Power consumption and flow field characteristics of a coaxial mixer with a double inner impeller☆

Baoqing Liu,Yikun Zhang,Mingqiang Chen,Peng Li,Zhijiang Jin*

College of Chemical and Biological Engineering,Zhejiang University,Hangzhou 310027,China

Keywords:Coaxial mixer Power consumption Flow field characteristics Numerical simulation

ABSTRACT A coaxial mixer meeting the actual demand of a system with high and variable viscosity is investigated.It has an outer wall-scraping frame and a double inner impeller consisting of a four-pitched-blade turbine and Rushton turbine.The power consumption and flow field characteristics of the coaxial mixer in laminar and transitional flow are simulated numerically,and then the distribution of velocity field,shear rate and mass flow rate are analyzed.The simulation results indicate that the outer frame has little effect on the power consumption of the double inner impeller whether in laminar or transitional flow,whereas the inner combined impeller has a great effect on the power consumption of the outer frame.Compared with the single rotation mode,the power consumption of the outer frame will decrease in co-rotation mode and increase in counter-rotation mode.The velocity,shear rate and mass flow rate are relatively high near the inner impeller in all operating modes,and only under double-shaft agitation will the mixing performance near the free surface be improved.In addition,these distributions in the co-rotation and counter-rotation modes show little difference,but the co-rotation mode is recommended for the advantage of low power consumption.

1.Introduction

Mixing is widely used in chemical,petrochemical,pharmaceutical,food,metallurgical,paper and sewage treatment industries.It plays a significant role in unit operations like homogenization,emulsification,fermentation,crystallization and polymerization[1].As the core part of a mixing vessel,the agitator directly determines the mixing effect and power consumption of the mixing system,thus influences the quality of the product and the production cost.Therefore,it is meaningful to develop a new-and high-efficiency agitator.

Most traditional agitators have only one type of impeller with the advantages of simple geometry,easy operation and mature design methods,which can meet the needs of most industrial processes.However,single shaft mixers are usually adaptable to limited and specific technological processes.Actual chemical processes are complex.Firstly,under actual conditions,phase transition,heat transfer and viscosity changes happen simultaneously in chemical reaction processes.For example,at the beginning of the process of producing high-purified formic acid and sodium tripolyphosphate through the polyphosphate acidification of sodium formate,viscosity of the material in the mixing tank is high,but it decreases as the process goes on with the flow property of the mixing system improved[2].For systems with high and variable viscosity,traditional single-shaft mixers are difficult to satisfy the need to agitation at different stages with changing viscosities.Secondly,single-shaft agitators can usually achieve a single function.Radial flow agitators are good at shearing and beneficial to the turbulent diffusion with the disadvantage of long mixing time and bad global mixing effect[3].Axial flow agitators can strengthen axial flow of materials with the circulation of the mixed system,but its shearing effect and local mixing effect are relatively poor[4,5].Thus,coaxial mixers are being developed to meet the different needs at different mixing stages of some industrial processes.

Coaxial mixers can satisfy the different mixing stages of systems with high viscosity.Because of its complex geometry and the space-time variable viscosity,there are quite few reports on its mixing performance[6].The earliest work was reported by Schneider and Todtenhaupt of EKATO Company[7].Afterwards,Canadian Tanguy's group did systematic researches on the performance of coaxial mixers,which were composed of an anchor agitator and Rushton turbine impeller or Sevin propeller or Deflo-Sevin impeller[8-11].Their studies were mainly focused on the influences of rotation modes and speed ratios on power consumption and mixing performance.Some researchers in China also researched on coaxial mixers in recent years[12-15].Earlier researches were mainly focused on coaxial mixers with only single inner impellers,but it is well known that coaxial mixers with composite inner impellers are more advantageous in those occasions with high and variable viscosity[16].This paper is about a coaxial mixer,which has an outer wall-scraping frame and a double inner impeller consisting of a four-pitched-blade turbine(abbreviated as PBT-4)and Rushton turbine(abbreviated as RT-6).

