The effect of liquid co-flow on gas fractions, bubble velocities and chord lengths in bubbly flows. Part II

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The effect of liquid co-flow on gas fractions, bubble velocities and chord lengths in bubbly

flows. Part II

Asymmetric flow configurations

Muilwijk, Corné; Van den Akker, Harry E.A.

DOI

10.1016/j.ijmultiphaseflow.2021.103562

Publication date

2021

Document Version

Final published version

Published in

International Journal of Multiphase Flow

Citation (APA)

Muilwijk, C., & Van den Akker, H. E. A. (2021). The effect of liquid co-flow on gas fractions, bubble velocities

and chord lengths in bubbly flows. Part II: Asymmetric flow configurations. International Journal of

Multiphase Flow, 138, [103562]. https://doi.org/10.1016/j.ijmultiphaseflow.2021.103562

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International Journal of Multiphase Flow 138 (2021) 103562

ContentslistsavailableatScienceDirect

International

Journal

of

Multiphase

Flow

journalhomepage:www.elsevier.com/locate/ijmulflow

The

effect

of

liquid

co-ﬂow

on

gas

fractions,

bubble

velocities

and

chord

lengths

in

bubbly

ﬂows.

Part

II:

Asymmetric

ﬂow

conﬁgurations

Corné Muilwijk

a,∗

_,

_Harry

_E.A.

_Van

_den

_Akker

a,b

a Bernal Institute, University of Limerick, Limerick, V94 T9PX Ireland

b Transport Phenomena Lab, Department of Chemical Engineering, Delft University of Technology, Van der Maasweg 9, 2629 HZ Delft, The Netherlands

a

r

t

i

c

l

e

i

n

f

o

Article history: Received 8 April 2020 Revised 8 December 2020 Accepted 3 January 2021 Available online 10 January 2021

Keywords:

Inhomogeneous Bubble column Bubble Image Velocimetry Optical ﬁbre probe CFD Validation Gas hold-up Mixing pattern

a

b

s

t

r

a

c

t

Thispaperdescribestheeffectsofuniformandnon-uniformliquidco-flowonthebubblyflowina rect-angularcolumn (withtwoinlets) deliberatelyaeratedunevenly.Thetwoverticalbubblystreams, com-prisinguniformbubbles,startedinteractingdownstreamofthetrailingedgeofasplitterplate.Thisstudy quantifiestheemergenceofbuoyancydrivenflowpatternsas afunctionofthedegree ofa-symmetric gasspargingand(non-)uniformliquidco-flowbyusingBubbleImageVelocimetry(BIV)anddual-tip op-ticalfibreprobes.Withoutliquidco-flow,smalldifferencesinthegasfractionoftheleftandrightinlet hadalargeeffectonthemixingpattern,whereasaliquidco-flowstabilizedahomogeneousflowregime andtheflowpatternwaslesssensitivetogasfractiondifferences.Voidfractions,bubblevelocitiesand chordlengthsweremeasuredattwofixedpositionintheflowchannel,whereasBIVprovidedaglobal overviewoftheflowstructures.Acorrelationwasdevelopedtopredict(a-symmetric)operating condi-tionsforwhichthegasfractionoftheleftandrightinletarebalanced,suchthatthebubblemotionis governedbyadvectionandnobuoyancydrivenflowstructuresarise.Thedataobtainedishighlyvaluable forCFDvalidationanddevelopmentpurposes.

1. Introduction

Besides classic symmetric bubble columns (with or without a liquid co/counter-current flow), a-symmetric bubble configura-tions are also widely encountered in the form of air-lift reac-tors and photobioreactors. It has been found that depending on the degree ofa-symmetry andthe emerging large scalemotions, mixing times in laboratoryscale setupsare significantly reduced [Alméras et al. (2018); McClure et al. (2016)] and heat transfer ratesincreased[Gvozdićetal.(2019b)].

Scaling-up of bubble columns and aerated vessels requires detailed CFD modelling of the dispersed gas-liquid flow [Becker et al. (1994)]. Most of the available models work well for homogeneously dispersed bubbly flows and are used with increasing confidence, but modeling of a-symmetrically (or half) sparged bubble columns has proven to be a real challenge [Huang et al. (2018)]. Therefore, systematicand accurate experi-mental data,comprisinggas fractions,bubblevelocities andsizes andliquidvelocities,ina-symmetricbubblecolumnconfigurations

∗_{Corresponding author.}

E-mail addresses: Corne.Muilwijk@ul.ie (C. Muilwijk), Harry.VanDenAkker@ul.ie

(H.E.A. Van den Akker).

is crucialforCFD validation anddevelopmentpurposes, butit is sparselyavailable[DeTournemineandRoig(2010)].

Operatingour rectangular bubble columna-symmetrically, i.e. by applyingdifferentairand/or waterflow ratestothe left-hand andright-hand sides, may createtwo parallel bubbly flows with different(mixture)velocitiesand/or (mixture)densities.Theshear betweenthesetwo parallel flows mayresultin Kelvin-Helmholtz (KH) instabilities which have been widely studied under single-phase conditions. Brown and Roshko (1974) experimented with parallelflowsoftwodifferentgasesandobservedorganized vorti-calflowstructureswhichbypairing(seee.g.,WinantandBrowand (1974)) gave rise to a mixing layer between the two gas flows. The lateralgrowth ofthe mixinglayer then followsfrom engulf-ment of outer fluid by these vortical structures. When conceiv-ing bubbly flows as single-fluid flows comprising interpenetrat-ing phases and exhibiting a mixture velocity, one could argue a similarity with the above single-phase KH instabilities. An anal-ogy between single-phase and two-phase vortical structures has alreadybeensubmittedalongtimeago[Rietema(1982);VanDen Akker(1998)].Groen etal.(1996)aswell asMuddeandVanDen Akker(1999)observedanddescribeddynamicbehaviourofbubble columnscomprisingcoherentvorticalstructures.

https://doi.org/10.1016/j.ijmultiphaseﬂow.2021.103562

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Loth andCebrzynski(1995)studiedmixinglayers betweenjust a liquid and a liquid with bubbles 2 and 4 mm in diame-ter. They found these bubbles modulated shear layer thickness.

Roigetal.(1998)reportedresultsfromjustfourexperimentsfora mixinglayerbetweentwobubbly ﬂowswithalow holdup(<2%) of bubbles with an average chord length of some 2 mm. They found the global behaviour of such bubbly,ows to be very sensi-tive to (initial)voidfractioncontrasts. Ayedetal.(2007)injected millimetresizedoxygenbubblesby576smallcapillaries(0.33mm internaldiameter)atthelowvelocitysideofamixinglayer,while no bubbles were introduced atthe high velocity side. In a simi-lartest facility,DeTournemineandRoig(2010) foundstableﬂow patterns characterized by so-called frontiers between the bubbly streams from the left and right inlets. They only observed such frontiers when bubbles were injected on the low liquid velocity side, whereas oscillating boundaries occurred for all cases when bubblesweresuppliedatthehighliquidvelocityside.

These previous investigations of bubbly mixing layers [Roig et al. (1998); Ning et al. (2009); De Tournemine and Roig (2010)], seeded with (polydisperse) small bubbles and operated at low gas fractions, reported data for a very small numberofcasesonlyatseeminglyarbitraryoperatingconditions. Therefore we identified an urgent need of a broader and more accurate database for a-symmetrically operated bubble columns: how asymmetric gas sparging induces dynamic buoyancy-driven flow behavior and how uniform andnon-uniform liquid co-flow modifiesthis. Aparametricstudythen deliversuniqueandhighly valuable experimental data to serve as a reference for CFD val-idation in an Euler-Euler framework. While two parallel bubbly flows (separated by a boundary) develop in vertical direction, the strength of the buoyancy driven flow structures (e.g. liquid entrainment rates into a dense bubble swarm) as a function of the degree ofa-symmetry can serve asa very strongbenchmark case to calibrate sub-models for interfacial momentum transfer, two-phaseturbulenceandlateraldispersionofbubbles.

All these sub-models are strong functions of the (local) void fractionandbubblesize (distribution).Therefore,computationally simulating half-sparged bubblecolumns asinAyed etal.(2007);

De Tournemine andRoig (2010); McClure et al.(2017, 2016) and

Gvozdi´c et al. (2019a), axisymmetric non-uniform aeration in a cylindrical bubble column as in Harteveld et al. (2003), or symmetric non-uniform sparging in a shallow 2D column as in

Harteveld (2005) is essentially easier when there is only a sin-gle bubble size (distribution) present. Of course, the bubble size depends on the gas flow rateand co-flowvelocity Muilwijk and Van denAkker(2019a,b); MuilwijkandVandenAkker (2021). A-symmetric sparging in a bubble column then imposes different bubblesizesforeachinlet,unlesssinglebubblesareformedwitha constantdiameteratlow,constant,gasflowratesinquiescent wa-ter asinAlméras etal.(2018),orincasea differentsplitterplate designisusedasinNingetal.(2009),wheretheindependent con-trolofbothinletswascompromised.Inourcase,wedesignedthe gasspargerinsuch away,that(in eachinlet)uniformlarge bub-bles were produced, which essentially have constant rise veloci-ties, suchthatlateraldispersionduetosize/velocitydifferences,is minimized(asexplainedinPartI)andbreakupandcoalescenceof bubblesisavoided.

