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2011ANSYS,Inc. June21,20131
PhaseChangeModeling
Vedanth Srinivasan
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qqtqqq
n
p
qpqpqqqqqqqqq
qqqmp
t ,vm,lif
1
FFFuRguuu
MultifluidConservationEquations
Continuity:
Momentum for qth phase:
The inter-phase exchange forces are expressed as:
Energy equation for the qth phase can be similarly formulated.
n
p
pqqqq
qqm
t 1u
qppqpq K uuR
transient convection pressure shear
interphase
forces
exchange
interphasemass
exchange
body external, lift, andvirtual mass forces
Volume fraction for the qth phase
Solids pressure term is
included for granular model.
PhaseChange!!
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Solvesoneequationforcontinuityofmixture
Solvesoneequationforthemomentumofthemixture
Solvesforthetransportofvolumefractionofeachsecondaryphase
MixtureModelConservationEquations
r
k
r
kk
n
kkm
T
mmmmm
m
uuFguupuut
u
1eff
0
mm
m ut
).().()( rpppmpppp uut
PhaseChangesourcesadded
+Sp
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Interfacialmasstransfer
Masstransferrateperunitofvolume sourcetermsinphasemass
conservationequation
secm
kg
312 iiS Am
Mass flux vector,
kg/(m2 sec)
Interfacial area
density, 1/m
Phase 1 Phase 2
Interface
12S
Mass transfer
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Masstransferdefinedthroughphaseinteractionpanel
MasstransfermodelsavailablewithmixtureandEulermodels Cavitation
Evaporationcondensationmodel
Userdefinedmasstransfer
Boiling
Masstransferduetoheterogeneousreactions
Nucleationandgrowthinpopulationbalancemodels
Mass transfer
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Latentheatisaccountedforwhenmasstransferis
prescribedthroughstandard
means. Latentheatiscalculatedfrom
standardstateenthalpyof
species/phaseparticipatingin
massexchange.
Materialtypemustbefluid
Beawareofvaluesofstandard
stateenthalpy only
enthalpydifferencematters. For
example,vaporenthalpy
mustbelargerthanliquid
enthalpy.
Mass transfer
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CavitationModeling
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Cavitationoccursinmanyengineeringdevices.
Aliquidatconstanttemperaturecanbesubjectedtoadecreasing
pressure,whichmayfallbelowthesaturatedvapourpressure Theliquidalsocontainsnoncondensablegases(dissolvedoringested)
Hydrofoils,Propellers,Inducers,Nozzles,Biomedical,
Needforcavitationmodelswhichaccountfor
Nphaseflowswithmultiphase
speciestransport.
Effectsofslipvelocitiesbetween
theliquidandgasphases.
Thermal
effects
and
compressibilityofbothliquid
andgasphases.
CavitationModels
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PhysicalChallenges
PhaseChange(bubblegeneration&collapse)
Largedensityratioofliquidtovapor(e.g. water300K,theratiois4e+4)
Strongdependenceofgeometryandflowconditions
Incavitating zones,staticpressureremainsaconstant (=saturationpressure)
Turbulenceeffects
Thermalinfluence
Numericalchallenges:
Handlethelargeliquidtovapordensityratios
Dealwithcavitationmasstransferandpossiblyheattransfer
Phasictransitionswithinthedomain(vaporflooding,liquid/vaporregimes)
CavitationCharacteristics& NumericalChallenges
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Cavitationzonesareprevalentlynotedinfluidpumps,valves,sharpedgedorifices,injectorsetc.
Cavitationisanundesirable(mostly)andcancause: Significantdegradationinperformance,asmanifestedbyreducedmass
flowrates,lowerheadriseinpumps,loadasymmetry,vibrationand
noise.
Physicaldamagetoadevice(duetobubbleimpactonsurfacesCavitationErosion)whichcanultimatelyaffectstructuralintegrity.
