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doi:10.1016/j.flowmeasinst.2006.08.003
FlowMeasurementandInstrumentation17(2006)291–297
Effectofupstreamflowdisturbancesontheperformancecharacteristicsofa
V-coneflowmeter
S.N.Singh ,V.Seshadri,R.K.Singh,R.Gawhade
AppliedMechanicsDepartment,IITDelhi,HauzKhas,NewDelhi110016,India
Received9November2005
Abstract
TheperformancecharacteristicsofaV-coneflowmeterwithdifferentdiameterratioshavebeenevaluatedexperimentallyasafunctionof
Reynoldsnumberandupstreamdisturbance.TheexperimentshavebeenconductedusingwaterandoiltocoverawiderangeofReynolds
numbers.TheeffectofupstreamvelocityprofilehasbeeninvestigatedbyplacingagatevalveupstreamoftheV-coneflowmeteratadistanceof
5D,10Dand15Dandperformingtheexperimentsat25%,50%,75%andfullyopenconditionsofthevalve.Fromthestudy,itisseenthatthe
dischargecoefficientofaV-coneflowmeterisnearlyindependentofReynoldsnumber.Thevalueofthedischargecoefficientis0.7256±1.78%
for=0.64,andfor=0.77thedischargecoefficientis0.7315±1.97%.Thevalueofthedischargecoefficientisnotaffectedbytheupstream
disturbanceifthedisturbanceisplacedatadistanceof10Dormore.Thevariationinvalueofthedischargecoefficientisapproximately6%for
adisturbanceplacedatadistanceof5D.
c 2006ElsevierLtd.Allrightsreserved.
Keywords:V-coneflowmeter;Dischargecoefficient;Reynoldsnumber;Flowdisturbance;Equivalentdiameterratio
1.Introduction
variablearea,annularflowetchavebeendevelopedoverthe
yearsforspecialapplicationsandarecurrentlyavailableinthe
openmarket[ 2–4 ].Towardtheendofthelastcentury,afew
moredifferentialpressuretypeflowmeters,namelythewedge
flowmeter,variableareaorificemeterandV-coneflowmeter
weredevelopedtoimprovetheturndownratioandalsotomake
thedischargecoefficientlesssensitivetoReynoldsnumber.The
otherefforthasbeentominimizetherequirementofupstream
anddownstreamlengthscombinedwithimprovedaccuracy.In
someoftheindustrialapplications,upstreamflowishighly
disturbedcausinginaccuracyinthemeasurement.Underthese
conditions,Shenmin[ 5 ]hasopinedthattheV-coneflowmeter
provedtobeaviablealternative.
TheliteratureavailableonthedesignofV-coneflowmeter
isscanty,probablyduetoconfidentialityandpatentrequire-
ments[ 6 ].ItisclaimedthattheV-coneflowmeterprovides
flowmeasurementwithanaccuracyofupto±0.05%overa
turndownratioof30:1.Inaddition,therepeatabilityofthe
V-coneflowmeterisclaimedtobe±0.1%comparedwith
±0.2%fortheotherflowmeasurementdevicesanditdoesnot
requirefrequentrecalibration.Besidestheseadvantages,the
V-coneflowmeterisalsomoreresistanttoabrasionandwear
Theaccuratemeasurementoffluidflowisvitalforcustody
transferandprocesscontrolinmanyindustries.Insome
operations,theabilitytoconductaccurateflowmeasurementis
soimportantthatitcanmakethedifferencebetweenmaking
aprofitandincurringaloss.Forsuchapplications,special
flowmetersliketheturbineflowmeter,vortexflowmeteror
Coriolisflowmeterareusedasthesecanhaveahighaccuracy
oftheorderof±0.1%ifusedunderidealconditions.Formost
normalindustrialapplications,differentialpressuredevices
suchasanorificemeter,aventurimeter,anozzlemeterortheir
variantsareused.Thelimitationofthesemetersisthattheturn
downratioofthesemetersisoftheorderof5andminimum
upstreamanddownstreamstraightlengthsneedtobeprovided
toensureproperflowconditions.Orificemetersarewidely
usedduetotheirlowcost,simpledesign,lowmaintenance
requirementsandhighreliability[ 1 ].Specialtypesoforifice
meterssuchareeccentric,quadrantedge,conicalentrance,
Correspondingauthor.Tel.:+91116591180;fax:+91116581119.
