Experimentalstudyofpowerconsumption,localcharacteristicsdistributions and homogenization energy in gas-liquid stirred tank reactors☆

Facheng Qiu,Zuohua Liu*,Renlong Liu*,Xuejun Quan,Changyuan TaoYundong Wang

1School of Chemistry and Chemical Engineering,Chongqing University,Chongqing 400044,China

2Department of Chemical Engineering,Tsinghua University,Beijing 100084,China

3School of Chemistry and Chemical Engineering,Chongqing University of Technology,Chongqing 400054,China

Keywords:Stirred tank Gas-liquid two-phase Power consumption Local characteristics Homogenization energy

A B S T R A C T In this paper,the power consumption,the vertical local void fraction and the local gas-liquid interfacial area are investigated in the aerated stirred tank reactors(STRs)equipped with a rigid-flexible impeller.Meanwhile,the regressive correlation based on power consumption and interfacial area is proposed.Then a novel homogenization energy(HE=RSDPtm)expression based on power consumption and local interfacial area is redefined and used to indicate the mixing efficiency.The optimal operating mode is selected based on the change of the HE value.This paper can provide research ideas for structural optimization of stirred reactors.

1.Introduction

The stirred aeration reaction tanks have been extensively applied in chemicaland biochemical industries[1,2].In generalterms,theeffectof agitation is to make the material system even state,which is conducive to the uniform and heat transfer of the reaction.Nevertheless,the purpose of gas-liquid homogenization cannot be realized easily owing to thecomplexityoffluidflowbehavior[3].Eventhepooragitationresults in an increase in reaction by-products that affect the progress of the entire chemical process[4].Indeed,the lack of research on the factors affecting the mixing performance of the stirred reactor tanks leads to the unreasonable design of its structure and operation mode in the gas-liquid mixing system.Therefore,the better understanding of mixing performances including flow field characteristics,power consumption,local characteristics distribution,homogenization energy,etc.is conducive to providing considerable insight for optimal design of STRs in the gas-liquid mixing process[5].

Recently,many researches on flow field characteristics,power consumption,local characteristics distribution,homogenization energy have been published in the mixing process[6].In terms of flow field characteristics,Jeanmeure et al.[7]proposed a direct method to draw a distinction between circular and stratified flow patterns without imaging based on the electrical capacitance(ECT)technology.Specifically,the method depends on capacitance data and features extracted from raw data measurements.Ji et al.[8]proposed a new method,which based on empirical mode decomposition and least squares support vector machine,to identify the flow pattern of gas-liquid.Tatterson[9]investigated the gas disperses flow regimes that would occur under the factors of the agitation speed and the air injection flow rate.

In terms of power consumption research,Dohi et al.[10]found that the power consumption reduced because of the aeration and presented an empirical correlation for power consumption.Taghavi et al.[11]discussed the changes of local and overall power consumption in the aerated stirred tank using six-blade Rushton turbines(RT).Moreover,an empirical correlation formula was used to describe the relationship between power consumption and flow pattern transitions.Kazenin et al.[12]experimentally discussed dimensionless-number correlations for determining the power consumption and mass transfer characteristics in designing laminar-and turbulent-flow stirred vessels by flexible impellers.Scargiali et al.[13]proposed a novel total correlation for the predictionofthepowernumberwhichcouldhandleboththesubcritical and supercritical patterns.In terms of local characteristics distribution,Geng et al.[14]used the photography techniques to research the distribution laws of gas holdup,the local Sauter mean bubble size and interfacial area under different air flow rates with a half elliptical blade disk turbine.Laakkonen et al.[15]employed the particle image velocimetry equipment to simultaneously study the local bubble size distribution,interfacial area,air void fraction and fluid velocity in a flat aeration stirred tank.Bao et al.[16]adopted thedual electric conductivity probe method to investigate the local gas holdup,the mean bubble size and the gas-liquid two-phase interfacial area in a fully baffled dished base stirred tank.

