PIVMeasurementforRayleighConvectionandItsEffectonMassTransfer☆Wei Chen,Shuyong Chen,Xigang Yuan*,Huishu Zhang,Botan Liu,Kuotsung Yu

State Key Laboratory of Chemical Engineering and School of Chemical Engineering and Technology,Tianjin University,Tianjin 300072,China

Fluid Dynamics and Transport Phenomena

PIVMeasurementforRayleighConvectionandItsEffectonMassTransfer☆Wei Chen,Shuyong Chen,Xigang Yuan*,Huishu Zhang,Botan Liu,Kuotsung Yu

State Key Laboratory of Chemical Engineering and School of Chemical Engineering and Technology,Tianjin University,Tianjin 300072,China

A R T I C L EI N F O

Article history:

Rayleigh convection

Particle image velocimetry

Mass transfer coeff i cient

Enhancement of mass transfer

The velocity distribution in Rayleigh convection caused by acetone volatilization in acetone-ethyl acetate binary system was observed in a vertical cross section of an initially quiescent liquid layer by utilizing particle image velocimetry.Obvious turbulent vortexes that were induced by Rayleigh convection appeared in the bulk liquid, and its statistic features indicated thatRayleigh convection became moreintensewith theincrease of Ranumber and ReGnumber.Mass transfer coeff i cient was measured and the computed enhancement factor indicated that Rayleigh convection could promote the surface renewal of the liquid phase and intensify the interfacial mass transfer signif i cantly.A method was proposed for the prediction of mass transfer coeff i cient based on the measured velocity vector,and the predicted mass transfer coeff i cients are in reasonable agreement with the experimental results.

©2014TheChemicalIndustry andEngineeringSocietyofChina,andChemicalIndustryPress.Allrightsreserved.

1.Introduction

Rayleigh convection phenomenon has long been investigated since the work of Rayleigh[1]and Bénard[2].In gas-liquid or liquid-liquid mass transfer processes,when the liquid concentration gradient near the interface generated by species diffusion across the interface leads to a density gradient opposite to the direction of gravity,the system is said to be Rayleigh instable.When the density gradient attains a critical value,the denser liquid layer at the interface may collapse,and convection occurs near the interface.Such a density gradient driven convection,termed as Rayleigh convection,def i nitely affects the mass transfer in chemical engineering processes such as absorption,extraction,and distillation[3-6].

AgooddealliteratureelaboratedtheconvectionpatternsofRayleigh convection,for instance,Okhotsimskii andHozawa[7],Sha et al.[8]and Kutepov et al.[9]observed differentinterfacial convective f l ow patterns by using optical methods,such as the Schlieren technique,and describedthestructuresofconvectionpatternsingas-liquidmasstransfer processes.Lotsof researchers analyzedtheeffectof Rayleighconvection on the interfacial mass or heat transfer.Atmane et al.[10]discussed the f l ow characteristics and heat f l ux around a horizontal cylinder with Rayleigh convection.Arendt et al.[11]investigated the effect of Rayleigh convection and Marangoni convection on mass transfer of CO2-water system.Sun et al.[12]analyzed the enhancement of mass transferbyinterfacialconvectioninthephysicalabsorptionanddesorption of CO2into and from nonaqueous solvents.Guo[13]investigated the liquid phase concentration distribution via the real-time laser holographic interferometry,and near-interface turbulence and periodic burstwereobservedinthevicinityoftheinterface.Also,numericalsimulations of interfacial convection can be found in literature[14-16].

