Annular two-phase flow in vertical smooth and corrugated pipes

Annular two-phase flow in vertical smooth and corrugated pipes

van Eckeveld, A. C.; Gotfredsen, E.; Westerweel, J.; Poelma, C.

DOI

10.1016/j.ijmultiphaseflow.2018.07.004

Publication date

2018

Document Version

Final published version

Published in

International Journal of Multiphase Flow

Citation (APA)

van Eckeveld, A. C., Gotfredsen, E., Westerweel, J., & Poelma, C. (2018). Annular two-phase flow in

vertical smooth and corrugated pipes. International Journal of Multiphase Flow, 109, 150-163.

https://doi.org/10.1016/j.ijmultiphaseflow.2018.07.004

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ContentslistsavailableatScienceDirect

International

Journal

of

Multiphase

Flow

journalhomepage:www.elsevier.com/locate/ijmulflow

Annular

two-phase

flow

in

vertical

smooth

and

corrugated

pipes

A.C.

van

Eckeveld

a,∗

_,

_E.

_Gotfredsen

b

_,

_J.

_Westerweel

a

_,

_C.

_Poelma

a a Delft University of Technology, Leeghwaterstraat 21, Delft, 2628CA, The Netherlands

b Technical University of Denmark, Nils Koppels Allé, Building 403, Kgs. Lyngby, 2800, Denmark

a

r

t

i

c

l

e

i

n

f

o

Article history: Received 26 April 2018 Revised 25 June 2018 Accepted 2 July 2018 Available online 1 August 2018

a

b

s

t

r

a

c

t

Two-phaseflowinribbedorcorrugatedpipesisofinterestinmanyindustrialapplications.Experiments areperformedtoassesstheflowregimecharacteristicsinupwardannularflowthroughverticalsmooth andcorrugatedpipes.Fromhighspeedrecordings,theflowregimeandtemporalfilmcharacteristicsare obtained.Anovelimplementationofaplanarlaser-inducedfluorescence(PLIF)methodisusedto mea-surethefilmthickness,preventingstrongreflectionsfromdeterioratingthemeasurements.Liquid accu-mulationbetweentheribsofthecorrugatedpipeisalsomeasuredusingaPLIFtechnique.Furthermore, dropletsizingisperformedcombiningshadowgraphicandinterferometrictechniquestocapturealarge dropletsizerange. Themeasurementsshow thatthepresenceofpronouncedcorrugationsatthe pipe wallcausesastrongincreaseinentrainmentofliquidintothegasflow.Theentrainmentiscorrelated tothefillingofthecorrugationswithliquid; itissignificantlyreduced(from90%entrainmentto50%) whenthecorrugationsareentirelyfilledwithliquid.Theamountofliquidfillingofthecorrugationsis relatedtothesuperficialliquidfilmflowvelocity.Theliquidfillingfraction (α)scales withthe Weber and liquidReynoldsnumber, and the obtainedscaling alsoholdswhen theexperiments arerepeated withadifferentliquid(mono-ethyleneglycol)andwithalargercorrugationgeometry.Dropletsoccurring incorrugatedpipefloware30–50%largercomparedtothesmoothpipe,asaconsequenceofthelocally (atthelocationsofthecavities)increasedfilmthickness.

© 2018ElsevierLtd.Allrightsreserved.

1. Introduction

Ribbedorcorrugatedpipesareusedinmanyindustrial applica-tions.Theyareforexampleappliedasflexibleflowlinesandrisers intheoilandgasindustry.Otherapplicationsareprimarilyfound in processing units in production plants (e.g. food and chemical industry),where heat and mass transfer are important. Axisym-metric or helical inserts have been shown to increase heat and mass transfer coefficients drastically under certain conditions. In manyof these applications two-phase flows occur, having a low liquidloading.Thereis,however,limitedunderstanding ofthe ef-fectofribsandcorrugationsontheflowregimesoccurringin two-phase flows through thesepipes. This work aims at contributing tothisknowledge. Experimentsarecarried out toinvestigatethe two-phaseflowbehaviorinsmooth andcorrugatedverticalpipes, operatingin the annularflow regime. In thisregime, a thinfilm transportsapartoftheliquidalongthepipewall.Liquid entrain-mentfrom thefilm into the gascore resultsin a fractionof the totalliquidflowratebeingtransportedasdroplets.

∗ _{Corresponding author.}

E-mail address: a.c.vaneckeveld@tudelft.nl (A.C. van Eckeveld).

Co-currenttwo-phase flow in smooth vertical pipeshas been subject of many studies. Azzopardi (1997) provides a thorough summaryofthiswork.Morerecentcontributionsare providedby e.g. Belt etal.(2010); van‘t Westende etal. (2007), andSawant etal.(2008,2009).Inliterature,theoccurrenceofupwardannular flowisrelatedtoeithertheabilitytosuspendthedispersedphase (Turneretal.,1969)orthestabilityofthefilmatthewall(Zabaras et al., 1986). Either way, there exists a critical gas flow velocity below which the film is not sustained anda transition to churn flowisobserved.Forpipeswitha50mminnerdiameter,this crit-icalgasflowvelocity isapproximately14m/s(Taiteletal., 1980). Pressure drop,entrainment ratio, voidfraction and wave charac-teristics invertical annularflow are reasonably well understood. Forverylowliquidflowrates,afullfilmisnotsustained:thefilm breaksupandliquidistransportedinrivuletsalongthepipewall (Hewitt,1965).Forhigherliquidflowrates,thefullfilmismainly characterizedby twotypesofwaves: capillaryripples and distur-bance orrollwaves(Azzopardi,1997).Disturbance wavesare the main source ofliquid entrainmentinto the gascore (Arnoldand Hewitt,1967; Cousins andHewitt,1968; Azzopardi andWhalley, 1980). The inceptionof disturbancewavesis thereforean impor-tantparameterwhen studyingliquidentrainmentinannularpipe flow. Azzopardi (1997) is one ofvarious other authors proposing

https://doi.org/10.1016/j.ijmultiphaseflow.2018.07.004

Fig. 1. Schematic representation of the two main droplet formation mechanisms in upward annular smooth pipe flow: bag break-up (left) and ligament break-up (right).

acriterionfortheinceptionofdisturbancewaves,belowwhichno significantentrainmentisexpected.AccordingtoIshiiandGrolmes (1975),entrainmentissuppressedifthefilmReynoldsnumber1_is

smallerthen160,duetotheabsenceofdisturbancewaves.Sawant etal.(2009) showedthat thepresence ofdisturbancewaves isa necessaryconditionfortheonsetofentrainment,butnotsufficient initself. Especiallyatlower gasflow ratesdisturbancewavescan occurwithoutsignificantentrainment.

Twomechanismsfordropletformationfromdisturbancewaves have been identified (Azzopardi, 1997). Fig. 1 gives a schematic representation of these two mechanisms. At lower gas and liq-uid flow rates,thebag break-up mechanismisdominant. Partof the wave is undercut by thegas flow, resulting in theformation of droplets. The second mechanism, occurringat highergas flow speeds, istheligamentbreak-upmechanism, wherealigamentis sheared fromthewavesby thehighspeedgasphase.This mech-anism occurs overa large range ofoperating parameters. Several studiesaimedtomodeltheentrainmentrateinannularpipeflow.

