urift

, J

35, 1

ersit

a r t i c l e i n f o

Article history:

Received 30 September 2010

Received in revised form

28 January 2011

Accepted 31 January 2011Available online 5 February 2011

Keywords:

Airlift

CFD

Hydrodynamics

Multiphase ow

Multiphase reactors

a b s t r a c t

of biochemical processes are ease of long term sterile operation,

d thend intion.hereloop

by a draft tube inserted into the column. The external loop airlift

Contents lists available at ScienceDirect

w.e

Chemical Engine

Chemical Engineering Science 66 (2011) 32683279liquid circulation.E-mail address: simcik@icpf.cas.cz (M. Simck).and a hydrodynamic environment suitable for fragile biocatalysts, consists of two separate columns connected with pipes. Otherimportant part, which may or may not be present, is the gasseparator. Its purpose is to prevent bubbles from being entrainedinto the downcomer, which would decrease the driving force for

0009-2509/$ - see front matter & 2011 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ces.2011.01.059

n Corresponding author.simplicity of construction, absence of moving parts, and lowpower consumption. Their other advantageous features in case

airlift reactor and the external loop airlift reactor. The internalloop airlift reactor is a bubble column divided into the two partsamong different types of multiphase reactors. They possess goodmixing, mass and heat transfer characteristics and they are usedin a wide range of industrial applications such as waste watertreatment, chemical (e.g. hydrogenations and oxidations) andbiochemical processes, and others. The other advantages are

the riser and the downcomer. Gas is injected into the riser anresulting difference between average densities in the riser athe downcomer provides a driving force for liquid circulaAlso solid particles can be present (catalyst, biomass, etc.). Tare two main groups of airlift reactors namely, the internal1. Introduction

Airlift reactors are pneumatically agitated vessels, and are one

which are susceptible to physical damage by uid turbulence ormechanical agitation (Chisti, 1998).

The airlift reactor consists of two interconnected main parts,SimulationThis paper documents experiments and CFD simulations of the hydrodynamics of our two-phase

(water, air) laboratory internal loop airlift reactor (40 l). The experiments and simulations were aimed

at obtaining global ow characteristics (gas holdup and liquid interstitial velocity in the riser and in the

downcomer) in our particular airlift congurations. The experiments and simulations were done for

three different riser tubes with variable length and diameter. Gas (air) supercial velocities in riser

were in range from 1 to 7.5 cm/s. Up to three circulation regimes were experimentally observed (no

bubbles in downcomer, bubbles in downcomer but not circulating, and nally the circulating regime).

The primary goal was to test our CFD simulation setup using only standard closures for interphase

forces and turbulence, and assuming constant bubble size is able to capture global characteristics of the

ow for our experimental airlift congurations for the three circulation regimes, and if the simulation

setup could be later used for obtaining the global characteristic for modied geometries of our original

airlift design or for different uids. The CFD simulations were done in commercial code Fluent 6.3 using

algebraic slip mixture multiphase model. The secondary goal was to test the sensitivity of the

simulation results to different closures for the drag coefcient and the resulting bubble slip velocity

and also for the turbulence. In addition to the simulations done in Fluent, simulation results using

different code (CFX 12.1) and different model (full EulerEuler) are also presented in this paper. The

experimental measurements of liquid interstitial velocity in the riser and in the downcomer were done

by evaluating the response to the injection of a sulphuric acid solution measured with pH probes. The

gas holdup in the riser and downcomer was measured with the U-tube manometer. The results showed

that the simulation setup works quite well when there are no bubbles present in the downcomer, and

that the sensitivity to the drag closure is rather low in this case. The agreement was getting worse with

the increase of gas holdup in the downcomer. The use of different multiphase model in the different

code (CFX) gave almost the same results as the Fluent simulations.

& 2011 Elsevier Ltd. All rights reserved.CFD simulation and experimental measinterstitial velocity in internal loop airl

M. Simck a,n, A. Mota b, M.C. Ruzicka a, A. Vicente b

a Institute of Chemical Process Fundamentals, Czech Academy of Sciences, Rozvojova 1b Institute for Biotechnology and Bioengineering, Centre of Biological Engineering, Univ

journal homepage: wwement of gas holdup and liquidreactor

. Teixeira b

6502 Prague 6, Czech Republic

y of Minho, Campus de Gualtar, 4710-057 Braga, Portugal

lsevier.com/locate/ces

ering Science

However, the quality of the CFD simulation predictions, of course,greatly depends on how well or how badly the employed CFD

M. Simck et al. / Chemical Engineering Science 66 (2011) 32683279 3269The knowledge of the airlift hydrodynamics is needed for thedesign of the airlift reactor. Basic global quantities such as gas holdupand liquid velocities in the riser and in the downcomer, totalinterfacial area, and others are needed to be known. The hydrody-namic and other relevant parameters such as the airlift geometry areinterrelated and their relationship can be quite complex and theydirectly or indirectly inuence each other in sometimes not soobvious ways (Chisti, 1998), e.g. the driving force for the liquidcirculation is the difference in gas holdups between the riser and thedowncomer. This driving force is balanced by friction losses in theriser and the downcomer and in the bottom and top parts of thereactor (inuence of bottom and top clearances in the case of internalloop airlifts or losses in connecting pipes in the case of external airliftsand of the airlift geometry in general). However, the resulting liquidcirculation in turn affects the riser and downcomer gas holdup andthus the driving force. The gas holdup depends also on bubble slipvelocity, which depends on the bubble size. Bubble size is inuencedby the gas distributor, coalesce properties of the involved uids andby turbulence. Turbulence is inuenced by liquid circulation, etc.

The relevant hydrodynamic parameters need to be eitherobtained experimentally or predicted by models of various types.A lot of experimental data have been published in the past onglobal quantities (holdup, liquid velocities) in airlift reactors andcorrelations based on these data. A large number of correlationsfor these parameters are compiled in Chisti (1989), other can be,e.g., in Chisti (1998).