E-mailaddress: sidhnathsingh@hotmail.com (S.N.Singh).
0955-5986/$-seefrontmatterc2006ElsevierLtd.Allrightsreserved.
693163520.008.png 693163520.009.png 693163520.010.png
292 S.N.Singhetal./FlowMeasurementandInstrumentation17(2006)291–297
51to0.90atRe=22,000usingwaterasthe
workingfluidwithupstreamdisturbance.Theyhaveshownthat
theV-coneflowmeterislesssensitivetothepresenceofswirl.
Irving[ 14 ]hasanalyzedthetypeofdisturbancecausedbya
rangeofpipefittingsanddiscussedthewayinwhichvarious
typeofdisturbancesaffecttheflowthroughorificemeters.
Heconcludedthatstandardsareinadequateinspecifyingthe
sufficientlengthofstraightpipe.Joshi[ 15 ]hasreportedthe
specialfeaturesoftheconeflowmeteranditsadvantages.From
hisstudies,hehasconcludedthatunderallconditions,the
V-coneflowmeter’sperformanceisbetterthanthatoftheother
typesofflowmeteroverawiderangeofReynoldsnumbers.In
thepresentstudy,theperformanceofaV-coneflowmeterhas
beenexperimentallyevaluatedasfunctionofReynoldsnumber
andthentheeffectofupstreamdisturbancehasbeenanalyzed.
Theupstreamdisturbancehasbeencreatedbyplacingagate
valveatdifferentupstreamdistances.
=0
.
Symbols
Equivalentconediameterratio
Re Reynoldsnumber
m 3
p Staticpressure,Pa
C d Dischargecoefficient
1h Differentialhead,mmWC
Hg Mercury
o SAE-20oil
W Water
Q Dischargerate,kg
Density,kg
/
/
s
u Meanvelocity,m
/
s
µ
Dynamicviscosityofthefluid,Pas
Kinematicviscosityoffluid,m 2
/
2.V-coneflowmeter
becauseofitsgeometry.Thetaperdesignminimizeswear(ero-
sion)byreducingthecontactoftheprimaryelementwithhigh
velocity[ 7 ].AV-conemetercanalsomeasureevenindis-
turbedflowconditionswithshorterupstreamstraightpipesas
comparedtootherflowmeasuringdevices.Thishasresulted
intheincreasinguseofV-coneflowmetersintheoffshore
andpetroleumrefiningindustries[ 8 ].Thebasicdesignofthe
V-coneflowmetermakesitrelativelyinsensitivetooutside
vibrationsaswellasconegeometryandpressuretaplocations.
AtlowReynoldsnumbers,thevelocityprofileisnolonger
flat(asinhighlyturbulentregimes)andtakestheshapeofa
parabola,withmaximumvelocityatthecenterofthepipe.
Liptak[ 9 ]hasreportedthattheannularregionbetweenthepipe
andtheconeelementtendstoflattenthevelocityprofileby
slowingtheflowatthecenterwhileincreasingitnearthewall
resultinginamoreuniformvelocityprofile.Genesietal.[ 10 ]
haveshownthattheV-conecreatesacontrolledturbulence
regionthatreshapesthevelocityprofileinthepipelinewhich
isdesirableforflowmeasurements.Flowisalsodirectedaway
fromconeedgeduetoboundarylayerformationonthecone
surface,thereforetheedgeisnotlikelytowear.
BritishandISOstandardcodesrecommendtheminimum
straightlengthsupstreamanddownstreamoftheflowmeter
dependingontheReynoldsnumber,pipediameter,
TheV-cone’simprovedperformancecharacteristicsarea
resultofitsuniquedesign( Fig.1 ).Itfeaturesacentrally
locatedconeinsideatube.Theconeinteractswiththefluid
flow,reshapestheincomingfluid’svelocityprofileandfinally
createsaregionoflowerpressureimmediatelydownstream
ofthecone.Thepressuredifferenceexhibitedbetweenthe
staticpressureatadistanceofonediameterupstreamof
theconeandthelowpressurecreateddownstreamofthe
cone,canbemeasuredandcorrelatedtotheflowrate.The
pressuredifferentialmeasuredisincorporatedintothestandard
flowmeterequationfordifferentialpressuredevicestoevaluate
theflowrateprovidedthedischargecoefficientisknown:
Q=C d × 1
p 1−
4 × 4 ×(
D 2 −d 2
)× p 2××1
P(1)
s
D 2 −d 2
D 2
where
=
(2)
and
1
P=( Hg − w )×g× 1
h
1000 .