Experimentswerecarriedoutinthetestsetup asdescribedin ourprevious paper[Muilwijk andVan denAkker(2019b)], where the superﬁcial liquidandgasvelocities ofboththe left andright inlet compartmentscanbe varied independently.The bubblesize d_b in each inlet can be calculated using a correlation developed inourprevious paper[MuilwijkandVandenAkker(2019b)] asa functionofthesectionalUsgandUsl.

For this Part II paper, we used the same techniques as de-scribedinPartIofthistwinpaper,viz.BubbleImageVelocimetry

(BIV)anddual-tipoptical fibreprobes (OFP),whereBIVwasused to perform analyses of the large scale flow structures, while the OFPs were used to measure local gas fractions, bubble velocities andchord lengthsat fixed positions. Experimentswere designed tocover awide rangeofflow behaviors,such that a comprehen-sivesetofexperimentaldatawasobtained.

Amodeltodescribethegasfractionwasadoptedtopredict a-symmetric operatingconditions forwhich a higher gasflow rate iscompensatedwithahigherliquidco-flowsuchthatthereisno gasfractiondifferenceatspargerlevel.Fortheseconditions,where nobuoyancydrivenflowstructuresemergeandthebubblemotion wasgovernedbyadvection,bubblymixinglayerpatternsoccur.We then also identified operating conditions for which there are, in addition to an equal gas fraction atleft andright inlet, (almost) equalbubblesizesformedinbothinletsections.

The structureof thispaperisthen asfollows.An overviewof experimentalparametersandthedifferentflowconfiguration sce-nariosisgiveninSec.2;Sec.3showsresultsontheeffectofa uni-formliquidco-flow onthe flowpatterns andthedeparture from symmetric operation withincreasing degreesof a-symmetric gas sparging.Sec. 4presentsresultsontheeffectof uneven(leftand right inlet) liquid co-flows on flow patterns.Concluding remarks andsuggestionsforfutureworkaregiveninSec.5.

2. Methodsandparameters

Measurements were carried out in the ”LimBuRig” test facil-ity[MuilwijkandVandenAkker(2019b)].Two,initiallyseparated, parallelstreamsofbubblyﬂowswithdifferentsuperﬁcial(gasand liquid) velocities, started interacting downstream of the trailing edge of a splitter plate (see Fig. 1a). While Part I of this paper showed results for a symmetric operation (uniformUsg andUsl),

a-symmetric bubble column configurations were studied for this part,wherethesuperficialgasvelocitiesUsg and/orsuperficial

liq-uidvelocitiesUsl (L)eftand(R)ightwere varied independently. In

Fig. 1a, the gas flow is higher at the right hand side, while the liquid flow rateis highest in the left compartment. Downstream ofthe splitterplate,the fastliquidflow fromthe left inletslows downandexpandslaterally,pushingtheflowwiththehighervoid fractiontotheright;thelatterthen startsacceleratingdueto in-creasedbuoyancy.K-Hinstabilitiesdevelopthegrowthofwhichis restrictedbythecloseproximityoftherightsidewall.Thevarious flow cases are describedwiththe help of the following parame-ters:

U sg

= 1 2

(

U sg,L+U sg,R

)

(1)

U sl

= 1 2

(

U sl,L+U sl,R

)

(2)

U sg=U sg,R− Usg,L (3)

U sl=U sl,R− Usl,L (4)

whereL,Rdenotetheleftandrightinlet,respectively.Thedegrees ofa-symmetryinthesuperﬁcialgasandliquidvelocity,

λ

gand

λ

l

respectively, werethen definedasthe ratioof thesuperficial gas orliquid velocity difference (between left andright inlet) to the meansuperficialvelocity:

λ

g=

U sg

(5)

λ

l=

U sl

(6)

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C. Muilwijk and H.E.A. Van den Akker International Journal of Multiphase Flow 138 (2021) 103562

Fig. 1. (a) Raw image corrected for lens distortion. (b) Bubble parcel velocity vec- tors as calculated using Bubble Image Velocimetry (see Part I). Reference vector (1 m/s) given on the right. Average of 5 image pairs, ≈40 ms. Inlet conditions: U sg,L =

0.63 cm/s; U sg,R = 1.87 cm/s; hence U sg = 1 . 25 cm/s and λg = 1 . U sl,L = 0.2 cm/s;

Usl,R = 0 cm; hence U sl = 0 . 1 m/s; and λl = −2 .

The meansuperﬁcial gasvelocity

Usg

waskept ata value of

1.25cm/s (unless otherwisementioned), while

λ

gwasvaried

be-tween -1and1.Therefore,thesuperﬁcial gasvelocityofeach in-let (L,R) wasinthe range0.63-1.88cm/s, which isinthe regime where bubblesare formed individually witha veryuniform bub-blesize[MuilwijkandVandenAkker(2019b)].Themean superﬁ-cialliquidvelocity

U_sl

wasvariedbetween0-0.2m/s.Thedegree ofa-symmetry ofthe liquidco-ﬂow

λ

l wasvaried between0,-1,

and -2,the latterindicating no liquidﬂow atthe rightinlet and U_sl,L=2

U_sl

.

More detailson thedesignofthe testfacilitycanbe found in ourprevious paper[Muilwijk andVan denAkker(2019b)], where correlations were developed to describe the bubble diameter d_b and (overall)gas hold-up asa function ofthe applied superficial liquidandgasvelocities.Localgasfractions,bubblevelocitiesand chordlengthsforuniformgasspargingandliquidco-flowwere re-portedinPartIforsuperficialgasvelocitiesintherange0.63-6.25 cm/sandliquidvelocitiesupto0.2m/s.Sincewefoundthat Bub-ble Image Velocimetry can only be applied for low to moderate void fractions, we limit ourselves to show organizedflow struc-turesatrelativelylow

Usg

,suchthattheassumptionofa2Dﬂow

patternisplausible.

Exploratory bubblestreaklineexperimentswere performedin ordertoinvestigatethevarioustypesofﬂowpatternsasafunction

of

U_sl

,andthedegreesofa-symmetry

λ

gand

λ

l.Bubble

streak-lineswerecaptured(JaiGo2400Mcamera,KowaLMVZ166HC 16-64mmvarifocallens)forvariousoperatingconditionsusinga fo-cal lengthof_{≈ 25} mm f /5.4 andanexposure timeof1_/

10 sand showninFigs.2,8.Wefoundthatthebubblevelocitiesataheight of ≈ 50 cm above the trailing edge of the splitter plate show mostlyuni-directional flow behavior. Part Iof thispapershowed that at the gas fraction andbubble velocities at x=±15 cm are verymuchrepresentativeforthebulkofthebubblecolumn,where xis thehorizontalcoordinate,withx₌0beingthe centerofthe column (see Fig. 1b). So here, we kept the dual-tip optical fibre probesata fixedposition ofy=63cmabovethe trailingedgeof the splitter plate(80 cmabove the gas sparger level) and 5 cm from the column side walls (x=±15 cm). The mean reason for measuring gas fractions, bubble velocities, and chord lengths at thesepositionsisthatthebubblesmoveinamostlyvertical direc-tion,alignedwiththeopticalfibreprobes.Measuringthe hydrody-namicparametersattheselocationsmaketheOpticalFibreProbe measurementsmostreliable.Measuringatlowerelevationswould misssubstantialnumbersofbubbles.MeasurementswiththeOFPs were takenfor a duration of300 s to obtain themean gas frac-tion and its standard deviation over 30 second intervals aswell asbubble velocity andchord length distributions. Series of bub-blevelocityandchordlengthmeasurementswhererejectedwhen thepairing ratedropped below25% asaresultoftheoccurrence ofdownflowingbubbles.Meanbubblevelocitiesarecalculatedas thegasfractionweightedmeanbubblevelocity, seePartIofthis paper.

A Bubble Image Velocimetry (BIV) technique, as explained in Part I, was adopted to calculate bubble parcel velocities and to quantifyglobalﬂowstructures.Forthispart,imageswerecaptured ofthe bubble columnfor 10 s ata rate of120 Hz and a spatial resolutionof _{≈ 0.7}mm/pix.The size ofan interrogationwindow wasreducedto32×32pixelstoobtain ahigherspatialresolution tobettercapturehighgradientsinthehighshearregions.Fig.1b showsavectorplotofthe(5_/

120saverage) bubbleparcelvelocity ascalculatedusingBIVforthecaseshowninFig.1a.

Contour plots ofthe parcel velocity magnitude, calculated ac-cordingto:

|

v

b

|

=

v

b,x2+

v

b,y2 (7)

and bubble traces were obtained by integrating the mean bub-bleparcelvelocities.Theroot-mean-squarebubblevelocity ﬂuctu-ationswerecalculatedaccordingto:

v

b=

v

2

b,x+

v

b,y2 (8)

where

v

_b_,iistheinstantaneousvelocityﬂuctuation(i=x,y).

