Xiaolong Li,Hongliang Zhao,Zimu Zhang,Yan Liu,*,Ting’an Zhang

1 Key Laboratory for Ecological Utilization of Multimetallic Mineral,Ministry of Education,Shenyang 110819,China

2 School of Metallurgy,Northeastern University,Shenyang 110819,China

3 School of Metallurgy &Ecological Engineering,University of Science and Technology Beijing,Beijing 100083,China

Keywords:Intermig impeller Solid-liquid mixing Stirred tank CFD

ABSTRACT The multiphase flow in the solid–liquid tank stirred with a new structure of Intermig impeller was analyzed by computational fluid dynamics (CFD).The Eulerian multiphase model and standard k–ε turbulence model were adopted to simulate the fluid flow,turbulent kinetic energy distribution,mixing performance and power consumption in a stirred tank.The simulation results were also verified by the water model experiments,and good agreement was achieved.The solid–liquid mixing performances of Intermig impeller with different blade structures were compared in detail.The results show that the improved Intermig impeller not only enhances the solid mixing and suspension,but also saves more than 20% power compared with the standard one.The inner blades have relatively little influence on power and the best angle of inner blades is 45°,while the outer blades affect greatly the power consumption and the optimized value is 45°.

1.Introduction

The solid–liquid mechanical stirred reactors are applied widely in chemical engineering and nonferrous metallurgy,such as crystallization,leaching processes and catalytic reactions.The fluid mixing,particle suspension,concentration distribution and power consumption are mainly determined by the type,structure,and operations of an impeller in a stirred tank.EKATO,a Germany company,put the first Mig impeller into practical production as early as 1964.Then,the Mig impeller was redesigned after absorbing the characteristics of the common pitch blade turbine.An outer blade inclined in the opposite direction to the inner blade was added to promote the overall circulation,as shown in Fig.1a.Ever since,EKATO altered its outer blade into two-layer structure and obtained the Intermig impeller (shown in Fig.1b) with a further improvement on solid–liquid mixing performance.These two impellers belong to the multi-section counter-flow impeller and could generate axial flows,so they have the advantages of high circulation and low power consumption [1].In 1994,PingGuo Aluminum Plant (in Guangxi,China) applied the Intermig impeller to seed precipitation tanks[2]and configured the inner part of blade inclined downward slightly.To avoid scabbing and depositing of solid particles,Shenyang Aluminum Magnesium Design Institute,China,then optimized blades and designed the improved Intermig impeller [3]shown in Fig.1(c).The improved Intermig impeller lengthens the outer blades,which promotes the scouring force significantly.Shear force generated by the impeller and baffles also increases noticeably when the feed solution flows through baffles,having positive effect on the decrease of deposition and scab at the bottom and corners of tanks,while enhancing mixing performances.Compared with the common pitch blade turbine,the power consumption of the improved Intermig impeller reduces dramatically,to only about 1/5–1/4 of blade impeller’s [4].

Nowadays,a few investigations on the solid–liquid suspension process by employing the Intermig impeller have been reported.The suspension behaviors of solid particles in the Newtonian fluids were studied by Ibrahim et al.,who compared mixing performances of five agitators (including the Intermig impeller) in low viscosity liquids[5,6].The results showed that fewer particles were suspended in the case of higher viscosity.When the fluid viscosity increased from 10-3Pa·s to 0.01 Pa·s,the stirring performance of two-layer Intermig impeller improved remarkably,and the Intermig impeller had the highest stirring efficiency when the viscosity of fluid was 1 Pa·s.Bujalski et al.adopted the discoloring and conductivity methods in high solid hold-up systems,to investigate the mixing time of Lightnin 310,315 and Intermig impellers[7,8].The mixing time for high solid hold-up system was usually more than two orders of magnitude than that for single-phase liquid,but for Intermig impellers to achieve suspension,the mixing time increased by five-fold only.

Fig.1.Structures of Mig,Intermig and improved Intermig impellers.

