CFD-PBM Coupled Simulation of an Airlift Reactor with Non-Newtonian Fluid

12 Pages·2017·5.22 MB·English

Oil&GasScienceandTechnology–Rev.IFPEnergiesnouvelles(2017)72,26
(cid:1)M.Hanetal.,publishedbyIFPEnergiesnouvelles,2017
DOI:10.2516/ogst/2017017
IFPEnergiesnouvellesInternationalConference
RencontresScientifiquesd'IFPEnergiesnouvelles
DynamicsofEvolvingFluidInterfaces–DEFIGatheringPhysico-ChemicalandFlowProperties
Dynamiquesdesécoulementsàinterfacesfluides–aucroisementdelaphysico-chimieetdelamécaniquedefluides
CFD-PBM Coupled Simulation of an Airlift Reactor
with Non-Newtonian Fluid
Mei Han1,2*, Zuoliang Sha2, Arto Laari1 and Tuomas Koiranen1
1SchoolofEngineeringScience,LappeenrantaUniversityofTechnology,P.O.Box20,Lappeenranta53851-Finland
2TianjinKeyLaboratoryofMarineResourcesandChemistry,TianjinUniversityofScienceandTechnology,Tianjin300457-PRChina
e-mail:mei.han@lut.fi
*Correspondingauthor
Abstract— Hydrodynamics ofan AirLift Reactor (ALR) with tapwater and non-Newtonian fluid was
studied experimentally and by numerical simulations. The Population Balance Model (PBM) with
multiple breakup and coalescence mechanisms was used to describe bubble size characteristics in
the ALR. The interphase forces for closing the two-fluid model were formulated by considering the
effect of Bubble Size Distribution (BSD). The BSD in the ALR obtained from the coupled
Computational Fluid Dynamics (CFD)-PBM model was validated against results from digital
imaging measurements. The simulated velocity fields of both the gas and liquid phases were
compared to measured fields obtained with Particle Image Velocimetry (PIV). The simulated results
show different velocity field profile features at the top of the ALR between tap water and non-
Newtonian fluid, which are in agreement with experiments. In addition, good agreement between
simulations and experiments was obtained in terms of overall gas holdup and bubble Sauter mean
diameter.
NOMENCLATURE
F Turbulent dispersionforce, Nm(cid:1)3
Symbols TD
F Wall lubrication force, Nm(cid:1)3
W
a Volumefractionof gas/liquidphase,1 k Liquidshear-inducedturbulencekineticenergy,
g/l l
Cl, Cɛ1,Cɛ2k-ɛModel parameters m2 s(cid:1)2
C Satomodel parameter k Turbulence kinetic energy due to bubble-
lb l,g
C Added mass coefficient inducedturbulence, m2 s(cid:1)2
VM
C Drag coefficient j Consistency index, Pa sn
D
C Lift force coefficient n Bubble number
L
C Turbulent dispersionforce coefficient n Flow index
TD
C Wall lubrication force coefficient U Gas superficial velocity, ms(cid:1)1
W g
d Bubble Sauter mean diameter, m Eo Eotvos number
s
d Bubble equivalent diameter, m Re Reynolds number
b
f Volume fraction of the bubble phase with size b(d) Bubblebreakuprateduetoturbulenteddies,s(cid:1)1
i
class ibased on thegas phase b(f |d) Daughter bubble size distribution
v
f Volumefractionof bubbleswithvolumev b (d) Bubble breakup rate dueto instability, s(cid:1)1
v 2
F Drag force, Nm(cid:1)3 - (d,d) Collision rate due toturbulent eddies,s(cid:1)1
D T i j
F Lift force, Nm(cid:1)3 P (d, d) Coalescence efficiency due toturbulent eddies
L T i j
ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommonsAttributionLicense(http://creativecommons.org/licenses/by/4.0),
whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Page 2 of12 Oil&GasScienceandTechnology–Rev.IFPEnergiesnouvelles(2017)72,26
- (d,d) Collision rate due tobubble wake, s(cid:1)1 and even production yield in the reactor. Bubble size
W i j
P (d, d) Coalescence efficiency due to bubble wake influencesgasholdup,gasresidencetime,specificinterfacial
W i j
- (d,d) Collisionrateduetodifferentrisevelocities,s(cid:1)1 area,andmassandmomentumtransferbetweenthegasand
U i j
P (d,d) Coalescence efficiency due to different rise liquid phase. Meanwhile, bubble size and its behavior are