(3)
ratio
andpipefitting.Ifftetal.[ 11 ]haveconductedexperimentsto
examinetheeffectofflowdisturbanceonaconicalflowmeter.
Theflowdisturbancewascreatedbyinstallingsingleand
doubleelbowsindifferentplanes.Fromtheresults,itcan
beconcludedthattheperformanceofaV-coneflowmeter
isnotverymuchaffectedbythisdisturbanceevenifthe
upstreampipelengthissmallornegligible.Prabhuetal.[ 12 ]
haveconductedexperimentsfor
Allothertermshavetheirusualmeaningsandarementioned
inthenomenclatureand Fig.1 .
Forthepresentstudy,thepipediameterchosenis52mm
(50mmNB)andthehighestdiameteroftheconeis40mm
for
=0
64and33mmfor
=0
.
75.Thelengthofthe
75and
itwasheldinthepositionbythreethinradialstrutsprovided
onthecylindricalportionupstreamofthevertexofthecone
asshownin Fig.1 .Thestrutsweregivenanaerofoilshapeto
minimizeflowdisturbance.Pressuretapsareprovidedatone
pipediameterupstreamandatthebaseoftheconeasshownin
Fig.1 .
=0
.
64and32mmfor
=0
.
75intheReynolds
numberrangeof30,000to49,400withairastheworking
fluidwithsingleanddoublebends.Theyhaveconcludedthat
thedischargecoefficientinthecaseofaV-coneflowmeter
islesssensitivecomparedtotheotherflowmeteringdevices
andpumpinglossesarealso50%lessincomparisonwiththe
orificemeter.Sarkaretal.[ 13 ]haveconductedexperiments
=0
.
3.Experimentalsetupforwaterandoil
Inordertoanalyzetheeffectofupstreamvalvedisturbance
ontheV-coneflowmeter,twoexperimentaltestsetupsfor
with
D Pipediameter,m
d Conediameter,m
s
.
conewas38mmfor
693163520.011.png 693163520.001.png 693163520.002.png
 
S.N.Singhetal./FlowMeasurementandInstrumentation17(2006)291–297 293
Fig.1.DesignanddrawingdetailsofaV-coneflowmeter.
Fig.2.Sketchoftheexperimentalsetupforflowmeasurements.
waterandoilexperimentswerefabricated.Theschematic
arrangementoftheexperimentalsetupforwaterisshownin
Fig.2 and Fig.3 showstheplacementoftheconeinsidethe
pipe.Waterissuppliedtothesetupfromalargesizedover-
headtanklocatedatanelevationof15mabovetheground.The
waterlevelinthetankwasmaintainedconstantbyoperating
suitablepumpslocatedinthebasementofthelaboratorywith
theprovisionofanoverflowpipe.Flowratewasregulatedbya
gatevalve‘V 3 ’locatedat22Ddownstreamoftheflowmeter.
Duringexperimentation,valve‘V 1 ’waskeptfullyopenand
valve‘V 3 ’wasusedtoregulatetheflowrate.Theflowrate
wasmeasuredusingthegravimetricmethod.Forthispurpose,
abeamtypebalanceof1000kgcapacitywithaweighingtank
wasused.Theresolutionofthebalancewas0.10kg.Inthis
methodthetimeforaknownweightofwatertogetcollected
inthetankwasaccuratelymeasuredusinganelectronicstop
watchhavingaresolutionof0.01s.Thepressuredifferentialis
measuredusingeithermercuryU-tubemanometersorinverted
U-tubemanometers(resolution±1mm)dependingonthe
magnitude.
Anothergatevalve‘V 2 ’wasincorporatedupstreamofthe
V-coneatdifferentdistancesandoperatedat25%,50%,75%
andfullyopenconditionstostudytheeffectofaskewed
velocityprofileontheperformanceoftheV-coneflowmeter.