In terms of homogenization energy,the homogenization energy,defi ned with two parameters including power consumption and mixing time,couldreflectthemixingefficiencyinthemultiphasemixingprocess.Ochiengetal.[17]definedthehomogenizationenergyandstudiedtheeffect of draft on homogenization energy.They found a more obvious decrease in power consumption and mixing time when a lower impeller off-bottom clearance was chosen.Meanwhile,the mixing efficiency increased by approximately 61%when compared to a system without draft.Bouaifietal.[18]definedthehomogenizationenergyastheproduct ofpowerconsumptionandmixingtime(Ptm)toobtainaquantitativeexpression of mixing efficiency.In general,the optimal mixing efficiency means the minimum homogenization energy Ptm.Based on this viewpoint,they found that the axial configurations presented a better mixing performance.Jafari et al.[19]utilized the homogenization energy Ptm to discuss the relationship between the agitated speed and the mixing performanceandfoundthatthegassingoperationcanreducethemechanical powerconsumptionandimprovethemixingefficiencyforagivenimpellerspeed.Inthiswork,anovelhomogenizationenergycorrelation,whichfirstly took into account the local distribution characteristics in the slot,was proposed to characterize the effect of impeller type,rotational speed,flexible piece length,etc.on power consumption.

In the present work,the objectives of this study are to carry out the research on gas-liquid two-phase mixing performance in rigid-flexible combination STRs.In order to deepen the knowledge of the gas-liquid mixing behavior and optimize structure and operation parameters of rigid-flexible combination STRs,theeffects of flexible piecelength l,impeller types,gas flow number Fl,agitated speed N on power consumption,local void fraction and gas-liquid two-phase interfacial area have been investigated.Then the mixing efficiency research based on the power consumption,local distribution characteristics and mixing time is conducted in a single-impeller gas-liquid STR.

2.Material and Methods

Fig.1 shows the investigated schematic diagram of rigid-flexible stirred tank in aerated system.Specific parameters are shown in Table 1.The transparent cylindrical Plexiglas tank was with an inner diameter of T=0.48 m,liquid height of H=T,and a thickness of 5 mm.Height of Plexiglas draft tube from the bottom was T/3.Four equally spaced baffles with a width of 5 mm were symmetrically installed on the inner wall of the draft tube.Tap water and air were selected for the experimental medium.The air was phase introduced via a ring sparger with 4-mm orifices and the ring sparger was 8 mm above the tank bottom.A Rushton disc turbine(RDT),a 45°pitched blade turbine(PBT),a rigid-flexible Rushton disc turbine(RF-RDT)and a 45°rigidfl exible pitched blade turbine(RF-PBT)impeller were used in the research system.The experimental impellers were shown in Fig.2.The rigid-flexible combined impellers are made up of stainless steel and silicon piece.Flexible piece lengths l,made of silicone,ranged from 2.0 to 4.0 cm.Gas flow rates ranged from 1.0 to 2.5 m3·h?1.Rotational speeds ranged from 1 to 3 s?1.As shown in Fig.1,the measuring points of the local void fractions and the local Sauter mean bubble size are 0.06 m away from the inner wall of the tank in the radial direction,i.e.,the ratio of the radial position r to the tank radius R is 0.75.There are 5 data collection points in the axial direction of the probe with a distance between consecutive points of 0.100 m.

Table 1 Experimental system specific structural parameters

3.Results and Discussion

3.1.Power consumption

In an aerated system,the agitation power consumption was measured by using the torque sensor(Da Yang Company,Model:HX-90D)installed on the stirring shaft.Agitation power consumption is calculated as following[20]:

Fig.1.The experimental process and test system.1—Chaotic motor;2—Programmable Logic Controller;3—Torque transducer;4—Stirring shaft;5—Baffles;6—Measuring points;7—Impellers;8—Computer;9—Data acquisition card;10—Pressure transducer;11—Ring gas sparger;12—Gas flow meter;13—Air compressor.