2.Experimental

The schematic of the mixing tank which contains a semicircle spiral jacket and 2 ellipsoidal heads is shown in Fig.1.The vessel diameter D is 1000 mm,the overall height H is 1500 mm,and the height of liquid hlis 1050 mm.The central coaxial mixer is composed of an inner high-speed impeller and an outer low-speed impeller.The inner impeller has 2 stirrers,whose upper part is PBT-4 and lower part is RT-6 as shown in Fig.1(b).The outer impeller is a frame paddle.Specific size is shown in Table 1.This coaxial mixer has two independent driving systems.The speed of the agitator can be adjusted by controlling the frequency of the driving system.Four operating modes,namely,single rotation of either inner or outer impeller,co-rotation and counter-rotation of two impellers,can be achieved.

Coaxial mixers are desirable in systems with high and variable viscosity,and the high-viscosity maltose syrup is selected as the experimental material.Maltose syrup with the concentration of 80%,purchased from Hangzhou Zixiang Co.,is colorless,tasteless and non-toxic.And it is a typical Newtonian fluid.The numerical simulation is performed at constant temperature of 28.1°C.Under such conditions,the viscosity of the material is 10.01 Pa·s and the density 1376.54 kg·m?3.

3.Computational

3.1.Finite element model

In order to get detailed information,the power consumption and flow characteristics were analyzed with the help of Fluent,a CFD numerical simulation tool.As the simulation is focused on the power consumption and flow characteristics of the fluid and does not involve heat transfer,the jacket and elliptical head are ignored when modeling.The entire flow region is divided into three regions:the inner impeller region,the outer impeller region and the other region.Considering the complex geometry of the coaxial mixer,the tetrahedral elements are selected to mesh each region and the size function is used to re fine the grid of the impeller region.Based on these conditions,the appropriate number of cells is determined as 1259914 through grid independence test.Specific meshing is shown in Fig.2.

The upper surface,assumed as always flat,of the material in the mixing tank is set as free surface,whose normal velocity is zero.Faces of the tank wall,shaft and impellers are all no-slippage wall boundaries.The speed of the shaft and the impellers are particularly specified.The inner impeller region and the outer impeller region belong to the moving region and the other region is static,so the momentum interactions among the three regions are transferred across the interfaces.The coordinate systems of the moving regions rotate at the same speed as that of the corresponding rotating shaft.

3.2.Numerical simulation method

A laminar flow model is chosen for calculation according to the operating conditions.As a result,controlling equations composed of the continuity equation and momentum equations are enclosed[17].

MRF which uses two reference frames for calculation is adopted in calculating the flow field.Impeller regions(moving region)use a reference frame rotating in the same speed as that of the corresponding impeller.Other regions(static regions)use a static reference frame to calculate the flow field.Coupling of pressure and speed is done by means of SIMPLE algorithm.The momentum equation is discretized with second order upwind scheme[18,19].

Fig.1.Structure of the coaxial mixer.1-jacket entrance;2-thermometer;3-jacket;4-tank body;5-electromotor of outer impeller;6-torque sensor of outer impeller;7-electromotor of inner impeller;8-torque sensor of inner impeller;9-agitator drive or gearbox;10-thermocouple;11-jacket exit;12-thermal resistance;13-frame paddle;14-PBT-4;and 15-RT-6.

Table 1 Main size parameters of coaxial mixer

4.Analysis and Discussion

4.1.Verification of numerical simulation

Fig.2.Mesh of coaxial mixer.

In order to test the reliability of the numerical simulation,it is necessary to compare the result of the numerical simulation with the experimental data.The experiment is conducted in a stainless agitator vessel,which has the same geometry as described in Section 2.The power consumption of the double inner impeller rotating alone in the experiment is compared with that from the simulation,both having the outer impeller present but stationary,and the detailed information is shown in Table 2.It can be seen that the average absolute relative error of power consumption in the simulation to that in the experiment is about 5%,and the error is larger when the inner impeller rotates alone at low speed.The reason is that the torque of the inner impeller rotating at low speed accounts for a small fraction of the range of the torque sensor(200 N·m),which leads to measurement errors.Meanwhile,the torque of the inner impeller equals to the difference between the load torque and the non-load torque,and the actual frictional resistance moment between the inner and the outer shafts under load condition is smaller than that under non-load condition because of the lubrication of the material.This is one of the reasons why the power number obtained from the experiment is always smaller than that obtained through the numerical simulation,as shown in Table 2.We can conclude that the reliable computational model and method used in the numerical simulation can meet the accuracy requirement and be used to predict the power consumption and flow characteristics of the coaxial mixer.

