LH2Absorbers–SimulationsandProposedFlowTest

AleksandrV.Obabko,KevinW.CasselandEyadA.Almasri

FluidDynamicsResearchCenter,Mechanical,MaterialsandAerospaceEngineeringDepartment,

IllinoisInstituteofTechnology,Chicago,IL

AbsorberReviewMeetingFermiNationalAcceleratorLaboratory

February21-22,2003

Introduction:ApproachestoHeatRemoval

Twoapproachesunderconsideration:

ÀExternalcoolingloop(traditionalapproach).

+BringtheLH2tothecoolant(heatremovedinanexternalheatexchanger).

ÁCombinedabsorberandheatexchanger.

+Bringthecoolant,i.e.He,totheLH2(removeheatdirectlywithinabsorber).

LH2

MuonBeam

Heater

He Cooling Tubes

Introduction(cont’d)

Advantages/disadvantagesofanexternalcoolingloop:

+HasbeenusedforseveralLH2targets(e.g.SLACE158).

+EasytoregulatebulktemperatureofLH2.

+Islikelytoworkbestforsmallaspectratio(L/R)absorbers.

−Maybedifficulttomaintainuniformverticalflowthroughtheabsorber.

Advantages/disadvantagesofacombinedabsorber/heatexchanger:

+Takesadvantageofnaturalconvectiontransversetothebeampath.

+Flowinabsorberisselfregulating,i.e.largerheatinput⇒moreturbulence⇒enhancedthermalmixing.

+Islikelytoworkbestforlargeaspectratio(L/R)absorbers.

−MoredifficulttoensureagainstboilingatveryhighRayleighnumbers.

HeatExchangerAnalysis

EnergybalancebetweenLH2andcoolant(He).

3Parameters:Ti=coolantinlettemperature

To=coolantoutlettemperature

TLH2=bulktemperatureofLH2

A=surfaceareaofcoolingtubes

hLH2=convectiveheattransfercoefficientofLH2

hHe=convectiveheattransfercoefficientofHe

∆x=thicknessofcoolingtubewalls

kw=thermalconductivityofcoolingtubewalls

cp=specificheatcapacityofHe

HeatExchangerAnalysis(cont’d)

3Rateofheattransfer:

q=−A(To−Ti)

(

1

hLH2

+∆xkw+

1

hHe

)

ln(

TLH2−To

TLH2−Ti

)

3MassflowrateofHe:

mHe=q

cp(To−Ti).

hHe⇒fromappropriatecorrelation(flowthroughatube).

hLH2andTLH2⇒fromCFDsimulations(nocorrelationsfornaturalconvectionwithheatgeneration).

ComputationalFluidDynamics(CFD)

FeaturesoftheCFDSimulations:

3ProvidesaverageconvectiveheattransfercoefficientandaverageLH2

temperatureforheatexchangeranalysis.

3TrackmaximumLH2temperature(cf.boilingpoint).

3Determinedetailsoffluidflowandheattransferinabsorber.

⇒Betterunderstandingleadstobetterdesign!

CFD(cont’d)

Take1:ResultsusingFLUENT(M.Boghosian):

3Simulateonehalfofsymmetricdomain.

3Steadyflowcalculations.

3HeatgenerationviasteadyGaussiandistribution.

3Turbulencemodeling(RANS)usedforRaR≥4×108.

Take2:ResultsusingCOAcode(A.ObabkoandE.Almasri):

3Simulatefulldomain.

3Unsteadyflowcalculations.

3AllscalescomputedforallRayleighnumbers.

åInvestigatestartupbehavior,e.g.startupovershootinTmax.

åInvestigatepossibilityofasymmetricflowoscillations.

åInvestigateinfluenceofbeampulsing.