U i j
velocities affected by several factors, such as gas holdup, liquid
velocityfieldandliquidphysicalproperty.Extensivestudies
[4-8] have shown that bubble size characteristics have
Greek Symbols
significant effects on the hydrodynamics and mass transfer
l Liquid apparent viscosity,kg m(cid:1)1s(cid:1)1 performance of ALR, especially for liquids with high
app
l Laminarviscosity, kg m(cid:1)1 s(cid:1)1 viscosity. For example, Hwang and Cheng [5] found that
lam
gas holdup decreased with increasing Carboxyl Methyl
l Dynamic viscosity of liquid due to shear-
tl inducedturbulence, kgm(cid:1)1s(cid:1)1 Cellulose (CMC) concentration due to formation of large
bubblesinhighlyviscousliquid.Dengetal.[6]showedthat
l Dynamic viscosity of liquid due to bubble-
tb Bubble Size Distribution (BSD) for highly viscous liquids
inducedturbulence, kgm(cid:1)1s(cid:1)1
became broader in heterogeneous flow regime and increase
l Turbulence viscosity of the gas phase,
tg of gas holdup slowed down with aeration rate due to
kg m(cid:1)1 s(cid:1)1
formation of large bubbles. Gumery et al. [8] reported that
l Effectiveviscosity, kg m(cid:1)1 s(cid:1)1
eff liquidcirculationvelocitydecreasedintheALRbyincreas-
c Shear rate, s(cid:1)1 ing liquid apparent viscosity due to enhanced bubble
q Liquid/gas density, kg m(cid:1)3 coalescence.
ɛ Overall gas holdup, % Computational Fluid Dynamics (CFD) simulation is a
g,o
ɛ Turbulentdissipationrateduetoshear-induced powerful tool to investigate and predict hydrodynamics in
l
turbulence, m2s(cid:1)3 multiphase reactors. However, it is required that the CFD
ɛ Turbulent dissipation rate due to bubble- models describe the phenomena behind the physics accu-
l,g
inducedturbulence, m2 s(cid:1)3 ratelyinordertopredictresultswithgoodconfidence.This
is still difficult and challenging since fluid mechanics in
multiphase flow is quite complex and far from fully under-
Subscripts
stood.Therefore,itisnecessarytovalidatetheCFDsimula-
tions of ALR experimentally, particularly with different
m Gas-liquidmixture
liquid physical properties. The two-fluid model with the
l,L Liquid phase
assumption of a single bubble size can give reasonable
g Gas phase
predictions for multiphase reactor only in cases where the
i,j Classesof bubble size bubble size isnarrowly distributed.Coupling ofPopulation
BalanceModel(PBM)intoCFDmodelscouldmakeitpos-
sibletoextendthesimulationandpredictionofflowregimes
INTRODUCTION fromhomogeneoustoheterogeneouswherethebubblesize
is widely distributed. PBM is an effective method to calcu-
Airlift Reactors (ALR) attract more and more interests in late BSD for gas-liquid flows on the condition that bubble
manyprocessapplications,suchassyngasfermentation[1], coalescenceandbreakupmodelsareprovidedasmodelclo-
direct coal liquefaction [2] and waste water/gas treatment sures. Many researchers have used the coupled CFD-PBM
[3]. The advantages of ALR over bubble columns include model to predict the hydrodynamics and mass transfer in
enhanced mixing efficiency and good suspension of multiphase reactors [9-14]. Their studies showed that a
particles due to improved liquid circulation. In comparison better agreement between simulations and experiments was
to mechanically stirred tanks, simple structure and low obtained when BSD was considered compared to using a
energy consumption make ALR even more attractive, constant mean bubble diameter. Chen et al. [10] found that
particularly considering the current stringent energy and the coupled CFD-PBM simulation was able to predict the
safety demands. effects of aeration rate and liquid surface tension on the
Airlift loop reactors are an important type of pneumati- gasholdupinbubblecolumns.Theypointedoutthatsimu-