Although investigations on solid–liquid flow systems in stirred reactors have been carried out,most of them were focused on single-phase [9,10]or solid–liquid systems with low solid holdup[11].There were few reports[12–14]on the multiphase stirring systems with high solid hold-up by the improved Intermig impeller.

This paper adopts CFD methods to investigate the effects of the structures of the improved Intermig impeller on the solid–liquid mixing performance,particle suspension and power consumption in the high solid hold-up system.The simulation results are also verified by the cold model experiments.The optimized structure of the Intermig impeller is obtained and the present results may provide significant guidance to the design of impellers and the scale-up of stirred reactors.

2.Experimental

2.1.Water model experiment

A lab-scale stirred tank of 425 mm in diameter was manufactured according to the geometric structures of the industrial cylindrical stirred tank with the diameter of 14 m.Fig.2 shows the experimental equipment with diameter (T) and height (H) are 425 mm and 500 mm,respectively.Two baffles are installed off the wall of the stirred tank with a gap of 10 mm,and the lower ends of two baffles stretch downstream the stirred suspension with a radius of 50 mm.Top of the tank is equipped with a cover plate,which has 48 holes for sampling and measuring particle concentration across the whole reactor.The diameter of the impeller(D)is 0.624 T.Meanwhile,the ratio for the distance(between lower blade and the bottom of reactor) and diameter of reactor is C/T=0.071.Agitation speed is kept at N=250 r·min-1.The impeller rotates in a clockwise direction and baffles bend to the downstream direction to allow high speed flow around the bottom corner.The agitator pushes the fluid flow downwards.As the fluid moves to the wall baffles,it turns upwards along the bending baffles,alleviating the probability of particle settling.Water and glass powder are utilized in the liquid–solid system,which maintains the average of solid hold-up (Cavg) at 800 g·L-1in the reactor (the volume fraction is 0.33).Table 1 shows the geometric structure of impeller and physical properties of test materials.

2.2.Method to measure concentration

In cool water model experiments,a particle concentration measurement device (PC6D,Institute of Process Engineering,Chinese Academy of Sciences) based on the optical method [15]is used to measure local solid hold-up in the stirred tank.Two optical fibers are arranged parallelly in a probe and each of them can transmit the laser beam.When particles pass by the probe,they will reflect the laser,which is received by the reflex optical fiber to a photoelectric detector and then converted into a voltage signal proportional to solid hold-up.Thus,the phase volume fraction of solid particles is acquired by analyzing the average of voltage signals.Shan et al.applied the same instrument to measure the distribution of solid hold-up in a stirred tank without baffle,with the relative error within 0.5% [16].

3.Modeling Details

The Eulerian multiphase model and the standard k–ε turbulence model[17]are selected to predict the three-dimensional unsteady flow field and the solid–liquid mixing performance.The effects of mass transfer,lift force and virtual mass force are ignored due to their minor effects in the present situation.

3.1.Governing equations

The continuity equation for each phase(i=l or s)can be written as:

Fig.2.Experimental system of cold water model (unit:mm).

Table 1 Geometry of impeller and physical properties of test materials

The volume fractions of the phases add up to unity in each control volume,namely:

Gidaspow model [18]is adopted to calculate the momentum exchange coefficient in the high solid hold-up system in this paper.When the liquid volume fraction αlis bigger than 0.8,the momentum exchange coefficient Kslcan be calculated as:

When αlis below 0.8,Kslcan be calculated as:

The standard k–ε turbulent model is used for turbulence modelling.The following transport equations for the turbulent kinetic energy (k) and the turbulent energy dissipation rate (ε) are adopted.

where G corresponds to the production of the turbulent kinetic energy.The turbulent viscosity of the liquid phase,μt,is determined by:

The parameters for turbulent model are chosen as follows:Cμ=0.09,C1=1.44,C2=1.92,σk=1.0,σε=1.3.

3.2.Boundary condition

The whole fluid region in the stirred tank is selected as computational domain,and the value of each variable on the solid wall is calculated with the standard wall function.The liquid level is set as symmetric interface,namely gradients of all physical variables are zero in the normal direction on the free liquid surface.Unsteady sliding mesh method is employed to handle the rotation of the stirrer zone [19].The SIMPLE algorithm based on the couple of the pressure and velocity,and the second-order upwind scheme is adopted to discretize the governing equations.All residuals need converge to 10-4.

