1、?.t+4 *.* ?wpfid ; i -=%NATIONALADVISORYCOMMITTEEFORAERONAUTICSTECHNICALNOTENo. 1451AN INVESTIGATION OF AIRCRAFT HEATERSXXVII-DISTRIBUTIONOF HEAT-TRANSFER RATEINTHE ENTRANCE. SECTION OF A CIRCULAR TUBEBy L.M. K. Boelter, G.Young,andH.w. IversenU+versity of California .=q-JlWashington jldy 1948 ._FOR
2、 bFENCEProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-IwrIoNALADVISORYCOMMITCEEFORAEROMMJTICSTECHNICALNYI!ENo;1451 31176013460432ANINVESTIWTIONOFAIRCRAFTHEATERSXXVII- D3!RmIONOFEXATJIX/ANSFERRATEINByL.= ENTRANCESECTIONOFA CIRCUIARTUBEM.K.Boelter,G.Y
3、oungendH.W.IversenSUM4ARYExperimentaldataonthevariationofthepointunitthermalconductanceintheentrancesectionofa circulartubearepresentedfor .16differentflowconditionsoftheenteringair.Resultsarecomparedwithvaluescalculatedfromexistinganalyticalsolutions.Theaverage(integratedman withlength)unitthermalc
4、onductanceIsslsocslculat%dforeightentering-airconditionsendfscoaredwithvaluesresultingfromsnal.yticalluhhods.h msnycasestheexperimentalvaluesareappreciablyhigherthanthosederivedfromecnzationswhiaharebasedonover-aid.dat-n onlongpipes.INTRODUCTIONThepresentinvestigationwasconductedtodeterminethedistri
5、butionofheat-transferrateresultingfroma variationoftheunitthermalconductanceattheentrancetoa tubeforvariouscondltionsofthe enteringfluid.Heretoforeexperimentaldatafortheunitthermalconductancefc( (intheequationq =fcA - ta) havebeenobtafnedasenaverageoverthstubelength.Equationsforthedeterminationof fc
6、 haveusuallybeenexpressedintermsofthefluidpropertiesandsom fixedphysicaldimensionofthesystem, .suchasthetubedi- ter.Inmanycases,when. itismoreimportanttohow thevalueofthetemperatureattheparticularpointalongtheheat-transfersurfacethantolnlowtheove rateofheattransfer,anaveragevalueoftheunitthermalcond
7、uctancefc isin-. adequate-endal valuef mustbedetermined.Theequationsforxtheunitthermalconductanceshouldthenbeexpressedintem ofavariablephysicaldimensionx.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-,:. .=,: -.-2 -HACATNNoo1451.Dataonthelocalunitc
8、onductancemaybeappliedtothedesignof-anexhaueasandalrheatexchanger.Forexample,thelifeofanexhaust-gasandairheatexchangermaydendonthedistributlonoftemperaturewlthlntheunit,whichdepnxlsonthevariationofthelocalunit conductancewithintheexchanger.Pointsofhightemperaturemayoftencausenwtalfailure,andregionso
9、flargetemperaturegradientscausedmgemnm thermalstresswhtchdecreasesthelifeoftheheater.A thoroughlnmwledgeofthedistributlonofthelocalorpointunitthermalconductancef wouldallowapredictlonoftheseeffects,andCxthusa properdesigncouldbeestablished.Theresultsofexperimentsreportedhereinshowthatthe f in,1 Cxth
10、e“entrsncesection ofa heatedcirculartubeIsverymuchgreaterthsnthatwhichwouldbepredictedfromequationsderivedfromexperimentsonverylongtubesenddependsonthetypeoffluidentrance.Theunitthermalconductancemaynotreacha constantvalueasfaras15 tubediamtersdownstream. =2 Thefollowingentranceconditions(fig.1)were
11、lnvestigated: .-(a)(b)()(d)(e)(f)($3)(h)(f)(J)(k)(1)(m)(n)(0)(P)BellnnuthBeltiuthtithonescreen3Bellmmthwithscreenholder .Bell.muthwithsixscreens Right-angle-edgeentranceBaxesharp-edgeentranceLarge-orificeentranceSmall-orificeentranceShortcalmlngsectionLOngcslmingsection45-cn.e-bendentrance90-ane-ben
12、dentrsnce90-$n$-bendentrancewithcalmingsection.45round-bendentrance90round-bendentrance180round-bendentrancelIntlrlspaperthe“entrancesection”16theinitialportionofthetubeInwhichthelocalunitthermalconductancefc isapproachingthecon-%stantvalueattaineddownstreaminthetube. .?orsmothpipeendconstanttubesur