Fig.2.Impeller types.(a)Rushton disc turbine(RDT),(b)pitched blade turbine(PBT),(c)rigid-flexible Rushton disc turbine(RF-RDT),(d)rigid-flexible pitched blade turbine(RF-PBT).

where Pgis the net power consumption.M and M0representthe torque under normal working conditions and under no loaded,respectively.N is the measured agitation speed.In order to enhance accuracy in the results presented in the subsequent sections,the validation of torque has been conducted under different sampling frequencies(500,1000,1500 Hz).The differences in measurement of torque are within±4%.Then the selected sampling frequency can be deemed to have been validated and theresults toberepeatable.When thesamplingfrequency is determined,each of torque in the experimental system is determined by the average of three-repeated measurement.Thus,the sampling frequency of torque is set to 1000 Hz.In addition,the power consumption with aeration and no-aeration wascharacterizedbytherelative gassed/ungassedpower demand(RPD)Pg/P0.Inour initialstudy,wefoundthat thegasflownumberunderdifferentconditionshasaneffectonchanges in RPD.In the following figures,it is expressed as a certain fluctuant behavior.When the external operating conditions change,the fluctuation behavior of the RPD changes.For this reason,the relative standard deviation(RSD)is employed to quantitatively quantify the degree offluctuation.For the gas flow number Fl,the following points need to be addressed.In Section 3.1.1(Effect of impeller types on RPD),the parametersNand Q areconstants.TheFl canbedirectly obtained fromgasflow rates.In Section 3.1.2(Effect of impeller speeds on RPD),the parameters N and Q are variable when the parameter N is set to constants,equal to 1,2 and 3 s?1,respectively.Then relationship between relative power demand(RPD)and gas flow number under different impeller speeds is obtained.In Section 3.1.3(Effect of flexible length on RPD),the D is equal to the rigid structure diameter D0plus the length of theflexible length l.As with the above method,the parameter D is set to constants,equal to 2.0,3.0 and 4.0 cm,respectively.Then the result has been obtained.

3.1.1.Effect of impeller types on RPD

Fig.3.Relative power demand(RPD)characteristics with different impeller types under different gas flow numbers(l=3.0 cm,N=2.0 s?1).

As shown in Fig.3,the RPD values are gradually decreasing,then will remain almost unchanged as the Fl continues toincreasefor fourselected impellers.As can be seen from the Fig.3,the RPD values of rigid-flexible impeller system(RF-RDT,RF-PBT)are higher than those of rigid impeller system(RDT,PBT).That might be due to the addition of a flexible piece.For the rigid impellers system(RDT,PBT),RPD values of disc impeller are higher than those of pitched impeller because of the more projected width in the vertical direction.In terms of the impeller diameter,the additionoftheflexiblepiecefurtherincreasestheprojectedwidthandform dissipationof energybehindtheimpeller.Furthermore,maximum difference percentage in RPD values of RDT is 5.65%larger than that of PBT.As for the rigid-flexible system,the maximum difference percentage in RPD valuesis4.20%.Whentheflexiblepieceisadded,themaximumdifference percentage in RPD values moves in the direction in which the Fl value increases.Indeed,it is well known that the impellers worked in different regimes,so cavities behind the impeller blades were different because of the different quantities of gas received[18].For the same consumption,disc turbines produced more turbulent and less mean flow when compared with the pitched turbines[21].These factors may be the cause of the above difference.