In numerical simulation,the method of surface integral for all force components on the blade is utilized to calculate the resultant moment.Then the stirred power consumption can be expressed as:

where P/W:the stirring power consumption;M/N·m:torque;ω/rad·s-1:angular velocity.N/r·min-1:stirring speed.

3.3.Mesh model

Gambit was utilized for modeling and meshing of the stirred tank and impeller.Unstructured grids,including the tetrahedron and hexahedron are employed to divide the stirred tank.The complex region near the solid walls is discretized by tetrahedral mesh while hexahedral mesh occupies the inner zones.The thickness of baffles is neglected during model building and meshing,meanwhile the grid is more refined around the baffle surfaces.Fig.3 shows the meshing for the stirred tank and impeller.

3.4.Independence verification

The effects of grid size,time step on the simulation results were investigated,followed by the verification of CFD results against the experiments under the same conditions.The main structures of the tank and physical properties of solid–liquid two-phase system are described in Table 1.The stirring speed of impeller is set at 250 r·min-1and the ratio of liquid level to tank diameter is 0.94.The volume fraction of solid particles is controlled at 0.33.The impeller with the inner impeller angle of 60°,the inner blade angle of 30°and the outer blade angle of 30° is employed in the calculation to verify the simulation results.Those operating conditions and geometric parameters are suitable for the results in Figs.4–6.

3.4.1.Verification for grid independence

Grids consisting of 520 k,390 k and 260 k cells on the whole computing domain are employed to simulate the liquid–solid two-phase flow in the stirred tank.The liquid phase velocity and solid hold-up distributions are compared in the context of different grids[20].What we can see from Fig.4 is that differences of liquid phase velocity and solid hold-up distributions are very small (less than 5%) under different grids.Therefore,we decide to adopt the 260 k grid for the subsequent simulation,which cuts down computational loads but also obtains reliable results.

3.4.2.Test for time step independence

In unsteady numerical calculation,setting a suitable time step is also vital.When the time step is too short,computing time will increase significantly and round-off error may accumulate.While if the time step is overlong,it will lead to a greater cut-off error,which makes the residual error difficult to converge.Now,some methods rely on choosing time step by trial and error.For instance,the ratio of the minimum length of grid cell and mean velocity of flow field is set as t1.The ratio of characteristic length and characteristic velocity is defined as t2.When t1is lower than t2two or more orders of magnitude in unsteady sliding mesh methods,some scholars believe it suitable to choose 10%of the reciprocal of rotating speed as the time step.The rotating speed varies from 150 to 250 r·min-1in this work,so the longest time step will not exceed 0.006 s.Therefore,three time steps,0.0005 s,0.002 s and 0.005 s,are chosen in the initial computation.The results are shown in Fig.5.The distributions of velocity and solid hold-up in both axial and radial directions show less difference(<3%)with different time steps.For a solid–liquid suspension system of high solid hold-up and small particle sizes,particles normally fall slowly,which means that particles need 1–2 min to reach steady motion.In this work a short time step of 0.002 s was chosen at the beginning of calculation,leading to convergent results.Then the time step increased to 0.005 s to accelerate computing processes.

3.4.3.Validation against water model experiment

After the tests on grid and time step independence,water model experiments were used to further verify the reliability of simulation.Solid-liquid two-phase flow in a stirred tank is simulated by using water as the continuous liquid phase and glass powder as the solid phase.Both calculations and experiments are implemented in the same conditions.Three impellers with 0.624,0.67 and 0.714 in D/T are used in water model experiments.Fig.6 compares experimental and simulation results in terms of solid holdup distributions.Distributions of particles become more homogeneous as the diameter of impeller increases when the rotational speed is same.The increase of diameter not only shrinks the particle accumulation area near the bottom and wall of tank,but also improves mixing effects in the axial direction,contributing to the decrease of concentration gradient on the surface of liquid.For the solid hold-up in the axial direction,the results of simulation and experiments are identical,which verifies the reliability of CFD model.