However,most of the previous studies focused on the investigation of macroscopic convective f l ow patterns caused by interfacial convection in gas or liquid phases,limited in qualitative analysis.In recent years,the local hydrodynamics of interfacial convection,such as liquid velocity distribution and turbulent structures,have been quantitatively investigated by experimental measurements.Buffone and Sef i ane[17] undertook an experimental study on evaporation driven convection in a vertically oriented capillary tube by using a μ-PIV(particle image velocimetry)technique.Corvaro and Paroncini[18]performed an experimental analysis by PIV to study the Rayleigh convection induced by heat transfer in a square cavity heated from below and cooled by the sidewalls,and indicated that the velocity module grew up with the increase of the Rayleigh number while the velocity distribution did not show the main differences.Baumann and Mühlfriedel[19] described the measurement of concentration prof i les near the liquidliquid phase boundary by the laser induced f l uorescence and computed the diffusion coeff i cient of the plain interface between two immiscible liquids.Xu et al.[20]measured the velocity distribution of near-surface turbulence by PIV and proposed an empirical correlation relating the mass transfer coeff i cient across the turbulent interface to the gradient of the vertical f l uctuating velocity(Hanratty's β).

However,the mechanism of interfacial convective hydrodynamics and the inf l uence of interfacial convection on mass transfer are still not clear.There are many models to depict the mass transfer across the gas-liquid interface in literature,but most models fail to take the randomness of interfacial instability and complexity of mass transfer mechanism across the interface into account.The previous experimental studies did not quantitatively observe the detailed f l ow structures ofinterfacialturbulence,andthereforecouldnotbeabletorevealtherelationship between interfacial convection and mass transfer.

In this study,Rayleigh convection in the gas-liquid mass transfer of acetone volatilization in acetone-ethyl acetate binary system is quantitatively measured utilizing PIV.The liquid mass transfer coeff i cient is obtained by measuring the liquid concentration change during the mass transfer process,and the mass transfer enhancement factor is analyzed to investigate the inf l uence of Rayleigh convection on gasliquid mass transfer.According to the velocity distribution obtained by PIV,the surface residence time,an important parameter for theoretical models of mass transfer,is computed based on the characteristic scale and surface velocity and used to predict the mass transfer coeff i cient via penetration theory.Then the predicted mass transfer coeff i cients are compared with the experimental data.

2.Experimental

With the volatilization of acetone from the liquid,the liquid density increases in the vicinity of the interface and Rayleigh instability is induced.The intensity of Rayleigh effectcan be characterized by a dimensionless Rayleigh number

wheredisthecharacteristiclength,whichisthethicknessofliquidlayer here,g is the gravity acceleration,Δρ is the liquid density difference between liquid surface and bulk liquid,D is the diffusivity of diffusing species in the liquid phase,and μ is the liquid viscosity.A positive Ra number is the necessary condition for Rayleigh convection.

The experimental apparatus,as illustrated schematically in Fig.1, consists of a gas-liquid interfacial mass transfer system and a PIV measurementsystem.Theinterfacialmasstransferappearsintheinterfacial mass transfer simulator with initially quiescent liquid of acetone-ethyl acetate solution and nitrogen gas f l owing above.

ThePIVsystemusedinthisstudywasmadebyLaVisionCorporation (Germany),and a double cavity Nd-YAG laser(made by Beamtech Optronics Corporation,China)with a maximum energy of 200 mJ and a wavelength of 532 nm was used as the light source.The laser beam, with 10 ns duration of the pulsed illumination,had a variable pulse frequency up to 15 Hz.The laser was also equipped with a lens system to produce a diverging laser sheet with a thickness not exceeding 1 mm. A CCD camera with a resolution of 1376×1040 pixels was used to capture the images,and was equipped with a f i lter with a wavelength of 532 nm to capture only the light scattered from the laser lightened particles.Hollow glass microspheres with diameters of 8−12 μm were seeded in the liquid as tracer particles.In the experiments,the laser was run at 4 Hz and the measurement time was 30 s.The PIV system grabbed and processed the digital particle images utilizing the crosscorrelation approach of the FlowMaster software to give the measured velocity vector distribution.