cally agitated multiphase reactors where the bubble phase lations made by implementing PBM produced much better
functions as the agitation source and reactant. Bubble size comparison to experiments for gas holdup and liquid
characteristics,determinedbytheinitialbubblesize,bubble velocity than by using mean bubble diameter. Wang and
breakup and coalescence, is an important hydrodynamic Wang [12] investigated mass transfer in bubble column
parameter and closely related to mass transfer performance with the coupled CFD-PBM model and showed that the
Oil&GasScienceandTechnology–Rev.IFPEnergiesnouvelles(2017)72,26 Page 3of 12
CFD-PBM coupled model could predict effectively the
1
hydrodynamicsandmasstransfer.Liuetal.[13]performed
CFD-PBMcoupledsimulationsofairliftbioreactorforhairy 5
root culture and presented good agreement between
simulations and experiments in terms of bubble number
density. Xing et al. [14] investigated the ability of the 6
8
CFD-PBM coupled model to account for the effect of
viscosityonthegasholdupinabubblecolumn.Thefeature
that the increased viscosity resulted to a decrease in the
volume fraction of small bubbles and an increase in the
volume fraction of large bubbles was captured well using 9 2
the developed CFD-PBM model [12, 15]. The coupled
CFD-PBM simulations of ALR are relatively rare, espe-
ciallywiththeviscousornon-Newtonianfluid.Inindustrial 11RRiisseerr
applications, many processes [16-18] are operated in the 22DDoowwnnccoommeerr((ddrraaffttttuubbee)) 7
viscousmediumsorwithcatalystsshowingnon-Newtonian 33OO--rriinnggggaassddiissttrriibbuuttoorr
44GGaassmmaassssfflloowwccoonnttrroolllleerr
behavior.
55SSqquuaarreettaannkk
The aim of this study was to develop a CFD model for 66DDaavviiss88..33ssooffttwwaarree
ALR with non-Newtonian fluid in order to contribute to 77LLaasseerr
the design and optimization of ALR in practical applica- 88CCaammeerraaffoorrggaasspphhaassee 3
99CCaammeerraaffoorrlliiqquuiiddpphhaassee
tions. A PBM with the coalescence mechanisms by turbu-
4
lent eddies, wake entrainment and different rise velocities
of bubbles is coupled into the two-fluid model. Bubble
breakupsduetoeddycollisionandeddyinstabilityaretaken
into account. Gas holdup, bubble size and liquid and gas
velocity fields obtained by Particle Image Velocimetry
Figure1
(PIV) were used to validate the CFD model.
Schematicdiagramoftheexperimentalsetup.
1 EXPERIMENT
1.1 Experimental Setup and Material
Theschematicdiagramoftheexperimentalsetupusedinthis
work isshown inFigure 1.
The AR_ALR is composed of a riser (outer column),
downcomer (draft tube) and gas distributor. The riser is
0.15 m in inner diameter and 1.2 m in height. The down-
comer is 0.60 m high with the inner diameter of 0.10 m.
The downcomer was co-axially mounted with the riser
locating at 0.05 m above the column bottom. A plastic
O-ring gas distributor with a diameter of 0.12 m was
installed in the annulus between the riser and the down-
comer and it was at 0.07 m above the bottom. Gas is fed
to the column through 36 pores, with hole size of
0.5 mm distributed equidistantly at the top of the O-ring.
The AR_ALR is located inside a transparent rectangular Figure2
box in order to diminish optical distortions during visual- Dynamic viscosity of water and CMC solution measured by
rheometer.
ization measurements.
Tap water and 0.14 wt% CMC (Finnfix 50000) aqueous
solution were employed to study the Newtonian and non- 302 (Anton Paar) and the curve is shown in Figure 2.
Newtonianfluids.ThedynamicviscosityoftheCMCsolu- As the reference, the viscosity of tap water was also tested
tion was measured with the Modular Compact Rheometer andisshowninFigure2.TheCMCsolutionexhibitedshear
Page 4 of12 Oil&GasScienceandTechnology–Rev.IFPEnergiesnouvelles(2017)72,26
TABLE1
GoverningequationsanddiscretePBMfortheALR.
