Meng Li,Yangbo Tan,Jianglong Sun,2,3,De Xie,2,3,Zeng Liu,2,3,*

1School of Naval Architecture and Ocean Engineering,Huazhong University of Science and Technology,Wuhan 430074,China

2Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration(CISSE),Shanghai 200240,China

3Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics(HUST),Wuhan 430074,China

Keywords:Light particles Drawdown mechanism Baffled stirred tank Submergence Numerical simulations KR impeller

A B S T R A C T To improve the efficiency of the desulfurization process,the drawdown mechanism of light particles in stirred tank is studied in this paper.For both up and down pumping modes,the just drawdown speeds(Njd)of floating particles in transformative Kanbara Reactor(KR)are measured in one and four baffled stirred tanks experimentally.Then numerical simulations with standard k-ε model coupled with volume of fluid model(VOF)and discrete phase model(DPM)are conducted to analyze the flow field at the just drawdown speed Njd.The torques on the impeller obtained from experiments and simulations agree well with each other,which indicates the validity of our numerical simulations.Based on the simulations,three main drawdown mechanisms for floating particles,the axial circulation,turbulent fluctuation and largescale eddies,are analyzed.It's found that the axial circulation dominates the drawdown process at small submergence(S=1/4T and 1/3T)and the large-scale eddies play a major role at large submergence(S=2/3T and 3/4T).Besides,the turbulent fluctuation affects the drawdown process significantly for up pumping mode at small submergence(S=1/4T and 1/3T)and for downpumpingmodeatlargesubmergence(S=2/3Tand3/4T).Thispaperhelpstoprovideamorecomprehensive understanding of the KR desulphurizer drawdown process in the baffled stirred tank.

1.Introduction

Solid-liquid stirred rectors are widely used in the process industry,such as iron,chemistry and pharmaceuticals industry.Especially in the KR mechanical stirring of the iron industry,the improvement of solidliquid mixing efficiency is important for desulphurization process.

To reutilize the resources and protect the environment,some researchers paid attention to the Kanbara Reactor desulfurization waste slag.In the study of Zhibo Tong et al.[1],a novel valorization process of KR desulfurization waste slag into iron-containing substances and desulfurization agent for hot metal pretreatment was investigated.The study of Guanghong Sheng et al.[2]focused on the physicochemical properties of the KR slag samples and its potential treatment of acidic mine drainage.Aiming at effective utilization of KR slag in the iron ore sintering process,Kazuya Fujino et al.[3]studied the characteristic of KR slag.

Some other researchers focused on the study of mixing process in the stirred tank.Jun-hong JI et al.[4]proposed a variable-velocity stirring method to improve the desulfurization efficiency of high-sulfur hot metal for KR desulphurization process.And Ouyang et al.[5]developed the structure of impeller with a new type WG-3Y stirrer and the new stirrer was proved to be more efficient to draw down particles than the conventional KR impeller.Referring to the work of Ouyang[5],transformative KR impeller was considered with up and down pumping modes.

The density of the desulfurizer is smaller than the iron water.Therefore,the efficient drawdown of the desulfurizer is the key of the KR mechanical stirring.

The baffles that affect the solid drawdown and dispersion in the stirred tank were studied by many researchers in recent works.Liu et al.[6]studied the particle dispersion in the unbaffled stirred tank andusedtheparticledistributioncurvestoconsiderthelightparticledistributioninthestirredtank.YoshieNAKAIetal.[7]investigatedtheeffect of flux dispersion on the hot metal desulfurization reaction to improve the efficiency of the desulfurization process.In their experiments,three kinds of particles dispersion behavior,non-dispersion,transition and complete dispersion,were observed in unbaffled stirred tank.Oscar Khazam et al.[8]found a stable central vortex an inefficient way to draw down and distribute solids in unbaffled stirred tank.Two alternate baffle configurations,half baffles and surface baffles were considered later by Oscar Khazam et al.[9].It showed that surface baffles performed better than either half-or fully baffled configurations for the drawdown of floating solids.Generally,it is believed that the baffles in the stirred tank are effective for the drawdown and dispersion of the light solid particles.Therefore,one andfour fully baffled stirred tanks were studied in our paper.