CavitationModeling
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EstimationoftherateofvapourproductionisbasedontheasymptoticgrowthrateofRayleighPlessetequation
Zwartetal.Model
Schnerr andSauerModel
SinghalModel (Mixturemodelonly)
TransportEquations
cevv
v RRvt
)(
InCavitation,theliquidvapor masstransfer(evaporationand
condensation)isgovernedbythevapor transportequation
Masstransfer
due
to
growth
and
collapse
of
vapor
bubbles
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Singhals FullCavitationmodel
CavitationModelCapability
vPP
vPP
l
vvl
gv
vap
PPkFRe
3
20.1,1max
l
vvl
vcond PPkFRc
32,1max
kPP satv 39.02
1
cevv
v RRVt
).(
)(
Fvap=0.02,Fcond=0.01
/solve/set/expert Singhal etal.module[No]Yes
Variableproperties
Turbulenceeffectsonsaturatio
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Zwarts &Schnerrs CavitationModel
VariablePsat
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Zwarts andSchnerrs CavitationModels
Cavitation Models Vapor Volume Fraction Transport Equation
Zwart-Gerber-Belamri Model Schnerr-Sauer Model
cevv
v RRV
t
).(
)(
l
v
B
vvnuc
vape
PPFR
)(
3
2)1(3
vPP
l
v
B
vv
condc
PPFR
)(
3
23
v
PP
01.0
50
105
10
4
6
cond
vap
nuc
B
F
F
m
l
v
B
lv
e
PPR
)(
3
23)1(
vPP
vPP
l
v
B
lv
c
PPR
)(
3
23)1(
1310
1
4
3
1
B
)3
41/(
3
4 33BB
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ForSchnerr andZwarts model
Keepunderrelaxationforvaporto0.5orhigher
KeepDensity/Vaporizationmassto1.0 Ifcoupledsolverisused,keepcourantnumberaround200(default),onlyfor
complicatedgeometry/cases,considerreducingittotherangeof20 50
ForSinghals model
momentumrelaxationfrom0.050.4 Pressurerelaxation:0.2 0.4
Vaporizationmass:0.1 1.0
Tips/Tricks
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NoneofthecavitationmodelscanbeusedwiththeexplicitVOFoptionbecausethesurfacetrackingschemesareincompatiblewiththe
interpenetratingcontinuaassumptionofthecavitationmodels.
Theycanonlybeusedforasinglecavitationprocess.
TheSinghaletal.modelrequirestheprimaryphasetobealiquidandthesecondaryphasetobeavapour.
Singhals modelisonlycompatiblewiththemultiphasemixturemodel.
TheSinghaletal.modelisnotcompatiblewiththeLESturbulencemodel.
LimitationofCavitationModels
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WallBoilingModels
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Threeboilingmodelavailable:
RPIBoilingmodel Applicabletosubcoolednucleateboiling
NonequilibriumBoiling ExtensionofRPItotakecareofsaturatedboiling
CriticalHeatFlux ExtensionofRPItotakecareofboilingcrisis
Contours of vapor volume fraction
in a nuclear fuel assembly
Boiling Model Options
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BoilingModels
Boilingmodels:
RPIboilingmodel
Nonequilibriumboiling
CriticalHeatFlux
InterfacialAreaandBubbleDiameter
AlgebraicformulationsandUDFoptions
IACequationcompatiblewithboilingmodelsInterfacialTransfermodels
Arangeofsubmodelsfordragandlift,and
turbulentdispersion
Liquid/vaporinterfaceheatandmasstransfermodels
Flowregimetransitions frombubblytodroplets
Contours of vapor volume fraction
in a nuclear fuel assembly
Current ANSYS
Capabilities
Transitional
or Unstable Film
boiling
Critical
Heat
Flux Minimum
Heat Flux
StableHea
tFlux
Wall Superheat (Twall - Tsat)
Subcoole
d
Nucleate
boiling
Sa
turated
Single
Phase
3.0V
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RPIWallBoilingModel
Tw
Tbulk
Tsat
bwdBubble nucleating site
Departing bubbleHeated wall
Thin superheated layer
Subcooled boilingoccurswhenwallandthinliquidboundarylayer
havetemperaturehigherthansaturationtemperatureatlocal
pressure,i.e.,Superheated
Ex:Heatexchangers,Heatedpipeflows,Coolingjackets,Quenchheat
treatment..
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ThemodelwasdevelopedatRensselaerPolytechnicInstituteandiscalledRPImodelforsubcooled boiling
ThemodelisimplementedwithinEulermodel
Itincludesatleasttwophases:liquid(primaryorcontinuousphase)andvaporbubbles(secondaryordiscretephase)
TheRPIWallBoilingModelwasdevelopedduetothefailureofpurelysinglephaseconvectiveheattransferforwallboiling.
RPIaccountsforsteambubblegenerationaswellasquenchingeffects:
Nucleation,bubblegrowthanddeparturefromthewall
KeystepsintheRPImodel
Partitionthewallheatfluxintothreecomponents.
Closureofeachcomponentusingsubmodels
Canbeusedwithdifferentboundaryconditions.