FLUENTCFDResults

AverageNusseltNumbervs.RayleighNumber:

Nulam = 0.8114Ra0.1931

Nuturb = 0.3079Ra0.2184

Nu = 0.5754Ra0.1979

Nu = 0.6789Ra0.1859

NuJSME = 0.5042Ra0.2126

10

100

1000

1.0E+061.0E+071.0E+081.0E+091.0E+101.0E+111.0E+121.0E+131.0E+141.0E+15

RaD

Nu

D

x = 7.4e-02 laminarx = 7.4e-02 turbulentx = 0.5x = uniformJSME cylinder - uniform

turbulentregime

laminarregime

FLUENTCFDResults(cont’d)

Non-DimensionalMaximumTemperaturevs.RayleighNumber:

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+061.0E+071.0E+081.0E+091.0E+101.0E+111.0E+121.0E+131.0E+141.0E+15

RaD

T* m

ax.

x = 7.4e-02x = infinityx = 0.5

T*max = (Tmax-Tw)/(q'''D2/k)

ParameterMapforLH2

0.010.020.050.10.20.51R,m

1

10.

102

103

104Σ=0.007

Σ=0.250

Ra=1015

1014

1013

1012

1011

1010

109

Ra=108

DT*=2K 4K DT

*=8K

q¢  ,W����m

Note:Propertiestakenat18K,2atm.

COAFormulation

Propertiesandparameters:

R=radiusofabsorber

Tw=walltemperatureofabsorber

q′′′(r)=rateofvolumetricheatgeneration(Gaussiandistribution)

q′

=rateofheatgenerationperunitlength

ν=kinematicviscosityofLH2

α=thermaldiffusivityofLH2

k=thermalconductivityofLH2

β=coefficientofthermalexpansionofLH2

GoverningEquations(T-ω-ψformulation)

Energyequation:

∂T

∂t+vr

∂T

∂r+vθ

r

∂T

∂θ=∂

2T

∂r2+

1

r

∂T

∂r+

1

r2

∂2T

∂θ2+q(r)

Vorticity-transportequation:

∂ω

∂t+vr

∂ω

∂r+vθ

r

∂ω

∂θ=Pr

[

∂2ω

∂r2+

1

r

∂ω

∂r+

1

r2

∂2ω

∂θ2

]

+RaRPr

[

sinθ∂T

∂r+

cosθ

r

∂T

∂θ

]

Streamfunctionequation:

∂2ψ

∂r2+

1

r

∂ψ

∂r+

1

r2

∂2ψ

∂θ2=−ω

vr=1

r

∂ψ

∂θ,vθ=−

∂ψ

∂r

Formulation(cont’d)

Initialandboundaryconditions:

T=ω=ψ=vr=vθ=0att=0,

T=ψ=vr=vθ=0atr=1.

Non-dimensionalvariables:

r=r∗

R,vr=

v∗

r

R/α,vθ=

v∗

θ

R/α,t=

t∗

R2/α,

T=T

∗−Tw

q′

/k,ψ=

ψ∗

α,ω=

ω∗

α/R2,

q(r)=q′′′(r)

q′/R

2=1

2πσ2e

−r2

2σ2,σ=

σ∗

R.

Formulation–Non-DimensionalParameters

PrandtlNumber:

Pr=ν

α

RayleighNumber:

RaR=GrPr=gR

3βq

′/k

να

(

=π

32RaMB

)

Nusseltnumber:

NuR=hLH2R

k

(

=NuMB

2

)

Results–FlowRegimes

Thefollowingflowregimesareobserved:

+Steady,symmetricsolutions:RaR≤1×108

+Unsteady,asymmetricsolutions:RaR≥1×109

Steady,symmetricresultsforRaR=1.57×107

(uniformheatgeneration):

Streamfunction:Temperature:Vorticity:

X

Y

-1-0.500.51-1

-0.5

0

0.5

1

X

Y

-1-0.500.51-1

-0.5

0

0.5

1

X

Y

-1-0.500.51-1

-0.5

0

0.5

1

Steady,SymmetricResults(cont’d)