Many researchers studied the drawdown mechanism of the light particles in the stirred tank.In the work of Oscar Khazam et al.[8],two mechanisms,turbulent fluctuation and mean drag,for the drawdown of floating solids had been identified in baffled stirred tanks.In the study of Gul Ozcan-Taskin et al.[10],the solid drawdown mechanisms,recirculationloopandsurfaceaeration,fordownpumping impellers was discussed.In subsequent work of Gul Ozcan-Taskin et al.[11],the main circulation loop for up pumping mode was discussed.So,the pumping mode is a critical factor to be considered in the investigationofdrawdownmechanism.Inthestudy of ShengchaoQiaoetal.[12],CFD simulations were carried out to find a CFD methodology to predict thecritical impeller speed for the complete drawdown of floating solids in a stirred tank with an up-and down-pumping pitched blade turbine.Shengchao Qiao et al.[12]found the solids drawdown and dispersion is affected by another drawdown mechanism,the large scale energycontaining eddies that can be characterized by the integral length scale of turbulence.Nenad Kuzmanic et al.[13]reported that large anisotropic eddies which was responsible for the complete drawdown of floating solids in full baffled mixing tank were important.The large primary eddies gave rise to smaller isotropic eddies by energy transfer.Therefore,the large scale eddies shouldbe considered as oneof the critical solid drawdown mechanisms in the baffled stirred tank.

Fig.1.(a)The impeller(D=97 mm)and the baffled stirred tank(T=290 mm),(b)the sketch of the water model used in the experiments.

For a comprehensive understanding of the solid drawdown process in the KR desulphurization process,three drawdown mechanisms,the axial circulation,turbulent fluctuation and large scale eddies,were investigated in this paper.The axial circulation was characterized by large swirls and waves which developed over the entire free liquid surface.Strong mean circulation leaded to a better distribution of particlesinthestirredtank.Theturbulentfluctuationwascharacterized by a wavy surface with energetic surface eddies.The large scale eddies were characterized by the integral length scale of turbulence with its characteristic structure scale being proportional to k3/2/ε.

In Section 2,the water model experiment set-up and computationalfluiddynamics(CFD)simulationmethodswereintroduced.Stirredtank withbothoneandfourbaffleswereconsideredinfivesubmergences.In Section 3.1,the drawdown speed and power were measured directly from the experiments.The experimental and computational results were compared in Section 3.2.In Section 3.3,CFD simulations were used to analyze the flow field near the surface in the stirred tanks.The main drawdown mechanisms were analyzed in Section 3.4 and conclusion was shown in Section 4.

2.Experimental

2.1.Water model experiments

Fig.2.The detailed size of the transformative KR impeller.

In the experiments,we considered a flat bottom cylindrical tank with the diameter T=0.29 m and height H=0.45 m,as shown in Fig.1(a).The still liquid height h=T=0.29 m and purified water with density ρ =997 kg·m?3and dynamic viscosity μ =0.896 × 10?3Pa·s was used.Fig.1(b)shows the sketch of the equipment in experiments.The detailed size of the transformative KR impeller is shown in Fig.2.Two kinds of baffle configuration,one and four baffles,were considered.The width,height and thickness of the baffles were T/10,1.38T and T/145,respectively.Intheexperiments,whenthenumberofparticlesismorethan 500,the drawdown rotation speed will not be affected.Therefore,1000 EVA(ethylene-vinyl acetate copolymer)particles(density ρp=920 kg·m?3and diameter dp=3 mm)were used in the experiments.The submergence,S,was defined as the distance from the liquid surface to the centerline of the impeller.S=1/4T,1/3T,1/2T,2/3T,and 3/4T were considered.The mixing process was actuated by the Lightnin LB2 L2Y15N Mixer to control and display real-time rotational speed.The torque on the impeller was measured by self-propulsion apparatus(CUSSON with a precision of 10?4N·m).