Many of the correlations presented in the literature arerestricted in their validity to the same reactor size, type and gasliquid system used in their development (Young et al., 1991). As arule, these correlations are system specic, being of little use indesign or scaleup, where the usual requirement is for estimation ofexpected performance in larger or geometrically different reactorsor uids (Chisti, 1998). Some authors employed models based onmechanical energy balance in the airlift reactor, e.g. Verlaan et al.(1986), Chisti (1989), and Heijnen et al. (1997). However, informa-tion about friction losses (friction coefcients) must be provided asan input parameter for these models. More recent experimentalmeasurements of airlift global hydrodynamic characteristics (riserand downcomer holdup and velocities) can be found, e.g., in vanBaten et al. (2003), Blazej et al. (2004), Merchuk et al. (1998)and van Benthum et al. (1999) (internal loop airlifts) or in Freitaset al. (2000) and Vial et al. (2002) (external loop airlifts). Therewere also papers published on local gas holdup and/or local liquidvelocity measurements. Luo and Al-Dahhan (2008, 2010) measuredliquid velocity proles, turbulent quantities using the CARPTtechnique and gas holdups proles using computed tomographyin an internal loop airlift reactor. They observed signicant effect oftop and bottom clearances on the ow. They also observed that thebubbles are prone to concentrate in the riser center in radialdirection and the change from bubbly to churn-turbulent ow atsupercial gas velocity of 2 cm/s. Local gas holdups and/or liquidvelocities in external loop airlift reactors were measured, e.g.by Young et al. (1991), Vial et al. (2002), Wang et al. (2004), Caoet al. (2007), Utiger et al. (1999), or Lin et al. (2004).

Apart from experiments, empirical correlations or theoreticalmodels such as the models based on mechanical energy balance,CFD simulations can be an another tool, which can be used to studyairlift hydrodynamics. There are two main groups of multiphaseowmodels usable for simulations on bubble column/airlift scale. InEulerEuler models all phases are treated as interpenetrating con-tinua, while in EulerLagrange models the motion of individualparticles is tracked through the continuous uid. The EulerLagrange models, which track the motion of every single particle(approximated as a mass point with closure equation for theinterphase forces), can be used for smaller scale problems with

low gas holdup. Only EulerEuler models (mixture model and fullmodels, submodels and closure equations describe ow phenomenaoccurring in the airlift reactor. Since the gasliquid ows are verycomplex with ow phenomena occurring on a wide range of spaceand time scales, modeling of gasliquid ows is still an open subjectand far from being complete. It is still necessary to validatesimulation results against experiments. EulerEuler models needclosures for all relevant interphase force (drag, lift, added mass, etc.),for the turbulence (due to single phase ow and due to bubbles) andmodels for bubble coalescence and break-up, because the bubblesize gures in most of the closure equations. Sokolichin et al. (2004)discussed the relevance of individual interphase forces for thesimulation and also turbulence modeling issues in their reviewpaper. They observed a weak dependency of simulation results (inpartially aerated rectangular bubble column) on the employed valueof the bubble slip velocity. They explained this weak dependence bythe fact that the bubble total velocity was the sum of the bubble slipvelocity and the liquid velocity, which can be relatively high, so thechange in the bubble slip velocity had lower impact on thecalculated gas holdup. It could be expected from the same reasonthat the similar behavior (weak dependence of gas holdup on thebubble slip velocity) could be found in airlift simulations, if bubblesare present only in the riser and the downcomer holdup is zero, andmay be the dependence could be even weaker due to the moreordered ow in the airlift if compared to the bubble column.However, if there is nonzero gas holdup in the downcomer, thenthe effect of the bubble slip velocity could be much stronger due tocountercurrent ow of both phases in the downcomer. It is then notsurprising that some authors did simulations of airlifts and obtainedgood agreement with experiments even when inappropriate closurefor drag force was used (e.g. SchillerNaumann correlation for rigidsphere drag used for 5 mm equivalent diameter air bubble in water)in cases with zero downcomer gas holdup.

There are a number of papers dedicated to the EulerEuler CFDsimulations of airlift reactors.

External loop airlift simulation comparisons of radial prolesof gas holdup and liquid velocity can be found, e.g. in Vial et al.(2002), Roy et al. (2006), or Cao et al. (2007). The comparison ofaverage gas holdup and liquid velocities with experiments forinternal loop airlifts and for zero downcomer gas holdup can befound, e.g. in Mudde and van den Akker (2001) (rectangularairlift), van Baten et al. (2003), or in Huang et al. (2008), whoalso reported weak dependence of the simulation results on thebubble velocity prescribed on the top boundary condition. Simu-lations for cases with nonzero downcomer holdup were done, e.g.by Oey et al. (2001), Huang et al. (2010), Talvy et al. (2007) or Jiaet al. (2007). Talvy et al. (2007) compared vertical and horizontalproles of gas holdup in riser and downcomer, and horizontalliquid velocity proles in downcomer with experiments in arectangular airlift. Jia et al. (2007) compared simulated andexperimental horizontal proles of gas holdup and liquid in arectangular airlift and found a good agreement.

2. Goals

The primary goal was to test the ability of our CFD simulationsetup to capture global characteristics of the ow in our experi-mental 50 l internal loop airlift with enlarged degassing zoneEulerEuler model) were used in the presented work, thus onlyEulerEuler models are considered in the following text. The mainadvantage of CFD simulations if compared to experiments is that noexperimental apparatus has to be built; the equipment dimensionsand working uids can be easily changed in simulations; etc.(riser and downcomer mean liquid interstitial velocities and gas

holdup) in the three experimentally observed bubble circulationregimes, and so verify if the simulation setup could be later usedfor obtaining the global characteristic for modied geometries ofour original airlift design or for different uids. The comparisonwas done for three different riser tubes. The CFD simulations weredone in commercial code Fluent 6.3 using algebraic slip mixturemultiphase model. Simulations results using different model (fullEulerEuler) in different code (CFX 12.1) are also presented in thepaper. The experimental and simulation setups are describedin Sections 3 and 4, respectively.

The secondary goal was to test the sensitivity of the simula-tions to the different bubble slip velocity, and to the differentturbulence closure models (variants of ke, ko). This was doneusing the mixture model in Fluent 6.3 code.

3. Experimental setup

The experiments were done in an internal loop airlift reactorwith enlarged degassing zone. The total volume of the apparatus

the airlift was 10 and was set by the addition of NaOH solutionprior to the start of the measurement.