Models Equations
Massconservation rðq a u Þ¼0;k¼l;g
k k k
(cid:1) (cid:1) (cid:3)(cid:3)
rðq a u u Þ¼(cid:1)a rP0þr a l ru þruT þq a g
Momentumconservation k k k k k k eff k k k k
þFD;kþFL;kþFW;kþFT;k
(cid:1)(cid:1) (cid:3) (cid:3)
rðqlalklulÞ¼r alllam;lðltlþltbÞ=rk rkl þalðGk;l(cid:1)qlelÞ
(cid:1) (cid:1) (cid:3) (cid:3)
rðqlalelulÞ¼r al llam;lþðltlþltbÞ=re rel þ alel=klðCe1Gk;l(cid:1)Ce2qlelÞ
Moedqifiueadtiokn-ɛ[2tu0r,b2u1le]nce lt;l¼Clðql=k2lelÞ;leff ¼lapp;lþlt;lþltb;ltb¼Clbqlagdbs(cid:4)(cid:4)ug(cid:1)ul(cid:4)(cid:4)
kl;t¼klþkl;g;el;t¼elþel;g;kl;g¼1=2agCVMu2slip;el;g¼agguslip
ltg¼lt;lqg=ql
P (cid:1) (cid:3)(cid:4) (cid:4)
FD;k ¼ Mi¼1fiagql34CdDbii ug(cid:1)ul (cid:4)ug(cid:1)ul(cid:4)
Dragforce[22] (cid:5) (cid:1) (cid:3) (cid:6)
C ¼max 24Re(cid:1)1 1þ0:15Re0:687 ;8=3Eo=ðEoþ4Þ
Di i i
P (cid:1) (cid:3)
FL;k ¼(cid:1) Mi¼1CLifiagql ug(cid:1)ul oourl
8 (cid:1) (cid:1) (cid:3)(cid:3)
<min 0:288tanhð0:121Re;f Eo0 ; Eo0<3:4
i i i
Liftforce[23] CLi: fðEo0iÞ; 3:4<Eo0i<5:3
(cid:1)0:29; Eo0>5:3
i
fðEo0Þ¼0:00925Eo03(cid:1)0:099Eo02þ1:088
i i i
P (cid:1) (cid:3) h i
Walllubricationforce[23] FW;k ¼(cid:1) Mi¼11=2CWifiagdbiql ug(cid:1)ul 2 ðR(cid:1)rÞ(cid:1)2(cid:1)ðRþrÞ(cid:1)2
Turbulentdispersionforce[24] F ¼(cid:1)C a qk oa
TD TD g l lor
(cid:1) (cid:3) jP(cid:3)k (cid:1) (cid:3)
ootðagfiÞþr agubfi ¼ j;k 1(cid:1)12dj;k gi;jkcj;kagfiagfkvi=vj=vk
Populationbalancemodelfor xi(cid:1)1(cid:4)ðxjþxkÞ(cid:4)xiþ1
bubblesintheALR[11]
XM XM
(cid:1)agfi ci;jagfk=vkþ ni;kagfkbkvi=vk(cid:1)biagfi
k¼1 k¼i
thinningbehaviorandtheapparentviscosity,l ,couldbe mass flow controller (Bronkhorst E-7000). Gas superficial
app
describedby the following powerlaw model: velocity,U ,wascalculatedbasedonthecross-sectionalarea
g
oftheriser(theannulus).Allexperimentswerecarriedoutat
l ¼jcn(cid:1)1 ð1Þ atmospheric pressure and room temperature.
app
wherejandnaretheconsistencyindexandtheflowindex 1.2 MeasurementTechniques
ofthefluid,respectively.jis0.118Pasnandnis0.68forthe
CMCsolutionobtainedbyfittingEquation(1)withtheleast- The overall gas holdup in the reactor, ɛg,o, was determined
squaresmethod. by theheight expansion method:
Tap water and CMC solutions were operated in experi- eg;o ¼ðHm(cid:1)HlÞ=Hm ð2Þ
mentsinbatchmode.Thestaticlevelforbothliquidphases
was0.8m.Oil-freecompressedairasthegasphasewasrun where H is the static liquid level and H is the gas-liquid
l m
in once-through mode. Gas flow rate was controlled by a mixture height after aeration.
Oil&GasScienceandTechnology–Rev.IFPEnergiesnouvelles(2017)72,26 Page 5of 12
TABLE2
Modelsofbubblesbreakupandcoalescencerate.