Ishii andMishima(1989) usedtheonset ofentrainmentcriterion developed by Ishii andGrolmes (1975), to come up withan en-trainment correlation.Thecorrelation isbasedontheassumption that the excess liquid, above the entrainment onset limit, is en-trainedintothegasflow.TheyfoundaliquidReynoldsnumber de-pendencyinthetransitionregime(160 <Ref< 1635),andalso

in-troducedaviscositydependency. Thisviscositydependencyisnot warrantedaccordingtoWallis(1968).PanandHanratty(2002) de-velopedasimilarcorrelation,withouttheliquidReynoldsnumber andviscositydependency.

Theinfluenceofnon-smoothpipewallsonthetwo-phaseflow is lesswell understood, butvery relevant incertain applications, such as corrugated risers (Belfroid etal., 2013), ribbed wall heat exchangers forboilingandcondensation(AgarwalandRao,1996), and mass transfer applications (Kukreja et al., 1993). Two-phase flow in corrugated pipesis mainly studied in the context of in-ternalhelicalwiresorothertypesofinsertsinsmoothpipes.Heat transfercoefficientscanbesignificantlyincreasedwhenthesetype ofinserts areused.Thisbehavior, however,isstronglydependent on the appearing two-phase flow regime. Severalstudies are de-voted tothe flow regime boundariesintwo-phase flows through pipeswithinserts.AgarwalandRao (1996)foundasignificant in-creaseoftheheattransfercoefficients, relatedtotheexistenceof annularflowoveralargerrangeofflowparameters,accompanied by anincreasedfilmthickness.Kim etal.(2001) showedthat, for counter-current two-phaseflow inacoiled pipe,theflow pattern transitionlinesmoved tolower gasflowvelocities.Thiswas

con-1 Re

f = 4 ρl u fδ/μl , with u f the average film velocity and δthe film thickness.

Fig. 2. Typical cavity flow in a corrugated pipe, subject to dry gas flow. The incom- ing gas flow separates at the upstream cavity edge, forming a shear layer where vortical structures can appear. The shear layer separates the bulk flow inside the main pipe from the recirculating flow in the cavities.

firmed by e.g. Ansari and Arzandi(2012) forhorizontal channels withribs. Recently, new attention wasgiven to two-phase flows in corrugated pipes in the framework of the mitigation of flow-induced vibrations in these pipes(Belfroid et al., 2013; van Eck-eveld et al., 2017). The presence of liquid was found to reduce, andeventually mitigate,flow-inducednoise.Inthisapplication, it is important to determine the minimum liquid loading required topreventvibrationstooccur,whichisstronglyinfluencedbythe flowregime.

Thereisverylimitedknowledgeabouttheeffectofwall rough-ness on two-phase flow behavior in the annular regime. The present work aims at understanding the effect of axisymmetric ribsalong a pipe wall on the flow pattern in vertical co-current two phase flow. In dry gas flow through thesepipes, the quasi-stagnant flow inside the corrugations isseparated from theflow throughthecoreofthepipe.Arecirculationcellisformed inside thecavities,whichscaleswiththecavitysize.Thereisalarge va-riety of cavities, classified based on their geometryand internal flow structure.The geometries studied inthiswork are so-called shallowopencavities,wheretheshearlayerextendstothe down-streamendofthecavity,andasinglerecirculationzoneisformed insidethecavity.Thisregimeoccurswhentheratioofthelength overdepthratioofthe cavityis ࣠8.The specificthresholdvalue forthisregimeiscaseandflowdependent.Aschematic represen-tationofthistypeofflowisprovidedinFig.2.

Thisworkaddstounderstandingtheeffectofacorrugatedpipe wallonthe flowbehavior intheannularregime.The behaviorof liquid atthe pipe walls, the entrainment ratio and the resulting dropletsizesareassessed, bothforsmooth andcorrugatedpipes. Twodifferent corrugation geometries are studied,and waterand mono-ethyleneglycol(MEG)areusedasworkingliquids,withair asthe gas phase. The measurements are carried out in an open flow loop, described in Section 2, together with the experimen-talmethods.Differentmeasurementtechniquesareusedto inves-tigate the flow behavior. The film thickness in smooth pipes is measuredusingaplanarlaser-inducedfluorescence(PLIF)technique, adapted to remove the effect of total internal reflections at the gas-liquidinterface.Dropletsizingiscarriedoutusing shadowgra-phyandinterferometry,alongsideentrainmentmeasurements. Liq-uidaccumulation insidethe cavities isalsoassessed usinga PLIF basedtechnique. Measurement resultsforthe smooth and corru-gatedpipesareprovidedinSections3and4,respectively.The re-sultsarediscussedinSection5.Section6providestheconclusions fromthepresentstudy.

2. Experimental

2.1. Experimentalset-up

Themeasurements arecarriedoutinan openflowloopwitha verticaltest section (depictedinFig. 3).The airflowthrough the pipeis provided bya blower (EsamMediojet 2V). Gasflow rates

Fig. 3. Schematic representation of the experimental set-up. The gas flow is created using a blower, followed by an expansion vessel which reduces the noise amplitude from the blower. Liquid is injected with a spray nozzle at the pipe center. The test section is transparent and can be replaced by a corrugated pipe section.

are measured witha zero

β

-ratio, long-radius ASME flow nozzle (Leutheusser, 1964). The superficial gas and liquid velocities are usedtocharacterizetheseflowrates(usg=Ql/Ap andusl=Qg/Ap,

withQ being the volume flow rate of the respective phase and

Ap the pipe cross sectional area). After passing through the

ex-pansionvessel, theflowis directedupward andliquidisinjected withspraynozzleslocatedatthepipecenter(BetePJ8,PJ10,PJ15, PJ24 andPJ32). The various nozzles are used for different liquid flowrates.Althoughtheyproducesslightlydifferentsprays,the ef-fecton theresults isfound tobe negligible.A rotary vanepump (Fluid-O-TechPA111) drives the liquid flow. The nozzles produce a dispersed sprayof droplets with a nominaldiameter lessthan 150μm.Theliquidflowrateismeasuredwithacoriolismassflow meter (Bronkhorst M14 CORI-FLOW). For flow development pur-poses,a3.7-mlongsmoothpipesection(Lp/Dp≈ 75,withDpbeing

theinnerpipediameter,whichis50mm)isplacedbehindthe liq-uid injectionpoint. It is made of steel, with a wall thickness of 5mm.Itisfollowedbya transparentplexiglasmeasurement sec-tion,whichalsohasawallthicknessof5mm.Themeasurements aretakenatapproximately84pipe diametersdownstreamofthe liquidinjection point. The flow loop is terminated with an open outflow. Temperature measurements are performed at the outlet usinga Pt100 temperatureprobe located at the pipe center-line. Thetemperaturemeasurements, together withpressure measure-mentsupstream of theliquid injectionpoint, areused to correct themassdensityofthegas.Fortheexperimentswithcorrugated pipes, the last three meters (Lp/Dp≈ 61) of theflow loop are

re-placed witha PVC corrugated section. Due to the wide range of applications (from different heat-exchangers to industrial risers), there is a large variety in geometrical characteristics that are of

Fig. 4. Cross-section of the corrugation geometry. The symbols are explained in text and numerical values for the used geometries are given in 1 .