4.2.Power characteristics

As an important foundation of selecting the right driving system,the power consumption of the mixing process is closely related to themixing intensity and fluid flow conditions.Power number is an important parameter representing the mixing power:

Table 2 Comparison of power number under single rotation mode of inner impeller

which is in turn influenced by flow conditions,which is in general represented by the Reynolds number:

The power curves in Figs.3 and 4 show the relationship between the power number of inner impeller and the Reynolds number under different operating modes and speed ratios.The speed ratio,α,is the ratio of the inner impeller speed(Ni)to the outer impeller speed(No),that is α=Ni/No.

The power curve of the double inner impeller in Fig.3 shows the following:(1)With the same Reynolds number and different speed ratios,the power numbers are of little differences in the laminar flow,approximately equal to the power number of the inner impeller rotating alone.This means that rotation of the outer frame has little influence on power consumption of the inner impeller as the inner impeller speed and outer frame speed are both low in laminar flow,which makes tangential flow generated by the slower rotation of outer impeller has little effect on the inner impeller.(2)In the transitional flow(Re＞30),the outer frame speed becomes relatively high with the speed ratio decreasing,and the tangential flow generated by high-speed outer frame affects the inner impeller region,influencing its power consumption.As a consequence,the influence on power consumption becomes appreciable and increases with the speed ratio decreasing.The power consumption decreases due to the outer frame rotation under corotation mode and increases under counter-rotation mode.

The power curves of the outer impeller under different speed ratios in Fig.4 indicate that the inner impeller has significant influence on the power consumption of the outer impeller under both co-rotation and counter-rotation modes,and the influence increases with the speed ratio increasing.Comparing to single rotation of the outer impeller,the power number increases under counter-rotation mode and decreases under co-rotation mode.Because the tangential flow generated by the inner impeller exerts extra resistance on the outer frame under counter-rotation mode,the power consumption of the outer impeller is increased.On the contrary,the rotation of the inner impeller helps to drive the outer frame under co-rotation mode,leading to the decreasing power number of the outer impeller.

Fig.3.Power curve of inner impeller under different operating modes.

From the discussion above,the power consumption of the inner combined impeller under co-rotation or counter-rotation mode is almost the same as that under single rotation.So its power consumption can be estimated based on the existing power curve.Furthermore,considering the drive efficiency and the frictional resistance loss between inner and outer shafts,the driving system of the inner impeller can be chosen or designed.The power consumption of the outer impeller under counter-rotation mode is larger than that under single rotation mode,which can be seen from Table 3.In Table 3,ΔNp/Np0means the percentage of power number increases under counter-rotation mode compared to that under single rotation in laminar flow with different speed ratios.Generally speaking,the power number increases more intensively with the speed ratio increasing.If the selection of driving system is still based on the power curve of the outer impeller rotating alone,the power of the drive system may be insufficient.

4.3.Mixing performance

High-efficiency mixing of medium or high-viscosity Newtonian fluid needs the mixer to meet the following two requirements:(1)It provides intensive shearing,which is necessary to reduce the size of concentration patches;and(2)It makes the material circulate widely and rapidly.These two factors can guarantee that the fluid in the high-shearing area and low-shearing area exchange rapidly,leading to the uniform mixing in the whole vessel.Hence,it is essential to improve the mixing performance of coaxial mixers based on the flow field,shear rate and mass flow.

4.3.1.Flow field

Fig.4.Power curve of outer impeller under different operating modes.