The gas holdups in the riser and downcomer were estimatedusing U-tube manometers. The agreement of this estimate withthe real gas holdup in the apparatus may be affected by a pressuredrop due to ow.

4. Simulation setup

The main part of the simulations was done in CFD code Fluent6.3 using the algebraic slip mixture model and the simulationsetup is described in detail in Section 4.1. A part of the Fluentsimulations was later recalculated in the CFX 12.1 code using thefull EulerEuler model and their results are also presented in thispaper, although the case B CFX simulations were not nished dueto convergence problems and the results are not shown. The CFXsetup is described in Section 5.2. The airlift geometry is shown

D4 142 28 142 28 142 28

D5 420 28 420 28 420 28

M. Simck et al. / Chemical Engineering Science 66 (2011) 326832793270Fig. 1. Airlift geometry (not in scale).was 50 l. The downcomer inner diameter was 14.2 cm. Measure-ments were done for three different riser tubes: 1206.2 cm(case A), 1208.7 cm (case B) and 1406.2 cm (case C)(height inner diameter). The airlift geometry is depicted inFig. 1 and the relevant dimensions are summarized in Table 1.The gas was entering the airlift through the 10 cm diameterporous plate sparger. The diameter of the active zone of thesparger, through which the gas ow was passing, was 8 cm. Airand tap water were used as the gas and liquid phase. Gassupercial velocities in the riser were in range from 1 to 7.5 cm/s.The net water ow through the airlift was zero.

The liquid interstitial velocity in the riser and in the down-comer were measured with four pH probes (two Methrom model620 probes in the riser and two model 691 probes in the down-comer) and evaluated from the probe signal response to asulphuric acid solution injection. The probe signal was monitoredand the data stored using Labview program. The signal samplingrate was 10 Hz. The mean liquid interstitial velocity (VLUL/aL),was estimated as VL(x2x1)/(t2t1), where x1,2 are probevertical positions and t1,2 are probe signal peak times. The probeswere placed at x8.4 and 117.5 cm in the riser, and at x9.0 and117.5 cm in the downcomer (x0 being the sparger level). Thereported values of interstitial liquid velocity are four measure-ments averages. The interstitial liquid velocity was measured inthe downcomer in cases A and C, and the riser velocity wascalculated from a continuity equation. It was done the oppositeway in case B.

The tracer was injected into the downcomer 18.4 cm above thegas distributor (10 ml of 4.5 M H2SO4 solution). Initial pH inside

H1 23 5 23 5 23 5

H2 1200 60 1200 60 1400 70

H3 200 16 200 20 0 0

H4 170 14 170 12 170 14

H5 120 6 120 6 120 6Table 1Airlift dimensions for congurations case A, case B and case C, and # of grid cells

per these dimensions in simulations (See Fig. 1).

Case A Case B Case C

(mm) # of

grid cells

(mm) # of

grid cells

(mm) # of

grid cells

D1 100 12 100 12 100 12

D2 62 12 87 12 62 12

D3 70 14 92 14 70 14in Fig. 1. The gas distributor in the simulation domain geometry

M. Simck et al. / Chemical Engineering Science 66 (2011) 32683279 3271had the same diameter as the riser. The computational grid wasthe same for both Fluent and CFX simulations and contained48,100 (case A), 49,100 (case B) and 44,700 (case C) grid cells. Thecomputational grid (at the airlift cross-section) is shown in Fig. 2and number of grid cells per each airlift dimension can be foundin Table 1. The grid was sufcient to obtain grid independentresults (see Section 5.1 for the grid independence test result). Thetimestep in all simulations was 0.005 s.

4.1. Fluent simulations

The mixture model was employed for simulations done inFluent 6.3 code. The model assumes that two or more phases areinterpenetrating. It can solve cases, where two or more phasesmove at different velocities and it assumes local equilibrium overshort spatial length scales, i.e. dispersed phases move at theirterminal velocities. This model is simpler than full EulerEulermultiphase model. The mixture model solves the continuity andthe momentum equation for a mixture with averaged mixtureproperties (density, velocity, and viscosity), an algebraic equationfor the dispersed phase(s) slip velocity and a volume fractionequation for the secondary phase(s). The mixture model shouldrequire less computational resources than the EulerEuler model,since it solves fewer equations. However, it can be sometimesmore difcult to converge with more iterations required to bedone, thus diminishing the mentioned advantage over the EulerEuler model. Model equations, boundary conditions and othersolver parameters are described in following paragraphs.

The algebraic slip mixture model solves the continuity andmomentum equation for the mixture, the algebraic equation fordispersed phase slip velocity and volume fraction equation for thesecondary phase to update the composition of the mixture due toow (Manninen et al. 1996), and nally the turbulence model issolved to provide the closure for the turbulent viscosity, which

Fig. 2. Computational grid for cases A and C (left), and case B (right) at the airliftcross-section.appears in the momentum equation for the mixture.Continuity equation

The mixture continuity equation is

@rm=@trUrmvm 0 1where vm(1/rm)

Pk1n akrkvk is the mixture mass averaged

velocity, and rmP

k1n akrk is the mixture density, ak is the

k-th phase volume fraction. The sums are over all (n) phases (k).Momentum equation

The mixture momentum equation is

@rmvm=@trU rmvmvm rprUmmrvmrvTmrmg

rU Xnk 1

akrkvdr,kvdr,k

!2

where n is the number of phases (2 in our case),mm(

Pk1n akmk)+mt is the mixture effective viscosity, mt is theturbulent viscosity and mk is the molecular viscosity of phase k.The k-th phase drift velocity is calculated as vdr,kvkvmvkc(1/rm)

Pi1n airivic, where vkcvkvc is the slip velocity of the

phase k (c index is for the continuous phase).Equation for the k-th phase slip velocity

The k-th phase slip velocity is calculated from the followingalgebraic equation:

vkc tkrkrca=frkZt=strak=akrac=ac 3The rst term on the right hand side of Eq. (3) is due to the

drag force, where tkrkdk2/(18mc) is k-phase particle relaxationtime, fCD Re/24 is a drag function, Redk9vkc9rc/mc, accelerationag(vm r)vm@vm/@t and CD is drag coefcient. The dragcoefcient CD was calculated from Tomiayama