3. Uniformliquidco-ﬂowata-symmetricairsparging

3.1. Theboundarylayerbetweenthetwobubblystreams

Fig. 2 shows the influence of a uniform liquid co-flow on theflow patternsinsidethe column. Themiddlecolumn(

λ

g=0)

showsbubble streaks foruniformaeration withincreasing liquid co-ﬂow from the top to the bottom, where

U_sl

₌0 m/s (top);

Usl

=0.1m/s(middle);and

Usl

=0.2m/s(bottomrow).

The left (

λ

g=−0.75) andright (

λ

g=0.75) columns of Fig. 2,

withtheira-symmetricairsparging,show strongbuoyancydriven ﬂow structures at the side with the highest gas fraction (which showsuplighter).Thedevelopingboundarybetweenthetwo bub-blyﬂowsofdifferentdensitiesisclearlyvisible.Inallthreerowsof

Fig.2,theﬂowﬁeldsfor

λ

g=−0.75and

λ

g=0.75areeachother’s

(5)

Fig. 2. Bubble streaklines for U sg = 1.17 cm/s. From left to right: varying the de-

gree of a-symmetric gas sparging λg . From top to bottom: increasing liquid co-ﬂow

velocity (uniform). U sl = 0, 0.1 0.2 m/s. λl = 0 .

Intheabsenceofaliquidco-ﬂow(toprow),theliquidcarried upwardsinthebuoyantplumereturnson theotherside, thereby creatinghighlyunsteadyrecirculationvortices.Thebuoyantplume acceleratedwithincreasingheight anddeﬂectedfromthecolumn wall ata height of ≈ 1 m above the edge of the splitter plate, whereaftertheplaneshearlayerdisappearedbydisintegratinginto a3Dchaoticturmoil.

Aliquidco-flowwasfoundto organizethe vorticalstructures, thereby preservinga quasi-2D shear layer. At a liquid co-flowof 0.1 m/s (middle row), a somewhat more organized vortex ap-peared higherin the column, while a recirculatory flow was not observedfor

Usl

=0.2m/s(bottomrow).Also,theﬂuctuationsof

theboundarydampenedwithincreasing liquidco-ﬂow,whilethe ”angleofdeparture”,thedevelopmentofthelateralpositionofthe boundary,becamesmallerwithincreasingco-ﬂowvelocity.

Thecases with

λ

g=0all show unstable(wavy)interfaces

be-tweenthetwobubblyflows.Itseemsthatmainlyintheabsenceof liquidco-flowK-Hinstabilitiesare abletogrow intowell-defined rollupvortices.Obviously,a(stronger)co-flowhasastabilizing ef-fect. Itis knownfromsingle-phase K-Htheory that a Richardson number,denotingtheratioofa velocitydifference squaredanda difference in specific weight between the parallel flows, governs theformationofK-Hinstabilities.Thecomplexinterplaybetween flowratesand(local)voidfractionimpedesa moredetailed fore-castoftheoccurrenceofsuchvortices.

3.2. Globalﬂowpatterns

Fig. 3 showscontour plots ofthe mean(10s) bubble velocity magnitudeobtainedbymeansofBIV.The(uniform)superﬁcial liq-uid velocity is

U_sl

₌0(top); 0.1 (middle);and 0.2m/s(bottom rows), while the degree of a-symmetric gas sparging is

λ

g= -1

(left);

λ

g=0(center);and

λ

g=1(right).

The middle columns show almost uniform bubble velocities (Figs.3b,3eand3h)andvelocityfluctuations(Figs.4b,4eand4h), wherethebubblevelocitiesincreasewithincreasingliquidco-flow velocity (top tobottom), whilethe velocity fluctuations decrease withincreasing

U_sl

,whichconﬁrmsthecalmingeffectofaliquid co-ﬂowasshowninPartI.

Somesmallgradientsof

|

v

b

|

arevisibleevenwhen,without

liq-uid co-ﬂow,the aeration rates left andright were set equal (see

Fig.3b).Thebubblesfromtheleftinletacceleratedslightlydueto averysmallinequalityofthesuperficialgasflowratesattheleft andrightside ofthe splitterplate(dueto theaccuracy ratingof theMassFlowControllersandaslightlyoff-centeredsplitterplate [MuilwijkandVandenAkker(2019b)]).Aliquidco-flowthenhad an equalizingeffectonthe flow, seeFigs.4b,4e and4h,andthe flowbehaviorislesssensitivetosmallvariationsin

λ

g.

TheleftandrightcolumnsinFigs.3,4showvelocitymagnitude contoursandbubbletraces(Fig.3)andvelocityﬂuctuations(Fig.4) forunevenly spargedconﬁgurations(

λ

g=-1fortheleftand1for

therightcolumnsrespectively).

Inall3rowsofFigs.3and4,theﬂowstructuresfor

λ

g=-1and

1are verysimilarwhen mirroredinx₌0.Forall caseswith un-evengassparging,abuoyancydrivenﬂowpatternemerged,where thebubblesmigratedhorizontallytothesidewiththehighestgas fraction and accelerated in vertical direction. Without liquid co-ﬂow,seeFigs.3aand3c,bubbles weremovingdownwardsatthe side ofthe lowestgas fraction,indicatinga strong liquid recircu-lationloopasaresultofliquidentrainmentinthebuoyantplume andmassconservation.

Withincreasingliquidco-ﬂowrates,bubblesmigrated horizon-tallytoa lesserextent,hence,thedevelopingboundaryremained morecentered inthecolumnandabubblerecirculationloop did notemergeintheﬁeldofviewuptoy=1.2m.

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Fig. 3. Bubble traces and contours of the velocity magnitude, see Eq. (7) , with a uniform co-ﬂow. From left to right: λg = -1, 0, 1; From top to bottom: U sl = 0, 0.1,

0.2 m/s. U sg = 1.25 cm/s.

Fig. 4. Contour plots of the root-mean-square velocity ﬂuctuations as calculated ac- cording to Eq. (8) . λg = -1, 0, 1; From top to bottom: U sl = 0, 0.1, 0.2 m/s. U sg =

(7)

Fig. 5. Parcel velocity proﬁles obtained by BIV measurements at y = 63 cm for various λg . From left to right: increasing liquid co-ﬂow velocity (uniform; λl = 0 ). The dashed

lines at x = ±0 . 15 m denote the OFP locations. The velocity proﬁles in (a) are extracted from Figs. 3 a- 3 c; those in (b) from Figs. 3 d- 3 f; and those in (c) from Figs. 3 g- 3 i for

λg = −1 , 0 , 1 respectively.

The organizing effect of a liquid co-flow on the flow pattern is evident fromthevelocity fluctuationcontours showninFig. 4. Withoutliquidco-flowandnon-uniformgassparging,(Figs.4aand

4c),very strongﬂuctuationswere foundinthetopcorners ofthe column. Asthe velocitygradientsincreasedwithheight,the bub-bleplumedetachedfromthecolumnwallaty_{≈ 1}m,andthe2-D planeshearlayerdisintegratedintochaotic3-Dswirlingstructures. Similar behaviorwasobservedby Almérasetal.(2018),wherean inhomogeneously sparged rectangular bubble column was oper-ated ina regime witha planar (2D) recirculationvortexat small gasvolumefractiondifferences:

α

/

α

<0.4.

A uniform liquid co-ﬂow controlled the development of the boundary,organizedtheﬂowpatternsanda2-Dplaneshearlayer was preserved. Due to the high gradients of

α

at the boundary, someorganizedvortex-rollupoccurredbetweenthehighandlow

α

layer(seerightcolumnofFig.2),whichexplainsthedeveloping contours (width and intensity)of the velocity ﬂuctuationsatthe locationoftheboundary.

3.3. Parcelvelocityproﬁles

Fig. 5 showsvelocity proﬁles of the mean vertical parcel ve-locities (y−direction), as measured by BIV over a 10 s interval, at a height of y₌ 63 cm above the trailing edge of the splitter plate.Theuniformliquidco-ﬂowvelocity

U_sl

wasﬁxedat0.0m/s (a),0.1m/s(b),and0.2m/s(c), whilethedegree ofa-symmetric sparging

λ

gwasvariedintherange-1...1(seelegend),with

λ

g=0

indicatingequalsuperﬁcialgasﬂowratesattheleftandrightinlet. ThesmoothcurvesinFig.5illustratethattheimagecorrelation

al-gorithmforcalculatingparcelvelocities,whichisdescribedinPart I,worksratherwell.

For

λ

g<0

(

,Usg,L>Usg,R

)

, a plume ofhigh bubblevelocities

developedattheleft handsideofthecolumn.Abuoyancydriven accelerationoccursofthebubblystreamthathasinitiallyahigher gas fraction at the left inlet. When

λ

g>0

(

,Usg,L<Usg,R

)

, this

buoyancy driven bubbleplume developed atthe right hand side ofthecolumn.

