Availableonlineatwww.sciencedirect.com
ScienceDirect
j ou rn a l h o m e p a g e :w w w . e l s e v i e r . c o m / p i s c
Experimental
study
on
two-phase
flow
pressure
drop
in
small
diameter
bends
夽
A.T.
Autee
a,
S.V.
Giri
b,∗aDepartmentofMechanicalEngineering,MarathwadaInstituteofTechnology,Aurangabad,India bDepartmentofMechanicalEngineering,DeogiriInstituteEngineeringandManagementStudies, Aurangabad,India
Received20February2016;accepted13June2016 Availableonline 5July2016
KEYWORDS Two-phase; Pressuredrop; Elbow; Returnbend; Curvaturemultiplier; Air—water
Summary Measurementoftwo-phaseflow pressuredrop anditsprediction acrosscurved
tubesandbendsisimportantfortheenhancementoftheperformanceandsafetyoftheheat
exchangers andflowtransmitting devices. Thecomparative study ofsome ofthe available
two-phasepressuredropcorrelationsrevealsthatthepredictedvaluesofpressuredropsby theseleadingmethodsmaydifferbylarge.Theapplicabilityofthesecorrelationstothesmall diametertubesofrange4.0—8.0mmanddifferentbendanglesoftherange90—180◦isnotfully established.Thebasicobjectiveofthepresentexperimentalinvestigationistogeneratethe experimentaldatatodeveloptheunifiedcorrelationapplicableforthesmalldiametertubesof range4.0—8.0mmanddifferentbendanglesoftherange90—180◦.Hence,experimentalfacility wasdevelopedtoconducttheexperimentstogeneratethedataandtoassessthepredictive capabilityofsomeoftheavailabletwo-phasepressuredropcorrelations.Itwasobservedthat thecorrelationsconsideredforcomparisonswereunabletosatisfactorilypredictthemeasured experimentaldatawithinthe±50%errorbands.Anew correlationisdevelopedintermsof curvaturemultipliertothestraighttubetwo-phasepressuredrop.Thecorrelationisvalidated withthepresentmeasuredexperimentaldata.Thestatisticalanalysissuggeststhatcorrelation showssatisfactoryresults.
©2016PublishedbyElsevierGmbH.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
夽 ThisarticlebelongstothespecialissueonEngineeringand Mate-rialSciences.
∗Correspondingauthor.Tel.:+919850884540. E-mailaddress:[email protected](S.V.Giri).
Introduction
Reliableandaccuratepredictionoftwo-phasepressuredrop isimportantin designandanalysisinmany process indus-tries for the enhancement of safety and performance of equipmentssuchasboilers, condensers,heat exchangers, airconditioningunits.Curvedtubesandbendsofdifferent http://dx.doi.org/10.1016/j.pisc.2016.06.038
2213-0209/©2016PublishedbyElsevierGmbH.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense(http://creativecommons.org/ licenses/by-nc-nd/4.0/).
x quality,drynessfractionorgasfraction
Greekletters
P pressuredropbetweentwopoints,N/m2
curvaturemultiplierintheproposed
correla-tion
bendangleindegree
N standarddeviation,% Subscripts a accelarational f frictional G gas g gravitational Hom homogeneous L liquid SP singlephase TP Two-phase
TPrb Two-phasereturnbend
anglesrangingfrom90◦to180◦indifferentorientationsare
widelyemployedinheatexchangersandflowtransmitting
devices.Two-phaseflowinabendismoredifficultto ana-lysethanthatofthestraighttube duetocurvaturewhich generatesacentrifugalforce andcauses thedenserphase (i.e.,liquid) tomove awayfromthe centreof curvature, whiletheairflowstowardsthecentreofcurvature.
The first study on two-phase pressure drops in return
bends was conducted by Pierre (1964), who proposed a
correlation basedonexperimentsincludes effects of fric-tionandturning.Geary(1975)withR-22usingvariousbend geometries pointed to the importance of the centre-to-centre distance and developed model based on friction factorandvapourflow.Chisholm(1983)andPaliwada(1992) proposedcorrelationsfortwo-phasepressuredropsinreturn bends.Chenetal.(2004a)andChenetal.(2004b)studied water—airmixtureandR-410Aflows,respectively,through differentbendgeometriesandstudiedtheeffectofliquid surfacetensionandgasinertia.DomanskiandHermes(2008) proposedanewcorrelationfortwo-phaseflowpressuredrop in180◦ returnbendswhichconsistofatwo-phasepressure dropforstraighttubesandamultiplierthataccountsforthe bendcurvature.Padillaetal.(2009)collected325pressure dropdatapointsofthreedifferentfluids(R-12,R-134aand
theseleadingmethodsmaydifferbylarge.Theapplicability ofthesecorrelationstothesmalldiametertubesofrange 4.0—8.0mmanddifferentbendanglesoftherange90—180◦ isnotfullyestablished(Autee,2014).Smalldiametertubes areusedformanufacturingofheattransferequipmentsto improvetheperformanceandreduce themassof working substance.