0s correlation(Tomiyama et al., 2002) for a single bubble:

CD max min 24=Re10:15Re0:687,72=Ren o

,8=3Eo=Eo4h i

4a

where Eo(rLrG)gd2/s. The bubble equivalent diameter d insimulations was set to 5 mm. Previously done visual observationsof the bubbly ow using a high speed camera, suggest that thisbubble diameter could reasonably well represent the typicalbubble size in our airlift, at least for lower gas ow rates.(However these experiments were done for a bubble columnand not the airlift conguration of our experimental unit, andwere done only for low gas ow rates due to the opaqueness ofthe bubbly layer.) The drag coefcient calculated from (4a) isCD1.215 for a single 5 mm bubble, with a corresponding slipvelocity 0.23 m/s. All bubbles were assumed to be of the samesize, there was no bubble break-up/coalescence model employedin our simulations.

Another closure, SchillerNaumann, was employed just for testpurposes to examine an effect of bubble slip velocity on thesimulation results (see Section 5.1)

CD 24=Re10:15Re0:687 for Reo1000CD 0:44 for Re41000 4b

However, all other presented simulations used the previousEq. (4a) for calculating the drag coefcient.

The second term on the right hand side of Eq. (3) appears dueto a dispersion of secondary phase by turbulence. The st is theturbulent Prandtl number and Zt is the turbulent diffusivitycalculated from

Zt Cmk2=egg=1gg1Cbz2g 1=2

zg 9vkc9=2=3k1=2Cb 1:81:35 cos2yy vkcvk=9vkc99vk9Cm 0:09

The gg is a time ratio between the time scale of the energeticturbulent eddies affected by the crossing-trajectories effect, seeFluent users guide. The value of st was set to 0.01. The defaultvalue was 0.75. The lower value, which was used in our Fluentsimulations, enhances a turbulent dispersion. The lower valuewas chosen, because for case B bubbles owing into the riser didnot disperse fast enough across the whole riser cross section as itwas visually observed in experiments.

Phase volume fraction equation for the secondary phase

The mixture composition is updated by solving the transportequation for the dispersed phases (only one dispersed phase inour case)@akrk=@trUakrkvm rUakrkvdr,k 5

@acrcvc=@trUacrcvcvc acrprUacmc,eff rvcrvTc

M. Simck et al. / Chemical Engineering Science 66 (2011) 326832793272Turbulence model

The standard ke model was used to model turbulence. Thismodel belongs to a group of Reynolds averaged NavierStokesequation models. The instantaneous velocity in the momentumequation is divided into the average and uctuating partuvm+v0. Then the momentum equation is ensemble averagedand the resulting term r (rv0v0) is modeled asr [mt(rvm+rvmT )], where mt is the turbulence viscosity, whichagain requires a closure equation. The closure is

mt rmCmk2=e 6The turbulent kinetic energy k and turbulent dissipation rate e

are obtained by solving their transport equations

@rmk=@trUrmvmk rUmt,m=skrkGk,mrme 7

@rme=@trUrmvme rUmt,m=seree=kC1eGk,mC2erme8

Thus unlike the molecular viscosity, the turbulent viscosity isnot a constant, but it depends on the local ow eld. The termGk,m is a turbulence production due to mean velocity shear.

Gk,m mtrvmrvmT : rvm 9The turbulent model constants were Cm0.09, sk1, se1.3,

C1e1.44, C2e1.92.The boundary conditions were no-slip condition on all airlift

walls. Standard wall function was used to model a velocity prolein the walls vicinity and to provide inner boundary conditionfor Reynolds averaged velocity eld. Zero liquid velocity and0.25 m/s gas vertical velocity were prescribed at the inlet for allphases. Gas volume fraction was then set to a constant value toobtain the desired gas ow rate into the airlift. Zero liquidvelocity was set at the outlet boundary and zero gradients wereset for gas velocity and gas volume fraction (user dened functionwas used to do this). The initial condition was zero liquid velocityand gas volume fraction, initial turbulence kinetic energy wask0.001 m2/s2, and dissipation rate e0.0001 m2/s3. The timeinterval of 30 s was then simulated to let the ow reach a steadyor pseudosteady state. Then another 120 s or more of a ow timewas simulated to obtain time-averaged quantities for evaluation.

The segregated pressure-based solver in Fluent was used tosolve the model equations, node based gradient option was usedto evaluate variables gradients. PISO scheme was used as apressurevelocity coupling algorithm, PRESTO! scheme was usedfor pressure discretization and the QUICK scheme for velocity, gasvolume fraction, turbulence kinetic energy, and dissipation rate. Arst order implicit scheme was employed for the timediscretization.

4.2. CFX simulations

In addition to the simulations run in Fluent code (setupdescribed in Section 4.1), some simulations were later recalcu-lated in CFX 12.1 using EulerEuler two-uid model. Their setupis described in this section. Unlike the mixture model, this modelsolves continuity and momentum equation for each phase. Thusfor a two phase ow there are two continuity and two momen-tum equations, one set for continuous phase c and one for dispersedphase d. The two momentum equations are coupled together viapressure (pressure eld is shared by both phases), and viainterphase force terms, which accounts for various forces (drag,lift, added mass, turbulent dispersion force, and others) andcancel each other out when momentum equations of individualphases are added together. Drag force and turbulence dispersionforce were accounted for in our CFX simulations. Other forces

were not considered.acrcgMcd 12

@adrdvd=@trUadrdvdvd adrprUadmd,eff rvdrvTdadrdgMdc 13

whereMcdMdc is a force acting on the phase c due to phases d(drag, lift, etc.), and mc,eff and md,eff are effective viscositiesconsisting of a molecular and a turbulent viscosity

mc,eff mcmtc and md,eff mdmtdOnly drag and turbulence dispersion force were considered in

our simulations

Mcd Mcd,DMcd,TD 14

Mcd,D Kcdvdvc 3=4CD=dadrc9vdvc9vdvc 15where d is dispersed phase particle (bubble) equivalent diameter.Drag coefcient was set to CD1.215 resulting in a bubble slipvelocity 0.23 m/s (5 mm bubble in water).Mcd,TD CTDKcdntc=stcrad=adrac=ac 16where CTD1, Kcd is momentum transfer coefcient for drag force,ntc is turbulent kinematic viscosity of the continuous phase,stc0.9.