The interfacial mass transfer simulator was made of quartz glass with an inner size of 200 mm in length,20 mm in width and 40 mm in height.The determination of the width of the simulator was to conf i netheconvective vortexes distributingin the center of the simulator but avoid limiting the development of Rayleigh vortexes in that direction[21].The liquid was initially quiescent in the simulator with a thickness of 10 mm.Nitrogen gas successively passed through activated carbon,silica gel and molecular sieve to remove the impurities and water,and then presaturated by the solvent in a tank in order to reduce the inf l uence of solvent evaporation.The liquid was likewise presaturated by nitrogen gasto avoid the gas absorption into the liquid. The reagents were provided by Kewei Chemical Corporation(Tianjin, China)with a declared purity of 99.5%.And the purity of the nitrogen gas was 99.99%(mass content).The liquid concentrations near the gas inlet and outlet positions of the simulator were measured via the gas chromatography(HP 4890,Agilent Technologies,USA)to analyze the liquid side mass transfer coeff i cient.

PIV system was used to measure the f l ow velocity distribution in a centralverticalcrosssectionoftheliquidphaseparalleltothegasf l owing direction(the sheet with green dots shown in Fig.1)by observing the motions of the tracer particles lightened by the laser sheet.

Theexperiments were carried out ata pressure of 101.325 kPa and a temperature of 298.2 K.Under such a condition,the densities of acetone and ethyl acetate are 785 and 895 kg·m−3,respectively.In our experiments,the density of the liquid solution was estimated based on isochoric mixing of the two species.It is diff i cult to estimate the solute concentration and the liquid density at the interface in the desorption process.However,a low concentration of thesoluteat the liquid surface could be expected because the acetone concentration in the gas side should be very low due to the nitrogen gas continuously f l owing by.In an extreme case,the liquid at the surface could be pure solvent.A nominal density difference Δρ of the liquid phase in Eq.(1)could be characterized as the density difference between the solvent and the solution.

3.Results and Discussion

Fig.1.Schematic diagram of the apparatus for PIV experiments.1—nitrogen vessel;2—gas purif i er and presaturator;3—rotameter;4—interfacial mass transfer simulator;5—laser sheet;6—laser head;7—computer;8—CCD camera.

3.1.Velocity vector distribution

Desorption of acetone from the system increases the liquid density at the surface,and as a result,the liquid surface becomes instable and the denser liquid tends to descend into the bulk liquid by gravity.

From the measured velocity vector distribution in the acetone desorption process via PIV at different time shown in Fig.2,the occurrence and development of Rayleigh convection can be observed.At t=5 s,an evident two-celled convection pattern appears near the interface.The convection cells develop into the bulk liquid at t=15 s. At t=25 s,the old convection cells vanish and new convection cells occur.

Fig.3 depicts the velocity distribution in the measured cross section of the liquid at 10 s for theacetonedesorption process with different Ra and ReGnumbers.The velocity vector becomes greater and the convective vortexes go into chaos with the increases of Ra number and ReGnumber.Theconvection patternsshowninFig.3 areingood agreement with the Schlieren images obtained by Sha et al.[8,22]for Rayleigh convection,whichexhibittypicallyaninverse-mushroomconvectivestructure with two symmetrical vortexes.

In our experiments,the momentum attributed to the initial injection of liquid and sweeping effects of gas will generate bulk f l ow in the liquid,so the velocity distributions shown in Figs.2 and 3 are the ensemble results of both the Rayleigh convection and the bulk f l ow induced by the initial liquid injection and gas sweeping.Generally,the characteristic scale of Rayleigh convection should be much smaller than that of the unavoidable bulk f l ow.

In order to capture f l ow patterns of Rayleigh convection in terms of vertex,a f i ltering approach based on large eddy simulation(LES) decomposition[23,24]is employed to f i lter out the velocity of the unavoidable bulk f l ow.According to LES decomposition,the measured velocity can be decomposed into a f i ltered velocity that forms large eddies and remaining velocity that forms small eddies[24]:

where U is the two dimensional velocity measured by PIV,U is the fi ltered(large-scale)velocity,U′is the remaining(small-scale)velocity,x and y are the coordinates,t is the time,f is the fi ltering kernel function, whichis Gaussian fi lter[24]inthis paper,and Ð is thedomainof thevelocity fi eld.According to the size of the simulator,the characteristic scale of the Rayleigh convection should be the minimum size of the liquid layer,i.e.,the thickness of the liquid layer 10 mm.