Mechanisms Equations
R R
bðdÞ¼ 0:5bðfjdÞdf;bðf;dÞ¼2bðfjdÞ= 1bðfjdÞdf
0 v v v v 0 v v
R
bðfjdÞ¼0:923ð1(cid:1)a Þne1=3 db P ðfjd;kÞðkþdÞ2k(cid:1)11=3dk
v g k b v
min
R
P ðfjd;kÞ¼ 1P ðfjd;eðkÞ;kÞP ðeðkÞÞdeðkÞ;P ðeðkÞÞ¼ð1=(cid:1)eðkÞÞexpð(cid:1)eðkÞ=(cid:1)eðkÞÞ
Bubblebreakupdue b v 0 b v e e
toturbulenteddies (cid:7) (cid:1) (cid:3)
P ðfjd;eðkÞ;kÞ¼ 1 fv;max(cid:1)fv;min fv;max(cid:1)fv;min(cid:3)d fv;min<fv<fv;max
b v 0 else
(cid:1) (cid:3) (cid:1) (cid:3)
fv;min¼ pk3r=ð6eðkÞdÞ 3; ðfv2;m=3axþð1(cid:1)fv;maxÞ2=3(cid:1)1Þ¼min ð21=3(cid:1)1Þ;eðkÞ=ðpd2rÞ ; (cid:1)eðkÞ¼p6k3ql(cid:1)u22k
Bubblebreakupratedue b ðdÞ¼b(cid:5) ðd(cid:1)dc2Þm ; bðf;dÞ¼2dð0:5Þ
toinstability 2 ðd(cid:1)dc2Þmþdmc2 v
pffiffiffi
- ðd;dÞ¼ðp=4Þa ða (cid:1)aÞ(cid:1)1C 2e1=3ðd þdÞ2ðd2=3þd2=3Þ1=2
T i j max max ij i j i j
Ctooatluesrbceunlecnetreadtedideuse PTðdi;djÞ¼exp(cid:9)(cid:1)(cid:9)0:75ð1þn2ijÞð1þn3ijÞ(cid:10)1=2ðqg=qlþcÞ(cid:1)1ð1þnijÞ(cid:1)3Wei1j=2(cid:3)
Cij¼lmbt;ij=ðlmbt;ijþhmb;ijÞ; lbt;ij¼(cid:9)l2bt;iþl2bt;j(cid:10)1=2; lbt¼0:89db;hb;ij¼(cid:1)NiþNj(cid:3)1=3
(cid:1) (cid:3) pffiffiffiffiffiffiffi
-W di;dj ¼12:0Hd2i(cid:1)uslip;i; (cid:1)uslip;i¼0:71 gdi
P ðd;dÞ¼expð(cid:1)0:46q1=2e1=3r(cid:1)1=2ðdd=ðd þdÞÞ5=6Þ
W i j l i j i j
Coalescenceratedue ((cid:1) (cid:3) (cid:9)(cid:1) (cid:3) (cid:10)
tobubblewake H¼ dj(cid:1)dc=2 6= dj(cid:1)dc=2 6þðdc=2Þ6 dj(cid:3)dc=2
0 else
(cid:4) (cid:4)
- ðd;dÞ¼p=4ðd þdÞ2(cid:4)u (cid:1)u (cid:4); P ðd;dÞ¼0:5
U i j i j ri rj U i j
PIVmethodwasadoptedtomeasureflowvelocityfields eachconditionandusedtocalculatethebubbleSautermean
forbothgasandliquidphasessimultaneously.ThePIVsys- diameter,d :
32
tem (LaVision GmbH) mainly included a double pulsed Nd
Yaglaser,twohighresolutionCCDcameras (1600pixel9 XN .XN
d ¼ nd3 nd2 ð3Þ
1200pixel)andDaVis8.3software.Theliquidvelocityfield 32 i bi i bi
i¼1 i¼1
was traced by PMMA-RhB fluorescent particles with the
diameter range of 20-50 lm. The measuring range of the where d and n are the bubble equivalent diameter and
bi i
flow field was from the wall to the centerline of the ALR the number of bubbles corresponding to the equivalent
in the radial direction. Each measurement window is diameter, and i indicates the size class that refers to the
75 9 50 mm in physical size. Eight hundred (800) pairs of bubble equivalent diameter.