Assume that the inner impeller speed is 240 r·min-1and the outer impeller speed is 20 r·min-1.The numerical simulation of the flow field under single rotation of inner impeller,co-rotation and counter rotation modes are performed,as shown in Fig.5.We can see that under single rotation mode of the inner combined impeller,a vortex forms below the PBT-4 impeller and RT-6 impeller respectively,but the liquid velocity in the upper area of the tank is very low,which results in a bad performance of global mixing.Under counter-rotation mode,another vortex appears in the upper area of the tank to improve the mixing of material in that area.However,too powerful the local circulation makes the material stay too long at some places and hinders the global mixing.Under co-rotation mode,the rotation of the outer impeller moves the vortex formed by the PBT-4 impeller up,which produces circular flow throughout the area above the RT-6 impeller.Meanwhile,the velocity of the material in the near-surface region is higher than that under single-shaft rotation mode,which improves the mixing of the material in the upper region of the tank greatly.So double-shaft mixing prevails in rapid mixing comparing to single-shaft mixing,and co-rotation is better than counter-rotation.

4.3.2.Shearing characteristics

Fig.6 shows the average shear rate separately on 20 cross sections perpendicular to the shaft.It can be seen that the shearing near thedouble inner impeller is the most intensive under all different operating modes,and the shear rate in the RT-6 region is larger than that in the PBT-4 region,showing the high shear characteristic of RT-6 impeller.In addition,Fig.6 indicates the average shear rate on each plane increases as the outer impeller speed increases,no matter under corotation or counter-rotation mode.Comparing to single rotation,the counter-rotation strengthens the shearing in all regions,and the corotation also improves the shear rate of all regions except the local RT-6 impeller region.In general,the average shear rate of the whole tank under co-rotation mode is larger than that under counter-rotation mode,which means that the shearing performance of co-rotation mode is better than that of counter-rotation mode.

Table 3 Percentage increase of the power number of outer impeller with different speed ratios

Fig.5.Flow lines under different operating modes.

4.3.3.Distribution of mass flow

The axial flow has a great effect on the mixing of the material in the tank,so the axial mass flow passing through the 20 planes perpendicular to the mixer shaft is calculated in Fig.7.Under each condition,the speed of the inner impeller is constant(240 r·min-1),while the speed of the outer impeller increases gradually from 10 r·min-1to 40 r·min-1.

Fig.7 indicates that the mass flow increases only in the upper region of the tank under counter-rotation mode,and it decreases in other regions,especially in the region between PBT-4 and RT-6 impeller.Under corotation mode,the mass flow in most regions increases except the region between the two impellers.Thus,the fluid circulation under the corotation mode is better than that under the counter-rotation mode.

5.Conclusions

(1)The outer frame impeller of the investigated coaxial mixer has little effect on the power consumption of the double inner impeller consisting of a four-pitched-blade turbine and a lower Rushton turbine no matter in laminar flow or in transitional flow,whereas the inner impeller has great effect on the power consumption of the outer frame.Usually,the power consumption of the outer frame will decrease under co-rotation mode but increase under counter-rotation mode.For design and selection of the driving system of the outer impeller,the increased power consumption caused by the rotation of the double inner impeller must be taken into consideration.

Fig.6.Distribution of average shearing rate of each cross section under different operating modes.

Fig.7.Distribution of mass flow of each cross section under different operating modes.

(2)Under all kinds of operating modes,the velocity,shear rate and mass flow near the double inner impeller are relatively high.Comparing to single rotation of inner combined impeller,the velocity,shear rate and mass flow improve significantly under the double-shaft mixing.

(3)In high-viscosity systems,the distributions of shear rate and mass flow under co-rotation and counter-rotation modes are of little difference.Because of its lower power consumption,the corotation mode is recommended in actual applications.

Nomenclature

C distance from the tank bottom,mm

D vessel diameter,mm

d impeller diameter,mm

e blade thickness,mm

H overall height of the tank,mm

hlheight of the liquid,mm

Nispeed of inner impeller,r·min-1

Nospeed of outer impeller,r·min-1

Np power number

Re Reynolds number

T torque,N·m

w blade width,mm

α speed ratio of inner impeller and outer impeller

μ viscosity of the liquid at bulk temperature,Pa·s

ρ density of the material,kg·m?3