Fig.3.Mesh models.

Fig.4.Velocity and solid hold-up distributions with different grids.

Fig.5.Velocity and solid hold-up distributions with different time steps.

Fig.6.Comparison of solid hold-up distributions between experiment and simulation.

4.Results

The mixing performances of blades with different angles(shown in Fig.7) are simulated with numerical methods.α1,α2,α3are the angle of inner impeller,inner and outer blade,respectively.It needs a long time for solid particles to achieve the final stable state because of high solid hold-up (average solid volume fraction of 0.33).Hence,the present simulation results are recorded when the stirring time is 60 s.After that,the distributions of solid hold-up and power consumption change very little.

4.1.The inclination of inner impeller

Fig.7.Setting angle of the blades.

The inner impeller of a standard Intermig impeller is installed horizontally in industry,while the improved Intermig impeller inclines the inner impeller downwards by 30° (α1=60°).From streamlines showed in Fig.8(a) and (b),we can see that the improved Intermig impeller (α1=60°,α2=30°,α3=30°) can form more intensive axial circulations which will be beneficial to axial mixing for particles at bottom.Two small circulations at the end of the impeller form on both two cases.The structure of the baffle also affects the flow state.The inclined baffle in the Fig.8(b)allows the incoming flow to climb up along the baffle,enhancing the axial circulation of the fluid.This also promotes suspension and reduces deposition of particles at the bottom of central regions.The main function of vertical baffle is to obstruct the flow of suspension and make it flow around the baffle,with little contribution to the axial circulation of the fluid.Fig.8(c)and(d)compares the velocity vectors of standard and improved Intermig impellers.The improved impeller combined with the bottom inclined baffles formed a stronger axial circulation,which is beneficial to the suspension of bottom particles.

Fig.8.Streamlines and velocity vector under the interaction between impeller and baffles.

Fig.9.Solid hold-up distributions with different types of impellers.

Fig.9 shows changes of solid hold-up distributions with different sorts of impellers.The standard impeller is matched with 4 upright baffles,so the thickness of clear liquid layer at surface is smaller and particles deposit seriously on the bottom.By contrast,the improved impeller has positive effect on particle suspension although the region of clear fluid is larger than that of the standard impeller.

Power consumption for agitator is meaningful in practice.Although the power consumption is mainly decided by the diameter and rotational speed,the structure of agitator also has a significant effect.Power consumption for the standard impeller is 40.6 W,while the improved impeller is only 31.7 W,saving approximately 20% energy.

4.2.Inner blade angle

Fig.10 shows that axial circulations are strengthened with α2increasing gradually from 15° to 45° (where α1=60°,α3=30°),before weakened when α2reaches 60°.Combined with the inner blade and the inclined baffles,the axial pumping performance becomes more forceful as α2increases to 45°.The axial circulation occupies the whole stirred tank and brings sufficient momentum exchanges for fluid.When α2further increases to 60°,although the effective agitation area enlarges,circulations are strengthened in the peripheral direction near sides of blade.This may have little or even a negative effect on the upward movement of fluid,and thus it will go against to developed axial circulation.Fig.11 illustrates the turbulent kinetic energy with different inner blade angles.With the increase of the inner blade inclination,the effective area driving the fluid will also increase,leading to the enhancement of turbulent kinetic energy.The turbulent energy around the baffle is higher when the α2ranges from 30° to 45°,causing more particles to float up along the baffle.

From solid hold-up distributions in Fig.12,we can see that with the increase of α2,mixing effects are improved in both axial and radial directions.When α2reaches 45°(α1=60°,α3=30°),a better mixing performance forms in tank where particle deposition decreases significantly at the bottom.As α2increases to 60°,despite the enhanced disturbance of the fluid,it does not obviously improve the axial movement of particles from flow field analysis above.Hence,particle concentration distribution has little change at the surface of fluid.Simultaneously,owing to the fact that axial pumping effects of blades are weakened in the vertical direction,it will have adverse impact on particle upward motion.As a result,solid hold-up is larger at the bottom of blades,and deposition is more serious.