Table 1

Dimensions of the different geometries used. Symbols are explained in the text, and a schematic of the corrugation lay-out is provided in Fig. 4 . geom A geom B Dp [mm] 49.25 49.25 Lc [mm] 4 6 Hc [mm] 4 6 Pc [mm] 6 10 red [mm] 2 2 Lp [m] 3 3.6

interest forcorrugated pipeflow. For thepresentstudy, we limit ourselves to two different general corrugation geometries. Both haverectangularcorrugationswithacavityheightoverlength ra-tioof1(Hc/Lc=1). Theupperedges are rounded(with theedge

rounding radius r_ed) asis found inmany applications (e.g. tape-wireinsertsinheatandmasstransferenhancementapplications). Thepitch(Pc)islimited,tofitasufficientnumberofcorrugations

inthe verticaldistance inorderto ensurefull flow development. Aschematicrepresentation oftheused geometries isdepictedin

Fig. 4. The dimensions are given inTable 1. For optical access a transparentcorrugatedsectionisplacedjustbeforetheendofthe corrugated pipe, at 49≤ Lp/Dp≤ 53 fromthe corrugated pipe

en-trance.

2.2. Highspeedimaging

Tocharacterizetheannularliquidfilmatthepipewall,a com-bination of high speed imaging and planar laser-induced fluores-cence(PLIF)isused.Fromthehighspeedimages,theflow regime andtemporalfilm statisticsare obtained. APhotronFastcamAPX 1MPcamera is used,equippedwith a105 mm Micro-Nikkor ob-jective. The transparent section is illuminated fromthe back us-ingan LEDpanel.Agridwithalternatingblackandwhitelinesis placedbetweenthelightsourceandthepipetoincreasecontrast ofthe gas-liquidinterface in thevisualizationimages.Images are recordedat700Hz,whichissufficienttocapturethedynamic be-haviorofthefilm.

2.3. Filmthicknessmeasurements

ThefilmthicknessisobtainedfromthePLIFmeasurements.The methodused beforeby e.g.Schubring etal.(2010) isadaptedfor thispurpose,withtheaimtoremovelarge reflectionsatthe gas-liquid interface. The set-up is schematically depicted in Fig. 5a. A laser sheet (from an Nd:YAG LitronLasers Nano L 50-50) il-luminates the liquid film. The liquid contains a fluorescent dye (150 μg/Lrhodamine WT).Thefluorescent light isrecordedusing aCCDcamera(LaVisionImagerLX16M),equippedwitha105mm Micro-Nikkorobjective witha red filter(B+W62 041)infrontof it.Theviewinganglehasbeenoptimizedintermsofwall-normal

Fig. 5. Principles of the liquid film thickness measurements.

Fig. 6. Comparison of film thickness from binarization (A) and using the novel line detection method (B). Large reflections can be detected in B because of the deviation of the lines.

spatial resolution of the film and the amount of reflections ob-served, resulting in an angle w.r.t. the laser sheet (

θ

in Fig. 5a) of75°.

Adrawback ofthe describedoptical techniqueisthe overesti-mationofthefilmthicknessduetototalinternalreflectionsatthe air-water interface. Häber etal.(2015) showed that the overesti-mation ofthefilmthicknesscouldreacha factoroftwoforsteep waves.Inordertoreducethiserror,theregularlightsheetusedby

Schubringetal.(2010)isreplacedbyalinedlightsheet.A compa-rablemethodispresentedbyCharogiannisetal.(2017)for down-wardannularpipeflow.Thelightsheetconsistsofalternatinglight and(smaller)darkregions,asisvisibleinFig.6.Thedarklinesare generatedbypassingthelightsheetthroughagrid,thereby creat-ing shadowsbehindthe gridlines. Areflectionofthe light sheet atthewavyair-waterinterfacewillcausethelinestodeviatefrom their straightpath,enablingadistinction betweenthe actualfilm andthereflections.Adrawbackofthismethodisthereduced spa-tialresolutionofthefilmthicknessmeasurement.Thespatial reso-lutioninthestreamwisedirectionisnowassociatedwiththe num-berofgridlinesinthelightsheet,insteadofthenumberofpixels in that direction.No prism is usedin theexperiments. Sincethe camera isrelatively faraway (paraxialapproximation isallowed), knowingthepipewallthicknessandthespacingofthedarklines inthelightsheetissufficienttospatiallycalibratethesystem.

Aninverseray-tracingtechniqueisusedtovalidatethemethod.

Fig.5bshowsanexampleimage obtainedwiththistechniquefor asimplesinewave.Theinitialpositionofthelinesisobtained us-ing apeak-find algorithm,withthe averageimageasinput. Devi-ation of the linesis detected using a run-lengthencoding script, determiningthefirstwall-normallocationwherethelinesshowa

2pixeldeviationfromtheinitialpositionoveratleast5pixelsin wall-normaldirection.Forthisartificialwave theimprovementin filmthicknessmeasurement isevident.Onlywherethe lightrays havea(near-)perpendicularangleofincidencewithrespecttothe gas-liquidinterface,thewaveheightisoverestimated.

Thistechniqueisappliedforthe filmthicknessmeasurements inasmooth pipe.Linespacingwaschosen tobe1 mm,whichis deemedsufficienttocapturemostwaves,keepinginmindthe cap-illary lengthscale (2.7mm inthe air-watercase).Decreasing the linespacingfurther wouldcomplicate theline detectionmethod.

Fig.6 showsa partofa typical image obtainedfromthese mea-surements, visualizing the improvement when the line detection methodisused.

2.4.Cavityfillingmeasurements

The liquid accumulation inside the cavities of the corrugated pipe is alsomeasured usinga PLIF-based method, similar to the film thickness measurements. In this case, the reflections at the air-waterinterfacearereducedbyreducingtheviewinganglewith respectto thelaser sheet. Anangle ofapproximately25° is used betweenthelaser sheetand thecamera. Witha steadyand per-fectly axisymmetric gas-liquid interface within the corrugations, thisyields a viewing angle well belowthe critical angle for air-water (=48.6◦) and air-mono-ethylene glycol (=44.0◦). The dye concentrationis optimizedfortherequiredintensityofthe emit-tedfluorescent light,resultinginaconcentrationof125μg/L. Fur-thermore,the optical box is filled with a Rhodamine solution of approximately50μg/L,andthefluorescentlightemittedfromthis regionis usedto correctfornon-uniformity in thelaser sheet. A typical image obtainedwithwaterinjection ina corrugatedpipe

Fig. 7. Typical image of liquid accumulation in cavities for a corrugated pipe with geometry B (see Table 1 ). Flow is from bottom to top. The corrugated wall is marked with the red line, the white boundaries are obtained from image processing and in- dicate the filling regions. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 8. Schematic representation of the slit used to remove the film from the pipe wall. δD indicates the gap width between the inner pipe wall and the slit edge, which is 2 mm at each side.

withgeometryB isdepictedinFig. 7. Highintensitycorresponds to regions of liquid accumulation. The white boundariesare ob-tainedafterprocessing, andindicatethe fillingarea. Moredetails aboutthedifferentprocessingstepscanbefoundinaprevious pa-perbyvanEckeveldetal.(2017).

2.5.Filmflowrateanddropletsizes

Dropletsizesaremeasuredatthepipeend,afterremovalofthe liquidfilm attachedto thewall. The film isremovedusing a slit (aswasappliedbye.g. Hayetal.1996).Theslitiscircular,witha wedgeshapededge.Theinternaldiameteroftheslitis4mmless thantheinternalpipediameter.Thefilmiscollectedbetweenthe slitandtheinnerpipewall,andisdirectedtoaseparatecontainer (seeFig.8).Themassofthecontainerisrecordedoveraperiodof atleasteightminutes,toobtainthefilmflowrate.

