Comparison of four models for thermal response test evaluation.docx

Comparison of four models for thermal response test evaluation.docx

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Comparisonoffourmodelsforthermalresponsetestevaluation

Comparisonoffourmodelsforthermalresponsetestevaluation

SignhildEAGehlin,GoranHellstrom.ASHRAETransactions.Atlanta:

2003.Vol.109Part1.pg.131

 » Jumptoindexing（documentdetails）

FullText （5896 words）

CopyrightAmericanSocietyofHeating,RefrigerationandAirConditioningEngineers,Inc.2003

[Headnote]

ABSTRACT

Fourtwo-variableparameterestimationmodelsforevaluationofthermalresponsetestdataarecomparedwhenappliedonthesametemperatureresponsedata.Twomodelsarebasedonline-sourcetheory,thethirdmodelisacylinder-source-basedsolution,andthefourthisanumericalone-dimensionalfinitedifferencemodel.Thedatasetscontainmeasuredtemperatureresponse,heatload,andundisturbedgroundtemperaturefromthreethermalresponsetests,togetherwithphysicaldataofthetestedboreholeheatexchangers（BHE）.ThemodelsestimategroundthermalconductivityandthermalresistanceoftheBHEandarecomparedregardingtestlengthanddataintervalused.Forthethreedefineddatasets,thelinesourceapproximationmodelshowstheclosestagreementwiththemeasuredtemperatureresponse.Thecylindersourceandnumericalmodelsshowsensitivitytotheinclusionofearlydata.Arecommendedminimumresponsetestdurationof50hoursisconcludedfromthemodelcomparison.

INTRODUCTION

Duringathermalresponsetest,adefinedthermalloadisappliedtoaboreholeheatexchangerandthetemperaturedevelopmentoftheinletandoutlettemperaturesaremeasuredovertime.Thistemperatureresponseallowsextrapolationofthethermalbehaviorinfuturetime.Onepossibleconceptualmodelfortheinterpretationistoassumethegroundtobeaconductivemediumandtodeterminetheapparentthermalconductivityandotherthermalparametersofthismedium.Thetestmaybeconductedusingatransportabledevicethatisbroughtonsitetotheborehole.

Sinceitsintroductionin1995-1996,thisin-situmethodhasspreadtomostcountrieswhereboreholesinthegroundareusedasaheatsource/sinkonalargerscale.Themethodservesprimarilytoassessthegroundthermalconductivityandperformanceofdifferentboreholeheatexchangerdesigns,whichareimportantforoptimaldesignandqualitycontrol.Themethodisdescribedinseveralpapers,e.g.,Gehlin（1998）,Austin（1998）,Austinetal.（2000）,ShonderandBeck（2000）,andKavanaughetal.（2000）.TheprincipleofathermalresponsetestsetupisoutlinedinFigure1.

Theboreholetemperatureresponseisthetemperaturedevelopmentovertimeoftheheatcarrierfluidcirculatingthroughtheboreholeheatexchangerwhenaknownheatingorcoolingloadisimposed.Byevaluatingtheincreasingfluidtemperatureversustime,informationaboutthethermalpropertiesinandaroundtheboreholeisobtained.Alowthermalconductivityis,e.g.,indicatedbyamorerapidtemperatureresponse.Theresponsealsogivesinformationaboutthetemperaturedifferencebetweentheheatcarrierfluidandthesurroundinggroundcausedbytheheattransfer,i.e.,thethermalresistanceoftheboreholeheatexchanger.

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Figure1Thermalresponsetestsetup.

Severalanalyticalandnumericalmethodsareusedfortheevaluationofresponsetesttemperaturedata.Thedifferentmodelsrequiresomewhatdifferentsetsofinputdata.Variousanalyticalmethodsforevaluationofboreholeresponsetestdataarediscussedbelow.

EvaluationMethods

Anumberofmethodshavebeenappliedovertheyearsforthesimulationofboreholeheatexchangerperformance.Bothanalyticalandnumericalmodelshavebeenusedandreportedinseveralpapers,reports,andbooks.Here,thefocusisonmodelsfortheevaluationofthermalresponsetestdatafordetermininggroundthermalconductivityandevaluationoftheefficiencyoftheboreholeheatexchanger.

Thethermalresponsetestmethodisbasedontheso-calledsingleprobemethodfordeterminingthethermalconductivityofsolidmaterialsinalaboratoryenvironment（StalhaneandPyk1931）.Initialanalyseswerebasedontheline-sourceapproximation,whichdoesnotconsiderthethermalpropertiesoftheprobematerial.In1954,Blackwellpresentedananalyticalsolutionincludingboththeprobematerialandapossiblecontactresistanceattheprobesurface.Inprinciple,thismethodmakesitpossibletoshortenthemeasurementperiods,especiallyforlargeprobediameters.Attemptstodetermineboththermalconductivityanddiffusivitysimultaneouslybytakingthecontactresistanceintoaccountwerenotsuccessful（Blackwell1954;Becketal.1956）.Thedeterminationofthethermaldiffusivitywasfoundtobeverysensitivetothecontactresistance.Sundberg（1988）developedadetailedFEMmodeloftheprobeinordertoshortenthemeasurementperiod.Hefoundthatboththermalconductivityanddiffusivitywereheavilyinfluencedduringtheinitialtimeperiodbysmallchangesintheprobeproperties.