13、facetemperature. .%versen(reference1)obtainedexperimentaldataforthiscaseandcomparedtheresultswiththeanalysesofLatzkoandofBoelter,Martlnelli,andassociates.-. . =. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Theresultsoftests(a)to(d)illustratetheef
14、fectsofturbulencesndtests(a),(1),and(J)showtheeffectsofentrancevelocitydistribution.Theremainderofthetestsshowtheeffectofthevariousnnrepracticaltentranceconditions,inwhicheddyingflow ispresent.Latzko(reference2)developedanalytical=thcdeforapproximatingthevsriatlonof the pointunitthermal.conductancef
15、orthreeentering-g- contions:CaseI: Bothvelocityandtemperaturedistributionsareuniformoverthecrosssectionattheentrance.(Thisisapproximatelytheactualsystimofaheatingsectionwithabellmmthattheentrance.)CaseII: Thevelocltydistributionatthsentrancecorrespondstothatforfullydevelopedturbulentflow,andthetempe
16、raturedistributionisuniformoverthecrosssectionattheentrance.(Theactualsystemmaybevisualizedasaheatingsectionwitha longcalmingsectionupstream.)CaseIII: TheintermediatecasebetweencasesI andII,inwhichthecaladngsectionofcaseIIistooshortforthefluidtohaveattaineda fullydevelopedvelocftydistributionbeforee
17、nteringtheheatingsection.(SeeappendixA fordescriptionofanalytical methods.)A mthodnotedinreference3approximatesthevexlationofthepointunitthermalconductanceforairforeaseI. Anexpressionforestimatingtheintegratedaverageunitthemmzlconductanceforanylengthofheatingsecttoneisalsodevelopedinreference3.= add
18、itiontothepointunitthermalconductance,theaverageunitthermal.conductanceforthecirculartubewerecalculatedasa functionoftubelengthforeightexperimmtelconditions(fig.15casesasbg,h,i,J,k,md 2). Fortwooftheseconditfonatheaverageunitthermalconductenzeawereanalyticallyobtainedbyusingtheequationsfor fCxgivenb
19、yLatzko,byBoelterandhisassociates,andbyIversen.Theaversgeunitthermalconductance,themmn valuetakenovertheentirelengthoftubeinquestion,isobtainedfromthefollowingequationzf 1. =- faxCav Zo Cx. Theeffectoftheenterinwhereaseddyingflowisconsideredtobethatcharac-terizedbyrelativelylargescalevortices,etc.Pr
20、ovided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.-=-4 l?ACATNHo.1451 “” .ThisworkwascomiuctedattheUniversityofCaliforniaunderthgsponsorsh,lpaniiwiththefinancialassistanceoftheNationalAdvisoryCommitteeforAeronautics. .Tineauthorswishtoextendtheirgratitu
21、detoItoMr.H.R.Poeland,whoconstructedtheheatexchanger;toMr.A.G.Guibert,whotranslatedtheGermanarticlebyH.Latzlm;andtoMessrs.C.H.Kilpatrlck,F.E.Maddocks,M.?4.Rubesfn,E.Barron,H.B.Fletcher,G.T.Dibble,andA.P.HuntingtonfortheiraidInobtainirigdata.A greatportionofthedatareportedhereinwasobtainedbytheJunior
22、authorsaspartoftheirfulfillmentoftherequirementsforthedegreeofmasterof -scienoeInmechanicalTh9apparatus1se*ineering.DESCRIPTIONOFAPPARATUSessentiallya doublysteea+jacketedtubethroughwhichairiowsandisheated.Me saturatedstathusitiscalledthe“no-load”heatlossendwasusedasa correctiontothe“load;values.The
23、n-loadvaluewasabout10percentoftheloadvaluesThe 19 glass condensate collector tubes were Installedbetweenadouble-glass-partition chsmber. This actedasb insulatingJackettoreducetheno-loadheatlosses.outsideoftheglasspanelsa sheetofpaperruledtotenthsof inchwasplacedinordertomeasurethswaterlevelinthetube
24、s.Thedownstreamendofthetestpipe was connectedWItha M-inch-longrubbertubebywayofa gatevalvetoa 3-inchpipeleadingtoa calibratedorificesectdonandthencetotheintakeofa centrifugalblowerwhichexhaustedtheairtotheatnnsphere.Therateofairflowwaeregulatedbytheblowerspeedandbyans ofthegatevalve.Entering+irtempe