Dropletsizedistributionsaremeasuredafterfilmremoval,with acombinationofshadowgraphicparticleimaging(SPI)and interfer-ometricparticleimaging(IPI,Gloveretal.1995).Thetechniquesare combined to capture a large range of droplet sizes. A schematic overviewof the SPI set-up is provided in Fig. 9. Images are

ac-quired using a CCD camera (LaVision Imager LX 16M) equipped with a 200 mm focal length Micro-Nikkor objective. Behind the pipe, a diffusewhite backgroundis litby a pulsed Nd:YAG laser (LitronLasersNanoL50-50).Thedropletshadowsaresubsequently recorded.Severalimage processingstepsareapplied.First,a back-groundcorrectionisapplied,followedbyamedianfilter(3x3 pix-els) to reduce noise. The droplet edges are found using a canny filter and the contours are filled with a convex hull technique (Gonzalez andWoods,2012).Fromtheresultingbinaryimage,the droplet sizes are obtained, assuming spherical droplets. A typi-cal example of an SPI image obtained after background subtrac-tion and the applicationof a spatialmedian filter is depictedin

Fig.9.Thedropletsizerangethatcanbemeasuredusingthis tech-niqueislimitedbythespatialresolutionoftheimagesandbythe optics. The spatial resolution in the reported experiments is ap-proximately12.5μm/pixel.Furthermore,thediffractionlimitofthe imagingsystemisaround25μm.Itisthereforedifficulttoobtain reliabledropsizesfordropletswithdp< 50μmusing

shadowgra-phy.

Aninterferometrictechniqueisusedto measuredropletswith smallerdiameters.Thedropletsareilluminatedwitha1mmthick lasersheet,asisschematicallydepictedinFig.10.Thesame cam-era is used for the SPI andIPI measurements. It is placed at an angleof 70° withthe laser sheet, andthe Scheimpflugcondition is fulfilled to obtain equal focusing over the entirefield of view (Adrian and Westerweel, 2011). The 70° angle results in a high signal-to-noise ratio of the interference fringes, especially when laser light witha parallel polarization isused (Damaschke et al., 2005). Aseparate aperture is placed justbeforethe camera lens. Illumination of a spherical droplet with a light sheet results in two glare-pointsat both sidesofthe droplet.A defocusedimage oftheseglarepointsyieldsadiskwithaninterferencepatterndue to the monochromatic laser light that is used. A typical raw IPI imageisdepictedinFig.10.Thereisadirectrelationbetweenthe spacingofthefringesandthedropletsize.When theratioof re-fractiveindicesofthedropletsandthesurroundingfluidislarger than unity(m= n_l

ng>1) thisrelationis (Damaschke etal., 2005):

dp= 2

λ



ψ



cos

(

θ

/2

)

+



msin

(

θ

/2

)

m2_{− 2mcos}

(

θ

_/2

)

₊₁



, (1)

withdpbeingthedropletsize,

λ

thewavelengthoftheusedlight,



ψ

theangularfringespacing,and

θ

the viewingangle.The ad-vantage of using an interferometric technique is that the size of theinterferencedisksisnotrelatedtothedropletsize,butrather totheopticalchoicesmadeindesigningtheset-up.Smalldroplets yield a large



ψ

, and the lower bound of the droplet size that can be measured is solely determined by the aperture size and theworkingdistance.Thedetectionoflargedroplets islimitedby thespatialresolutionofthecameraimageasitcorrespondstothe smallestfringespacingthatcanstill bedetectedaccurately.A cor-relationmethodis usedtolocate thedropletsin theimages.The entireimage iscorrelatedwithacircularmask,havingthesizeof theinterferencedisks.Peaksintheresultingcorrelationplane are associatedwiththelocationsofthedroplets.Overlappingpartsof the dropletsare removedandthe fringe spacingis found froma simpleperiodogram,obtainedusingaFastFourierTransformofthe vertically-averageddiskimages.Thefringespacingissubsequently usedtocalculatethedropletsize.

CombinationofIPIandSPI

SPI andIPI recordings are carried out subsequently, assuming stationaryandreproducibleconditionsatspecificflowsettings.The validityofthisassumptionisverifiedbyrepeatingexperimentson different measurement days. Fig. 11shows droplet size distribu-tions obtainedfromSPIandIPI atthe sameflow conditions.The

Fig. 9. Schematic representation of the shadowgraphy set-up (left), where δz depicts the depth of focus of the imaging system. A cut-out of a typical image obtained using the shadowgraphic measurement technique (right), after background subtraction and the application of a median filter. Dark spots are the shadows of droplets, used to find the droplet size.

Fig. 10. Schematic representation of the IPI set-up (left) and a cut-out of a typical image obtained with this method (right). The insert shows the normalized interference pattern obtained from the enlarged droplet image after normalization and the application of a moving average filter.

Fig. 11. Volumetric droplet size distributions obtained from IPI and SPI, and the resulting combined and fitted distribution. The vertical dashed lines indicate the combination region for this particular case.

overlapping region in droplet diameter, indicated by the dotted lines, isused to combinethe two distributions into a single dis-tributioncoveringtheentiredropletsizerangeobservedinthe ex-periment.Theprobabilityofadropletendingupintheoverlapping range(i.e.a_{≤ d}p≤ b)forthetwotechniquesis:

Pab ipi= Nipi[a≤ dp≤ b] Nipi , and Pab spi= Nspi[a≤ dp≤ b] Nspi , (2)

whereNipi andNspi are thenumberofdropletsobtainedfromIPI

andSPI, respectively.Since the distributions fromIPIand SPIare

subsetsofthefulldropletsizedistribution,itholdsthatC1· Nipi=

C2· Nspi=Ncom,whereC1/2areconstants.Knowingthatthe

proba-bilitythatadroplet hasa diameterbetweena andbinthe com-bineddistribution(Pab

com)should matchforIPIandSPI,the

follow-ingconversionisobtained:

Pcomab = 1 C1Nipi[a≤ dp≤ b] Ncom = 1 C2Nspi[a≤ dp≤ b] Ncom . (3)

Thecombineddropsizedistributionthenbecomes:

PcomNcom=



Nipi ifdp≤ b C1 C2Nspi ifdp>b, with C1 C2 = Nipi[a≤ dp≤ b] Nspi[a≤ dp≤ b]. (4)

Theresultofthisoperationforoneparticularcaseisshownin

Fig. 11. The figure also shows the fitted upper limit log normal (ULLN)distribution, aswasalso used bye.g. Azzopardi (1997) to describethedropletsizedistributioninannularsmoothpipeflow. Thisdistributionisfittedtothecombinedvolumetricdropletsize distributionandstatisticalmeasuresregardingthedropletsare ob-tainedfromthefit.

3. Two-phase flow in smooth pipes

Asareferenceforthecorrugatedpipe flow,two-phase flowin a smooth pipe isfirst assessed. Tothe knowledge ofthe authors thereis no literature dataavailable forthe very low liquid load-ing used in the presentedexperiments, andwhich is relevant in variousapplications.Theliquidvolumefractionattainedinthe ex-perimentsis

φ

l<2× 10−4.Thisoperatingrangeisparticularly

Fig. 12. Different film flow regimes observed from the high speed video recordings. (A/D) ripples, (B) ripples and disturbance waves, (C) rivulets. The superficial gas and liquid velocities are indicated on top, in m/s and cm/s, respectively. The black and white bands in the background are used to increase the contrast in the film shadowgraphs. The black arrows indicate the position of disturbance waves in B, whereas the white arrow shows the rivulet observed in C.