Analyticalmodels,suchastheline-sourceandcylinder-sourcetheories,requireseveralsimplifyingassumptionsregardingthegeometryoftheboreholeandheatexchangerpipes.Forthepurposeofthethermalresponsetestevaluation,theheatflowtoorfromtheboreholemayberepresentedasaninfinitelylongheatsourceorsinkinthegroundwithnegligibleinfluenceofheatflowsinadirectionalongtheboreholeaxis.Inthegroundoutsidetheboreholeitiscommonpracticetoassumethatthethermalprocessdependsonlyontheradialdistancefromtheboreholeaxis.Theone-ortwo-dimensionalheatflowprocessfromthecirculatingfluidtotheboreholewallisassumedtoberepresentedbyathermalresistancethatcharacterizesthetemperaturelossbetweenheatcarrierfluidandboreholewall.Somemodelsalsoincludethethermalmassofthematerialsintheborehole.

IngersollandPlass（1948）appliedtheline-sourcemodeltothedesignofgroundloopheatexchangers.Mogensen（1983）proposedtouseaboreholesimilartotheprobetoestimatethegroundthermalconductivityfromanexperimentalfieldtest.ThismethodisnowcommonlyusedforthermalresponsetestevaluationinEurope.

ThecylindersourceapproachmodelsthegroundloopheatexchangerasacylinderbyintroducinganequivalentdiametertorepresentthetwopipesofasingleU-pipeheatexchangerasasinglecoaxialpipe.CarslawandJaeger（1959）developedanalyticalsolutionswithvaryingboundaryconditionsforregionsboundedbycylindergeometry.DeermanandKavanaugh（1991）andKavanaughandRafferty（1997）describetheuseofthecylinder-sourcemodelindesigninggroundloopheatexchangers.Theeffectivethermalconductivity（anddiffusivity）ofthegroundformationiscomputedbyreversingtheprocessusedtocalculatethelengthofthegroundloopheatexchanger.Basedonashort-termin-situtest,themeasuredeffectivethermalresistanceofthegroundofadailyheatpulseisfittedtoavaluecomputedfromadimensionlesscylinder-sourcefunctionbyvaryingthethermalconductivityanddiffusivityoftheground.

Numericalmodelscanbedesignedtohandledetailedrepresentationsoftheboreholegeometryandthermalpropertiesofthefluid,pipe,boreholefilling,andground,aswellasvaryingheattransferrates.Themoreextensivesetofrequiredinputdataoftenmakethesemodelsmoredifficultandtime-consumingtousethantheanalyticalmethods,whichsometimesmaybeimplementedassimplespreadsheetapplications.

Berberichetal.（1994）describearesponsetesttypeofmeasurementingroundwater-filledductsinwater-saturatedclaystonewheretemperaturesensorswereplacedalongtheboreholewall.Themeasureddatawereanalyzedwithbothananalyticalline-sourcemodelandanumericaltwo-dimensionalfinitedifferencemodelusingparameterestimationwithgroundthermalconductivityandvolumetricheatcapacityasvariables.Thenumericalmodelcalculatestheheatflowsinboththeverticalandtheradialdirectionsforaboreholeoffinitelength.Theresultsfromthenumericalanalysesresultedin5%lowerthermalconductivityvaluesthantheanalyticalresults.Berberichetal.（1994）attributethisdifferencetoendeffectsofthefinite-lengthborehole,i.e.,increasedheattransfernearthetopandbottomoftheborehole.

ShonderandBeck（1999）developedaparameter-estimation-basedmethod,whichisusedincombinationwithaone-dimensionalnumericalmodel.Thismodelissimilartoacylinder-sourcerepresentationinthatitrepresentsthetwopipesoftheU-tubeasasinglecylinder.However,itaddstwomorefeatures-athinfilmthataddsaresistancewithoutheatcapacityandalayerofgrout,whichmayhaveathermalconductivityandheatcapacitydifferentfromthesurroundingsoil.Thismodelaccommodatestime-varyingheatinput.

Atransienttwo-dimensionalnumericalfinitevolumemodelinpolarcoordinatesforresponsetestevaluationisreportedinAustin（1998）andAustinetal.（2000）.ThegeometryofthecircularU-tubepipesisapproximatedby"pie-sectors,"overwhichaconstantfluxisassumed.TheconvectionresistanceduetotheheattransferfluidflowinsidetheU-tubesisaccountedforbyusingfluidpropertiesthroughanadjustmentontheconductivityofthepipewallmaterial.AthoroughdescriptionofthenumericalmodelisfoundinYavuzturketal.（1999）.Themodelhassincebeenimprovedbyintroducingaboundary-fittedgridsystemthatismoreflexibleandbetterrepresentstheU-tubepipegeometry（Spitleretal.2000）.Themodeliscomparedwiththeline-sourceandcylinder-sourcemodelsinAustin（1998）.

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TABLE1

SummaryofRequiredInputtotheFourAnalysisModels

Smith（1999）