy of the impinging droplet.The dimensionless total mixing time(τ_(m)) is calculated by a modified mixing function.With the Weber number(We) ranging from 5.65 to22.7 and the Ohnesorge number(Oh) ranging from 0.136 to 0.214,we find rm hardly changes with We and Oh.Whereas,θ_(i)and surface wettability are found to have a significant effect on τ_(m).We find that θ_(i)has no clear effect on τ_(m)on a hydrophobic surface,while on the hydrophilic surface,τ_(m)increase with the θ_(i).Thus,reducing the impinging angle is a valid method to shorten the τ_(m).

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.

H_-/H_∞ fault detection filter design for interval time-varying delays switched systems

The problem of the robust fault detection filter design for time-varying delays switched systems is considered in the framework of mixed H-/H∞. Firstly, the weighted H∞ performance index is utilized as the robustness performance, and the H- index is used as the sensitivity performance for obtaining the robust fault detection filter. Then a novel multiple Lyapunov-Krasovskii function is proposed for deriving sufficient existence conditions of the robust fault detection filter based on the average dwell time technique. By introducing slack matrix variable, the coupling between the Lyapunov matrix and system matrix is removed, and the conservatism of results is reduced. Based on the robust fault detection filter, residual is generated and evaluated for detecting faults. In addition, the results of this paper are dependent on time delays,and represented in the form of linear matrix inequalities. Finally,the simulation example verifies the effectiveness of the proposed method.

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.

Effect of gas blowing nozzle angle on multiphase flow and mass transfer during RH refining process

A three-dimensional mathematical model was developed to investigate the effect of gas blowing nozzle angles on multiphase flow,circulation flow rate,and mixing time during Ruhrstahl-Heraeus(RH) refining process.Also,a water model with a geometric scale of 1:4 from an industrial RH furnace of 260 t was built up,and measurements were carried out to validate the mathematical model.The results show that,with a conventional gas blowing nozzle and the total gas flow rate of 40 L·min^(-1),the mixing time predicted by the mathematical model agrees well with the measured values.The deviations between the model predictions and the measured values are in the range of about 1.3%–7.3% at the selected three monitoring locations,where the mixing time was defined as the required time when the dimensionless concentration is within 3% deviation from the bath averaged value.In addition,the circulation flow rate was 9 kg·s^(-1).When the gas blowing nozzle was horizontally rotated by either 30° or 45°,the circulation flow rate was found to be increased by about 15% compared to a conventional nozzle,due to the rotational flow formed in the up-snorkel.Furthermore,the mixing time at the monitoring point 1,2,and 3 was shortened by around 21.3%,28.2%,and 12.3%,respectively.With the nozzle angle of 30° and 45°,the averaged residence time of 128 bubbles in liquid was increased by around 33.3%.

Water modeling on fluid flow and mixing phenomena in a BOF steelmaking converter

A 1∶8 physical water model was constructed to investigate the fluid flow and mixing phenomena in the basic oxygen furnace(BOF)converter.The particle image velocimetry was employed to measure the velocity distribution of the bath and the high-speed camera was applied to capture the cavity shape in the combined blowing BOF converter.The mixing time for varied operating conditions was measured by the stimulus-response approach.The cavity depth increased with the decrease in the lance height and the increase in the top gas flow rate while the bottom blowing gas had little influence on the cavity depth.The minimum cavity depth was obtained under the condition of a 69.8 m^(3)/h top gas flow rate,a 287.5 mm lance height and a 0.93 m^(3)/h bottom blowing gas flow rate,which was 161.2 mm.The mixing time decreased as the lance height decreased and the top blowing gas flow rate increased.The mixing time was first decreased and then increased with the increase in the bottom gas flow rate.With the condition of 69.8 m^(3)/h gas flow rate of top blowing,the 287.5 mm lance height and the 0.93 m^(3)/h gas flow rate of bottom blowing,the mixing time in the converter was 48.65 s.The empirical formula between the stirring power and the mixing time in the converter was calculated.

Characterization on the hydrodynamics of a covering-plate Rushton impeller

A modified Rushton impeller with two circular covering-plates mounted on the upper and lower sides of the blades was designed.There are gaps between the plates and the blades.The turbulent hydrodynamics was analyzed by the computational fluid dynamics(CFD) method.Firstly,the reliability of the numerical model and simulation method was verified by comparing with the experimental results from literature.Subsequently,the power consumption,flow pattern,mean velocity and mixing time of the covering-plate Rushton impeller(RT-C) were studied and compared with the standard Rushton impeller(RT) operated under the same conditions.Results show that the power consumption can be decreased about 18%.Compared with the almost unchanged flow field in the lower stirred tank,the mean velocity was increased at the upper half of the stirred tank.And in the impeller region,the mean axial and radial velocities were increased,the mean tangential velocity was decreased.In addition,the average mixing time of RT-C was shortened about 4.14% than the counterpart of RT.The conclusions obtained here indicated that RT-C has a more effective mixing performance and it can be used as an alternative of RT in the process industries.

Flow field research on bottom argon blowing in a 40 ton ladle

In order to improve argon blowing efficiency in a 40 ton ladle, numerical simulation and water simulation experiments of the bottom argon flow were performed. Relationships among the ladle mixing time, slag eye area, different blowing flow rates, and different blowing positions （0,0.56R, 0. 62R, 0. 67R） are discussed. Results showed that the ladle mixing time decreased when the argon blowing brick distance （from bottom center of the ladle） increased, and decreased significantly when the blowing flow increased from 70 to 130 L/h. When the blowing flow increased and exceeded 130 L/h,the stirring effect tended to be stable, and there was little effect on the ladle mixing time. The slag eye area increased as the argon brick distance increased, and was larger when the argon blow brick was near the ladle wall. Wall shear stress significantly increased as the brick distance increased and was concentrated at the slag wall near the argon flow brick;this is called the most serious erosion wall. The average wall shear increased exponentially with increasing argon blowing brick distance.

Hydrodynamics and oxygen transfer in a novel extra-loop fluidized bed bioreactor

In this paper, the characteristics of fluid mixing time in a novel extra-loop fluidized bed were studied. The results showed that the mixing time was shortened with the increase of fluid velocity. All the discrete numbers of the reactor were above 0.2. The serial number n was 2.5 -3.0. It was judged accordingly that the reactor fluid state was continous stirred tank reactor （CSTR） mainly. When the inspiratory capacity increased the mixing time of the reactor was shortened. Thus the air input was beneficial for the fluid mixing. During the three phases mixing process, the mixing time of the reactor could be decreased by the n increase of carrier and air loading together, but the change was not significant. The parameters affecting the reactor fluid state were fluid velocity, inspiratory capacity and carrier. KLa could be increased with the air loading increase, and at the same gas/liquid ratio when the pressure drop was high, KL~ value was increased. The amount of carrier complex influence on KLa. As the carrier loading continued to increase, its value had been dropped but the changes was not significant, and optimization condition was found at above 800 1 000 g carrier loading （pouzzolane） or 600 g PVC. Under gas/liquid ratio of 0.8% -5.2%, KLa was （0.62-1.37）×10^-2· s^-1.