Fig.2.The velocity vector distribution at different times measured via PIV for Ra= 2.66×108and ReG=13.7.

Fig.3.The measured velocity vector distribution via PIV at 10 s.

Itshouldbenotedthat,forstabilityanalysis,thecharacteristiclength d*in the Rayleigh number is def i ned as the thickness of the liquid surface layer in which veritable density gradient develops before the onsetofRayleighconvection.However,becauseitisdiff i culttomeasure the concentration distribution,we simply take the thickness of the entire liquid layer 10 mm as the characteristic length d.Such way of handling d forestimatingRa by Eq.(1)is valid if thecharacteristic lengthd* is assumed constant,since for constant d*,Ra by Eq.(1)is proportional to Ra*that is based on the characteristic length d*,and all the variation behavior(averaged velocities forexample)withrespecttoRa shouldberetainedforthosewithrespecttoRa*,ofwhichtheonly differencefrom Ra is in their magnitudes.

Fig.4 shows the original velocity f i eld and small-scale velocity f i eld based on the LES decomposition.The small-scale velocity f i eld shows thestructuresofmeasuredRayleighconvectioninmoredetail.Symmetrical vortexes of Rayleigh convection with scales of about 2−6 mm are clear,and the vortex center is about 1-3 mm below the liquid surface.

3.2.Average velocity

In the ga-liquid mass transfer process studied in the present paper, the convection in bulk liquid was inf l uenced by both Ra and ReGnumbers.Because the Rayleigh convection is caused by the density gradient in the gravitational direction,the f l ow along the gravitational direction (vertical direction in this paper)will play a dominant role[25].In the experiments here,the Rayleigh convection developed continuously in the measurement time of 30 s.Therefore,the time-space averaged vertical velocity for the measured velocity f i eld in 30 s is employed to characterize the Rayleigh convection.

Fig.5showsthetime-spaceaveragedverticalvelocityvs.Ranumber with different ReGnumbers.It is found that Vavgis exponentially related to the Ra number and the regression equations are listed in Table 1.The pre-exponential factor is larger with the increase of ReGnumber.Thus Vavgincreases with the increase of the Ra number and ReGnumber, and the gas f l ow also inf l uences the interfacial convection signif i cantly with a large ReGnumber.The explanation on the positive effect of ReGontheverticalvelocityisthatthegasf l owcouldrenewthegasattheinterface and increase the concentration gradient at the liquid surface. Therefore,both high liquid concentration and gas f l ow rate promote the volatilization of acetone and intensify the Rayleigh convection,promoting the mass transfer signif i cantly.

3.3.Characteristic scale

Accordingtotheturbulentcascadetheory,thescaleofturbulentvortexes can be separated into three ranges[26]:injective range where the turbulent energy is injected by external forces,inertial sub-range where the energy is conserved and transported to smaller scales,and dissipative range(Kolmogorov range)where the viscous dissipation overcomes the movements and stops the cascade.In this paper,the characteristic scale is de fi ned as the size of the largest turbulent eddy which could be computed by velocity vector.To reduce the in fl uences of liquid injection and gas sweeping,the small-scale velocity fi eld decomposedbyLESdecompositionisusedtocomputethecharacteristic scale.The characteristic scale L can be decompounded into Lu,x,Lv,x,Lu,yand Lv,y,where the fi rst subscript corresponds to velocity components u or v and the second subscript means along coordinates x or y [26,27].Taking Lu,xand Lu,yfor example,root mean square values u″of fl uctuating velocity and autocorrelation coef fi cients Ru,x,Ru,yof each point in the fl ow fi eld can be computed as follows.

Fig.4.LES decomposition of measured velocity distribution for Ra=1.2×108and ReG=69.0 at t=10 s.

Fig.5.Time-space averaged vertical velocity in different experiments.

where u′is the f l uctuating velocities based on time averaged velocity, and n is the number of total images(n=120 in this study,images were grabbed by PIV measurement at 4 Hz for 30 s);

Table 1Correlations for time-space averaged vertical velocity vs.Ra number

Finally,L can be computed by orthogonal synthesis of Lu,x,Lv,x,Lu,yand Lv,y.A time-space averaged characteristic scale Lavgis computed toinvestigate the features of Rayleigh convection at different Ra and ReGnumbers.