In cases with

Usl

=0m/s, see Fig. 5a, a globalliquid

circu-lationwasestablishedduetotheabsenceofa netliquidthrough ﬂow.Thisratherunsteadyvortexdraggeddownbubblesattheside ofthelowestUsg,seealsothetop leftandrightbubblestreaksin

Fig.2.Duetothewanderingbehaviour ofthebubbleplume, vor-tices were generatedatthe freeinterface that traveleddown the column.Lowfrequencyflowinstabilities causedthis2D flow pat-terntodisintegrate intoachaotic turmoilatsome 1meterabove the trailing edge of the splitter plate, see also the contour plots inFigs.4a and4c.Therefore, itshouldbe notedthatthe velocity profiles are a 10s average anddifferentvelocity profiles may be measuredfordifferenttimeintervalsandfurtherstudyisrequired tostudythedynamicsofthecolumn.

With increasing

Usl

, see Figs. 5b and 5c, the development

of a liquid recirculation loop was inhibited due to advection of bubbles.Liquid co-ﬂowhadastabilizingandorganizing effecton the ﬂow patterns and low frequency instabilities for cases with

U_sl

₌0 m/s were removed. For the highest

U_sl

setting (5(c)), almost ﬂat velocity proﬁles were measured at both sides (left, right)oftheboundarieswherevelocitygradients occurred.Asthe bubblystreamwiththehighest/lowestinitialgasfraction

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acceler-C. Muilwijk and H.E.A. Van den Akker International Journal of Multiphase Flow 138 (2021) 103562

Fig. 6. The void fraction αat x = ±15 cm and y = 63 cm as a function of the degree of asymmetry λg . U sg = 1.25 cm/s. (a) U sl = 0 m/s; (b) U sl = 0.1 m/s; and (c) U sl = 0.2

m/s. The error bars indicate the standard deviation over 30 s intervals.

Fig. 7. c at x = ±15 cm and y = 63 cm as a function of the degree of asymmetry λg . U sg = 1.25 cm/s. (a) U sl = 0 m/s; (b) U sl = 0.1 m/s; and (c) U sl = 0.2 m/s. The error

bars indicate the standard deviation of the chord length distributions. See also legend of Fig. 6 .

ated/decelerated withtheﬂow directionrespectively, thevelocity difference betweenthe left andright plateau increased, seealso

Figs. 3g and 3i. Withincreasing/decreasing

λ

g,departing from 0,

theboundarylayersdriftedmoretotheright/leftsiderespectively, whilethicknessoftheboundarydecreasedwith

|

λ

g

|

.

In the idealcaseof symmetricgas sparging, a flatbubble ve-locity profile is expected. Due to slight inaccuraciesof the Mass Flow Controllers,theleftsideofthecolumnreceivedahighergas fluxat

λ

g=0.Thedevelopmentofthebubblevelocityproﬁleswas

foundtobehighlysensitivetoslightchangesin

λ

gintheabsence

ofaliquidco-ﬂow,see_{• in}Fig.5a.Thiseffectislargelyreducedin theeffectofaliquidco-ﬂowvelocity,seeFigs.5band5c.

The dashed lines at x=±0.15 m indicate the locations (at y₌63cm) oftheopticalﬁbre probes.Theresultsthereofare dis-cussedbelow.

3.4. Localﬂowmeasurements 3.4.1. Gasfraction

Fig.6 showsthedevelopmentof thegas fraction

α

at y= 63 cmandx=−15 cmandx=15cm asa functionof thedegreeof a-symmetricgassparging

λ

gfor(a)

Usl

= 0(openmarkers);(b)

Usl

=0.1(greymarkers);and(c)

Usl

=0.2m/s(blackmarkers).

Foreach

λ

g,themeasurement atx=−15()andx=+15cm()

weretakensimultaneouslyforadurationof300s.

Thehighestgasfractionwasobtainedatthesidewiththe high-est superﬁcial gas velocity; on theleft side when

λ

g<0 andon

therightsidewhen

λ

g>0.Themarkerson theleft(at

λ

g=−1),

correspond to the cases shown in the left column of Figs. 3, 4, whereas themarkers onthe right(

λ

g=1) resemblethecasesas

(9)

of

α

(at themeasurement locations)withrespectto

λ

g isalmost

symmetricin

λ

g=0.

For

Usl

=0(openmarkers), thelineofsymmetry(where the

gasfractions atx₌-15,_,andx₌₊₁₅ cm,_,areequal),isfound slightly right of

λ

g=0. This agrees well with our earlier

obser-vation that thecalibration ofthemassﬂow controllersis slightly different(yetstillwithinthespeciﬁcations),assymmetrywas ob-tained when

λ

g≈0.02. A liquid co-ﬂow then mitigated the

ef-fect ofa slight imbalancebetween both superﬁcial gasvelocities (Left/Right) asthe curves for

U_sl

₌ 0.1 and0.2m/s seemto be verysymmetricaround

λ

g=0.

For

Usl

=0.2m/s(black markers),thetwo gasfractions vary

almost linearlywith

λ

g inthe whole range

λ

g=−1...1, whereas

for

U_sl

=0m/s,

α

wasverysensitiveto

λ

ginthe range-0.3...0.3,

followed by a plateau for

|

λ

g

|

>0.4. As the width of the bubble

plumedecreaseswithincreasing

λ

gandy,the(average)boundary

surpassesx₌_±15cm(seeFig.3a,3c),suchthattheopticalprobes atthehighUsgsidealsoencounteredbubblesoriginatedatthelow

Usg side.Hence,the gasfractionasa functionof

λ

gleveled off at

high

|

λ

g

|

asthevoidfractionmaximumemergedclosertothe

col-umnsidewalls.

Without liquidco-ﬂow,seeFig.6a,a steepgradient of

α

with respect to

λ

gwasfoundcloseto

λ

g=0,indicating thatthe

over-all flow behavior is very sensitiveto small differencesofthe su-perficialgasvelocitiesbetweentheleftandrightinletandstrong buoyancydrivenflowstructuresemerged.Withliquidco-flow,see

Figs. 6b, 6c,the steep gradient close to

λ

g=0 disappears as the

ﬂowstabilizesandalignsmorevertically.

3.4.2. Bubblevelocities

The detailed velocitydata of individual bubbles arepresented separatelyintheAppendixastheymaybeusefulforvalidationof CFD simulations.A.1 showsacomparisonbetweenvertical parcel velocities

v

b,yandbubblevelocitiesmeasuredbytheOFPs.

3.4.3. Bubblechordlengths

Fig.7showsthemeanchordlengthcatx=±15cmandy=63 cmasafunctionofthedegreeofa-symmetricgassparging

λ

gfor

the same casesas outlined inFig. 6.Bubbles were formed sepa-rately(one-by-one)and,foreachoftheinlets(L,R),averyuniform bubblesizecanbeassumedforcaseswithalowUsg suchas

stud-iedinthispaper(seeMuilwijkandVandenAkker(2019b)). As, however, thebubble size formed in each ofthe inlet sec-tions(L,R)dependsontheappliedUsg andUsl,anoverallbi-modal

bubble size distribution was created when

|

λ

g

|

>0, where the

largerbubbleswereformedinthestreamwiththehighestUsg.

Mean bubble chord lengths were measured in the range 1.9-2.4 mm for

Usl

=0.1− 0.2 m/s, where the difference of c

be-tween x₌-15 and x₌15 cm decreased withincreasing

U_sl

. For

Usl

=0m/s, nodata could be obtainedwhenthe bubble

veloc-ities were not upwardsornot vertically alignedwiththeprobes. Bubblechord lengthswerefoundintherange2.1-2.6 mmforthe side withthehighestaeration rate(x=−15cmwhen

λ

g<0and

andx=15cmwhen

λ

g>0).

Thewidthofthechordlengthdistributionforthissetof exper-imentswasfoundtobe almostindependentof

λ

ganddecreasing

with

Usl

.

4. Non-uniformliquidco-ﬂowata-symmetricairsparging

4.1. Theboundarylayerbetweenthetwobubblystreams

Fig.8shows,inadditiontotheeffectofa-symmeticgas sparg-ingasinFig.2,alsotheinfluenceofana-symmetricliquidco-flow ontheflowpatternsinsidethecolumn.

Fig. 8. Bubble streaklines for U sg = 1.17 cm/s and U sl = 0.1 m/s. From left to

right: varying the degree of a-symmetric gas sparging λg . From top to bottom: in-

creasing degree of a-symmetric liquid co-ﬂow, λl = -0.5, -1, -2 (high liquid co-ﬂow

(10)

Fig. 9. Photographs of a vortex roll-up phenomenon. The time between each frame is 0.5 s. See Supplementary Material online for the embedded video. U sg,L = 0.81 cm/s; Usg,R = 1.69 cm/s; λg = 0.7; U sl,L = 0.2 m/s; U sl,R = 0 m/s; λl = -2;

The middle column (

λ

g=0) shows bubble streaks for

uni-form aeration. While the mean liquid co-ﬂow velocity

Usl

, see

Eq. (2) was kept at 0.1 m/s, the difference of liquidco-ﬂow be-tween the left and rightinlet increasesfromthe top to the bot-tomrowofFig.8.Thedegreeofa-symmetryfortheliquidco-ﬂow (

λ

_l) wasvaried between-0.5 (top); -1 (middle); and-2 (bottom row),withtheleftsideinlethavingthehighestliquidco-ﬂow ve-locity and

Usl<0,see Eq.(4). Therefore,all

λ

l values are

neg-ativeinthe presentedconﬁgurations.Forthebottom case, where

λ

l=−2,therewasnoliquidﬂowattherightinlet(Usl,R=0),while

Usl,L=0.2m/s. Asthebubbly ﬂowon theleft hasthelowest gas

fraction(duetothehigherU_sl),theboundarydevelopstotheright side dueto the buoyancydriven acceleration ofthe stream with thehighestgasfraction.