Theexperimentalsetupforoilwasexactlysameasthatfor
waterexceptthatoilfortheexperimentwasprovidedfromthe
693163520.003.png
294 S.N.Singhetal./FlowMeasurementandInstrumentation17(2006)291–297
Table1
Physicalpropertiesoftheworkingfluids
Workingfluid Temperature( C) Density
(
kg
/
m 3
)
Viscosity(Pas)
Water 18 998.97 0.0013
SAE–20(Oil) 32 799.82 0.018
storagetankusingagearpumpcoupledtoamotorof5hp
runningat980rpm.Theweighingmachineusedwasof100kg
capacity.Theweighingmachinewaskeptabovethestorage
tanksothatitcouldemptyintoitafterthemeasurement.Thus
thesetwasaclosedlooprecirculatingtype.Thissetupwasused
toconductexperimentsatlowReynoldsnumber.Thephysical
propertiesofoilandwaterusedinthestudyaregivenin Table1 .
4.Rangeofparametersinvestigated
Fig.3.PhotographoftheV-coneinsidethepipe.
TheV-coneflowmeterwasfirstcalibratedunderideal
conditionstoevaluatethedischargecoefficient.Thenavalve
‘V 2 ’wasplacedatadistanceof5D,10Dand15Dupstream
oftheV-conetoproduceskewedvelocityprofileupstream
oftheconebyadjustingtheopeningofthisvalveatfour
locationsnamely25%,50%,75%andfullyopenconditions.
Foreachopeningofthevalve‘V 2 ’andlocations,thevalueof
thedischargecoefficienthasbeenobtainedfortherangeofflow
ratesforboth
5.Resultsanddiscussion
TheV-coneflowmeteriscalibratedunderidealconditions
usingbothfluids,namelywaterandSAE20oil,forboth
.
54×10 5 . Fig.4
showsthevariationofthevalueofC d withReynoldsnumber
forboththe
.
25×10 3 –2
.
ratios.ItisseenthatthevalueoftheC d
atlowReynoldsnumbersissomewhathigherandreduces
withincreaseinReynoldsnumber.Theaveragevalueofthe
dischargecoefficientis0.7256for
ratios. Table2 givesthefullrangeofparameters
investigated.
Statisticalanalysiswasconductedforeachoftheflow
conditionsbycomparingthevalueofC d underidealconditions
tothatofdisturbedconditions.Uncertaintyinthevalueof
C d wasalsoestablishedonthelinesofANSI.Theformulae
usedtoevaluatethestandarddeviationanduncertaintiesofthe
experimentsare
64withapercentage
uncertaintyof1.78%,andthecorrespondingvaluefor
=0
.
77
is0.7310withapercentageuncertaintyof1.97%( Table3(a) )
intherangetested.ThereforeitcanbeconcludedthatC d is
nearlyindependentofReynoldsnumberintherangetested.
Havingestablishedtheindependenceofdischargecoefficient
withReynoldsnumber,furtherexperimentswereonlycarried
outwithwater. Figs.5 and 6 showthevariationofC d with
Reynoldsnumberandtheeffectofvalveopeningforboth
valuesof
=0
.
n P
C d
n .
MeanvalueofC d = ¯ C d =
i=1
(4)
. Fig.5 (a)givesthevaluesofdischargecoefficient
64)forthevalvelocationat5Danditisseenthat
C d isnearlyconstantforagivenopeningofthevalve.It
isalsoseenthatC d valuesincreasewithincreasingclosure
ofthevalve.ThisvariationofC d canbeattributedtothe
acceleratingflowandphenomenonofreshapingofthevelocity
profileintheannulusspaceasitapproachestheconeflowmeter
base.C d valuesat25%valveopeningwerefoundtobethe
highest,withanaveragevalueof0.7540.Theaveragevalues
forotheropeningswere0.7482for50%opening,0.7396for
75%openingand0.7142forfullyopenconditions.Thevalue
=0
.
v u u u t
n P
i=1 (
C d − ¯ C d )
2
n .
StandarddeviationinC d = C d =
(5)
r n
n−1 C d (6)
wherenisthenumberofmeasurementsineachrun.Theresults
oftheuncertaintyanalysisaregivenin Table3 .