25、ratureswereobtainedbymesnsoftwolaboratorythermometersanda thernmcouple,allsuspendedintheairneartheentrance.Thesurfacetemperaturesof the testsectionwereobtainedbymeansofthermocouplesWbeddedinslotsmadeinthepipe.Thedownstreamoutlet-airtemperaturewasobtainedbymwansofa thermocoupleinthe3fnchpipeandwasarr
26、angedfortraversingthecrosssectionofthestream.Theequipmentwasoperatedwiththevariousentranceappsratuattachedtotheupstreamendof thetestsection;forinstance,abellmouthnozzlewasusedtoobtaina conditionofuniformvelocitydistributionandwirescreenswereusedtoobtaingreaterturbulenceintheairstream. Schematicdiagr
27、smsofalltheentranceeffectsareshowninfigure1. Asshowninfigure5, the shortandlongcalmingsections,aswellasthetwoelbows,aremadeofpipeshatingthessmeinsidedimter (1.78s in. ) es the test pipe. The shortcalmingsectionis5 inches long ( 1A = 2.8) end thelongcalmingsectionis20incheslong(Z% =11.2).Thelegsofbot
28、hthe45 and90elbows=e about2 incheslongmeasuredalongthecentrelaxis.Thediametersofthetwoorificesexe1.04and1.41inches,respectively.Theroundbendshaveslightlysmallerimidedimters thauthetestpipe,butthedownstreamendsarechamferedtagivea snmo+fitwiththetastpipe.Provided by IHSNot for ResaleNo reproduction or
29、 networking permitted without license from IHS-,-,-6 .NACATNNo.1451 DESORIXTIONOFI!ESTIN3PROCEDURX .=Whenf;teematatnnspheric pressurewasadmittedtotheapparatusata lowflowrate(soadJustedthata strongwispofsteamcontinuouslydischargedfromthelasttestsectfontotheatmosphere),thesectionswerepurgedofairbythep
30、assageofthesteamthroughthemandbythesteamflowthroughtheglasstubewhenthecorksatthebottomswereremoved.kL8 soonasequilibriumtemperatureswereestablishedthroughout,alltemperCLtZUWSandallno-loadcondensatelevelsintheglasstubeswererecordedat,lwhereasthe f at A of 15.40Cxand 16.50 am disregarded because of th
31、e influence, ontheflowcondition,oftherubberhoeeconnecterprotrudingintothebackendofthetestpipe.Asidefromthesepoints,theexperimentaldataindicatea regularvarationof fCx dJngthOpipelengthforthedifferententrcecondftionsc . .CALCULATIONSEromthedatacollected,thefollowingitemswerecalculated:thehatgainedbyth
32、eairslxeamateachsection,thetemperatureriseoftheairstream,andfinallythelocalunitthermalconductanceateachsection.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATNNo.1451Forsczneoftheentrancecotitions(a,b,g,h,i,#,k,andZinfig.theaven%geunitthermalco
33、nduotance asa funotionofpipelengthwasalsocalculated.Theheatgainedbytheairstresmateachsectionisequaltotheproductoftheheatofvaporizationofwaterandthedifferencebetween71),heloadrateofcondensationandthen-loadrateofcondensation.TheneloadrateofcondensationvariedwiththeheightofthecondensatelevelintheKlaast
34、ubes.Itwasa linearvariation,however,andsothearithmeticavrageno-loadvaluesbetweentheinitilevellevelofthecondensateswereused.Thustheheattransferd thefinaltotheairS-treelnwhereload,levelsfromeachsectionwasqa ( )=Ah Rav-R:avVapIh5anglebend,90anglebend,90eaglebendwitha lorlhl -In fie 30, the fotiowkg ent
35、renceccnditicmsarecctheunitthezmalcozductcnceofincreasingthe .degreecftmbulencebyadditionofscreensianoible.4. Or.lyormidealsystemofturbulentflowincirculartubeshasbeensuccessfullyanalyzed.Forcase1,inwhichthevelooity andtemperaturedistributtonsareuniformattheentrante.thenointunltthe )=0.625ReO”(“-o.15
36、10x -2.844x_o 40- +o.o#e”25%rc =0.0384 “x o. -o.1510x -2.8Uxo.873ebO*25$.0,- q )inP(A2)where B“ isthetem inpmentheseatieqpation(A2).themlal Comblct-moe foav could beobtatidIntenuaof 1,the tube length measumd frm theleading edge. :%IProvided by IHSNot for ResaleNo reproduction or networking permitted