3.1.2.Effect of impeller speeds on RPD

The change characteristics of RPD as obtained with the RF-RDT under the different impeller speeds and gas flow number conditions is shown in Fig.4.The impeller speed has a more obvious effect on power consumption and the RPD shows a trend of decreasing with increasing Fl.Simultaneously,RPD values are above 0.4.Indeed,the aeration operation can be used as a potential energy to achieve specific flow regime requirements with the same power consumption[16].Moreover,with an increase in gas flow number,the change trend of relative standard deviation(RSD)of RPD values under different rotational speeds has also been studied.The value of relative standard deviation(RSD)can indicate the degree of influence of the change of gas flow rate on RPD value and help us control the operation mode of gas-liquid stirred reactor.One obvious change is that the RSD value of RPD increases as impeller speed increases.When the rotational speed is equalto2or3s?1,theRSDvaluesareincreasedby1.47%,3.88%,respectively when compared to that of impeller speed equal to 1 s?1.

Fig.4.Relative power demand(RPD)characteristics with different impeller speeds under different gas flow numbers(l=3.0 cm,RF-RDT).

3.1.3.Effect of flexible length on RPD

Fig.5 indicates a change trend relationship between relative power demand(RPD)variation and gas flow number under different flexible piece lengths.As shown in Fig.5,as the flexible piece length increases,the RPD values declines more rapidly.Actually,drainage capacity has a positive correlation with the diameter of impeller,which was raised by the increase in the flexible piece length.However,when air flow is large enough,gas flooding occurs in the stirred tank and the aeration operation cannot reduce the power consumption.Thus RPD value shows the changes as shown in Fig.5.From the perspective of RSD,when the flexible piece length is 3 cm,the RSD value is the smallest,that is,theinfluence of thegasflow number on thepower consumption is minimal.This finding provides guidance for the structural optimization of rigid-flexible stirred reactors.

3.1.4.Discussion on power consumption correlation

In order to propose a power consumption correlation suitable for rigid-flexible impeller system,four types of impellers(RDT,PBT,RFRDT,RF-PBT)are taken into consideration.Meanwhile,the gas flow number Fl(Fl=Q/ND3),the Froude number Fr(Fr=N2D/g)and power number NPG(NPG=Pg/ρLN3D5)are taken together to discuss.The power consumption correlation can be described as follows:

Table 2 shows the regression results based on power consumption correlation(3-2).As can be seen from the Table 2,the values of b are higher than those of c.This implies that aeration operation has a great influence on power consumption.In addition,the value of a0in the rigid-flexible impeller system is significantly greater than the value of a0in the rigid impeller system.

Table 2 Fitting parameters based on power consumption correlation

3.2.Local characteristics distribution profiles

In this work,the local void fraction(ε)and the local Sauter mean bubble size(d32)were obtained by using a dual electric conductivity probe(Jiu Zhang company,Model:BVW-2)and the measurement diagram is shown in Fig.1.Based on these measurement data,the local gas-liquid two-phase interfacial area values(a=6ε/d32)can be acquiredbythelocalvoidfractionandtheSautermeanbubblesize.Therefore,the vertical local bubble size distribution profile is not given in this section.The sampling frequency is set as 10 k Hz,and more than 500 bubbles were detected to obtain statistically representative data in eachmeasurement.Thethreemeasurementerrorsofthelocalvoidfractions and the local Sauter mean bubble size were within±4%,±6%,respectively.Thentheaveragevaluesofthree-repeatedmeasurementcan be deemed to have been validated and the results to be repeatable.In addition,the dotted line indicates the plane position of impeller inflowing Figures.It is worth mentioning that the he relative standard deviation(RSD)analysis of the local interfacial area is placed in the homogenizationenergysectionforbetterunderstandingofthecorrelation between energy homogenization behavior and local distribution characteristics.