Forthedesulfurizationprocess,thestageofsolidsstayingontheliquid surface is prohibited and the catalysts need to be drawn down to react with the sulfide in the molten iron.Following the work of Oscar Khazam et al.[8],the drawdown speed(Njd)is defined as the speed at which no particles remain floating on the liquid surface for more than 2-4 s.

2.2.CFD simulations

The ANSYS(Pittsburgh,Pennsylvania,USA)Fluent(version 16.1)CFD commercial software package was used in the numerical simulations.The standard k-ε turbulence model was chosen to simulate the turbulent flows in the stirred tank.Besides,the Sliding Mesh(SM)method that works for transient simulations was applied,though more computational efforts are needed when compared with the Multiple Reference Frames(MRF)method[14].

Tohaveabetterobservationoftheliquidsurface,thevolumeoffluid model(VOF)was used in the simulations.It simulates two or more immiscible fluids and can be applied for both the steady and transient tracking of liquid-gas interface with the advantage in tracking the volume fraction of fluids throughout the domain.Based on the conservation principles,the continuity equation can be written as follow:

where αistands for volume fraction,ρ anddenote density and velocity,respectively.The momentum equation is given below:

where the p and μ are pressure and viscosity,respectively.In every control volume,the volume fractions of all the phases sum to one.As long as the volume fraction of each phase is known at every simulation point,all variables and properties of the phase can be represented with the volume-averaged values.And the surface tension coefficients of the water and air were set as 0.072 N·m?1.

To simulate the movements of the light particles in the fluid field, thediscrete phasemodeling (DPM) was used. It treated the solid phase as dispersedphase in a Lagrangian framework [15]. The force balance equatesthe particle inertiawith the forces acting on the particles, and can bewrittenas:

the particle relaxation time,is the particle velocity,is the liquid velocity,μ is theviscosity of the fluid,ρ isthefluiddensity,ρpis the density of the particle,and dpis the particle diameter.Therelative Reynolds number Re is defined as:

The virtual mass force which is required to accelerate the fluid around the particle can be written as

where Cυmstands for the virtual mass factor with a value of 0.5 in the Fluent.And pressure gradient force can be expressed as:

The no-slip wall conditions were assumed for all the tank boundaries.And reflecting mode was chosen in DPM boundary condition for all parts of the model.The first-order upwind scheme for governing equations was applied and the residual for each time step was set to 10?4.And the time step is 0.001 s.

Following Sun et al.[16],Zhang et al.[17]and Tu et al.[18],nonstructural grid was used with ICEM in Fluent.Fig.3 shows the grid distribution in vertical section for the stirred tank.The sensitivity of mesh size in the numerical simulations was studied from 300 k to 800 k.The torques on the impeller in the case of S=1/4T,1/2T and 3/4T for down pumping mode in four baffled stirred tank were shown in Table 1.The torque of 300 k and 800 k is closer to the torque of experiments than 500 k.However,the results of 800 k are more reliable than 300 k.So,800 k grids were chosen finally.There are 73849 cells in the inner part and 776047 cells for the outer part.

Fig.3.The grid distribution for the stirred tank.

Table 1 The torques on the impeller and the relative error of the simulation and experiments results(S=1/4T,1/2T and 3/4T,down pumping mode,four baffles)

3.Results and Analysis

3.1.Just drawdown speed and power in experiments

Table 2 shows the just drawdown speed for different submergence with both up and down pumping modes for one and four baffles,respectively.For all four cases considered,the just drawdown speed increases with the submergence.And for one baffled tank,the just drawdown speed is higher than that for four baffled tank.In the work of Oscar Khazam et al.[8],the particles in the one baffled stirred tank accumulated at the surface of the vortex.They found that the four baffled configuration showed good solid distribution with the absence of a single vortex.Therefore,the four baffled configuration has a better suppression effect on the surface vortex than one baffled configuration.Besides,the particles drawdown and dispersion for four baffled configuration have a superior to one baffled configuration.