Two equation ke model was used to model turbulence and toobtain a closure for turbulent viscosity in the continuous phasemtc:

mtc Cmrck2c =ec 17

@acrckc=@trUacrcvckc rUacmcmtc=skrkcacGcacrcec18

@acrcec=@trUacrcvcec rUacmcmtc=serecacec=kcC1eGcC2ercec 19

where Gcmtc[rvc+(rvc)T]:rvcThe turbulent model constants were Cm0.09, sk1, se1.3,

C1e1.44, C2e1.92.Turbulence viscosity in the dispersed phase mtd was calculated

as

mtd rd=rcmtc=s 20where s1.

The boundary conditions were no-slip condition for liquid andfree-slip condition for gas phase on walls. Zero velocity for liquidand 0.25 m/s for gas phase were used. The volume fraction of gasphase was set to obtain the desired value of gas ow rate. Thedegassing condition was used at the outletliquid velocity is tozero, while the gas phase is allowed to escape.

5. Results

The results section has two main parts. Auxiliary simulationresults are presented in Section 5.1. The rst part consists of gridindependence test result, brief comparison of few simulationswith different turbulence models for a selected airlift congura-tion, and nally a comparison of two different closures for theThe continuity equations of continuous (c) and dispersed (d)phase are

@acrc=@trU@acrcvc 0 10@adrd=@trU@adrdvd 0 11

The momentum equations of phase c and d aredrag force. All of the simulation results discussed in Section 5.1

0.3

V

a dra

aum

M. Simck et al. / Chemical Engineering Science 66 (2011) 32683279 32730

0.1

0.2

0 0.06 0.08UG (m/s)

Tomiyama dragSchiller-Naumann drag

0.005

0.006

0.007

Tomiyam

Schiller-N

0.02 0.040.4

0.5

0.6

0.7

0.8

0.9

L (m

/s)were obtained from mixture model simulations done in Fluent 6.3(see Section 4.1 for simulation setup). The main simulation resultsand their comparison with experimentally measured data (liquidinterfacial velocity and gas holdup in the riser and in the down-comer) are presented in Section 5.2. The results for both simula-tion setups (Fluent, CFX) are presented. In experiments, therewere higher liquid velocities in the downcomer for the largerdiameter riser (case B) (lower downcomer cross section area) andthus gas phase was entrained into the downcomer. If cases A(shorter draft tube) and C (longer draft tube) are compared, thenfor the longer tube the gas separation was better resulting in nogas in the downcomer, while for the shorter draft tube (case A)bubbles were entrained into the downcomer for the highest gasow rate.

5.1. Auxiliary simulation results

The grid independence test was done for the case C(140062 cm riser) with riser air supercial velocity 2 cm/s(3.6 l/min). One simulation (Fluent) was run on a rened negrid with 8 more grid cells than in the standard coarse gridcase (357,600 vs. 44,700 cells). The difference in the liquidinterstitial velocity and gas holdup in the riser was within 1%.Thus it could be concluded that the standard grid was sufcient toobtain grid independent results.

(-

)

0

0.001

0.002

0.003

0.004

UG0 0.02

Fig. 3. Case A simulation results (Section 5.1). Comparison of two drag closures for 5 mmEq. (4b)). (a) Riser liquid interstitial velocity VL, (b) riser gas holdup a, and (c) downco0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

(-

)

UG (m/s)

Tomiyama dragSchiller-Naumann drag

g

ann drag

0 0.06 0.080.02 0.04Four additional turbulence models in addition to standard kemodel were tested for the case C, with gas ow rate 3.6 l/min priorto the main simulation campaign. These four models were RNGkemodel, RNG kemodel with swirl modication for turbulenceviscosity, realizable kemodel and standard (not SST) komodel.The models are not described in this paper and reader is referredto Fluents 6.3 User Guide (Fluent Inc. 2006) for details aboutthese models (simulations were run with default solver settings).The choice of the mentioned turbulence models had only a minorimpact on results of the simulations. The largest differencebetween standard ke model results and the other model resultswas 1.4% for interstitial liquid velocity and 4.9% for gas holdup inriser on coarse grid and 1.7% and 4.9% on the coarse grid,respectively. Standard kemodel was then kept for all subsequentsimulations. This turbulence model test was done because of ourprevious experience with the simulation of a partially aeratedrectangular bubble column, where a strong inuence of theseturbulence models was observed (qualitatively different owelds, 3 lower turbulent viscosity predicted by the RNG modelif compared to standard ke). However, the choice of the turbu-lence model had only a minor impact on the airlift simulationresults presented in this paper.

Different closures for drag coefcient were tested on cases Aand C to test the effect of changing the bubble slip velocity onsimulation results. Tomiyama closure for drag (4) for a singlebubble (5 mm equivalent diameter) and SchillerNaumann

(m/s)0.06 0.080.04

bubbles: Tomiyama (black marks, Eq. (4a)) and SchillerNaumann (white marks,

mer gas holdup a vs. riser gas supercial velocity UG.

Case A comparison between the drag closures is shown in

shown for case A and case C, simulations of case B were done only inFluent. Both setups (Fluent, CFX) gave very similar results. Althoughthere was a difference in their results in the radial gas holdupprole, it had only a minor impact on the global holdup and velocityvalues. In Fluent simulations the gas holdup radial prole wasalmost completely at, while in CFX simulations there was a relativedifference of 13% between the riser axis and the riser wall value.This was due to the stronger turbulent dispersion prescribed in theFluent simulation setup (st, Eq. (3)). The liquid velocity proles inCFX and Fluent simulations were similar, with relative difference inthe maximal velocity o3% (case A, UG7.5 cm/s). Nevertheless, asalready pointed out, the global values predicted by CFX and Fluentsimulations were almost the same.