Fig. 13. Flow map for the experimental parameter space, indicating the regions where a full film and rivulets occur in the smooth pipe.

theonset of condensation inheat exchangers orin dry-out con-ditions,mass fractions in thisrange will also occur. The present resultsarecomparedto dataobtainedbyBeltetal.(2010)andto thedatapresentedinthereviewpaperbyAzzopardi(1997),which arebothforahigherliquidloading.

The highspeedvideorecordingsoftheliquidfilmrevealthree different flow patterns: rivulets, regular ripples and disturbance waves.Fig.12 showssnapshotsofthedifferentflow regimes.Full high-speedrecordingsareaddedassupplementarymaterialtothis paper,andcanbefoundonline.Forlowliquidloadingathighgas flowratesthefilmisnotsustainedanddryspotsappear.This re-sultsintheformationofrivulets,transportingalltheliquidthatis attachedtothe wall (Cin Fig.12,supplementary recording‘R3’). Thewidthoftherivuletsvariesfromapproximately0.5to5.0mm. Theregionwhererivulets are observedinthedata isdepictedin

Fig.13.Formostoftheparameter spaceinthisstudy,thefilm is onlycoveredwithripplewaves(AandDinFig.12,supplementary recordings ‘R1’ and ‘R4’, respectively) which are smaller regular waves,witha limited azimuthal coherence. Forhighliquid load-ingatlowgasflow velocity,disturbancewavesstart toappear(B inFig.12,supplementary recording‘R2’). Thesewaveshavea

sig-nificantlylargeramplitudethantheripplesandtravelatahigher velocity.Theyalso show a strongcoherence along the circumfer-enceofthepipe.

Theoccurrenceof disturbancewavesbecomesveryclearfrom the time-space diagrams, obtained using the high speed images. Thesediagrams are obtainedfromthe centerline ofthe pipe im-ages, in streamwise direction. Figs. 14a and c show cases where onlyripplesarepresent.Increasingtheliquidloadingforthesame gas flow rate results in the onset of disturbance waves on top of the ripples (Fig. 14b). Theyare observed assteep bands with smallerwaves.Fromtheslopeofthesebandsthewave speedcan beobtained.ForthedisturbancewavesinFig.14bthisis approxi-mately0.45m/s,whereastheripplesinFig.14atravelata signif-icantly lower velocity (around 0.06 m/s). The difference inwave speed is caused by the increased penetration depth of the dis-turbancewaves intothe interfacialgasboundary layer. Thewave speed is compared to the correlation proposed by Kumar et al. (2002) andmore recently revisitedby Sawantet al. (2008). This correlation results in an over-prediction of the wave speed by a factor1.7.Itis,however,notvalidatedbelowtheonsetlimitof dis-turbancewaves.Furthermore,Sawantetal.(2008)report thatthe wave speed is dependenton the pipediameter, whichis smaller thaninthecurrentexperiments.

From literature it is expected that disturbance waves would notoccur inthereportedexperiments,althoughalargescatterof the experimental dataaround the onset boundary ofdisturbance waves hasbeen observed (Azzopardi, 1997; Sawant etal., 2009). The axial distribution of the disturbance waves observed in the high-speed video recordings is highly irregular, indicating opera-tion closeto the onset of thewaves. Decreasing the liquid load-ing results in their disappearance, in accordance with the onset boundary found by e.gSawant etal. (2009).Theyreport that an increase in the superficial gas velocity results in a higher liquid loadingrequiredfordisturbancewavestooccur,whichisalso ob-servedinourexperiments.FromthePLIFdataitisdifficultto dis-tinguish disturbancewaves fromother waves. Temporal informa-tion(wavespeed)is requiredtoseparate thesewavesfromother high-amplitudebursts(Belt,2007).

Fig. 14. Time-space diagrams of the image intensity along the pipe centerline for u sg = 20 (a,b) and 45 m/s (c), and u sl = 0.09 (a) and 0.25 cm/s (b,c). The white lines

indicate the wave speed of the ripple (a,c) and disturbance (b) waves. The letters in the top left corners correspond to the letters used in Fig. 12 .

Fig. 15. Film thickness ( δ) as a function of (a) superficial gas velocity and (b) superficial liquid velocity. The solid line in (a) and open symbols in (b) are experimental data by Belt et al. (2010) .

The instantaneousfilmthickness(

δ

) canbe obtainedfromthe PLIFmeasurements. Figs. 15a andb show theaverage film thick-ness with respect to the superficial gas velocity and superficial liquid velocity, respectively. A strong reduction in

δ

with an in-creasinggasvelocityisobserved,whichisrelatedtotheincreased film flow velocity.Althoughno experimental datais available for thelow liquidloadingusedinthepresentmeasurements,the re-sultsobtainedbye.g.Beltetal.(2010),whicharealsoincludedin

Fig.15a,show thesametrend.The effectoftheliquidloadingon

δ

is also significant, butconsiderably lower than that ofthe gas velocity.The standard deviation ofthe film thickness, whichis a measurefortheinterfacialwaveheight,showssimilartrendswith

usg and usl as the film thickness.Plotting it asa function ofthe

film thicknessitselfmakes alldatacollapseonto asinglestraight line,indicating the linear dependenceof thewave height on the film thickness, asis alsofound in literature(Beltetal. 2010,see

Fig.16).

At thecurrent operatingconditions,low liquid entrainmentis expected. Theabsenceofdisturbancewavesinthelargest partof themeasurement domaincorroboratesthisexpectation. Quantita-tive measures for the amount of entrainment are obtained from filmflow ratemeasurements, asdescribedinSection2.5.The en-trainment ratio is defined as E=Qtot−Qf ilm

Qtot , in which Q denotes

the respective liquid flow rate. The entrainment ratio as a func-tion ofthe gas flow rateisdepicted inFig. 17a.An expected in-creasewiththesuperficialgasflow velocityisobserved, originat-ing fromthe increase ofentraining shearforces atthe gas-liquid interface.Theentrainedliquidfractionseemstodecreasewith in-creasingliquidloading; theentrainmentmeasurements are, how-ever,somewhatcompromisedbytheevaporationofliquidintothe gas flow, effectively changing the total liquid flow rate through the smooth pipe. The actual liquid loading in the measurement

Fig. 16. Standard deviation of film thickness as a function of the film thickness. The solid line corresponds to a linear fit of all data (with a slope of 0.86).

section is therefore lower than the liquid loading at the injec-tionpoint.Theevaporationrateisestimatedusingthe correspond-ing Sherwood number for mass transport in internal pipe flow:

Sh=0.023Re0.83

g Sc0.44 (GillilandandSherwood, 1934), whereSc=

μ

g/

ρ

gDp isthe Schmidtnumber. Themasstransfer rateis

subse-quentlycalculatedaccordingto:n˙w=kcAf( pw−psatw)

RT ,wherekcisthe

masstransfercoefficient(kc=ShDv/Lp),Aftheinterfacialarea,pw

thepartial pressure of waterandR and T theideal gasconstant andthetemperature, respectively. Dependingonthe atmospheric humidity, the liquid flow rate could be corrected using this ex-pression. Unfortunately, no humidity measurements were carried outduringthemeasurements,henceanaccurateestimationofthe evaporationratecouldnotbeobtained.Usingdailymeteorological humiditydata,anestimateoftheevaporationrateisobtained,and

Fig. 17. Liquid entrainment ratio as a function of the superficial gas velocity u sg for different values of the superficial liquid velocity u sl , in smooth (a) and corrugated pipes(b,

geom A).

isfoundtobeinthesameorderastheentrainmentrateobserved inFig.17a.As expected, theactual entrainment willthereforebe closetozero.Theexactentrainmentratiois,however,notthemain purposeofthepresentstudy.Aqualitativeanalysisoftheeffectof corrugationsontheentrainmentratiocanbeperformedbasedon thereportedmeasurements.