Fortheleftcolumn,where

λ

g=−0.75(highgasﬂowleft),the

boundary evolvedto thecenter(fromthetop casetothebottom case)asthegasfractiondifferencedecreasedfromthetoprowto thebottomrowoftheﬁgure,hence,less-to-nonebuoyancy-driven ﬂow patterns were causedfor

λ

g=−0.75 and

λ

l=−2 at

Usl

=

0.1m/s.

Very unstable boundaries were observed for the cases shown inthe rightcolumnofFig.8,wherethehighestgasfractionisat the low liquidvelocity side.The boundaryconsistently gravitated towards the side with the highest gas fraction and signiﬁcantly larger angles ofdeparture were observed compared to the other casesshowninFigs.2,8.AKelvin-Helmolztypeofﬂowinstability seemedto occur onlyinextremecases anda clearvisiblevortex roll-upwasvisibleinthebubblestreaksfor

λ

g=0.75and

λ

l=-2.

Fig. 9 shows photographs (1_/

400 s) of the bubble column for a which a repeating vortex roll-up ﬂow pattern was observed (

Usg

=1.25cm/s;

λ

g=0.70;

Usl

=0.1m/s;and

λ

l=-2).Thetime

between each photograph is 0.5 s. As evident from the bubble streaks shown in Fig. 8, thislarge vortex roll-up only occurs for very speciﬁc conditions. The frequency of vortex formation and

movement of the vortex coreis clearly visible andthe period is estimatedat≈1.5s. Exploratory experimentsreveal that this fre-quencydependson

λ

gand

λ

l,butmoreexperimentsarerequired

forextendedperiodsoftimetoobtainasuﬃcientresolutioninthe frequency domain (when calculating a fast Fourier Transform of theboundarylocationorbubbledensityatamonitoringlocation). As the bubble detectionfrequency by the OFPs islow compared tothefrequencyoftheoscillationasvisualizedinFig.9,(spectral) analysisofthephaseindicatorfunctionorbubblevelocitydidnot yetyieldmeaningfulresults.

An advancedimage analysis technique(boundary detectionor spectralanalysisofthelocalbubbledensity)maybeusefulto con-structaregimemapofoperatingconditionsforwhichthistypeof organizedperiodicﬂowbehavioremerges.

4.2. Globalﬂowpatterns

Fig.10showscontoursofthemeanbubblevelocitymagnitude andbubbletracesfor

λ

g= -1,0,1(fromleft to right)and

λ

l =-1

(top)and-2(bottom),whereasFig.11showscontoursofthe ﬂuc-tuatingvelocityinasimilararrangement.Themeansuperﬁcial liq-uidvelocity

Usl

=0.1m/s. Hence,theconditionsarecomparable

tothoseofwhichthebubblestreaks aregiveninthesecondand thirdrowofFig.8.Figs.12,and13are similartoFigs.10and11, butfor

Usl

=0.2m/s.

Due to the difference of the liquid co-ﬂow velocity between both inlets (the left inlet having the highest Usl for all cases

shown), ﬂow patterns corresponding to

λ

g= -1 and 1 are no

longersymmetric.

Forall cases, the fluid at the side of the highestgas fraction (appearslighter inFig. 8)accelerated whileentraining fluidfrom thetrans-boundaryside.Iftheliquidco-flowvelocitywasthen in-sufficiently high, globalbubble recirculation vortices appeared as presentedinthetopregions(blue)ofFigs.11a,11cand11d,while

(11)

Fig. 10. Bubble traces and velocity magnitude contours. U sg = 1.25 cm/s; from left

to right: more gas ﬂow left ( λg = −1 ), even distribution ( λg = 0 ), more gas ﬂow

right ( λg = 1 ). U sl = 0.1 m/s; upper row: more liquid co-ﬂow left ( λl = −1 ); lower

row: all liquid co-ﬂow left ( λl = −2 ); see Figs. 3 d- 3 f for uniform co-ﬂow ( λl = 0 ).

nodownwardmovingbubbleswereobservedwhen

Usl

=0.2m/s

(Fig.12). Asnoticeablefromthestructures inthecontours ofthe velocityfluctuations,Figs.11,13,aliquidco-flowhasanorganizing effectontheflowpattern.Asaliquidco-flowstronglycontributed tothemomentumflux,emergingbuoyancydrivenflowstructures were moreorganized,anda2Dflowbehaviorwassustainedfora widerrangeof

λ

gandstreamwiselocationsy.

We observed vortex roll-up for various conditions at dif-ferent positions and at different scales. De Tournemine and Roig (2010) (half-sparged conﬁguration) reported oscillating boundarieswhenbubbleswereinjectedatthehighliquidvelocity sideattheinlet(

λ

g

λ

l>0).Thisagreeswellwithourexperiments

depictedinFigs.12aand13a(wherevortexroll-upoccurredatthe boundary), but toa lesserextent in Figs.10aand 11a where the liquidco-flowvelocitywaslower.Inthelattercase,a globalflow patternemerged duetoa larger influenceofbuoyancydifference

Fig. 11. Contour plots of the RMS velocity. U sg = 1.25 cm/s; from left to right: more

gas flow left ( λg = −1 ), even distribution ( λg = 0 ), more gas flow right ( λg = 1 ). U sl = 0.1 m/s; upper row: more liquid co-flow left ( λl = −1 ); lower row: all liq-

uid co-ﬂow left ( λl = −2 ); see Figs. 4 d- 4 f for uniform co-ﬂow ( λl = 0 ).

driven ﬂow pattern. At the opposite end of the spectrum when

λ

g

λ

l<0,(higherUsg atthelowUsl side asinFig.8for

λ

g=0.75

and

λ

l=−2,Figs.10fand12f),alsounstableboundarieswere

ob-served. Largebuoyancydrivenvortex roll-upstructures (of a size signiﬁcantlylargerthan10_{× the}bubblediameter)werecreatedas showninFig.9(seealsoSupplementaryMaterialonline),whereas

DeTournemineandRoig(2010)reportedsteadyboundariesinthis operatingregime.Thismaybe duetothelowerU_sl andhigher

α

andlargerbubblesinourcase,whichmaytriggerflowinstabilities. In specific cases, when the void fraction of both the left and rightstreamwere(exactly)equal,nobuoyancydrivenflow struc-tures were formed and a mixing layer type of flow patternwas then observed. Fig. 12d shows a case where there is almost no buoyancy driven global flow pattern. While the boundary was hardly detectable (no void fraction difference, which behavior is similar to the caseshownin Fig. 8for

λ

g=−0.75 and

λ

l=−2),

(12)

Fig. 12. Bubble traces and velocity magnitude contours. U sg = 1.25 cm/s; from left

to right: more gas ﬂow left ( λg = −1 ), even distribution ( λg = 0 ), more gas ﬂow

right ( λg = 1 ). U sl = 0.2 m/s; upper row: more liquid co-ﬂow left ( λl = −1 ); lower

row: all liquid co-ﬂow left ( λl = −2 ); see Figs. 3 g-i for uniform co-ﬂow ( λl = 0 ). See

Supplementary Material online for the videos of (d) and (f).

bubblevelocitieswere verymuch unidirectional(byinspection of bubblestreaks),andtheboundarylocationremainedcentered(see alsotheSupplementaryMaterialonlineforthevideoofthiscase). Also, the initial velocities of the left and right inlets, were pre-served for a large range of y (almost no color gradient in ver-tical direction in the vicinity of the left andright column wall). The contours ofthecorresponding velocity fluctuations(Fig. 13d) show averysymmetricgrowthpatternaroundx=0,which indi-catesthat thewidthoftheshearlayerincreasedwithheight and developed alignedwiththesplitterplateandamixing-layertype offlow pattern(seeBrownandRoshko(1974))wasrecovered.As buoyancy differences were (almost) absent, a liquid-shear driven vortex roll-ups occurred in the center of the bubble column for thisspecificcase,whichwasfoundtohavesmallerstructuresthan thebuoyancy-drivenvortexroll-upstructures.

Fig. 13. Contour plots of the RMS velocity. U sg = 1.25 cm/s; from left to right:

more gas ﬂow left ( λg = −1 ), even distribution ( λg = 0 ), more gas ﬂow right ( λg =

1 ). U sl = 0.2 m/s; upper row: more liquid co-ﬂow left ( λl = −1 ); lower row: all

liquid co-ﬂow left ( λl = −2 ); see Fig. 4 g-i for uniform co-ﬂow ( λl = 0 ).

