Pr 2 LH - capp.iit.educapp/mucool/lh2/Cassel-2-22-03.pdf · LH 2 + x k w + 1 h H e ln T LH 2 T o T...
Transcript of Pr 2 LH - capp.iit.educapp/mucool/lh2/Cassel-2-22-03.pdf · LH 2 + x k w + 1 h H e ln T LH 2 T o T...
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.