4. Two-phase flow in corrugated pipes

Withthesmooth pipecaseasareference,theflowbehaviorin corrugatedpipes isnow described. This is done for the corruga-tiongeometriespresentedinSection2,andforsuperficialgasand liquidvelocitiesasusedinthesmoothpipeexperiments.Asa con-sequenceofthepresenceofcorrugations,theflowregimechanges significantly.Itisimpossibletomakethesamedistinctionbetween afull filmandrivulets,asisdone forthesmooth pipe. Measure-mentsoftheliquidentrainment,dropletsizesandtheliquid accu-mulationinsidethecavities,however,canprovidephysicalinsight inthetwo-phaseflowbehaviorincorrugatedpipes.

4.1.Entrainment

The entrainment ratio measured forthe corrugated pipe with geometryAis depictedin Fig.17b.For highergas flow rates, al-mostall liquid is transported as droplets in the gas core of the flow.Evaporationinthispipeis expectedto belimited:thelarge entrainmentratioresultsin avery shortresidencetime of liquid inthepipe,comparedtothesmoothpipe.Reducingthesuperficial gasflowvelocity from42to 25m/scausesa strongreduction in theamountofliquidentrainment.Theentrainmentratiodecreases fromaround 0.95to0.6. Acriticalpoint occursforagasvelocity between30and 35m/s, where a stepin the entrainmentis ob-served.Theeffectoftheliquidflowrateisrelativelylimited com-paredtotheeffectofthegasflowrate.However, thetrendinthe liquidentrainmentbeforeandafterthe‘step’isopposite.Atlower gasflowrates,the lowestentrainmentis observedforthelowest liquidflowrate. Forusg≥ 35 m/s,thistrend isreversed.

Further-more,liquidentrainmentinto thegas coreisin allcases consid-erablyhigher inthe corrugated pipeas compared tothe smooth pipe(compareFig.17aandb).

4.2.Dropletsinthecore

Formostoftheparameterrange,themajorityofliquidis trans-portedasdropletsinthegascoreofthepipeflow.Thedropletsize distributions obtained fromSPI and IPI are combined by match-ingthemaround dp= 80μm,toobtain asingledistribution(see

Section2.5fordetailsonthecombinationofSPIandIPI). Droplet sizing is carried out fora subset of the parameter range,to ob-serve general trends. Fig. 18a gives a typical volumetric droplet size distribution(at usg=35m/sandusl=0.07cm/s). The dashed

line shows the fitted ULLN distribution for this case. The Sauter meandiameter (d32=6Vp/Ap, withVp andAp being thedroplet

volume and its diameter, respectively) is obtained from the fit, to quantitatively comparethe distributions fordifferentflow set-tings (seeFig. 18b).The superficial liquidvelocity doesnotaffect the dropletsize significantly. Thereis howevera strong decrease indroplet size withincreasing gas flow rate. Similartrends have beenobservedfordropletsinsmoothpipeflow causedbythe in-creasedshearingforcesexertedonthegenerateddroplets.Droplets observed in the corrugated pipe are significantly larger than ex-pectedfor asmooth pipe (approximately 30%). Entrainmentfrom corrugationsresultsinlargerfragmentsofliquidbeingintroduced tothe gascore, duetothelocallyincreasedfilm thicknessinside thecavities. Thishigherfilmthicknesscauseslarger fragmentsto be entrained into thegas flow. The smallpitch length of the in-vestigated geometries results inthe presence oflarger fragments throughouttheentiregascore.

4.3. Cavityfilling

Duetothe corrugationsandtheshortpitchlength,a continu-ousliquidfilmisnotformedformostoftheparameterspace. Liq-uidaccumulatesinthecavitiesbetweenthecorrugations.This liq-uidaccumulationismeasuredusingaPLIFtechnique(asexplained inSection 2).Thefractionofthecavityvolumeoccupiedbyliquid (indicatedwith

α

) hasbeen used toquantify the amountof liq-uidinthe cavities.

α

isobtainedfromthetemporal- and spatial-averaged data overall cavities inthe field of view.The resulting fillingisstronglydependentonthegasflowrate,asisdepictedin

Fig.19a.Forusg<30m/s,thecavitiesareentirelyfilledup.Thereis

aliquidfilmatthewall,skippingoverthecavities,essentially re-ducingthewallroughnessexperiencedbythegasflow.Forhigher values of usg, a linear reduction in

α

is observed. This

reduc-tion is mainly manifested at the downstream cavity side. Liquid isremovedfromthedownstreamsidebytheaugmentedshearing forcesexertedbythegasflow.Theremainingliquidinsidethe cav-ities isdragged towards the upstream cavityedge by themutual actionofgravityandtheinternalcavityflow.Liquidisre-entrained intothegascoreoftheflowbytheshearingrecirculatinggasflow abovetheinterface. Theeffectoftheliquidloadingisdepictedin

Fig.19(b).The fillingisplottedagainstthe liquidvolumefraction (

φ

_l=Q_l/Ql+g) to facilitatethe comparisonfordifferent superficial

Fig. 18. (a) Example of a combined droplet size distribution in the corrugated pipe (geometry A) for u sg = 35 m/s and u sl = 0 . 07 cm/s , the dashed vertical line indicates the

center of the SPI-IPI merging region. (b) Sauter mean diameter of the combined droplet size distributions in a corrugated pipe (geometry A) as a function of superficial gas flow speed. The solid line indicates a correlation for the droplet size in smooth pipes ( Azzopardi, 1997 ).

Fig. 19. Cavity filling as a function of the superficial gas speed u sg (a) and the liquid volume fraction φl (b). A–D in (a) correspond to the respective filling contours displayed

in Fig. 20 .

rate, due to thelarger liquid influx into thecavities. Typical fill-ingprofiles,illustratingthedifferentstagesoftheliquidfilling,are depictedinFig.20.

As showninFig. 17(b),thereis significant entrainmentinthe corrugated pipe. Entrained liquid in the core of the pipe is ex-pected to be spatially isolated from the cavities at the outer ra-dius ofthepipe. Mainlyliquidtransportedclose tothepipe wall interacts withthe internal cavity flow, affecting the liquidcavity filling. Therefore, the liquid entrainment ratio, averaged for dif-ferent liquid flow rates, is used to correct the superficial liquid velocity. This resultsin a superficial liquid film velocity (defined as usf=

(

1− E

)

usl). Plotting the filling

α

as afunction of thisusf

causes the datafor the various gasflow rates to collapseonto a single line(see Fig. 21). This indicates that the effect ofthe gas flowrateonthefillingismainlycausedbyanincreasein entrain-mentforincreasingusg.It,therefore,impliesthattheentrained

liq-uiddoesnotinteractwiththeinternalcavityflowandhence,does notresultinadditionalliquidbeingtrappedinthecavities.