RPI Wall Boiling Model
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Activating/WorkingwithRPIBoilingModel
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DecidewhichBoilingmodeltochoose IfTbulkbelowTsat Subcooled flow
UseRPIwallboilingmodel
IfTbulkcloseto(within3K)Tsat Saturatedflow Usenonequilibriumwallboilingmodel
ForCriticalHeatFlux/Burnout/DeparturefromNucleateBoiling(DNB)situation
Usecriticalheatfluxmodel
CommonmistakesinBoilingModel EnsuregravityisONtoseeanyheattransfer
Ensuresurfacetensionisspecified
Neededfornucleationandgrowthofbubbles
Ensurecorrectphasesinmasstransfermechanism
BoilingModels Tips&Tricks
VaporVolumefraction
Vertical location(m)
dia
meter=15.4mm
length=2000mm
Subcooled
water
Gravity
Bartolemei & Chanturiya Validation
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Solutionstrategies UselowerenergyURF(~0.6)
Y+forRPIcanbe>30(standardwallfn apply)
Youcanrunboilingcalculationinsteadystate
CangoforcoupledsolverwithratherlowerCourantnumberslike10orevenlessattimesorpseudo
transientsolver
Ifyoufaceproblemswithcoupledsolvers,lowertheexplicitrelaxationfactorsforbothpressureand
momentumto0.75orevenupto 0.5.
Ifcoupledsolverdoesnotworkatall,goforSIMPLE.
Ifsteadycalculationiscausingissues,checkifthe
reverseflowiscausinganytrouble. Ifyouaresurethatthereisnoreverseflowinthefinal
solution,specifyreverseflowquantitiessuchthatthey
helpconvergence.
BoilingModels Tips&Tricks
VaporVolum
efraction
Vertical location
(m)Bartolemei & Chanturiya Validation
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Evaporation/Condensation
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Evaporation/Condensation
Evaporation/Condensationisasurfacephenomenaunlikeboiling(volumetric)
Condensationisthetransformationofasubstancefromvaportoliquidresultingfromenergyremovalfromthevaporphase.
Incondensationprocesses,thevaportemperatureisatorbelowthesaturationtemperature.
Evaporationisthetransformationofasubstancefromliquidtovaporresultingfromenergyaddition.
Condensationoccursinvariousmodes.
Dropletformation
in
vapor
Liquiddropletformationonacooledsurface
Liquidfilmcondensationonacooledsurface
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Mechanisticmodelwithaphysicalbasis
Evaporation/CondensationModel
lvvlvv
v
mmvt
)(
Tl>Tsat
sat
satvvvclv
sat
satlllcvl
T
TTm
T
TTm
Tv
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Evaporationcondensationmodel
Positivemasstransferrateisdefinedas
being fromliquidtovapor.
Saturationtemperaturecanbeprovidedas
functionofpressure.
Ifsaturationtemperatureisafunctionof
othervariablesuchasvolumefraction,
pressureandothersolutions,aUser
DefinedFunctions(UDFs)maybe
necessarytodefinetheentirephase
changemechanism
Mass transfer
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Masstransferfromliquidtovapor
SpecifyLatentHeatasStandardStateFormationEnthalpy Standardstateenthalpyofvapor=latentheat(inj/kgmolunits)
Standardstateenthalpyofliquid=0
Samemolecularweightforliquidandvapor
Referencetemperature=298.15K
Calculationstrategy UsecoupledsolverwithlowCourant
numbers
Lowertheexplicitrelaxationfactors
forpressureandmomentumto0.5
Ensurereverseflowvolumefraction
properlydefinedatoutletboundaries
EvaporationCondensation Tips&Tricks
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Tuningevaporationandcondensationfrequency
Comparethenumericalresultswithexperimentalresults
Usesimplecalculationtoestimateevaporation Evaporationexpected=(Htotal Hsensible)/LatentHeat
Adjustevaporation/condensationfrequencies (0.001 100)
InEvaporationCondensationModel,departurefromsaturationdeterminestherateofmasstransfer
(TcellTsat)isthedrivingforce
Formasstransfertohappen,Tcell>or
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Dropletformationandvaporization(inpipelines,mixingTs,Valves,Pumpscompressingandexpandinggases)
Volatilephasebehavior(evaporation/condensationintanksstoringvolatilecompoundsthatchangephasebasedonstoragepressure)
ModelingFlashingbothusingCavitationmodel(Pdriven)andalsousingEvaporation/Condensation(Tdriven,superheatedflows)
L.N.GFlashing CryogenicLiquidFlashing
RefrigerantFlashing
FuelTankflashing
FlashTank
PhysicsModelingusing
Evaporation/Condensation
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WetSteamModel
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Duringtherapidexpansionofsteam,acondensationprocesswilltakeplaceshortlyafterthestatepathcrossesthevaporsaturationline.