4.3. Parcelvelocityproﬁles

Fig.14 showsvelocity proﬁles ofthe meanvertical parcel ve-locities (y-direction), as measured by BIV, at a height of y=63 cmabove the trailingedge ofthe splitterplate. The uniform liq-uidco-ﬂowvelocity

Usl

wasﬁxedat0.2m/sandthedegreeof

a-symmetricsparging

λ

gwasvariedintherange-1...1(see legend).

Theeffectofa-symmetricliquidco-ﬂowisshowninFigs.14aand

14bfor

λ

l equal to -1and-2,respectively. The lattercase

repre-sentsthecaseofnoliquidco-ﬂowattherightinletanda superﬁ-cialliquidvelocityof2

U_sl

₌0_.4m/sfortheleftinlet.

Thereaderisreferred back toFig.5cfor

λ

_l=0for

U_sl

=0.2 m/s. While thevelocity proﬁles Fig.5cshow symmetric behavior around x=0m forthevarious

λ

gconditions,velocity proﬁles in

Fig.14areno longersymmetricaroundx=0cm,nor

λ

g=0due

(13)

Fig. 14. Bubble parcel velocity proﬁles obtained by BIV measurements at y = 63 cm for various λg . U sl = 0 . 2 m/s. From left to right: increasing asymmetry of the liquid

co-flow, λl . The dashed lines at x = ±0 . 15 m denote the OFP locations. The velocity profiles in (a) are extracted from Figs. 12 a- 12 c, and the velocity profiles in (b) are

extracted from Figs. 12 d- 12 f for λg = −1 , 0 , 1 respectively.

AsUsl,L>Usl,R,thegasfractionofthebubblystreamoriginating

fromtheleftinletbecamelowerthanthatfromtherightinletfor themajorityofthecases.Therefore,duetothegasfraction differ-ences,thebubbly streamfromtherightinletacceleratedandthe streamfromtheleftinlet,withaninitiallyhighervelocityaty=0 decelerated,seeFigs.10b,10c,10e,10fandFigs.12b,12c,12d,12e,

12f.

For some cases, the region with highestbubble velocities re-mainedattheleftside.Thisoccurredfor

λ

g≤ −0.3when

λ

l=−1

(a)orfor

λ

g<−0.7when

λ

l=−2(b).Whenthereducingeffectof

theliquidco-flowonthegasfractionwas(over)compensatedbya sufficientlyhighsuperficialgasvelocity (U_sg,L>>U_sg,R),the result-ing gasfractionofthestreamfromtheleft inletwashigherthan thatoftherightinlet.Thisresultedtheninabuoyancydriven ac-celerationofthestreamcomingfromtheleftinlet.

Aroundthetippingpoints,

λ

g≈ −0.3for

λ

l=−1andespecially

λ

g≈ −0.7for

λ

l=−2,themeasuredvelocityproﬁles appearvery

sensitive towards changesin

λ

g.Forhigh(positive)

λ

g,whenthe

initial gasfractioncontrastishigh, velocityproﬁles arebecoming less dependent on variations of

λ

g. For those cases, the bubbly

stream from the rightinlet accelerated ina very strong manner, whilebeingpushedevenmoretotherightsideduetothehigh(er) co-ﬂowvelocityattheleft side.Thisresulted,partlyduethenear vicinity ofthe columnrightwall,in strongvelocity andgas frac-tion gradients, leadingtovortex roll-upbehavior asillustrated in

Fig.9.

4.4. Localﬂowmeasurements 4.4.1. Gasfraction

Fig.15showsthedevelopmentof

α

atx=±15cmandy=63 cmasafunction of

λ

gfor

λ

l=0(whitemarkers),-1(grey

mark-ers)and-2(blackmarkers)andfor(a)

Usl

=0.1and(b)0.2m/s.

Forthesakeofcomparison,thewhitemarkersinFig.15aand15b showthesameresultsasthegreyandblackmarkersinFig.6 re-spectively. The triangles pointing right () denote measurements takenatx=15 cm,whiletheleftpointingtriangles() represent measurementstakenatx=−15cm.

While the open markers

λ

_l=0 exhibit a symmetric pattern around

λ

g=0, where the highest gas fraction was measured at

thesideofthehighestaerationrate(leftif

λ

g<0andviceversa),

symmetryaround

λ

g=0waslostfor

λ

l=0.Inextremecases,for

Usl

=0.2,

λ

l=−2 and

λ

g≥ 0, see Fig. 15b and Figs. 12e, 12f,

the boundary drifted to the right side in a very strong manner. As the widthof the bubbleplume becamelessthan or equal to 5 cm, the OFP atx=15 cm was no longer located solely in the bubble swarm originating fromthe right inlet, butin the centre of the highlyunstable boundary, (where vortex roll-up occurred, seeFigs.13e, 13f).As thebubbleplumebecamethinnerwith de-creasing

λ

l andincreasing

λ

g,theprobeatx=15cmincreasingly

dwelledinthetrans-boundaryside(the bubbleswarmoriginating fromtheleftinletwithalowgasfraction),hence,thegasfraction measuredatx=15 cm(blacktriangles)nolongerincreasedwith increasing

λ

g.

Dueto an uneven liquid co-ﬂow,the highestgasfractionwas not necessarily found at the side of the highest aeration rate. A co-ﬂow affects the (overall) gas fraction according to a corre-lation developed in our previous paper [Muilwijk and Van den Akker(2019b)]andvalidatedinPartI:

α

=_U U sg sg+U sl+

ξ

U t

(9)

withUttheterminalrisevelocityofanisolatedbubble(≈ 24cm/s)

(14)

Fig. 15. αas a function of the degree of asymmetry λg at x = ±15 cm and y = 63 cm for λl = 0 (from Fig. 6 ),-1 and -2. U sg = 1.25 cm/s. The circles show the interpolated

operating condition for which αx=−15 = αx=15 . The error bars denote the standard deviations based on 30 s intervals.

created for most cases when

λ

g=0 (Usg,L=Usg,R) and/or

λ

l=0

(Usl,L=Usl,R), thereby inducing a competition between buoyancy

drivenandadvectiongovernedﬂowstructures.

A highliquid co-ﬂow (left) resulted in an initially fast rising bubbleswarm(alsoleft),whichthen,dependentontheinitialgas fractionsofbothstreams,mightaccelerate(Figs.10a,10dand12a or decelerate(Figs.10b,10c,10e, 10f andFigs. 12b,12c, 12e, 12f afterthetrailingedgeofthesplitterplate.Inthelattercases,with a uniformaeration (Figs. 10b,10e, andFigs.12b,12e. andwitha higherUsg,R(Figs.10c,10f,andFigs.12c,12f,astrongliquidco-ﬂow

originating fromthe left inlet (witha lower gas fraction) broad-ened anddecelerated.Thiswasduetoentrainmentofliquidinto the bubblyﬂow rising fromtherightinlet, leavingjustanarrow zonewithahighergasfractionatthefarright. Underspeciﬁc cir-cumstances(seeFig.12dandblackmarkersinFig.15bat

λ

g=−1)

all bubbles risemore orlessrectilinearbecausethe gasfractions leftandrightaremoreorlessequal.

ByinvokingEq.(9),alongwithEqs.(5)and(6)for

λ

gand

λ

l,

respectively,thecondition

α

L=

α

R (10)

canbeconvertedinto

λ

g=

λ

l 1 1+

ξ

Ut

Usl

(11)

showinghowforaspeciﬁc valueof

Usl

non-uniformitiesin

aer-ationrateandliquidco-ﬂowmayneutralizeeachother andresult inaquasi-uniformﬂowbehavior.

AsPart Iofthistwinpapershowedthat

α

developedwith re-spect to the height in the column(for uniform gas sparging),it cannot beassumedthat Eqs.(10)-(11),with

ξ

=0.82, work prop-erly to estimate operatingconditions for which the gasfractions for theleft andrightinlets atgas spargerlevel are equal.In our experiments, we only measured gasfractions at two positions at y=63cm,see againFig. 15.Ratherthan requiringthe condition

ofEq.(10)tobe imposedatthelevelofthesparger,we now ap-ply this condition to the two measuring positions at y=63 cm. Therefore,operatingconditionsforwhich

α

x=−15

(

)

=

α

x=15

(

)

are interpolatedandindicatedascirclesinFigs.15aand15b.Itisthen assumedthat if

α

x=−15=

α

x=15, thereis also nogas fraction dif-ferenceattheinlet(y₌0),andbuoyancydrivenﬂowpatternswill notdevelop.

Fitting ofthe interpolated values of

λ

g to Eq. (11) yields

ξ

=

1.05± 0.02, andEq.(10) with

ξ

=1.05 maybe used to describe thegasfractionatinletconditions.Asahighervalueof

ξ

resultsin alower estimatedgas fraction,thisagrees well withtheﬁndings of Part I of thispaper, where lower gas fractions were found at a heightof 40cm abovethe spargeras comparedto 80cm (the spargerislocatedaty=−17cm).Thiscan beexplainedduetoa lesserdegreeofswarmingbehaviorinthevicinityofthespargeras thearrayofbubbletrains(ofuniform,separatelyformedbubbles) wasdevelopinginthevicinityofthespargeranddidnotmixupto aheight ofatleast5cmabove theneedleoutlets(dependenton Usg andUsl).Moreexperimentsarerequiredtostudya-symmetric

operating conditions for which the (initial) gas fractions at both inletsareexactlyequal.