3.2.1.Effect of impeller types on local distribution profiles

Theverticaldistributionoflocalvoidfractionandinterfacialareaasa functionofaxialheightZ/HisshowninFig.6.AstheZ/Hvalueincreases,thedistributionchangeoflocalvoidfractionisverysimilartothatofthe interfacial area for the four impeller types.For the vertical distribution ofthelocalvoidfraction(Fig.6a),therigid-flexibleimpellerhasahigher local void fraction value than that of rigid impeller system.The local void fraction of Rushton turbine impeller is slightly larger than that of pitched turbine impeller.For the vertical local interfacial area(Fig.6b),there are similar local interfacial area distribution profiles in the selected system.Meanwhile,an obvious maximum value is detected in the vertical distribution of local interfacial area near the liquid surface.That mightbe because of theexistence of highgas holdup and relativity small bubble in that region.

Fig.5.Relative power demand(RPD)characteristics with different flexible piece lengths under different gas flow numbers(N=2.0 s?1,RF-RDT).

Fig.6.Effect of impeller types on local distribution profiles(l=3.0 cm,N=2.0 s?1).

3.2.2.Effect of agitation speeds on local distribution profiles

TheFig.7showstheverticaldistributionoflocalvoidfractionandinterfacial area as a function of axial height Z/H under different agitation speeds.The local void fraction value increases as the agitation speed increased,but the trend becomes weaker.In terms of the maximum values of the local void fraction,the difference is not significant when the agitation speed is equal to 2.0 or 2.5 s?1.The maximum peak of local void fraction values at impeller speed of 2.0 and 2.5 s?1increase by 7.03%and 8.21%,respectively,when compared with that of agitation speeds of 1.5 s?1.Fig.7bshows thechange trendof local interfacialarea as Z/H increases.As for the maximum interfacial area,the maximum values at impeller speed of 2.0 and 2.5 s?1increase by 9.46%and 12.64%,respectively,when compared with that of impeller speed of 1.5 s?1.

3.2.3.Effect of flexible piece lengths on local distribution profiles

The vertical distribution of local void fraction and local interfacial area with the RF-RDT under the fixed impeller speed(N=2.0 s?1)are reported in Fig.8.The values of local void fraction and local interfacial area are both rise when the flexible piece length increases.This foundation is in agreement with the previous work.As for vertical local interfacial area,when the flexible piece length is 3.0 cm,the maximum value of vertical local interfacial area increased by 10.25%when compared with that of 2.0 cm.When the flexible piece length is 4.0 cm,the maximum value of vertical local interfacial area increased by 14.8%when compared with that of 2.0 cm.Therefore,thelarger flexible piece length helps improve gas-liquid dispersion performance in rigid-flexible combination system.

3.2.4.Discussion on local interfacial area correlation

The local interfacial area is linked to the power consumption Pgand superficial gas velocity Ug,which depend on the impeller type.Theflowing correlation is used to discuss the relationship between interfacial area and impeller types.The local interfacial area correlation is shown in Table 3,the value of k is the largest,which is directly affected by the impeller types.

3.3.Homogenization energy

Fig.7.Effect of agitation speeds on local distribution profiles(l=3.0 cm,RF-RDT).

Fig.8.Effect of flexible piece lengths on local distribution profiles(N=2.0 s?1,RF-RDT).