Theexpansionprocesscausesthesuperheateddrysteamtofirstsubcoolandthennucleatetoformtwophasemixture
Theformationofliquiddropletsinahomogeneousnonequilibrium
condensationprocess,isbasedontheclassicalnonisothermalnucleationtheory.
Assumptions
Thevelocityslipbetweenthedropletsandgaseousphaseisnegligible.
Theinteractionsbetweendropletsareneglected. Massfractionof thecondensedphaseissmall(
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WetSteamModel
Ivt
vt
v
1
TTCRTh
Pdtdr
eM
qI
op
llv
TK
r
ml
vc b
21
2
2
1
3
4
3
22
Nucleationrate
Dropletradius
(growthrate)
Mixturedensity
MassFractionTransport
NumberdensityTransport
Droplettemperature
NonEquilibriumCondensationProcess
LoadMaterialbyTextCommand:Define/models/multiphase/wet steam/compileuserdefinedwetsteamfunctions
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Adjusttemperaturelimits,minimumof273K
Makesuremaximumwetnessfactorisnotbeyond0.2sincethepresent
modelassumeslowwetnessfactor Withwetnessfactor,>0.1,solutionbecomeslessstable
Forwetsteammodels,solveflowsolutioninitiallywithoutcondensationandoncepropersolutionisachieved,switchoncondensation
SwitchingoffcondensationcanbedonebydeselectingWetsteamequationsinthesolutioncontrolpanel
SolutionStrategiesforWetSteamModel
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Melting/Solidification
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SolidificationandMelting
Solidificationisthetransformationofasubstancefromliquidtosolid
Temperaturedecrease(morefrequentlyencountered)andchangeofstateoccursatthefreezingpoint
Pressureincrease(inthiscasetemperatureremainsconstant)
Thesolidificationprocessstartswithsmallsolidnucleationintheliquidthatincreasesinnumberwithtime(untilliquidiscompletelysolidified)
Application Casting,Crystallization..
Meltingisthetransformationofasubstancefromsolidtoliquid
Temperatureincreases,thechangeofstateoccursatthemeltingpoint
Ingeneral,themeltingpointisrelativelyinsensitivetopressure
Application Decrystallization in
pipes
under
low
temperatures,
Deicing
windshields..
Freezing&meltingpointareoftenequal(certainmaterialscanhavedifferentvalues)
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Melting/SolidificationModeling
Procedure Possibletomodelmeltingorsolidificationinasinglephaseorin
multiplephases
Forphasesthatarenotchangingphase,setLatentHeat,Liquidus andSolidusTemperaturetoZero
ModelingThermal&Solutal Buoyancy
ThermalandSolutal Buoyancy
optionavailableonlywhensolving
thephasechangeproblemwith
SpeciesTransport
TUIdefine/models/solidification-melting? yes
Include Thermal Buoyancy? yes
Include Solutal Buoyancy? yes
Use reference mass fraction of solutes? yes
Reference mass fraction of the species-i "value"
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Recommendations
MushyZoneParameter:Valuerangesaround104 to107.Highervalueswillassistin
bringingdownlocalcellvelocitytozeroasmaterialsolidifiesbutmaycause
oscillationsinsolutions.
Notnecessarytousepullvelocitywithinthesolution moreimportantwhenmodelingcontinuouscastingwherevelocityboundaryconditionsarespecified
Convergencedifficultiescanbeexpectedinsteadystatecalculations,continuous
castingsimulations,simulationsinvolvingmulticomponentsolidification,and
simulationswherealargevalueofthemushyzoneconstantisused.Inthatcase,considerreducingliquidfractionupdateinthesolvercontrols
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UserDefinedFunctions
DEFINE_CAVITATION_RATE(ModifyCavitationSourceterms)
DEFINE_BOILING_PROPERTY(Modifyparameterslikebubbledepature diameter,
frequencyofdeparture,nucleationsitedensity,areacoefficient&liquidref
temperature)
DEFINE_LINEARIZED_MASS_TRANSFER(Userdefinedmasstransfersourceterms)
DEFINE_SOLIDIFICATION_PARAMS(modifymushyzoneandbackdiffusionparameters)