Taking the accuracy into consideration,we measure the torque(T0)when the shaft rotated without impeller.And the final torque was calculated by:

where the Teis the torque on the impeller which was measured by selfpropulsion apparatus in the experiments.Fig.4 shows thedrawdown power(P)for both up and down pumping modes in one and four baffled stirred tanks.The power consumption was defined[19]as:

Table 2 The torques on the impeller and the relative error of the simulation and experiments results(S=1/2T,down pumping mode,four baffles)

Fig.4.Thedrawdownpowerofdifferentdrawdownspeedwithupanddownpumpingfor one and four baffled stirred tank.

wherenstandsfortherotationspeedandMstandsforthetorqueonthe impeller.Itisevidentthatinfourbaffledstirredtankmorepowerisconsumed than that in one baffled stirred tank.Meanwhile,for each stirred tank,thepowerconsumptioncurvesstayclosetoeachotherforbothup and down pumping modes.

Fig.5.Thesimulationresults ofS=1/3Twith down pumpingmode infourbaffledstirred tank.

Table 3 The torque on the impeller in case of down pumping mode in four baffled stirred tank

3.2.Comparison between experimental and numerical results

To analyze the flow field quantitatively and assess the effect of the drawdown mechanism qualitatively,the CFD simulation was conducted.Fig.5 shows the simulation results of S=1/3T with down pumping mode in four baffled stirred tank.Most of the particles are drawn down into the liquid and this corresponds to the results in the experiments.Table 3 shows the comparison of torques on the impeller betweentheexperimentalandthenumericalresultsfordownpumping mode in four baffled stirred tank.The relative error(σ)is defined as:

where the Tnand Testands for the torque on the impeller in numerical simulations and experiments,respectively.

For most submergences,the relative error is quite small.It reaches 0.82%and 0.60%for submergences S=1/2T and S=3/4T,respectively.Only for submergence S=1/4T,we find a large relative error 10.07%.The impeller is too close to the liquid surface,so the torque measurement was affected by the vibration force on the impeller and shaft.Besides,the slight vibration may be caused by different types of impellers and one baffled stirred tank.In general,the simulation torques agree well with the related experimental records.

3.3.Flow fields analysis in numerical simulations

The central lateral planes of the flow field in the stirred tank for up and down pumping modes are shown in Figs.6 and 7,respectively.Fig.6(a)and(b)shows the flow field of up pumping mode in one baffl ed stirred tank with S=1/4T and S=1/2T,respectively.In Fig.6(a),the circulation near the surface moved toward to wall of the stirred tank.While in Fig.6(b),the circulation near the surface moved from wall to the shaft.As only one baffle appeared in the stirred tank,theflow field symmetry breaks.

Fig.6(c)and(d)shows the flow field of up pumping mode in four baffled stirred tank with S=1/4T and S=1/2T,respectively.Theflow field in Fig.6(c)and(d)had similar characteristic as shown in Fig.6(a)and(b).Besides,compared with the flow fields in Fig.6(a)and(c),two circulations appeared in the flow field in Fig.6(b)and(d)as the submergence increases.The mean circulation changed with the submergence.

Fig.7(a)and(b)shows the flow field with down pumping mode in one baffled stirred tank for submergence S=1/2T and 3/4T,respectively.For S=1/2T,the circulation near the liquid surface moved from the wall of stirred tank to the shaft.Meanwhile for S=3/4T,the circulation near the surface is too weak to identify the moving tendency.

Fig.6.Thecentrallateralplanesoftheflowfieldforuppumpingmode(thecentrallateralplanewasperpendiculartothebaffleinonebaffledstirredtankandthecentrallateralplanewas in the middle of two baffles in four baffled stirred tank),(a)S=1/4T,one baffle,(b)S=1/2T,one baffle,(c)S=1/4T,four baffles,(d)S=1/2T,four baffles.