NusseltnumberversusθforRaR=1.57×107

(uniformheatgeneration):

Nuvs.θ:

0.045.090.0135.0180.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

CodeComparisons–AverageNusseltNumber(Nu)

Uniformheatgeneration(σ→∞)withPr=1:

RaRMitachietal.1

FLUENT2

COACode

1.57×106

8.587.78.2

1.57×107

14.011.912.0

1Mitachietal.(1986,1987)-Resultsshownarefromnumericalsimulationswhich

comparedfavorablywithexperiments.2

FromM.Boghosian’scorrelationforPr=1.4,i.e.NuMB=0.7041·Ra0.1864

MB.

CodeComparisons–COAvs.FLUENT

Gaussianheatgeneration:σ=0.25

steadylaminar,steadyRANS(turbulent),unsteadyN–S

FLUENT1

COACode

RaRTavgTmaxNuTavgTmaxNu

1×108

0.01010.016916.40.01000.01815.6

1×109

0.00670.010125.10.00650.01125.4

1×1010

0.00450.006038.50.00390.007046

1FromM.Boghosian’scorrelations(TMB=

π

4T):

TavgMB=0.3130·Ra

−0.1771MB,TmaxMB

=1.3597·Ra−0.2233MB,NuMB=0.7041·Ra

0.1852MB

Steady,SymmetricResults:RaR=1×108,σ=0.25

Streamfunction:Temperature:Vorticity:

X

Y

-1-0.75-0.5-0.2500.250.50.751-1

-0.5

0

0.5

1

X

Y

-1-0.500.51-1

-0.5

0

0.5

1

Steady,SymmetricResults:RaR=1×108,σ=0.25

Nuvs.t:Tmaxvs.t:

Time

Nu(avg)

0.050.10.15

2

4

6

8

10

12

14

16

Time

T(m

ax)

0.050.10.15

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

Unsteady,AsymmetricResults:RaR=1×1010,σ=0.25

Nuvs.θ:

THETA

Nu

01230

20

40

60

80

100

120

140

160

180

200

Unsteady,AsymmetricResults:RaR=1×1010,σ=0.25

Nuvs.t:Nuvs.θ:

0.000.050.100.150.20

t

10.

20.

30.

40.

50.

60.

Nu

�����

0.045.090.0135.0180.0

Θ

20.

40.

60.

80.

Nu

�����

GaseousAbsorberParameters

FordE/dx=13.81M,1.5×1014

muons/s⇒q′=332W/m

Thenat100atmand80K⇒RaR=2.01×1015

forR=0.5m.

Characteristics:

+Noboiling!

−Morecomplexandtime-consumingtosolvethefluidflowandheattransferproblem:

+RaRisoneorderofmagnitudehigherthaninthecaseofliquidhydrogenabsorber.

+Compressibility?

?Treatmentofactualgeometry.

?Effectofionizationandmagneticfieldonfluidflowandheattransfercharacteristics.

Conclusions

âCurrentCOAresultscompareverywellwithlimitedexperimentaldataandFLUENTresults(bothlaminarandturbulentregimes).

âCriticalRayleighnumberforunsteady,asymmetricbehaviorisRaR>1×10

8.

⇒RoughlycorrespondstolaminartoturbulenttransitioninFLUENTresults.

âNostart-upovershootintemperatureathighRa.

⇒Heaternotnecessarytoimproveperformanceofabsorberasheatexchanger.

âCFDresultsofferguidanceforgaseousabsorber(additionalissuesmustbeaddressed).

ProposedFlowTest

Wishlist:

3Nearroomtemperatureflowtest⇒minimizecost;maximizepossiblesitesfortest.

3Workingfluidthatissafeandeasytoworkwith.

3Allowforflexibilityinprovidingheatsource.

3Maximizeinformationobtainedwithoutneedforinternalmeasurements(maybedifficultdependingonheatsource).

⇒Ifsuchmeasurementsarepossible,allthebetter.