Thebasicobjectiveofthepresent workistostudyand investigate,bothexperimentallyandanalytically,the char-acterizationofthetwo-phasepressuredropacrossthebends of different anglesin horizontal orientation and compari-sonofthemeasuredexperimentaldatawiththepredicted values,estimatedbysomeofthewidelyusedavailable two-phasepressuredropcorrelations,toassesstheirpredictive capabilitiesinthepresentrangeoftheexperimental param-eters.Finally,newcorrelationisdevelopedusingmeasured experimentaldata.
Experimental
facility
The experimental set-up was designed and fabricated to conductadiabaticair—watertwo-phaseflowexperimentsin small-diameter test sections at different orientationsand smalldiametertubebends(Autee,2014).This experimen-talset-upconsistsofairandwatercircuitasshowninFig.1. Air pressure is measured by bourdon pressure gauge and it is controlled by the air bass pass valve. Water is sup-pliedbywaterpumpanditsflowiscontrolledbythewater bypass valve.Airandwaterflowismeasured bytheRota meter,connectedinserieswithairandwaterline respec-tively.Measuredquantityofairandwaterismixedinmixing chamber. Test section isconnected aftermixingchamber. Air—watermixturecomingoutfromthetest-sectionis col-lectedinthewatertank.Inthewatertankairgetsseparated andthewaterisre-circulated. Differentialpressure trans-ducersmeasurepressureatinletoftestsectionandacross the bends. Data acquisition system records pressuredrop data.Fiveanglesofbendsviz.:90◦,112◦,135◦,157◦,180◦ with 40mm curvature radius and glass tubes of internal diameter 6.4 and 8.4mm were used during the investi-gation with 2R/D ratio of 10.95 and 14.21. The air and waterflowratesarevariedwithintherange7.5—77.3and 150.3—1554.24kg/m2srespectively.
Figure1 Schematicdiagramofexperimentalset-up.
Material usedfor test section is glasstubesof 6.4 and 8.4mminternaldiameter.Thebendingofglasstubeisskilled art and requires special equipments. Wooden pattern of requiredangleandcurvatureradiusarespeciallyprepared andusedtobendcircularglasstube.Carewastakenduring bendingoperation that the diameterof the tube remains constantthroughoutthetestsection.
Fig.2(a)showsthedetailofthestraighttube test sec-tionbeforebending.Section1is theentrancetothetest section,section2istheupstreampressuretap,section3is downstreampressuretapandsection4istheexitfromthe test section.Adistance of0.2 meteris keptbetween the entranceandupstreampressuretaptohavefullydeveloped flow.Section2islocatedwherecurvaturebeginsandsection 3is0.2mapart fromit.Astabilizationlengthof0.15mis keptdownstreamthesection3toavoidthebackpressure. Thepositionofsection3changesaspertheangleofbend whilesection2isfixed.Fig.2(b)showsthesectionalview of test-sectionwhereas Fig.2(c)shows the photographic viewofoneofthetest-section(112◦)afterbendingtothe requiredangleandcurvatureofradius.
Comparisons
of
the
experimental
data
with
existing
correlations
The experimental data is compared with some of the available two-phase pressuredrop correlations fromopen literaturetoassesstheirpredictivecapabilities.The corre-lationsconsideredforthecomparisonfor90◦ areChisholm (1983), Silva et al. (2010), Sookprasong (1980), Paliwada (1992)andMandalandDas(2001).Fig.3(a)showsthe com-parisonsoftheexperimentalpressuredropwithpredicted pressuredropvaluesforthediameterof 6.4mmusingthe correlationsconsideredforcomparisons.Itcanbeobserved thatnoneoftheabovecorrelationsatisfactorilypredictsthe experimentalpressuredropwiththeexceptionofSilvaetal. (2010)correlation.