4.4.2. Bubblevelocities

Locally measured bubble velocities in the presence of an a-symmetricliquidco-ﬂowarepresentedseparatelyinA.2and com-paredwithvertical(swarm)velocitycomponentsobtainedviaBIV.

4.4.3. Bubblechordlengths

Fig. 16 shows the mean chord lengths c at x₌_±15 cm and y=63 cm asa function of

λ

g and

λ

l=0,-1, -2 for(a)

Usl

=0.1

m/s;and(b)

Usl

=0.2m/s.ThewhitemarkersinFigs.16aand16b

showbubblechordlengthsobtainedwithauniformliquidco-ﬂow (

λ

_l=0)asshownbythegreyandblackmarkersinFigs.7band7c respectively.

(15)

Fig. 16. c as a function of the degree of asymmetry λg at x = ±15 cm and y = 63 cm for λl = 0, -1 and -2. U sg = 1.25 cm/s. The circular markers show the predicted chord

lengths for operating conditions where d b,L = d b,R , see Eq. (12) .

The largestbubbles were formed atthe inletwithhighestUsg

andlowestU_sl.Hence,thedevelopmentofcshowsasimilartrend asthedevelopmentof

α

showninFig.15.

Operatingconditionswerepredictedforwhich

d b,L= d b,R (12)

where d_b₌f

(

Usg,Usl

)

was developed in our previous paper

[MuilwijkandVandenAkker(2019b)]:

d b d n =

0.093 U l U g,n+

₆_.₁₈ Bo

+1.26F r 3/5

−1

−1 3 (13) where, Bo =

ρ

wgd n2

σ

≈ 0. 32 (14) F r =U 2 g,n gd n (15)

Ug,n is thelinear needle gasvelocity, 4Qg,n/

(

π

d2n

)

, dn the needle

diameter( 1.55mm)andUl theliquidco-ﬂowvelocity.

The valuesofdb attheleft andrightinletwere calculated

us-ingthesectional(inlet)valuesforUsg andUsl,andUsgiscorrected

forthe hydrostaticpressure atgasspargerlevel (asa function of the overallgas hold-up).Operatingconditions intermsof

λ

g, for

which Eq.(12) is satisﬁed,were calculatedfor

Usg

=1.25cm/s,

Usl

=0.1 and0.2 m/sand

λ

l=−1,−2.These bubble diameters

canbeconvertedintochordlengthsbytakingabubbleshape fac-tor of 0.50 (see Eqs. (5)-(6) ofPart I). These chord lengths have been inserted into Figs. 16a and 16b as circular markers for the various

λ

gvalues.ThechordlengthscalculatedfromEqs.(12)and

(13) agree ratherwell with the intersection points(

λ

g values in

Figs. 16a and 16b of the dotted lines through the experimental data.

Mostcalculatedchordlengths, attheintersectionpoints,were slightlysmallerthanthemeasuredchordlengths. Thiscanbe ex-plainedby(1)theaspectratioof0.50maybetoosmall;(2)some uncertainty of db as predicted by Eq. (13); and (3) the bubble

probes maybe biasedto larger chord lengthsasbubbles pierced attheedgeofabubblearemorelikelytosufferfromdrifting. 4.5. Theapotheosis:Anoperatingmap

Fig.17summarizestheoperatingconditionsoftheexperiments withana-symmetricliquidco-flowaspresentedinthisSection4. Thehorizontalaxisshowsthesuperficialgasvelocityandthe ver-ticalaxisdenotesthesuperficialliquidvelocity.Atrianglepointing left denotes the sectional inletconditions of theleft inlet,and a triangle pointing right stands forthe inlet conditions of the rightinlet.Thegreytrianglesshowtheexperimentswith

λ

l=−1,

whereastheblacktrianglesdenotetheexperimentswith

λ

_l₌₋₂. Athingray/blackline,hereafteroperatingline,connectsthe oper-ating conditionsof theleft andrightinlet foreach experimental conﬁguration.Asall experimentswere carriedout at

Usg

=1.25

cm/s, theoperating lines crossthe operating points

(

Usg

;

Usl

)

.

Thetwosetsofradialspokesat(1.25;0.1)and(1.25;0.2)showthe broad range of operating conditions and conﬁgurations we pre-sentedin thispaper.Note thatthe operatingpoints fortheright inlet () for

Usl

= 0.1 and

Usl

= 0.2 m/scoincide atUsl=0

asUsl,R=0when

λ

l=−2.Theoperatingconditionsfor

λ

l=0(see

Sec. 3)are omitted forclarity,asthe operatinglines wouldform horizontallinesintherangeUsg=0.63...1.88cm/sthroughthe

op-eratingpoints

(

Usg

;

Usl

)

={(1.25,0);(1.25,0.1);and(1.25,0.2)}.

Thegasfractionsattheinlet,asafunctionofthesectional(left orright)UsgandUsl arecalculatedaccordingEq.(9)with

ξ

=1.05.

Theiso-contoursofthegasfractionattheinletisshownbyblack solid(eachintervalof1%)anddashedlines(eachintervalof0.25%) andannotatedoutsidethe contourinFig.17.When an operating line isin parallel with the (solid/dashed black) contour lines for

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Fig. 17. Operating map as a function of the sectional U sg and U sl . Contour plot of d b according to the correlation proposed in Muilwijk and Van den Akker (2019b) . Dashed

white contours are drawn at an interval of 0.2 mm. The black contours show conditions for which αL = αR and the numbers denote the gas fraction at the inlet calculated

according to Eq. (9) with ξ= 1 . 06 . Dashed black lines are drawn at each 0.25% interval. Grey markers: λl = −1 ; black markers: λl = −2 . The thin solid grey/black lines

connect the operating conditions of the left inlet ( ) to the operating conditions of the right inlet ( ) for each setting λg , λl , and U sl .

thevoidfraction,thevoidfractionoftheleftandrightinletis bal-ancedandEq.(10)issatisﬁed.Forthesecases,nobuoyancydriven ﬂowstructures emergedand”bubblymixinglayer” conditionscan be predicted. Onthe contrary,whenthe operatinglines linesare rather skew, or even more or less normal,to the isocontours of

α

L,R,largecontrastsof

α

wereimposedatthetrailingedgeofthe

splitter plate and the ﬂow patterns were governed by buoyancy differences.

The colored contour map, withthe white dotted isocontours, showsthebubblesizeasafunctionofthesectionalUsgandUsl,see

Eq.(13).Similarly,whentheoperatinglineisparalleltothe isocon-tours ofd_b_,bubblesfromtheleftandrightinletare formedwith an equal equivalent diameter(but ata different formation rate). Theconditionsforwhichcx=−15=cx=15(thenassuming db,x=−15= db,x=15)donot necessarilycoincidewiththeconditionsforwhich

α

x=−15=

α

x=15.Therefore,regimesinFig.17can beidentiﬁed for which theisocontours ofdb,L,R and

α

L,R are (almost) parallel and

operating conditions can be predicted for which a bubbly mix-ing layerpatternoccurs(without buoyancydifference drivenﬂow

structures).Thelinesconnectingthepoints(1.88;0.4)and(0.63;0) for the case

Usg

=1.25 m/s;

Usl

=0.2 m/s;

λ

g=−1;

λ

l=−2,

are very parallel to both the isocontours of d_b and

α

L,R and the

ﬂowpatternsinthesecasesapproximatedabubblymixing conﬁg-uration,seeFig.12d.

Fig.17offersanexcellentstarting-pointfor(transient)CFD two-fluid simulations of bubbly flows with the view to validate the models for phase interaction forces, two-phase flow turbulence andlateralbubbledispersion(the latterparticularlydueto differ-encesinbubblevelocities).Firstofall,Fig.17presentsdataforgas fractionandbubblesizeasfunctionsofsuperficial gasandliquid velocities under various a-symmetric aeration and (non-)uniform liquidco-flowconditions.Aninterestingoptionwouldbeto simu-latevarious casesone.g.thelineconnectingthepoints(1.88;0.4) and(0.63;0),toseewhethersuchsimulationswouldresultinflow fieldsresemblingFig.12d,inspiteofdifferentsuperficialgasand liquidvelocities.Similarly, simulatingcasesona lineskewto the isocontoursof

α

_L,R shouldshowthedynamicsofbuoyancydriven ﬂowstructures.The varyingoperatingparametersfortheleftand

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rightinlet,leadingtoeithera smooth mixinglayer pattern(as in

Fig. 12d)orbuoyancydriven ﬂow structures, providea real chal-lengeforsimulationsinwhichthecontributionsofthethreeabove typesofmodelsmayvary.