Fig.13 compares power consumption at different α2.When the inner blade angle is 30°,the power consumption is relatively lower.With the increase of inner blade angle,the effective agitation area increases,so the power consumption rises slightly.Each increment of 15° is added to blades,power consumption normally rises less than 2%.As α2increases to 60°,blades suffer greater torques,and thus power consumption will have a significant increase,rising about 10% compared with the figure of 30°.

Fig.10.Streamlines with different α2 .

Fig.11.Turbulent kinetic energy with different α2 .

Fig.12.Solid hold-up distributions with different α2 .

Fig.13.Power consumption with different α2 .

4.3.Outer blade angle

Fig.14 shows streamlines with outer blade angles (α3) ranging from 15° to 60° and keeping α1=60° and α2=30°.As the agitator moves clockwise,the outer blades push the fluid downward.With the increase of α3,the downward pressure on fluid at bottom enhances,in conjunction with baffles,promoting the development of axial circulation flow.When outer blade angle is 15°,a certain area of circulations forms only in the central lower parts of the stirred tank.Flow field is relatively flat at the surface of fluid,where particles do not have enough suspending kinetic energy and it will produce more easily a clear liquid layer.As α3increases to 30°,axial circulation flows are enhanced and the flat area at surface has largely disappeared.When outer blade angle is 45° or larger,stable axial circulation flows form in the whole tank,and fluid mixes more fully,so it has little effect on flow field with an increasing α3.Turbulent kinetic energy distributions with different α3are shown in Fig.15.The changes of structure and size for outer blade have a great influence on the distribution of turbulent kinetic energy in the whole tank.The turbulent kinetic energy increases obviously,especially in the region around impeller,when the outer blade angle increases.

Fig.14.Streamlines with different α3 .

Fig.15.Turbulent kinetic energy with different α3 .

Fig.16.Solid hold-up with different α3 .

From solid hold-up distributions as shown in Fig.16,we can know that outer blades affect overall solid hold-up distributions significantly.When α3is smaller,the effective agitation area in the rotating direction is also smaller.Thus,particles are not mixed well and deposit at the bottom,while a thick clear fluid layer appears at the surface.The performance of particle suspension is improved with the increase of outer blade angle.As α3reaches 45°,the solid–liquid system is mixed uniformly except for the clear fluid in the central of axis.When α3is further increased to 60°,the solid–liquid mixing effects are improved slightly,but the distribution of particles tends to be uniform in whole tank.

Fig.17.Power consumption with different α3 .

Fig.17 shows that power consumption tends to grow exponentially with the increase of outer blade angle.The outer blade angle is the primary factor that affects the power consumption in the whole tank.This is mainly because outer blades are installed at the end of impeller and the radius is larger,leading to larger torques.In the meanwhile,considering mixing effects,outer blades make the fluid flow downward,which brings more fluid into the impeller zone.As α3increases to 45°,the system achieves the perfect solid–liquid mixing,although power consumption almost doubled.With the further increase of α3,the mixing performance improves little.Overall,outer blade angle should not be too large,and 45° is more suitable.

5.Conclusions

The Eulerian multiphase model,standard k–ε turbulence model and unsteady sliding mesh method are selected to simulate the solid–liquid mixing,suspension,and power consumption in the stirred tank.The simulated model with independence of mesh size and time step is verified by water model experiment and good agreements are obtained,verifying the reliability of the simulation method.

The improved Intermig impeller not only enhances the solid mixing and suspension but also saves more than 20% power compared with the standard one.The inner blades have relatively little influence on power and the best angle of inner blades is 45°.While the outer blades greatly affect the power consumption.The best angle of outer blades is 45°,which has a relatively uniform solid–liquid distribution.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China(U1760120,U1508217),National Key R&D Program of China (2017YFC0210403,2017YFC0210404) and Shenyang Science &Technology Project (17-500-8-01).