Fig.7.The central lateral planesof the flow field for down pumpingmode(the central lateral plane was perpendicular to the baffle inone baffled stirredtank and the central lateralplane was in the middle of two baffles in four baffled stirred tank),(a)S=1/2T,one baffle,(b)S=3/4T,one baffle,(c)S=1/2T,four baffles,(d)S=3/4T,four baffles.

The feature of circulation near the surface in Fig.7(c)(down pumping mode,four baffles,S=1/2T)and Fig.7(d)(down pumping mode,four baffles,S=3/4T)is similar as in Fig.7(a)and(b),except that the flow field symmetry is retained.Besides,two circulation loops appeared in Fig.7(a)and(c)and only one in Fig.7(b)and(d).

From Figs.6 and 7,it was found that the circulation pattern and strength are different for different submergences with both down and up pumping modes.The circulation near the surface was stronger at S=1/4T compared to that at S=1/2T in the same pumping mode and stirred tank.Therefore,the intensity of liquid fluctuation varies with the submergences in the same pumping mode and the same stirred tank.

Oscar Khazam et al.[8]found the intensity of turbulence and mean circulation velocity of the liquid are responsible for the solids drawdown and distribution in the tank.Besides,Nenad Kuzmanic et al.[13]found that the large anisotropic eddies are important for the complete drawdown of floating solids in baffled stirred tank.Therefore,to have a quantitative analysis of the particle drawdown mechanism,we comparedthethreekeyfactors,thedistributionofthemeancirculation,turbulent circulation and large scale eddies,at the surface.Near the surface,the flow in the radial and axial directions represents the mean circulation.To measure the mean circulation,the resultant velocity of the axial and radial velocities at the liquid surface was analyzed.The axial and radial velocities were obtained on a straight line in the radial direction from the shaft to the wall of the tank near the liquid surface.Define the resultant velocity(Vh)as:where Vzand Vrstand for the axial and radial velocities,respectively.Then,the data of large scale eddies were got from the same sample line as that of the resultant velocity.The surface-averaged turbulent kinetic energy of the liquid surface is defined to represent the turbulent circulation.

Fig.8 shows the resultant velocity of the axial and radial velocities at the surface in the diametral direction with down and up pumping modes for one and four baffled stirred tanks.The diametral line was perpendicular to the baffle in one baffled stirred tank and the diametral line was in the middle of two baffles in four baffled stirred tank.For each case in Fig.8,the resultant velocity tends to decrease as the submergence increases.For submergences S=1/4T,1/3T and 1/2T,the resultant velocity Vhis larger than that for submergences S=2/3T and 3/4T.Therefore,the mean circulation near the surface dominates the flow fields at small submergence and becomes weak at large submergence.

Fig.8.Resultantvelocityof axialvelocity andradialvelocityinthediametral direction attheliquidsurfacesfor different submergences.(thediametral linewasperpendicular to thebaffle inone baffled stirred tank and the diametral line was inthe middle of two bafflesin four baffled stirred tank),(a)down pumping mode,four baffles,(b)down pumpingmode,one baffle,(c)up pumping mode,four baffles,(d)up pumping mode,one baffle.

Fig.9 shows the surface-averaged turbulent kinetic energy of the liquid surface with up and down pumping modes in one and four baffled stirred tanks.It was found that for down pumping mode,the turbulent kinetic energy increases with the submergence.While for up pumping mode,the turbulent kinetic energy decreases with the submergences.For up pumping mode in one and four baffled stirred tanks,as shown in Fig.6,there is only one circulation loop in the flow field at S=1/4T and there are two evident circulation loops at S=1/2T.The major role which influences the liquid surface changes from the main circulation to the secondary circulation.Then the strength for the turbulent fluctuation decreases and the value of the turbulent fluctuation decreases with the submergence.For the down pumping mode in one and four baffled stirred tanks,the strength of main circulation loop becomes stronger with the submergence.So,the strength for the turbulent fluctuation increases with the submergence and the value of the turbulent fluctuation increases at the same time.Therefore,for small submergences the turbulent kinetic energy should be considered for up pumping mode and for large submergences the turbulent kinetic energy should be considered for down pumping mode.