Gas ow rates in the simulations were from 1.9 to 13.6 l/min(1.057.51 cm/s gas supercial velocity based on riser crosssection) for case A and C, and from 1.9 to 26.8 l/min (0.53

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Fig. 4. Case C simulation results (Section 5.1). Tomiyama drag closure (Eq. (4a))results for 3 mm (white marks) and 5 mm bubble (black marks). (a) Riser liquid

interstitial velocity VL, (b) riser gas holdup vs. riser gas supercial velocity UG.

M. Simck et al. / Chemical Engineering Science 66 (2011) 326832793274Fig. 3ac (riser liquid interstitial velocity and riser and downcomergas holdup vs. gas ow rate). We are aware that the SchillerNaumann closure is valid only for rigid spheres, which is certainlynot the case of 5 mm air bubble in water. However, the aim of thiscomparison was only to examine an inuence of changing a slipvelocity of bubbles on simulation results. The Tomiyama closuresresulted in bubble slip velocities (riser volume average) in range22.2 to 22.9 cm/s depending on the gas ow rate (was lower forhigher gas ow rates). The SchillerNaumann slip velocity was from37.6 to 38.6 cm/s, thus 70% higher. Nevertheless, even this ratherbig difference in slip velocities did not cause very signicant changesin simulation outputs. The relative difference between the gasholdups in riser was from 11.2% to 15.8% and was decreasing withincreasing gas ow rate (maximum absolute holdup differencebetween the two closures was 0.8%). The reason for this is theco-current ow of liquid and gas phases in the riser. The gas holdupin the riser is given by aGUG/VG, where UG is gas supercialvelocity given by air ow rate into the airlift and VG is gas interstitialvelocity in the riser, which is VGVL+Vslip. The effect of changing thebubble slip velocity Vslip on the holdup in the airlift riser is thensmaller then it would be in a case of bubbles rising through astagnant liquid (VL0), because the liquid velocity VL in the riser isrelatively high if compared to bubble slip velocity Vslip. The situationwould be different in the downcomer, where the phases owcountercurrently and the slip velocity value could have signicantimpact on the downcomer and also the whole airlift hydrodynamics.There was effectively zero gas holdup in the downcomer for all caseA gas ow rates except for the highest one with Tomiyama dragcorrelation, when the gas just started to be entrained into thedowncomer, and the downcomer holdup was 8% of the riserholdup. The difference between liquid interstitial velocities for thetwo drag coefcient correlations was from 1.6% to 8.5% and wasdecreasing with increasing of the gas ow rate with a sharper dropof this difference for the highest gas ow rate, where the drivingforce for liquid circulation was decreased by the small amount ofgas entrained into the downcomer (Tomiayama correlation case).

Case C comparison between simulations assuming 3 and 5mmdiameter bubbles is shown in Fig. 4a and b. Tomiyama dragcorrelation was used for both. The resulting volume averaged bubbleslip velocities in the riser were from 19.4 to 20.0 cm/s (3 mm bubble)and from 22.3 to 23.0 cm/s (5 mm bubble). There was only a verysmall difference between 3 and 5mm bubble simulations. Thereasons for this are the same as described in the previous paragraph.The relative difference between gas holdups in the riser was from 2.2%to 3.5%, and it was from 0.6% to 1.8% for the riser liquid interstitialvelocity. Again, the difference was decreasing with increasing of gasow rate. There was no gas in the downcomer.

It could be concluded that if the gas phase is present only inthe riser and not in the downcomer, then the impact of a bubbleslip velocity change is not so signicant due to co-current ow ofboth phases. However, if the gas phase is rising through astagnant liquid or even if the phases are owing countercurrently(downcomer), then, of course, this impact can be much moresignicant.

5.2. Main simulation resultscomparison with experiments

Simulation results for the three airlift congurations (cases A, Band C) and their comparison with experimentally measured data areclosure for 5 mm bubble were compared for case A, andTomiyama closure for 3 and 5 mm bubble were compared forcase C. Simulations were done for ve gas ow rates in range1.913.6 l/min for both case A and case C.presented in this section. Both Fluent and CFX simulation results are0.2

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Liquid interstitial velocities and gas holdups in the riser and inthe downcomer obtained from simulations (Fluent and CFX) and

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Fig. 5. Case A simulations vs. experiments (Section 5.2). Fluent simulations (black markvelocity VL, (b) downcomer liquid interstitial velocity VL, (c) riser gas holdup a, and (d

Fig. 6. Case A simulations (Section 5.2): Gas holdup elds for gas ow rates1.9, 3.6, 4.5, 9.1 and 13.6 l/min (riser gas supercial velocity 1.0, 2.0, 2.5, 5.0,7.5 cm/s).0.00

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0 0.02 0.04 0.06 0.08from experiments as a function of gas ow rate are shown inFig. 5ad. Gas holdup elds for different gas ow rates can beseen in Fig. 6. A very good agreement was obtained for liquidinterstitial velocity. The relative difference between simulations(Fluent) and experiments was from 0.7% to 4.4% and it wasincreasing with gas ow rate. The Fluent and CFX simulationsalso agreed very well with each other with CFX predicting slightlylower values. The situation was worse in the case of gas holdup.Simulations strongly underpredicted gas holdup in the riser(30% relative difference for the highest gas ow rate), and alsoin the downcomer, where the moment, when bubbles are startingto be entrained into the downcomer was shifted to higher gasow rates in simulations. The gas holdup from simulations in thedowncomer for the highest gas ow rate was less than 1/10 of theexperimentally obtained value. If a gas interstitial velocity isestimated from VGUG/aG, where UG is the gas supercial velocitygiven by gas ow rate, and aG is the experimentally measured gasholdup, then for the highest gas ow rate the VG would be74 cm/s, which is actually lower than the measured andsimulated liquid velocity and would result in a negative bubbleslip velocity, which is of course not possible. The reason of thediscrepancy between simulation and experiment is then probablydue to the experimental method used to obtain estimates of gasholdups. Holdup estimates measured with U-tube manometerscan be negatively inuenced by a pressure drop due to ow. Thiswill be discussed at the end of Section 5.2.

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) downcomer gas holdup a vs. riser gas supercial velocity UG.