imageswereacquiredbyeachcamerawithin10minforeach
testwhentheflowfieldwasinsteadystate.DaVis8.3soft-
ware was utilized to analyze the acquired images for each 2 MODELING AND SIMULATION
phase. The spatial resolution of the measured velocity field
was 3 9 3 mm (grid size). Ensemble- and time-averaged 2.1 Coupled CFD-PBM Model
velocity fields were calculated and used to compare to the
simulations. The governing equations of the time-averaged two-fluid
Digital imaging method was employed to evaluate the model and the discrete PBM model from Wang et al. [11]
bubblesizeandsizedistributionintheALR.Onethousand arelistedinTable1.BSDwasresolvedfromthePBMusing
(1000)digitalimageswereacquiredandusedtoanalyzethe the gas holdup and the kinetic energy dissipation rate
bubblesizeforeachcondition.Anoverlappingobjectrecog- calculated in CFD. Then BSD obtained from the PBM was
nition algorithm (Pixact Object Recognition and Analysis used to formulate the interphase forces and the turbulence
software, Pixact Ltd) developed byEloranta etal. [19] was modificationclosuretermsforthetwo-fluidmodel.Amod-
usedtorecognizeandanalyzethebubblesfromtheacquired ifiedk-ɛmodelbased onthetwo-timeconstantmodel from
digital images. More than 104 bubbles were detected for Lahey et al. [20] was used to describe the liquid phase
Page 6 of12 Oil&GasScienceandTechnology–Rev.IFPEnergiesnouvelles(2017)72,26
Pressure outlet boundary
condition at top surface
Center axis
b)
Periodic plane
Velocity inlet boundary condition
on surface of gas distributor
Figure4
Overallgasholdupfromexperimentsandsimulations.
a) c)
To describe BSD characterization in viscous fluid, the
Figure3
multiplebubblebreakupandcoalescencemodelsfromXing
Computational domain and grid profile: a) computational et al.’s [14] were used to close the PBM. The total bubble
domain,b)gridprofileatthetop,c)gridprofileatthebottom.
breakupratewascalculatedasthesumoftheratesfromeddy
collision and from the instability of large bubbles. For the
total coalescence rate three mechanisms were included,
turbulence, where both the shear-induced turbulence and
namely coalescence due to turbulent eddies, bubble wake
the bubble-induced turbulence were considered. The turbu-
entrainment,anddifferentbubblerisevelocities.Thedetails
lent viscosity of the gas phase was formulated using the
ofthebreakupandcoalescencemodelsfromXingetal.[14]
correlation proposed by Jakobsen [21]. The drag, lift, wall
used arelistedinTable 2.
lubrication and turbulent dispersion forces were taken into
account for gas and liquid momentum transfer. The drag
coefficient model from Tomiyama et al. [22] was used to 2.2 Numerical Details
calculate drag force for each bubble size group. The
Tomiyama drag coefficient model, being developed based Steady state simulations were performed for the ALR.
on the balance of forces acting on a bubble and available Two liquid phases, which are the CMC solution as the
theoretical and empirical correlations of terminal rising non-Newtonian fluid and tap water as the reference, were
velocity, is well suited for gas-liquid flows where the simulated. The apparent viscosity of the CMC solution
bubbles can be of different size to a certain extent. The lift was described with the power law equation, as measured
force was calculated with thelift force coefficient model of in the experiments. The numerical simulations were per-
Tomiyama et al. [23], which is applicable to larger-scale formed at two gas superficial velocities of 1.18 cm s(cid:1)1 and
deformable bubbles in the ellipsoidal and spherical cap 2.04 cm s(cid:1)1, which corresponded to the homogeneous and
regimes. The Tomiyama wall lubrication force model [24], heterogeneous flow regimes, respectively. The bubble size
which modified the formulation of Antal et al. [25], was was divided into 30 classes with the geometric method
employed for wall lubrication force calculation, as listed (v = vq), where the smallest bubble volume v was
i+1 i 1
in Table 1. 1.0 910(cid:1)10m3 with thefactorqof1.7.