Table 3 Fitting parameters based on local interfacial area correlation

As mentioned above,the preliminary research of homogenization energy can be described as Ptm.The highest mixing efficiency means the minimum energy homogenization.The power consumption was obtained from the previous research(Section 3.1).The mixing time tm was measured by two pH sensors placed at the bottom and top in the STRs.ThemixingtimeexperimentprocessisshowninFig.1.Themixing time measuring system based on the signal of two pH sensors placed at the bottom and top of a stirred reactor and a conventional stimulusresponse technique,in which the tracer signal was the difference between two pH measurements,so that the effect of the position of the probes in the tank was minimized and the initial and final values of the tracer becamezero beingeasier the determinationof mixingtimes[22].Meanwhile,asmixingtime is slightly shorter when using thedifference of the two signals,the position of each probe in that case does not play animportant role[23].Inaddition,we set theacquisitionpHto1000Hz so that the data collected under each measurement system is sufficient.For more accuracy of the data standpoint,the mixing time experiments wererepeatedthreetimesandtheaverageofthethreemeasuredvalues is taken as the mixing time.In this paper,the local feature distribution information(local interfacial area a)is taken into consideration.When considering local characteristic distribution,Montante et al.[24]adopted the mixing index(its mathematical expression is the same as the relative standard deviation,RSD)to quantitative analysis the local conductivity.The greater fluctuation of the distribution of local eigenvalues(gas hold-up,conductivity,etc.)measured in the vertical direction reveals that the value of the mixing index is larger(relative standard deviation)[24].It also indirectly indicates the mixed state within the gas-liquid mixing process.That is,the greater mixing index value of local characteristic distribution means a poorer mixing state[25].Therefore,the local characteristic distribution could be quantized and expressed by RSD values.In order to take the RSD of the local interfacialarea intoconsideration,theexpression of redefininghomogenizationenergy(HE)canbeexpressedasHE=RSDPtm.TheRSDofthelocal interfacial area,mixing time and power consumption have a consistent monotonic response to mixing performance(energy homogenization).In other words,the higher values of RSD of the local interfacial area,mixing time and power consumption all performed the worse mixing efficiency or homogenization energy.Therefore,the expression RSDPtm could indicate the mixing efficiency(homogenization energy).

As shown in Fig.9,the impeller type,impeller speed,flexible piece length and air flow rate are taken together to discuss the mixing ef ficiency based on the refined homogenization energy(HE).In general terms,the highest mixing efficiency means the minimum energy homogenization.Thus,the optimal operating mode can be selected based on the HE value.From Fig.9,we can see that the impeller type has a greater influence on HE value because of the highest HE value and the widest distribution of the HE value.An increase in impeller speed can slow down the HE value,which indicates higher mixing ef ficiency.Takentogether,fromthestandpointof changesinHEvalues,the preferred mode of operation is RF-RDT,2.5 s?1,3 cm,1.8 m3·h?1.

Fig.9.Refined homogenization energy(HE)at different conditions.

4.Conclusions

(1)As for power consumption,RPD decreases and then remains at a specific value with increasinggas flow number(Fl)and agitation speed.Inaddition,fromtheperspectiveofRSD,whentheflexible piece length is 3 cm,the RSD value of RPD is the smallest.

(2)As for local void fraction,two peaks of value distribution of vertical local void fraction are detected near the impeller location and below the liquid surface at a certain distance.As for local interfacial area,the rigid-flexible impeller has a higher local void fraction value than that of rigid impeller.The larger flexible piece length helps improve gas-liquid dispersion performance in rigid-flexible combination system.From the perspective of local interfacial area correlation,the influence of impeller types on interfacial area is greater than that of power consumption and gasflow rate in this work.

(3)Therefinedhomogenizationenergy(HE=RSDPtm)basedonthe power consumption and local interfacial area.From the standpoint of changes in HE values,the preferred mode of operation is RF-RDT,2.5 s?1,3 cm,1.8 m3·h?1.

Nomenclature

a interfacial area,m?1

C impeller off-bottom clearance,m

D impeller diameter,m

d32Sauter mean bubble size,mm

Fl gas flow number

Fr Froude number

g gravitational constant,m·s?2

H liquid height,m

h1location of the first measurement point,m

Δh interval adjacent measurement points,m

l flexible piece length,m

M torques under normal operating condition,N·m

M0torques under unloaded condition,N·m

N agitation speed,s?1

NPGpower number

P the net power consumption,W

Pgpower with sparged gas,W

P0power without sparged gas,W

Q gas flow rates,m3·s?1

R agitation tank radius,m

r radial coordinate,m

Δr radial position of measurement points,m

tm mixing time,s

Ugsuperficial gas velocity,m·s?1

VLliquid volume,m3

w impeller with,m

Z plane of measurement point

ε local void fraction

ρ fluid density,kg·s?3