5. Conclusions

An experimental investigation of a-symmetric bubble column configurationswasperformed, withunevengasspargingandwith auniformora-symmetricliquidco-flow.Underseveralconditions, Kelvin-Helmholtzinstabilitieswereobserveddevelopinginto orga-nized vorticalflow structures asa result oflateral differences in mixturevelocitiesand/orvoidfraction(i.e.,mixturedensity).

Bubble streaks were captured in order to study the occur-rence of (buoyancy driven) vortex roll-up structures. Bubble Im-ageVelocimetry(BIV),an imagecorrelationtechniquetocalculate the displacementofparcelsofbubbles, wasthenusedto capture globalflowpatterns.Dual-tipopticalfibreprobes(OFP)wereused tomeasurelocalvoidfractions,bubblevelocitiesandchordlengths attwofixedpositionsinthecolumnwherethebubblesmove pre-dominantlyupwardsandalignedwiththeprobe.

The verticalbubblevelocity andstandarddeviationthereof,as measured usingBIV andthe OFPs,were compared and generally good agreement was observed between both methods. Contour plotsofthebubbleparcelvelocitymagnitudeandthe root-mean-square(RMS)oftheitsvelocityﬂuctuationswereshownforawide rangeofa-symmetricoperatingconditions.

We presentedathoroughanalysisofthesteepdeparture from homogeneous bubbly flow to inhomogeneous bubbly flow as a functionofa-symmetricgassparging.Itwasfoundthatauniform liquidco-flowstabilizeda slightlyinhomogeneouslysparged bub-blecolumnasthedevelopingflowpatternswerelesssensitiveto a(small)degreeofa-symmetricsparging.

A model for the gas fraction was adopted to describe the gas fraction at the inlet as a function of both the degree of a-symmetricspargingandthedegreeofa-symmetricliquidco-flow. Operatingconditionswereidentifiedforwhichtherearenoinitial gasfractiondifferences, suchthat nobuoyancydriven flow struc-tures emerged.Inthiscase,thebubblesmove essentially rectilin-ear dueto advectionand a mixinglayer pattern(with its devel-opment alignedwiththesplitterplate)wasvisiblefromthe con-tours ofthe bubblevelocitymagnitudeandRMSfluctuations. For all other cases, when the gas fractionof the left and rightinlet were notequal,thebubbleswarm originatingfromtheinletwith thehighestgasfractionalwaysacceleratedasaresultofbuoyancy differencesandtriggeredlargeandunstableflowinstabilities.

An operating map wasconstructed to plot the gasfraction at theinletandthebubblediameterasfunctionsofthesectionalUsg

andU_sl andtorepresentall the experimentscarried out withan a-symmetricliquidco-ﬂow.Thisoperatingmapcanbeveryuseful toidentifyregimesatwhichbothinletsoperateatequalgas frac-tion(andequalbubblediameter),suchthatthereisnocompetition betweenbuoyancydrivenandadvectiondriven ﬂowstructures or opposite. For future reference, operating conditions may be pre-dictedforwhichmixinglayerpatternsoccurinorderto disentan-gle the effectof shear generated turbulence andbubble induced turbulence.

Futureworkmayincludefurtheranalysisof(the obtained)BIV data to study the dynamics of the bubble column, by means of Proper Orthogonal Decomposition and/or Dynamic Mode Decom-position.Also,regimescanbeidentiﬁedforwhichthemean bub-ble velocities can be describedby a parametric error function in termsofx,y,andtheoperatingconditions.

AfurtherexperimentalanalysismayfocusonLaserDoppler Ve-locimetryorphase-sensitiveHot-WireAnemometry(when optical access is impeded dueto the high void fraction) to study liquid

velocitiesandturbulence.Thebubble(parcel)velocitiespresented heremaythenactasareferenceforcalculating(local)slip veloci-ties.

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoconﬂictofinterest.

CRediTauthorshipcontributionstatement

Corné Muilwijk: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing -original draft, Visualization.HarryE.A.VandenAkker: Conceptualization, Writ-ing-review&editing,Supervision,Fundingacquisition.

Acknowledgements

Thisresearchwasmadepossiblethroughastart-upfundinthe contextoftheBernalProjectattheUniversityofLimerick.The au-thors want to acknowledge Saikat Bhowmick MSc. for his assis-tanceduringtheexperiments.

AppendixA. Bubblevelocitiesandparcelvelocities

A1. Theeffectofauniform-coﬂow(

λ

l=0)

Fig.A.1 showsthemean bubblevelocity

v

b asmeasured with

the dual-tip optical ﬁbre probes (a) and parcel velocities as ob-tainedbyusingBIV(b)asafunctionofthedegreeofa-symmetric gassparging

λ

g for

Usl

= 0 (open markers);0.1(grey markers)

and0.2m/s(blackmarkers).Theopticalﬁbreprobemeasurements atx₌₋₁₅andx₌₊₁₅cmweretakensimultaneously(300s aver-age).Thebubbleparcelvelocities(10saverage)aty=63cmwere linearlyinterpolatedatx=±15 cmfromtheproﬁles asshownin

Fig.5.Itshouldbenotedthatatrianglepointingright()denotes the measurements at location atx=+15 cm, whereas a triangle pointingleft()denotesmeasurementsatx=−15cm.

Ingeneral, good agreementwasobserved betweenthebubble (parcel)velocitiesasobtainedbybothmethods.InlinewithPartI ofthispaper,bothmethodsagreeverywellatintermediatebubble velocities(20<

v

b<40cm/s),whereasBIVresultsinvelocitiesup

to15%higherfor

v

b>60cm/s.AstheOpticalFibreProbesare

cen-teredbetweenthefrontandrearwall,whilethedepthofviewof thecamera coveredthewhole depthofthecolumn, this discrep-ancycanbe ascribeddueto3D effectsastheBIVresultsmaybe biasedtotheﬂow inthevicinityofthe frontcolumnwall (espe-ciallyforhigher

α

whenthetransparencydecreased).Gradientsof

α

and

v

b in thecollineardirection(between front andrearwall)

maycompromise thecomparability ofboth methods and further (numerical)researchisrequiredtostudythevalidityofa2D(x,y) ﬂowassumption.

Withoutliquid co-ﬂow,the bubblevelocity ishugely sensitive to a small degree of a-symmetric gas sparging (see white mark-ersaround

λ

g=0in Fig.A.1), evenmore stronglythan alpha (in

Fig.6).Alsofromthedevelopmentof

v

basafunctionof

λ

g,itcan

beseenthatthelineofsymmetryisslightlytotherightof

λ

g=0

duetoaslightimbalanceoftheMassFlowControllercalibrations. A-symmetric sparging induces a global liquid recirculation loop. Thestreamoriginatingfromtheinletwiththehighestgasfraction acceleratesandentrainsfluid.Thisentrainedfluidcomesdownat theothersideofthecolumn.Thedownwardvelocityoftheliquid dragsbubblesdown thecolumn,hencenegativebubblevelocities arerealisticallyobtainedfromtheBIVmethod.Duetothe config-urationoftheopticalfibreprobes,small(andnegative)bubble ve-locitiescouldnotbemeasured.Bubblevelocitymeasurements us-ingtheopticalprobeforthesetforUsl=0m/s(Fig.A.1a)were

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ig-C. Muilwijk and H.E.A. Van den Akker International Journal of Multiphase Flow 138 (2021) 103562

Fig. A.1. vb at x = ±15 cm and y = 63 cm as a function of the degree of asymmetry λg . Left: Optical ﬁbre probe; Right: Bubble Image Velocimetry. U sg = 1.25 cm/s;

Fig. A.2. Stdev( vb ) at x = ±15 cm and y = 63 cm as a function of the degree of asymmetry λg . U sg = 1.25 cm/s;

nored wheninsuﬃcientvalidbubblevelocitymeasurements were obtained.

Withincreasing

U_sl

,themeasuredvelocitiesatthetwo mon-itoringpointsinFig.A.1deviatedtoalesserdegreefromthemore homogeneousﬂowconditionsat

λ

g=0,asalreadyshowninFig.3,

whilethey arelesssensitiveto smallvariationsin

λ

g.Thisisdue

thereductionoftheoccurrenceof(ﬂuctuating)recirculationloops.

Fig. A.2 shows the standard deviation of the bubble velocity Stdev

(

v

b

)

asmeasured withthe dual-tip optical ﬁbre probes (a)

andparcelvelocitiesasobtainedbyusingBIV(b)asafunctionof

thedegree ofa-symmetric gassparging

λ

gforthe samecasesas

outlined inFig.A.1. Similarto thedevelopmentof

α

(Fig. 6)and

v

b (Fig. A.1) as a function of

λ

g, also the evolution of Stdev(

v

b)

isverysymmetricwithrespectto

λ

g=0.Thestandarddeviations

obtainedfromtheBIVmethod(b)showamoreirregularbehavior thanthoseobtainedbytheopticalﬁbreprobes(a)asthesampling periodofthe BIVis 10s, comparedto the 300s duration ofthe bubbleprobedataacquisition.TheobservedtrendsinStdev

(

v

b

)

as

capturedbybothOFPandBIVmethodsarerathersimilar.Although thestandard deviationsof thevelocity distributions measuredby