ThecouplingofPBMintoCFDmodelwasimplemented Thetwo-dimensionalaxis-symmetryassumptionwasused
in ANSYS Fluent 14.5 using user defined scalars that were inthisworkduetothegeometricsymmetryoftheALRand
defined for volume fractions of bubble group i in the gas low computational costs. The computational domain is
holdup. Bubble breakup and coalescence rate models were showninFigure3a.Thecomputationalgridwascreatedwith
loadedbytheuserdefinedfunction.Allbubblegroupswere ANSYS ICEM and the structural hexahedra gridding at
assumedtomoveatidenticalvelocitythatequalstothelocal thebottomandtopisshowninFigure3band3c,respectively.
ensembleaveraged gas velocity. The grid density and the corresponding cell size in the
Oil&GasScienceandTechnology–Rev.IFPEnergiesnouvelles(2017)72,26 Page 7of 12
a) c)
b) d)
Figure5
Bubblevolumefractionofexperimentandsimulation.
threemodeledzonesalongtheALRheightwere2393mm
(below the gas distributor), 21 9 1 mm (around the gas
distributor), and 284 9 2.5 mm (above the gas distributor).
Intheradialdirection,thegridwasfinednearthewallwith
the minimum edge size of 0.5 mm and the maximum edge
size of 2 mm. Grid independent solution was verified by
comparing to the experiments in terms of gas holdup and
liquidvelocity.
The wall function was used for the liquid phase and the
non-slip condition was used for the gas phase. The veloc-
ity inlet boundary was applied to the upper face of the gas
distributor, where the inlet velocity, gas holdup and
volume fractions of bubble groups were specified accord-
ing to the experiments. At the top surface of disengage-
ment zone, pressure outlet boundary condition was used.
The second order upwind scheme was used for the
momentum, turbulence kinetic energy and dissipation Figure6
rate equations and the first-order scheme for the volume
Bubble Sauter mean diameter from experiments and
fraction equations. simulations.
Page 8 of12 Oil&GasScienceandTechnology–Rev.IFPEnergiesnouvelles(2017)72,26
a) b) c) d)
Figure7
VelocityfieldsofAR_ALRwithwateratU =2.04cms(cid:1)1:a)liquidvelocity–PIV,b)gasvelocity–PIV,c)liquidvelocity–simulation,d)gas
g
velocity–simulation.
3 RESULT AND DISCUSSION gas superficial velocity U for both in tap water and
g
in CMC solution. The value of the overall gas holdup
3.1 OverallGasHoldup is lower in CMC solution than in tap water at the same
U . The simulated results for the overall gas holdup
g
The overallgas holdupsfor tap water andCMC solution at agrees well with the experimental data for both the
two different gas superficial velocities U , are shown in tap water and CMC solution with the relative error being
g
Figure 4. The overall gas holdups increase with increasing less than ±10%.
Oil&GasScienceandTechnology–Rev.IFPEnergiesnouvelles(2017)72,26 Page 9of 12
a) b) c) d)
Figure8
VelocityfieldsofAR_ALRwithCMCsolutionatU =2.04cms(cid:1)1:a)liquidvelocity–PIV,b)gasvelocity–PIV,c)liquidvelocity–simulation,
g
d)gasvelocity–simulation.
3.2 Bubble Size different liquid phases is shown in Figures 5a-5d. It can be
seen that the bubble sizes are narrowly distributed both in
ThesimulationresultsoftheBSDintheALRwithdifferent water and in CMC solution at low U . With increasing U ,
g g
liquid phases were obtained from the discrete PBM. The BSD becomes broad in water and even bimodal in CMC
comparison between the simulation results and experimen- solution. All these features are captured by the PBM with
tally determined bubble number densities in the ALR with the bubble breakup and coalescence models including
Page 10 of12 Oil&GasScienceandTechnology–Rev.IFPEnergiesnouvelles(2017)72,26
a)
a)
b)
b)
c)
c)
Figure9 Figure10
Radial profile of liquid axial velocity of experiments and Radial profile of liquid axial velocity of experiments and
simulationsatU =1.18cms(cid:1)1. simulationsatU =2.04cms(cid:1)1.
g g
several mechanisms. The relative errors between the exper- the ALR with different fluids at two investigated U . It can
g
iments and the simulations is less than ±10% for most of be found that the bubble Sauter mean diameter is slightly
thebubble groups, asshownin Figure 5. under-predicted in water and over-predicted in CMC solu-
Figure 6 shows a good agreement between the simula- tion. These results are obtained most probably because the
tions and experiments for bubble Sauter mean diameter in breakup models in the PBM are much more sensitive to