StandarderrorinC d =U C d =
Table2
Rangeoftheparametricinvestigation
S.no. ratio Upstreampositionofvalve‘V 2 ’ Extentofopeningofvalve‘V 2 ’ RangeofReynoldsnumber Parametermeasured
5D 25%,50%,75%andfullyopen 4.06×10 4 –2.19×10 5
Differentialheadacrossthe
conefordifferentflowrateand
C d calculatedforeach
combinationofvalveopening
andupstreamdistance
1 0.64
10D 25%,50%,75%andfullopen 6.12×10 4 –2.19×10 5
15D 25%,50%,75%andfullyopen 6.84×10 4 –2.21×10 5
2 0.77
5D 25%,50%,75%andfullyopen 5.49×10 4 –2.72×10 5
10D 25%,50%,75%andfullyopen 5.30×10 4 –2.72×10 5
15D 25%,50%,75%andfullyopen 1.43×10 4 –2.62×10 5
TherangeofRecoveredis1
(
693163520.004.png 693163520.005.png 693163520.006.png
S.N.Singhetal./FlowMeasurementandInstrumentation17(2006)291–297 295
Table3(a)
MeasuredvaluesofC d withoutvalve
S.no. Workingfluid Case Meanvalue Standarddeviation Percentageuncertainty RangeofReynolds
number
1 Oil
=0.64 0.7395 0.0023 0.36 1.25×10 3 –1.65×10 4
2 Oil
=0
77 0.7482 0.0030 0.43 1
.
50×10 3 –1
00×10 4
3 Water
=0.64 0.7145 0.0021 0.31 4.06×10 4 –2.18×10 5
54×10 5
5 Oilandwater =0.64 0.7256 0.0126 1.78 1.25×10 3 –2.18×10 5
6 Oilandwater
=0
77 0.7203 0.0024 0.36 9
.
10×10 4 –2
.
=0
77 0.7315 0.0139 1.97 1
.
50×10 3 –2
54×10 5
Table3(b)
MeasuredvaluesofC d andtheiruncertaintyforwaterflow
S.no. Case Valveopening Meanvalue Standarddeviation Percentageuncertainty RangeofRe
1
=0.643
L=5D
Full 0.7145 0.0021 0.31 4.06×10 4 –2.18×10 5
75% 0.7396 0.0023 0.32 6.19×10 4 –2.15×10 5
50% 0.7482 0.0016 0.23 6.14×10 4 –2.04×10 5
25% 0.7540 0.0047 0.70 5.88×10 4 –1.57×10 5
2
=0.643
L=10D
Full 0.7157 0.0023 0.34 9.61×10 4 –2.18×10 5
75% 0.7136 0.0022 0.35 6.53×10 4 –2.07×10 5
50% 0.7147 0.0025 0.38 7.17×10 4 –1.97×10 5
25% 0.7157 0.0026 0.39 6.12×10 4 –1.57×10 5
3
=0.643
L=15D
Full 0.7123 0.0020 0.30 7.61×10 4 –2.21×10 5
75% 0.7170 0.0015 0.23 6.84×10 4 –2.18×10 5
50% 0.7167 0.0023 0.35 9.07×10 4 –2.00×10 5
25% 0.7152 0.0036 0.58 7.93×10 4 –1.36×10 5
4
77
L=5D
.
72×10 5
75% 0.7277 0.0040 0.58 5.49×10 4 –2.62×10 5
50% 0.7490 0.0035 0.50 6
.
10×10 4 –2
.
35×10 5
25% 0.7790 0.0014 0.20 6.41×10 4 –1.66×10 5
.
36×10 4 –2
.
5
=0.77
L=10D
Full 0.7207 0.0017 0.25 9.10×10 4 –2.72×10 5
75% 0.7195 0.0017 0.24 5.31×10 4 –2.60×10 5
50% 0.7199 0.0018 0.27 8.23×10 4 –2.37×10 5
25% 0.7197 0.0005 0.08 8.01×10 4 –1.43×10 5
6
=0.77
L=15D
Full 0.7205 0.0005 0.08 1.43×10 4 –2.63×10 4
75% 0.7210 0.0020 0.29 1.15×10 4 –2.62×10 4
50% 0.7195 0.0014 0.21 1.10×10 4 –2.33×10 4
25% 0.7210 0.0014 0.24 1.03×10 4 –1.74×10 4
(a)=0.64.
(b)=0.77.
Fig.4.VariationofC d withReforundisturbedflows.
.
.
4 Water
.
.
.
=0
Full 0.7207 0.0026 0.38 9
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