Fig.9.Surface-averaged turbulent kinetic energy for the liquid surface of down and up pumping mode in one and four baffled stirred tank.

Fig.10 shows thelargeeddy scaleprofiles atthesurface with upand down pumping mode in one and four baffled stirred tanks.The diametral line was perpendicular to the baffle in one baffled stirred tank and thediametrallinewas inthemiddleoftwobafflesinfourbaffledstirred tank.For up and down pumping mode in four baffled stirred tank(Fig.10(a)and(c)),the curves of large eddy scales stay close to each other and decrease almost in a straight line with the increase of radial distance.This is because of the suppression effect of the four baffles in the stirred tank.For up and down pumping mode in one baffled stirred tank(Fig.10(b)and(d)),the strength of large eddy scales increases with the submergence.This is because the fluctuation near the surface in one baffled stirred tank is very intense and become strong with the submergence.And the range of large eddy scales in one baffled stirred tank is larger than that in four baffled stirred tank.This is because theflow field near the surface is more unsteady in one baffled stirred tank than that in four baffled stirred tank.

Fig.11 shows the power consumption of different submergences with up and down pumping in one and four baffled stirred tank.The power increases with the submergence for both two pumping modes and two baffled stirred tanks.So,the strength of the flow field in the stirred tank increases and the energy of the large scale eddies near the surface increases with the submergence.Therefore,the curves of large scale eddies increase with the submergence in one baffled stirred tank in Fig.10(b)and(d).Due to the inhibiting effect of the four baffles,the curves of large eddy scale stay close to each other for different submergences in Fig.10(a)and(c).Therefore,the large scale eddies dominate at large submergence for one baffled stirred tank and have an influence continuously at small and large submergences in four baffled stirred tank.

3.4.Analysis of the drawdown mechanism

For different pumping modes and different stirred tanks,the three drawdown mechanisms,the axial circulation,the turbulent fluctuation and the large scale eddies,can be found working together.One or two mechanisms will dominate at small or large submergence for specific pumping mode and stirred tank.

For down pumping mode in four baffled stirred tank,the peak value of the result velocity curves of S=1/4T is nearly twice larger than that at S=3/4T.Therefore,the axial circulation dominates at S=1/4T and 1/3T for down pumping mode in four baffled stirred tank.In Fig.9,the turbulent fluctuation for S=3/4T is three times larger than that of S=1/4T.So,the turbulent fluctuation dominates at S=2/3T and 3/4T.In Fig.10(a),the curves of large eddies scale are close to each other for down pumping mode in four baffled stirred tanks.Therefore,the large scale eddies have continuous and constant influence for all the submergences.

For up pumping mode in four baffled stirred tank,the peak value of the result velocity curves of S=1/4T is nearly four times larger than that for S=3/4T.So,the axial circulation dominates at S=1/4T and 1/3T.The turbulent kinetic energy for S=3/4T is four times larger than that of S=1/4T.So,the turbulent fluctuation becomes weak sharply and dominates at S=1/4T and 1/3T.For the large scale eddies,it keeps almost constant for different submergences.Therefore,large scale eddies have continuous and constant influence for up pumping mode in four baffled stirred tanks.

For the down pumping mode in one baffled stirred tank,the peak value of the result velocity curves for S=1/4T is over twice larger than that at S=3/4T as a whole.So,the axial circulation becomes weak sharply and dominates at S=1/4T and 1/3T.The turbulent fluctuation increases with the submergence and the value of S=3/4T is three times larger than S=1/4T.So,the turbulent fluctuation dominates at S=2/3T and 3/4T for the down pumping mode in one baffled stirred tank.The large scale eddies increase with the submergence.And the value of S=3/4T is nearly three times larger than S=1/4T as a whole in Fig.10(b).Therefore,the large scale eddies for the down pumping mode in one baffled stirred tank increase evidently and it dominates at S=2/3T and 3/4T.