The correlations considered for 180◦ return bends are Padilla et al. (2009), Chen et al. (2004b), Geary (1975), Chisholm(1983),MandalandDas(2001).Fig.3(b)showsthe
comparisons of the experimental pressure drop with pre-dictedpressuredropvaluesforthetubediameterof8.4mm usingthecorrelationsconsideredforcomparisons.Domanski correlationoverpredictsthemostofdataand91.66%data liesoutsidetheprescribedbands.Statisticalerroranalysis showseR of443.88% andNof17.7%. Itcanbeconcluded fromtheabovediscussionthatcorrelationsconsidered for comparisonsfailstopredictthepresentexperimentaldata satisfactorily.Though,Chenetal.(2004b)andGeary(1975) correlation for 180◦ bend predicts the present measured experimentaldatafordiameterof6.4mmreasonablywell butfailstopredictfor thediameterof8.4mm satisfacto-rily.SimilarconclusioncanbedrawnforSilvaetal.(2010) correlationfor90◦bend.Generalizedcorrelationdeveloped byMandalandDas(2001)fordifferentanglesinhorizontal planeisunabletopredictthedatasatisfactorilyforpresent rangeoftheanglesanddiametersofbend.Hence,itisfelt appropriatetodevelop thenewcorrelation topredictthe presentmeasuredexperimentaldata(Fig.4).
Development
of
new
correlation
Pressuredropwithinbendcanbetreatedasthesumofthree separatecomponents:friction,momentumchangeand grav-ityhencecanbeexpressedasfollows.
dP dx = dP dx f + dP dx a + dP dx g (1) Thepresentexperimentalinvestigationforvariousbends anddiameters is carried in horizontalorientation. There-fore gravitational effects are to be neglected. Also, the tube diameter is uniform across the test section hence momentumoraccelerationcomponentistobeneglected. Therefore,onlyfrictionalpressuredropisconsideredinthe presentanalysis.
Itisobservedfromtheopenliteraturethatmutualand complicatedinteractionof inertial, viscous, gravitational, surfacetensionforceshaslargeinfluenceontwo-phase pres-sure drop. However, parameters such as diameter of the tube,radiusofthecurvaturealsorequiredtobeconsidered
900 bend (D = 6.4 mm)
Experimental pressure drop (bar/m)
0.01 0.1 1 10 100 P re d ic te d p res sur e drop ( b a r/ m ) 0.01 0.1 1 10 100 Chisholm Silva et al. Kuhn et al Sookprasong Paliwada Mandal and Das
- 50 % + 50 %
(a)
1800 bend ( D = 8.4 mm)
Experimental pressure drop (bar/m)
0 1 1 1 . 0 1 0 . 0 P redi c te d pr ess u re dr op (b ar /m ) 0.01 0.1 1 10 Domanski et al. Padilla et al Chen et al Geary Chisholm Mandal and Das
- 50% + 50 %
(b)
Figure3 Comparisonofsomeoftheexistingcorrelationswithexperimentaldatafor90◦ elbowsofdiameter6.4mmand180◦ returnbendof8.4mm.
Proposed Correlation (Validation data) D = 6.4 mm
Experimental Pressure Drop (bar/m)
0 1 1 1 . 0 1 0 . 0 P re d ic te d Pr es s u re D rop (b ar /m ) 0.01 0.1 1 10 - 50% + 50% (a)
Proposed Correlation (Validation data) D = 8.4 mm
Experimental Pressure Drop (bar/m)
0 1 1 1 . 0 1 0 . 0 P redi cte d Pres s ure Drop ( b ar /m) 0.01 0.1 1 10 - 50% + 50% (b)
incalculationoftwo-phasepressuredropinbends.Hence, asimplifiedphysicalconceptisneededfordevelopmentof thenewcorrelation.
The curvature multiplier method adopted by Padilla etal.(2009)andDomanskiandHermes(2008),isbasedon straighttubetwo-phasepressuredropestimatedby Muller-SteinhagenandHeck(1986)correlation.Thissimplemethod isusedinthemodellingoftwo-phasepressuredrop across the different bends in the present investigation. Accord-ing to Muller-Steinhagen and Heck (1986), the two-phase pressure drop in a straight tube is predicted considering thepressuredropsofliquidandvapour phases,whichare calculatedseparately dP dl k =2fk D G2 k (2) wherekstandsforlorv,andfk=0.079Re−k0.25usingvapour
or liquid properties, as appropriate. The pressure drops computed for each phase are combined by the following equation: dP dl s−t = dP dl L +2x dP dl v − dP dl L (1−x)1/3 + dP dl v x3 (3)
where the index s−t denotes the straight-tube pressure drop.Thecurvaturemultiplier‘’isdefinedas
˝= dP dlbend dP dlst. (4) where dP
dlst. is estimated by Muller-Steinhagen and Heck
(1986)equation.