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The results are shown in Fig. 7ad (gas holdups and liquidinterstitial velocities) and in Fig. 8 (simulated gas holdup elds).This case B is interesting, because three different bubble circula-tion regimes were experimentally observed with the change ofthe gas ow rate. At rst, for the lowest gas ow rate, there wereno gas bubbles inside the downcomer. Then for higher rates thebubbles started to be entrained into the downcomer, but thebubble front did not reach the downcomer bottom yet. Andnally, for the highest gas ow rate, the front reached the airliftbottom and bubbles started to circulate with a correspondingchange of interstitial liquid velocity and gas holdup vs. gas owrate curve trends. Now the question was if our simulations areable to capture this behavior. The answer is that they can, butonly partially. There was an initially good agreement in liquidinterstitial velocities. The difference between the simulation andthe experiment for the lowest experimentally measured gas owrate was o3.5% and it was continually increasing with gas owrate. It was 8.5% for the second highest ow rate, which is still ok.But for the highest ow rate, where there was a steeper rise of theexperimentally measured liquid velocity due to the regimechange, the experiment/simulation difference was 46%. Gasholdup in the riser and in the downcomer and also the point atwhich bubbles start to enter the downcomer was captured verywell. However, the agreement for the highest gas ow rate wasbad again. The bubble front did not reach the airlift bottom in the

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Fig. 7. Case B simulations vs. experiments (Section 5.2): uent simulations (blac(b) downcomer liquid interstitial velocity VL, (c) riser gas holdup a, and (d) downcome0.35

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0.50simulations and there appeared no bubble circulation regimeeven for the maximal gas ow rate. The liquid interstitial velocitydid not change much with an increase in the gas ow rate in thesimulations, except for the lower rates (only 6.2% increase fromgas ow rate 4.526.8 l/min). The liquid supercial velocity insimulations (and thus a total circulating liquid ow rate), waseven decreasing with gas ow rate. The reason was that the

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k marks), experiments (white marks). (a) Riser liquid interstitial velocity VL,

r gas holdup a vs. riser gas supercial velocity UG.

Fig. 8. Case B simulations (Section 5.2): instantaneous gas holdup elds for gasow rates 1.9, 3.6, 4.5, 9.1, 13.6, 17.9 and 26.8 l/min (riser gas supercial velocity

0.5, 1.0, 1.3, 2.6, 3.8, 5.0, 7.5 cm/s).

driving force for the liquid circulation, the difference betweenaverage holdups in the riser and in the downcomer, was slowlydecreasing with gas ow rate from a certain point (QG4.5 l/min,UG1.26 cm/s), while the gas holdups in the riser and the down-comer were rising linearly. The absolute difference between them(riser/downcomer) was 1.7% at QG4.5 l/min (UG1.26 cm/s) and1.2% at 26.8 l/min (UG7.51 cm/s). The liquid supercial velocityin the riser dropped from 34.6 to 32.3 cm/s in this gas ow raterange in simulations.

For case B simulations, there was a very good agreement withexperiments for low gas ow rates. The deviation from experi-ments then started to increase slowly with gas ow rate and thenit rose suddenly for the highest gas ow rate with the onset of abubble circulation regime, which was not captured by thesimulations. As it was pointed out earlier, ow in a downcomer(countercurrent ow) is inuenced by a bubble slip velocity muchmore than a ow in a riser (co-current). Demands on the accuracyof drag force closure are then quite high if bubbles are present inthe downcomer. Drag coefcient and bubble slip velocity forgiven uids depend on bubble size, shape and on local gas holdup(and other factors such as a presence of surfactants). To obtain acorrect bubble slip velocity (a) a reliable closure equation for it isneeded and (b) correct inputs into this closure are required. Ourclosure was Eq. (3). A bubble size can be either prescribed directlyor it can be a result from a bubble coalescence/break-up modelsolution. The local gas holdup is then provided by solving

governing equations of the ow. In our simulations the bubblesize was prescribed directly (5 mm for all ow rates, all bubblesassumed to have a same size). The weak point of our simulationsand the cause of disagreement between simulations and experi-ments can be any of the above mentioned issues, probably thespecication of bubble size and/or the slip velocity adjustment onthe local gas holdup. Although measurements of bubble size weredone with a high speed camera, they could be done only for verylow gas ow rates. The bubbly layer soon became opaque as theholdup increased. Nevertheless, if extrapolated for the higher owrates, and taking into account the weak dependency of the bubblerise velocity on the bubble diameter in range of bubble equivalentdiameters cca 410 mm (see e.g. Jamialahmadi et al., 1994), ourassumption was that the 5 mm xed bubble size can reasonablywell represent the typical bubble slip velocities encountered inthe airlift. When the bubbles were entrained into the downcomer,this assumption was probably too crude.

5.2.3. Case C

Simulations (Fluent and CFX) and experiments of case C arecompared in Fig. 9ac. Gas holdup elds for different gas owrates can be seen in Fig. 10. A good simulation/experimentagreement was obtained for liquid interstitial velocity. Therelative difference between simulations (Fluent) and experimentsvaried from 4.6% to 8.3%. And again, as for the case A, the Fluent

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the three experimentally observed bubble circulation regimes,and to verify if the simulation setup could be later used for

M. Simck et al. / Chemical Engineering Science 66 (2011) 326832793278and CFX simulations gave very similar results with CFX predictingslightly lower values of liquid interstitial velocity. The agreementbetween the simulated and experimentally measured gas holdupin the riser was poor. The relative difference in the riser holdup forthe lowest gas ow rate was 40.4% and continually decreased to15.5% for the highest gas ow rate. Unlike as in the case A, the gasholdup in case C was overpredicted by simulations. If case Csimulations are compared with case A simulations (case C has20 cm longer draft tube), then it can be noticed that the predictedliquid interstitial velocities are very similar, with case C velocities2.72.9% higher if compared to case A except for the highest gasow rate, where the case C velocity is 6.1% higher, becauseof starting bubble penetration into the downcomer in caseA. Experimentally measured riser liquid interstitial velocities forcase Cwere 6.311.6% higher than for case A depending on the gasow rate. If the same comparison is done for gas holdups (case Avs. case C) then the relative difference between case A and case Csimulations is again low (case C riser holdup 1.74.6 relative %lower). However, the experimentally measured holdup in case Cwas 24.733.2 relative % lower than in case A except for the lowestgas ow rate. Thus the difference between case A and case C inexperiments was much higher than in simulations. It may suggestthat the reason for bigger discrepancy between experimental and

Fig. 10. Case C simulations (Section 5.2): gas holdup elds for gas ow rates 1.9, 3.6,4.5, 9.1 and 13.6 l/min (riser gas supercial velocity1.0, 2.0, 2.5, 5.0, 7.5 cm/s).simulation data in case C is probably again a consequence of theexperimental method used to estimate gas holdups (U-tubemanometers). As it was already said, holdup estimates measuredwith U-tube manometers can be negatively inuenced by apressure drop due to ow.