37、 without license from IHS-,-,-18( )(a) For Y 0.686 or ( ) $ =0.625Re0”25%.-.“f 1 z.%N=- 1.IJ fc (0.686)A”275$+ fc - cav w“%(cm1+ 0.144Ref )0.25= (A4) . -2Iversen(reference1)wassuccessfulinsimpliingtheccmrplexequationsgivenbyLatzko,andpresentedthefoXlawing.equation8forthevariationofthepointunitthenne
38、.1oonduota.nceintheentrancesect.ion withinitiallyunifomnvelooityandtemperaturedistributions.(a) For Re/4% ,.,r -_,. -.-.-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATNNo.1451Fortheaverageunitthermalconductancefora length1,hegave:(a) For Re 1/
39、4%f =fc( )1+ 0.128Re0”25Cav a z(A7)(A8)Themthod ofMartinellf (reference 3) presents an approximatemethodof solving case I by postulating that the fluid flow along the.entrance section is similsr to that along a flat plate until the boundarylayer builds up to the radius of the pipe. Thushe gives f r
40、air flowing?turbulently in the entrance section the followlng equations for the pointtit thermal conductance.(a) For 4.4%4 T0.3G0.8f = 5.4(10)Cx m%(A9)(A1O)ilBeinningwithpartXVIIIofthisseries,theexponentof T(and TfYandtheconstsntsintheseequationshavebeenslmpllfied.Provided by IHSNot for ResaleNo rep
41、roduction or networking permitted without license from IHS-,-,-.,.-20 .- NAOATNNO. 1451 .-Andfortheaverageunitthermalconductanceasa functIonoflength, -(a) For.-2 (-5)tlmfollowlng may be used%fc =f( )1 + O 067lle0”25av %“ 1Case IIIFor case III Latzko offers the following apprcmhmte graphl cal mthcd.
42、First the point uuittherml conductance at the particular Re of the problemiscalculatdasIfItwwreforcaseI,andthenthecalculationisrepeatedasifitwereforcaHeII.Bothcurmsforthepintunitthermalconductanceeralaidoutatadiaticeof x apart,equaltothedistancebetweenthebeginniwof the calming eectlon aud the heatin
43、g 8ection, uifor case II. “enmJ.op3” of * two cU,tveS WOWthe fc calculated for case I ahead Of thatxbe the solutionfortheirstapproximation.n)PProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-22Forexample,IfCx II.I X()r-%fcx . caseI- case case111.,1- t
44、-x)+46J%tube-wallbmperature,Fairtemperature,Fmfxed-mmnairtemperatureatmixedsnairtemperatureat-section,%weightrateoftluid,lbentrance,F QanyparticularU stance from entranceof tube, ftdistance into fluid streammeasuredfromthe tubewall, f t .specfftcweightofflufd,lb/cuftthfcknessof boundaryhyer, ftabsol
45、ute viscosityoffluid,(lb)(see)/sqftkinematicviscosityoffluid,sqftsecdi?mmsfonlessratioofdistanceg()massdensityoffluid,(lb)(sec2)ft4functiondefinedinappendixA()fc%Nusseltnumber T-.-_.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ItAcA NO. 1451Re.Pr
46、Prendtlnuniber(3600:0,)25Reynoldenumber( H %T = 3600pg)a71a15Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-26.- .NACATNNo.1451REFERENCES1. Iversen,H.W.: VariationofthePointUnttThermlConductanceonEntrancetoTubesfora FluidFlowingTurbulently.M.S. Thes
47、is,univ. of Cslir.,1943.2. Latzka,H.: HeatTransrinaNACATM No. 1068, 1944.3* Boelter,L.M.K.,Dennlson,H.TurbulentLiquidorGasStream.G.,Guibert,A.G.,endMorrin,E.H.:An Inve8tigation,ofAircrafHeaters.formmceof a Fluted-TypExhaustGasARR,lfarch194.3.4. Boelter,L. M. K.,Martinelli,R. C.,theAnalogybetweenHeat
48、l%ansferandx - edPer-andAirHeatExchanger.NACAandJonassen,F.: RemarksonMomentu.mTramfer. Trans.A.S.M.E., io1. 63, JUIY 1941, pp.447-455.3* Prandtl,L.: TheMechanicsofViscousFluids.Vol.IIIofAero-dynamicTheory,div.G,W. F.Durand,cd.,JuliusSpringer(Berlin),1935.5. McAdams,WilliamH.: HeatTransmission.Secondcd.,McGraw+?illBookCo.,Inc.,1942,PP.168, 171.-.-.-!.-.a71 -.Provid