Fig.6 shows the time-space averaged characteristic scale Lavgvs.Ra number for different ReGnumbers,and the regression equations are listed in Table 2.Lavgdecreases exponentially with the increase of Ra number and also decreases with the increase of ReGnumber.With the increase of Ra and ReGnumbers,the gas-liquid system is more instable and the induced Rayleigh convection is more intense,so that the convective vortexes become smaller.This result is in accordance with that discussed for the averaged vertical velocity in Section 3.2. The computed characteristic scale of the system can be further used to compute the surface residence time for the penetration mass transfer model.

4.Inf l uence of Rayleigh Convection on Mass Transfer

The liquid mass transfer coeff i cientis obtained bymeasuringthedesorption amount of acetone from the liquid phase,and the enhancement factor is then computed based on the theoretically predicted mass transfer coeff i cient without convection.Additionally,a method for mass transfer coeff i cient prediction is developed based on the measured velocity vector via PIV.

4.1.Mass transfer coeff i cient and enhancement factor

Withthe measured liquid concentrationsfor theacetonedesorption process of acetone-ethyl acetate system,the mean mass transfer coeff icient KL,expduring 30 s can be computed:

whereVListheliquidvolume,CL,0istheinitialconcentrationofsolution, CL,tis the concentration of solution at t=30 s,which is estimated by averaging the liquid concentrations near the gas inlet and outlet of the simulator with the sampling positions 5 mm below the interface,A is the mass transfer area,is the averaged mass transfer driven force at t=0 s and t=30 s,and(CL−is the logarithmic mean driven force at the gas inlet and outlet:

Fig.6.Characteristic scales in different experiments.

Table 2Correlations for characteristic scale vs.Ra number

where the interfacial concentrations are[28]

where m is the phase equilibrium constant,m=CGeq/CL,and CGeqis the gas concentration in equilibrium with the liquid concentration CL.In this study the inlet concentration of gaseous solute is zero and its outlet concentration is computed via the material balance.

For mass transfer process by means of molecular diffusion,Zhang et al.derived a model for the liquid mass transfer coeff i cient KL,theobased on the Higbie penetration theory[28]:

where τtheois the theoretical surface residence time.

Under the realistic condition considered in this paper,the liquid mass transfer coeff i cient should be enhanced by the interfacial convection compared with the hypothetical prediction.Thus an enhancement factor F,which indicates the inf l uence of interfacial convection on mass transfer,is def i ned as the ratio of experimentally measured liquid mass transfer coeff i cient to that predicted by Eq.(11):

Fig.7 displays the relationship between enhancement factor F and Ra number onsemilog coordinate for differentReGnumbers.F increases with Ra number and ReGnumber,and then becomes f l at.Theresults indicatethattheRayleighconvectionpromotes theliquidsurfacerenewal andintensifythemasstransfersignif i cantly,andtheexplanationforthe inf l uence of gas f l ow is the same as those for Figs.5 and 6.The results given in Fig.7 conf i rm the conclusion in Section 3.

By f i tting the experimental data,a new correlation for estimation of mass transfer coeff i cient is proposed for this system,

This correlation could predict the Sh number fairly well for this system as presented in Fig.8,with the average relative error of 8.2%and correlation coeff i cient of 0.95.

It should be noted that,according to the def i nition of Ra number by Eq.(1),Ranumberincorrelation(13)representsjusttheRayleighinstability of the gas-liquid systemitself,becauseΔρ used in thedef i nition is the density difference between the pure solvent and the bulk solution.The density difference attributing to Rayleigh convection in the real process should be smaller than Δρ and is affected by the gas fl ow that de fi nes the ReGnumber.Thus ReGin Eq.(13)re fl ects the interfacial instability under the operating condition.It should be also note d that,the Ra number,with a magnitude of 106-108in Eq.(13),is much greater than the ReGnumber,so the Rayleigh instability determined by the system is dominant in the enhancement of interfacial mass transfer.