4.4. Cavitygeometryandliquidproperties

Toassesstheeffectofcavitysizeandpropertiesoftheinjected liquidonthetwo-phaseflowbehavior, additionalexperimentsare carriedoutusingacorrugatedpipewithgeometryB(seeTable1) and/orwithmono-ethyleneglycol(MEG)asworkingliquid.

Geom-etry B issimilar to geometryA, butthe cavitydepth andlength areenlargedby50%.MEGisapproximately19timesmoreviscous thanwateratatmosphericconditions,whereasthesurfacetension issignificantly reduced(from72mN/mforwaterto48mN/mfor MEG,seeLide,1994).Attemptsweremadetouseaqueousglycerol solutionstokeepthesurfacetensionchangelimited.However, wa-ter evaporationfromthe solution causedthe liquidproperties to changeoverthelengthofthepipe,troublingtheresults.

ForthecorrugatedpipewithgeometryB,theentrainmentratio approachesone,irrespectiveofthegasflowrateandliquidloading (Fig.22(b)).Thestepintheentrainmentratio,observedfor geome-tryA,doesnotoccurforgeometryB,withinthecurrentparameter space.Thisisrelatedtothefillingfraction

α

,whichneverattains valuesabove 0.6forthisgeometry,even forlower gasflow rates (asisdepictedinFig.23(b)).Thefillingshowsthesamesteady in-creasewithincreasingliquidloading,buttheupperlimitisnever reached, anditprobablyoccursata higherliquidloading. Itwas shownforgeometryA, thatat totalcavityfilling (

α

→1) the en-trainmentsignificantly reduces.Forlower fillingratios,nearlyfull entrainmentisexhibited(E_→1).Similar principlesholdwhen in-jectingMEGinsteadofwater(Figs.22(a)and23(a)).Theabsolute valuesof the entrainment ratiofor MEG are slightly lower com-paredtowater,forbothcorrugationgeometries.Alsothefilling ra-tioislower.Thetrendsinbothfillingandentrainmentaresimilar forwaterandMEG.Thelargeincreaseinviscositywhenswitching

Fig. 20. Liquid cavity filling profile, measured with the PLIF method described in

Section 2 , for the four different cases indicated in Fig. 19 a. Flow is from bottom to top and dark regions are regions of liquid accumulation, for u sl = 0 . 11 cm/s.

Fig. 21. Liquid filling fraction αas a function of the superficial liquid film velocity ( u sf ) for different values of superficial gas velocity ( u sg ).

fromwaterto MEGdoesnothaveastrongeffectoneitherfilling orentrainment.

5. Discussion

Theentrainmentofliquidintwo-phasecorrugatedpipeflowis stronglyrelatedtothecavityfilling.TheliquidentrainmentratioE

sharplyincreaseswhenliquidisremovedfromtheindividual cor-rugations.Therecirculatinggasflowinsidethecavitiesdragsliquid back intothegascore(asdepictedinFig.24).It isassumedthat thisprocessisgovernedbyshearing-off ofwavesatthegasliquid interfaceinsidethecavities.Duetotherelativelyhighgasflow ve-locityandthelocallyincreasedfilmthicknessasaconsequenceof the presenceof thecavities, it issafe to assume that indeedthe ligamentbreak-upmechanism(see Fig.1) isdominant.Thereisa balancebetweendragforce,exerted bytheshearinggasflow,and theretainingforceduetosurfacetension.Wheneverthedragforce ontheinterfacialwavecrestsexceedstheretainingforce(Fd≥ Fσ),

liquidpacketsareremovedfromtheinterfaceandentrainedinthe gasflow. The dragforce is givenby: F_d=C_d

λ

hw

ρ

gu2w/2,withthe

dragcoefficientCd,thewavelength

λ

,thewaveheighthw andthe

relativevelocitydifferencebetweentheliquidandgasflowuw.The

retainingsurfacetensionforce isgivenbyF_σ=Cs

λσ

,withCs

de-pendingonthewaveshape.Using thisforce balanceasastarting point,IshiiandGrolmes(1975)derivedthefollowingentrainment criterion:

μ

lug

σ



ρ

g

ρ

l ≥ 11.78N0.8 μ Re−1l .3, (5)

whereNμ istheviscositynumber,whichwillbedefinedinEq.6.

Inalaterstudy,IshiiandMishima(1989)derivedacorrelationfor theentrainedfractionofliquid,basedonthepreviouslypostulated onsetcriterion. Assumingthat allexcess liquid(abovethecritical entrainment limit from Eq.(5)) is actually entrained, they found that the entrainment ratioE is a function of the liquidReynolds number and the Weber number

(

E= f

(

We1.25Re0_l.25

))

. The We-ber number

(

We=ρgu2cL

σ

)

indicates the balance between the

re-tainingforces(surfacetension)anddisturbingforces(shearatthe gas/liquidinterface).Thecavityrecirculationvelocityisdefinesas

uc=usg/4, which is representative for a cavity flow (Koschatzky

etal., 2011). The liquid Reynolds number

(

Re_l= ρluslL

μl

)

is a

mea-surefortheeffectoftheviscous forcesinsidetheliquid.The crit-ical Re_l for annulargas-liquidflow isnot reachedin mostofthe currentexperiments,duetotheverylowliquidloading.Therefore,

Fig. 22. Liquid entrainment as a function of the superficial gas velocity in a corrugated pipe, for different liquid loadings. Pipe with geometry A (a) and geometry B (b). Solid lines are for water, dashed lines for MEG. Results for water injection in geometry A are depicted in Fig. 17 (b).

Fig. 23. Cavity filling as a function of liquid volume fraction φl , for different superficial gas flow speeds. (a) Filling for MEG injection in geometry A, and (b) for water

injection in geometry B.

Fig. 24. Schematic of the internal cavity flow, removing liquid from within the cor- rugation.

theentrainmentinthesmoothpipeflowisverylow(seeFig.17a). Thisiscausedbythethinliquidfilm,entirelysubmergedinthe in-terfacialgasboundarylayer(IshiiandGrolmes,1975).Thecavities in thecorrugated pipe, however,causelocal liquidaccumulation, resultinginasignificantlyincreasedfilmthicknessfromwhich en-trainment will occur. The dependency on Rel is therefore

differ-ent incorrugated pipe flow. In smooth pipes, the entrainmentis positivelycorrelated totheliquidReynoldsnumber.Incorrugated pipes, however, entrainment is related to liquid accumulation in thecavities.AlargerliquidReynoldsnumber(indicatingmore liq-uidbeingtransported)leadstoanincreaseincavityfilling,which reducestheentrainment.ToarriveatEq.(5),itwasassumedthat

N0.8

μ ≈ 3Nμ.TheviscositynumberNμisafluidproperty,andis

de-finedas: N_μ=

μ

l



ρ

l

σ



σ g(ρl−ρg)

1/2. (6)

The assumption holds for low viscosity liquids, typically when

Nμ<0.01.ForMEG,used inthepresentstudy,itisnot valid, and

N0.8

μ isused instead of3Nμ. Assuming that the gas-filled part of

the cavityvolume

(

1−

α

)

isrelated tothe amount ofliquid en-trainmentfromthecavity,itcanbeapproximatedby:

(

1−

α

)

=f

(

We1.25Ren

l

)

. (7)

TherelevantlengthscalesfortheWeberandReynoldsnumberare associated with the cavity filling. The length scale inthe

defini-tionofWeistakenashalftheemptycavitysize(L₌1_/2

(

1₋

α

)

Lc),

whereasforRel,itistakenasL=

α

Lc.Applyingthesedefinitionsto

thedataacquiredinthereportedexperiments,n=−0.25givesthe bestcollapseofalldatapoints(aspresentedinFig.25a). Thereis stillsomescatter ofthedataobservedinthefigure.Aswas men-tionedbefore,insteadof scalingwiththetotal liquidflow rate, a betteragreementisfoundbyusingthesuperficialfilmvelocityu_sf.