3ProvideforcomparisonsofessentialdatawithCFDresults.

ProposedFlowTest(cont’d)

Inatypicaltestonewouldchoosethegeometry,workingfluidandheatinputtogiveaparticularRayleighnumber.Thenthetemperature(e.g.maximumtemperature)andflowconditionswouldbemeasured.

⇒ChoosetheRayleighnumberanddetermine∆T∗.

Thekeyinsight:

+Wecanmeasuretemperaturechangebyheatingfromaknownwalltemperaturetoboiling,i.e.∆T

∗=T

∗

boil−T∗

w.

⇒Intheproposedtest,thegeometry,workingfluidandtemperaturerangearechosen,andtherequiredheatinputisdetermined.

⇒Choosethe∆T∗

anddetermineRayleighnumber.

ProposedFlowTest(cont’d)

Features:

3Setup:absorberencasedincoolingsheath(similartoactualabsorber).

3Heatsource:electriccurrentinabsorberfluid,beam,etc.

3Absorberfluid:waterisacandidate.

→Couldpossiblyuseadditivetoincreaseelectricalconductivityand/orlowerboilingpoint.

ParameterMapforWater

0.010.020.050.10.20.51R,m

10

102

103

104

105

Σ=0.007Σ=0.250

Ra=1015

1014

1013

1012

1011

1010

109

Ra=108

DT*=0.1

ëC

1ëC

10ëC

DT*=100

ëC

q¢  ,W����m

Note:Propertiestakenat100◦C,1atm.

ProposedFlowTest(cont’d)

Procedure:

ÀChoose∆T∗⇒AbsorberwalltemperatureT

∗

w=T∗

boil−∆T∗.

ÁCirculatecoolantuntilabsorberfluidreachesuniformtemperatureequaltoT

∗

w.

ÂTurnonheatsourceandincreaseinaquasi-steadymanner,i.e.slowly,untilincipientboilingoccurs.

ÃRecordvideotonotelocationofincipientboilingandvisualizeflowusingbubbles.

ÄDetermineheatoutputfromabsorberbymeasuringmassflowrateandinlet/outlettemperaturesofcoolant.

ÅAtconclusionoftest,drainfluidfromabsorberanddeterminebulk,i.e.average,temperature,T

∗

avg,ofabsorberfluid,i.e.drainatconstant,knownmassflowrateandmeasuretimeseriesoftemperatureofdrainingfluid.

ÆRuntestforaseriesof∆T∗’s.

ProposedFlowTest(cont’d)

Analysisofflow-testresults:

ÀDetermineactualRayleighnumberoftestfrommagnitudeofheatinputnecessarytoproduceboiling,i.e.selected∆T

∗=T

∗

boil−T∗

w.

ÁDetermineheatinputpredictedfromCFDtoproducetemperaturerisecorrespondingto∆T

∗.

ÂCompareactualheatinputrequiredforboilingwiththatpredictedfromCFD,i.e.compareactualandpredictedRayleighnumbersforgiven∆T

∗.

ÃEstimateaverageNusseltnumberusingactualheatinput,heattransfersurfaceareaandT

∗

avg−T∗

w.

ÄCompareestimatedNusseltnumberfromflowtestwithpredictedvaluefromCFD.

ProposedFlowTest(cont’d)

Featuresofflow-test:

3Choose∆T∗

ratherthanRayleighnumberforeachtest.

3Noexoticfluidflowortemperaturemeasurementsnecessary.

→Wemeasurethemaximumtemperaturevisuallybyheatinguntilboilingoccurs.

⇒Thefluidmaybeheatedinthemostpracticalmannerwithoutregardforitseffectonmeasurementtechniques.

3Thebubblesprovidesomelimitedvisualizationcapability.

3Measuringmaximumtemperatureisaquantitythatisinfluencedstronglybybothfluiddynamicandheattransferaspects,i.e.itisacompositeoftheentirefluidflowandheattransferenvironment.