4.2.Mass transfer coeff i cient prediction

It is diff i cult to obtain the surface residence time of the liquid for masstransferprocesses.Inthispaper,itcanbecomputedbytheaverage interfacialvelocityandtheaveragecharacteristicscale[29],whichisthe realgas-liquidcontacttimewithinterfacialconvection.Basedontheassumption that the liquid surface renewal is controlled by the large scale vortex,the surface residence time can be def i ned as

Fig.7.Enhancement factors for different cases.

With the real surface residence time,the liquid mass transfer coef ficient can be computed by using the Higbie penetration theory:

Fig.8.The graph of Shfitvs.Shexp.

Fig.9.Predicted and measured values of mass transfer coeff i cient for different cases.

Fig.9 compares the predicted mass transfer coeff i cients based on the calculated surface residence time with the experimental data.The characteristic scale for surface residence time calculation is computed by the measured velocity vectors as described in Section 3.3.The mass transfer coef fi cients computed via the Higbie penetration theory are in reasonable agreement with the experimental data.Therefore,the mass transfer enhancement is attributed to thepromotion of liquid surface renewal by interfacial Rayleigh convection.The computed mass transfer coef fi cients are well accorded with the experimental data for low ReGnumber.However,the deviations increase with the increase of ReGnumber.For the method proposed here,the mass transfer coef ficientpredictionis basedonthePIVmeasurementdata inacross section in the center of the simulator with the weakest boundary effect and the strongest turbulence,so the predicted mass transfer coef fi cients should be greater than the experimental data.For the case of low ReGnumber, thesweepingeffectofthegas fl owontheliquidsurfaceisweak,andthe liquid fl ow at liquid surface is mainly induced by Rayleigh convection. For the case of rather high ReGnumber,such as panels(e)and(f)in Fig.9,thegas fl owmightinduceevidentliquid fl owattheliquidsurface. Thus the average tangential liquid velocity at the liquid surface used in Eq.(14)is the combined effect of gas sweeping effect and Rayleigh convection,and the measured uiavgshould be larger than that caused by Rayleigh convection.The estimated value of surface residence time is lower,which would make the calculated mass transfer coef fi cient larger than the measured value.Additionally,Rayleigh convective vortexes would become chaos with high impetus but not in a symmetricalstructure as we assumed.These limits in PIV measurements will introduce inevitable deviations into the predicted results.

5.Conclusions

The two-dimensional velocity f i eld of Rayleigh convection for acetone-ethyl acetate system was investigated via PIV.Rayleigh convection was found to have an inverse-mushroom convection pattern and a maximum convective vortex about 6-7 mm in the 10 mm thick liquid layer.Statistical analysis on the velocity vector indicates that both Ra number and ReGnumber have signif i cant inf l uence on Rayleigh convection:with the increase of the two numbers,the average vertical velocity increases and the average characteristic scale decreases.These results suggest that both high concentration and high gas f l ow rate could induce a great density gradient between the interface and bulk liquid,leading to intense Rayleigh convection.

According to the measurements of mass transfer,the enhancement factor of mass transfer increases with the Ra number and ReGnumber.And the mass transfer coeff i cient could be increased up to four-fold by Rayleigh convection.With a proposed method, the mass transfer coeff i cient estimated based on the surface residence time computed from characteristic scales is in satisfactory agreement with the experimental data especially for the case of small ReGnumber.However,with the limitation in our experiment, the two-dimensional velocity distributions were used in the mass transfer estimation,which is the main sources of the errors in estimating mass transfer coeff i cient and will be improved in our future work.

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21 November 2012

☆Supported by the National Natural Science Foundation of China(20736005).

*Corresponding author.

E-mail address:yuanxg@tju.edu.cn(X.Yuan).

http://dx.doi.org/10.1016/j.cjche.2014.06.022

1004-9541/©2014 The Chemical Industry and Engineering Society of China,and Chemical Industry Press.All rights reserved.

Received in revised form 14 March 2013 Accepted 24 March 2013

Available online 18 September 2014