One of the sources of error involved in using the U-tubemanometer is the pressure drop due to ow. Usually the pressuredrop effect is neglected. It was done also in measurementspresented in this paper. If the pressure drop in the riser isestimated as a pressure drop for a fully developed single phaseow in a pipe (turbulent ow, hydraulically smooth pipe) usingthe measured liquid velocities, then the estimates for the pressuredrop (taken for 1.2 m pipe length) for 7.5 cm/s gas supercialvelocities would be 150 Pa (case A), 70 Pa (case B), and165 Pa (case C). This would mean an underprediction of thereal gas holdup due to the pressure drop error by 1.31.4% forcases A and C, and 0.6% for case B (in absolute values notrelative). These are the maximal estimated errors for the threecongurations due to pressure drop and would be lower for thelower gas ow rates and the resulting lower liquid circulationrates. This would mean a better agreement between the simula-tion and the experiment for the case C holdup, if the pressure drop

CD drag coefcient ()

D distance, diameter (m)g acceleration due to gravity (m s2)G turbulent kinetic energy production due to mean

velocity gradient (J m3 s1)H distance, height (m)k turbulent kinetic energy (m2 s2)K momentum transfer coefcient (kg m3 s1)

3obtaining the global ow characteristic for modied geometriesof our original airlift design or for different uids. The secondarygoal was to test the sensitivity of the simulations to the differentbubble slip velocity, and to the different turbulence closuremodels (variants of ke, ko).

It was shown that there was a good agreement regarding theliquid interstitial velocities in the riser and the downcomer witherrors mostly well below 10% with an exception of higher gasow rates (and especially the highest one) in case B (largerdiameter riser). The agreement between simulations and experi-ments of the gas holdups in the riser and the downcomer waspoorer. The simulations overpredicted the riser gas holdup in caseA and underpredicted it in case C. However, as it was discussed inthe results section, it could be an error in experimental measure-ments rather than a simulation error. The agreement of the gasholdups in both the riser and the downcomer for case B wassurprisingly good, except for the highest gas ow rate, where aow regime had already changed to a bubble circulation regime,which was not captured by simulations. To conclude, theemployed simulation setups were able to predict reasonably wellsituations, when there was no gas phase entrained into thedowncomer. Care must be taken however, if the airlift operatesin the other two bubble circulation regimes. It was shown thatthere was only a weak inuence of the bubble slip velocity (andthus the drag coefcient) on the simulation results in cases withzero downcomer gas holdup. The reason for this weak inuence isthe co-current ow of the gas and the liquid phase in the riser.The phases ow countercurrently in the downcomer and then forthe cases with nonzero downcomer gas holdup a more accuratemodeling of the drag force/bubble slip velocity, probably inconnection with a bubble break-up coalescence model, wouldbe needed to obtain better agreement with experiments. Threeversions of the ke turbulence model and one ko model weretested. The choice of the turbulent model had only a minor impacton the simulation results.

Nomenclature

a acceleration (m s2)d bubble (equivalent) diameter (m)f drag function ()correction would be accounted for. Regarding the case B, notmuch would be changed, because there is smaller pressure dropdue to larger riser diameter. The agreement would get worse forthe case A, if the pressure drop correction would be included. Thesource of error in the case A experimental measurements isprobably different than the pressure drop.

6. Conclusions

The primary goal was to test the ability of our CFD simulationsetup to capture global characteristics of the ow in our experi-mental 50 l internal loop airlift with enlarged degassing zone inM force one phase is acting on another phase (N m )

p pressure (Pa)t time (s)u instantaneous velocity (m s1)U supercial velocity (m s1)v mean (ensemble averaged) velocity (m s1)v0 velocityuctuating part (m s1)

D drag (force)

Chisti, Y., 1989. Airlift Bioreactors.. Elsevier, London.Chisti, Y., 1998. Pneumatically agitated bioreactors in industrial and environmen-

tal bioprocessing: hydrodynamics, hydraulics, and transport phenomena.Applied Mechanics Reviews 51 (1), 33112.

Fluent Inc., 2006. Fluent 6.3 Users Guide.Freitas, C., Fialova, M., Zahradnik, J., Teixeira, J.A., 2000. Hydrodynamics of a three-

phase external-loop airlift bioreactor. Chemical Engineering Science 55,49614972.

Heijnen, J.J., Hols, J., van der Lans, R.G.J.M., van Leeuwen, H.L.J.M., Mulder, A.,Weltevrede, R., 1997. A simple hydrodynamic model for the liquid circulationvelocity in a full-scale two- and three-phase internal airlift reactor operatingin the gas recirculation regime. Chemical Engineering Science 52, 25272540.

M. Simck et al. / Chemical Engineering Science 66 (2011) 32683279 3279i,k index of a phasem mixture propertyTD turbulent dispersion (force)L liquidG gas

Others

Eo Eotwos numberRe Reynolds number

Acknowledgements

We gratefully acknowledge the nancial support of GACR(Grant no. 104/07/1110) and from FCT (Fundac~ao para a Cienciae Tecnologia, SFRH/BD/37082/2007). We also wish to thank ourcolleague S. K. Orvalho for reading the manuscript and providingvaluable feedback.

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Subscripts

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V interstitial velocity (m s1)

CFD simulation and experimental measurement of gas holdup and liquid interstitial velocity in internal loop airlift reactorIntroductionGoalsExperimental setupSimulation setupFluent simulationsCFX simulations

ResultsAuxiliary simulation resultsMain simulation results--comparison with experimentsCase ACase BCase C

ConclusionsNomenclatureAcknowledgementsReferences