For up pumpingmode in the onebaffled stirred tank,thepeakvalue of the result velocity curves for S=1/4T is more than four times larger than S=3/4T.Therefore,the axial circulation dominates at S=1/4T and 1/3T.The decreasing tendency of the turbulent fluctuation for up pumping mode in the one baffled stirred tank can be found in Fig.9 and it dominates at S=1/4T and 1/3T.The large scale eddies increase with the submergences and the peak value of S=3/4T is nearly three times larger than S=1/4T.So,the large scale eddies dominate at S=2/3T and 3/4T.

4.Conclusions

This paperconsideredthedrawdownmechanism ofthetransformative KR impeller with both up and down pumping modes in one and four baffled stirred tanks.The drawdown speed and power consumption were measured experimentally.The flow fields in the stirred tank were simulated with CFD to study the drawdown mechanism.The drawdown mechanism was considered from three aspects,axial circulation,turbulent fluctuation and large scale eddies.Some conclusions can be summarized from the results:

(1)AtS=1/4Tand1/3T,theaxialcirculationdominatesforthesolid drawdownforbothupanddownpumpingmodeinoneandfour stirred tanks.However,the axial circulation becomes weak with the submergence.So,it is not the main reason for the solid drawdown at S=2/3T and 3/4T.

(2)For the down pumping mode impeller in one and four baffled stirred tanks,the turbulent fluctuation increases with submergence and dominates at S=2/3T and 3/4T.However,for the up pumping mode impeller in one and four baffled stirred tanks,the turbulent fluctuation decreases withthe submergence and dominates at S=1/4T and 1/3T.

(3)Thecurvesoflargeeddyscalehaveanincreasingtendencyinone baffledstirredtank.Andinfourbaffledstirred,thecurvesoflarge eddy scale stay close to each other for different submergences.Therefore,the large scale eddies dominate for the solid drawdown at S=2/3T and 3/4T in one baffled stirred tank and have aneffectcontinuouslyonthesoliddrawdownforallthesubmergences in four baffled stirred tank.

Fig.10.Large eddyscales of the liquid surfacesfor different submergences.(the diametral line was perpendicular to the baffle inone baffled stirred tank and the diametral line was inthe middle of two baffles in four baffled stirred tank),(a)down pumping mode,four baffles,(b)down pumping mode,one baffle,(c)up pumping mode,four baffles,(d)up pumping mode,one baffle.

Fig.11.Thepowerconsumptionofdifferentsubmergenceswithupanddownpumpingin one and four baffled stirred tank(s).

This study on the drawdown mechanisms helps to provide a more comprehensive understanding of the KR desulphurizer drawdown process in the baffled stirred tank.Further optimization works of the impeller and the tank can be conducted based on the drawdown mechanism of floating particles.

Nomenclature

Cυmvirtual mass factor

D diameter of the impeller,mm

dpdiameter of the particles,mm

F additional force,N

Fppressure gradient force,N

Fvvirtual mass force,N

H height of the stirred tank,mm

k turbulent kinetic energy,m2·s?2

M torque on the impeller,N·m

n rotation speed,rad·s?1

P power consumption,W

p pressure,Pa

Re relative Reynolds number

S submergence

T diameter of the stirred tank,mm

Tetorque on the impeller in experiments,N·m

T0unloaded torque,N·m

Tntorque on the impeller in numerical simulations,N·m

u fluid velocity,m·s?1

upparticle velocity,m·s?1

Vhresult velocity,m·s?1

Vrradial velocity,m·s?1

Vzaxial velocity,m·s?1

W width of the baffles,mm

αivolume fraction

ε turbulent dissipation rate,m2·s?3

μ dynamic viscosity,Pa·s

ρ fluid density,kg·m?3

ρpparticle density,kg·m?3

σ relative error

τrparticle relaxation time,s