Fig.25bshowsthefillingasafunctionofWeandRef

(

=ρl u_sfL

μl

)

.It

shouldbenotedthattheliquidviscosityhasnoeffectonthe fill-ing,whenthisscalingisapplied.Thisisalsofoundinthepresent work.Thebehavior oftheliquidfilmiscompletelydominatedby surfacetension andthe shearinggasforce. AccordingtoIshii and Grolmes (1975), this holds in the low viscosity number regime (whereN_μ≤ 1

15).

In the low liquid filling regime, entrainmentfrom within the corrugationsaugmentsthetotalentrainmentratio.Apartfrom liq-uidentrainmentoriginatingfromwithinthecavities,asecond en-trainmentmechanismseemstooccursimultaneously.Fromthe en-trainment measurements forgeometryA(depicted in Fig.17b) it appears that even for entirely liquid-filled cavities (at the lower

usg range), around 60% of the total liquid flow rate is entrained.

This can not be causedby the previously described entrainment from within the cavity. It is expected that the corrugations de-creasethestabilityofthefilmandincreaseitswavystructure.The standard entrainment mechanisms then will be activated, where entrainmentisagainafunctionoftheliquidReynoldsnumberand theWebernumber:E= f

We1.25_Re0.25

l



,aswasfoundbyIshiiand Mishima (1989).The typical entrainment ratiofor waterexceeds thatforMEG underthe sameconditions.Due tothesignificantly higherviscosityforMEG, comparedto water,the liquidReynolds numberdecreases andhence,theentrainmentis expectedto de-crease. The lower liquidReynolds number indicates a lower film thicknessatthesameflowconditions,penetratinglessfarintothe interfacialgasboundarylayer.Theshearinggasvelocityatthe in-terfaceis lower, hence the entraining forcesdecrease, leading to alowerentrainmentratio.Forthelowerfillingcases,entrainment fromwithinthecavitiesandfromtheseparatingribswillco-exist. However, the interplay of these two entrainment mechanisms is stillunclear.

Allreportedexperimentsareconductedinupwardverticalflow direction.Itisanticipatedthatthedirectionofgravitywillhavea strongeffectontheobtainedresults.Inapreviousstudy,van Eck-eveldetal.(2017)foundthattheflowdirectionwithrespecttothe gravityhassignificantconsequencesfortheliquidcavityfilling be-havior.Theliquidfillingratioisconsiderablyhigherfordownward

Fig. 25. Gas-filled part of the cavity (1 −α) as a function of the Weber number and the Reynolds number based on the total liquid flow rate (a) and the film flow rate (b).

directed flow. Assuming a similar relation between cavity filling andentrainment to hold in downward flows, the liquid entrain-mentisexpectedtobereduced(seeFigs.17band19a).

6. Conclusions

Two-phaseflow experimentsare carriedout inasmooth pipe andincorrugatedpipestoassesstheeffectofthepresenceof cor-rugationsontheliquiddistributionintheverticalpipe flow.Film thicknessmeasurementsareperformedusinganovel implementa-tionofplanarlaser-inducedfluorescence.Shadowsareaddedtothe incominglaser sheet, wherethey appear asdarklines.The devi-ationof theselines atthe gas-liquidinterface isused to identify andremove large reflectionsin the PLIF measurements. Gas and liquidphase Reynoldsnumbers (based onthe pipe diameter)are

Reg=O

(

105

)

andRel<250.Attheseconditions,liquidentrainment

isnotexpectedtobesignificantinsmoothpipes.Theentrainment ratio(correctedforevaporation)isclosetozero.Furthermore,only fora very limited rangeof flow parameters, the onset of distur-bancewavesisobserved,whicharethemain sourceofliquid en-trainment.The filmthicknessisinthe orderof100

μ

m, andthe observedtrendswiththechangingsuperficialgasandliquid veloc-itiesareconfirmedbyotherexperiments(withhigherliquid load-ing),reportedinliterature.Forverylowsuperficialliquidvelocities athigh superficial gas velocities the annular film breaks up and liquidistransportedasrivuletsalongthepipewall.

Two-phaseflowincorrugatedpipesshowsaverydifferent be-havior compared to smooth pipes, at the same flow conditions. Droplet sizing in the corrugated pipe reveals that considerably largerliquidfragmentsaretransportedinthegascoreofthepipe, compared to the expected droplet distribution in smooth pipes. This is most likely caused by the locally (at the location of the cavities)increasedfilmthickness,resultinginlargerentrained frag-ments.Anupperlimitlognormaldistribution isusedtodescribe the droplet size distribution. The liquid entrainmentratio is sig-nificantly higher in corrugated pipes than in smooth pipes. Liq-uidisfoundtoaccumulate intheaxisymmetriccavitiesalongthe pipewall,andtheentrainmentstronglycorrelateswiththe liquid-fillingratio (

α

). Asharp increase inthe liquid entrainment ratio isobserved when the filling is decreased; for totally liquid-filled cavities the entrainment is significantly lower than for partially filledcavities.Thisshowsthattheinternalgasflowinsidethe cav-itycausesadditionalentrainment.Thecavityfilling

α

istherefore an important parameter when it comes to entrainment in these corrugatedpipes. It isfound to scale withthe Weber and liquid Reynoldsnumber,basedonthe filmflow rate:thegasfilled

cav-ityvolume

(

1₋

α

)

scaleswithWe1.25_Re−0.25

f .Thescalingwiththe

Webernumberissimilartothescalingforentrainmentinsmooth pipes. The liquid Reynolds number scaling, however, is opposite. Anincrease inRefinsmooth pipesleadstoan increased

entrain-ment.Forpartiallyfilledcavitiesincorrugatedpipesthefilling ra-tioandhencetheentrainmentdecreaseswithincreasingRef.

Itisshowninthisworkthattheliquidentrainmentratioin cor-rugatedpipesisstronglydependentontheamountofliquid accu-mulatinginthecavities ofacorrugatedpipe.Futurework should assessthisrelationfora broaderrangeofcorrugation geometries andfurtherinvestigatetheinfluenceofthedirectionofgravityon theobtainedresults.

Acknowledgments

Thisworkisfundedby Shell,forwhich theyaregratefully ac-knowledged. The authorsthankR.W.A.M. Henkesforhis valuable remarks,andE.F.J.OvermarsandJ.Ruijgrokfortheirpracticalhelp inthedesignofthemeasurementsandtheexperimentalsetup.

Supplementary material

Supplementary material associated with this article can be found,intheonlineversion,atdoi:10.1016/j.ijmultiphaseflow.2018. 07.004.

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