Halfoftheexperimentaldataobtainedisusedfor train-ingthemodelandremainingisusedtovalidatethemodel. Valuesofareobtainedfromtheaboveequation.Multiple linearregressionanalysisiscarriedoutforexperimental val-uessoobtained.Thefollowingexpressionisobtainedusing theregressionanalysisanditishavingR2valueof0.9.The
expressionobtainedforisas
˝=A x−0.619Re−1.2176 L 2R D −2.5403 (5) whereA=1.453×106.
Statistical analysisofthecorrelation suggeststhatitis havingacceptableaccuracy.Theproposedcorrelationshows meandeviationandstandarddeviationas22.31%and3.97% respectively. It hasbeen observedthat 75% of the exper-imental data predicted by the proposed correlation lies withinthe±30%errorbands(Giri,2014).
Conclusions
Thepredictivecapabilitiesofsomeofthetwo-phase pres-suredropcorrelationsfor90◦elbowsand180◦returnbends
available from open literature were assessed by compar-ingwithpresentmeasured experimentaldata.Ithasbeen foundthatnoneofthecorrelationwasabletopredictthe present experimental data satisfactorily. However, it has beenobservedthatsomeoftheavailable two-phase pres-sure drop correlations studied has reasonable predictive capability for one diameterof particular typeof bend at oneinstance but fails for other diameters. Hence, anew correlationisproposedfor thecurvaturemultiplier tothe straighttubetwo-phasepressuredrop.Thestatistical anal-ysissuggeststhatthecorrelationisofacceptableaccuracy forthepresentexperimentalrangeoftheparameters.
References
Autee,A.T., (Ph. D.Thesis) 2014. Experimental investigationon pressure dropfor adiabaticair-watertwo-phase flowinsmall diametertubesandbends.
Azzi,A.,Alger,U.S.T.H.B.,Friedel,L.,2005.Two-phaseupwardflow 90◦bendpressurelossmodel.ForschungimIngenieurwesen69, 120—130.
Chen,I.Y.,Huang,J.C.,Wang,C.-C.,2004a.Single-phaseand two-phasefrictionalcharacteristicsofsmallU-typewavytubes.Int. Comm.HeatandMassTransfer31(3),303—313.
Chen,I.Y.,Wang,C.-C.,Lin,S.Y.,2004b.Measurementsand corre-lationsoffrictionalsingle-phaseandtwo-phasepressuredrops ofR410AflowinsmallU-typereturnbends.Int.J.HeatMass Transfer47,2241—2249.
Chisholm,D.,1983.Two-phaseflowinpipelinesandheat exchang-ers.GeorgeGodwin,London,pp.154—166.
Domanski,P.A.,Hermes,C.J.L.,2008.Animprovedcorrelationfor two-phase pressure drop of R-22 and R-410A in 180o return bends.Appl.Thermal.Eng.28,793—800.
Geary,D.F.,1975.Returnbendpressuredropinrefrigeration sys-tems.ASHRAETrans.81(1),250—265.
Giri,S.V.,(M.E. Thesis)2014. Experimentalanalysisof adiabatic air—water two-phase flow pressure drop in small diameter bends.
Lockhart,R.W.,Martinelli,R.C.,1949.Proposedcorrelationofdata forisothermaltwo-phasetwocomponentflowinpipes.Chem. Engg.Progress45,39—48.
Mandal, S.N., Das, S.K., 2001. Pressure losses in bends during two-phasegas-Newtonianliquidflow.Ind.Eng.Chem.Res.40, 2340—2351.
Muller-Steinhagen,H.,Heck,K.,1986.Asimplepressuredrop cor-relation for two-phase flow inpipes. Chem.Eng.Process 20, 297—308.
Padilla,M.,Revellin,R.,Bonjour,J.,2009.Predictionandsimulation oftwo-phasepressuredropinreturnbends.Int.J.Refrig.32, 1776—1783.
Paliwada,A.,1992. Generalisedmethod ofpressure drop calcu-lation across pipe components containing two-phase flow of refrigerants.Int.J.Refrig.15(2),119—125.
Pierre,B.,1964.FlowResistancewithboilingrefrigerants—PartII. ASHRAEJ.,73—77.
Silva,S.F.,Resendiz,L.,CarvajalMariscal,J.C.,Eslava,T.,2010. Pressure drop models evaluation for two-phase flow in 90 degreehorizontalelbows.Ing.Mecá.Tecnol.Desarrollo3(4), 115—122.
Sookprasong,P.,PhDThesis1980.Two-phaseflowinpiping compo-nents.UniversityofTulsa.