i nationaladvisorycommiitee foraeronautics · 1 i.:. nationaladvisorycommiitee foraeronautics...
TRANSCRIPT
1
i
.:
.
NATIONALADVISORYCOMMIITEEFORAERONAUTICS
TECHNICAL NOTE 4383
A COOLED -GAS PYROMETER FOR USE INHIGH-
TEMPEWTURE GAS STREAMS
By LloydN. Krause,RobertC.Johnson,
andGeorgeE.Glawe
LewisFlightPropulsionLaboratoryCleveland,Ohio
Washington
September1958
https://ntrs.nasa.gov/search.jsp?R=19930085276 2020-03-19T06:17:33+00:00Z
99-.*i .’...--ADDENDUM
NACATECH&X ;~
By LloydN.tiausejRobert
*--
4383
C.Johnson,andGeorgeE.Glawe
September1958
Thelogarithmicftmctiononthelefthandsideofequation(14)(whichisalsotheordinateforthecorrelationcurveof fig.8) isap-plicableto theinternalheat-transferprocessinwhichthegasis inequilibriumandthespecificheatisessenttdlyconstant.However,ifthespecificheatofthegaschangesappreciablyduringtheprocessofcoolingintheprobe,itisnecessarytotreattheprocessonthebasisof enthalpydifferencesinsteadoftemperaturedifferences.Suchisthecase,forexample,whenthemeasurementismadeina dissociatedgas.
Iftheenthalpyofthegasat station2 canbe determinedfYomknowledgeof itscompositionandtemperature,andiftheenthalpyofthegasatwallt~peratureTw isconstantalongthetubewall,thetexmsinthelogarithmicfunctioncanbe replacedby enthalpytermssothatthecorrelationfunctionbeccmes
()
Ho - Hw‘H2-HW
where
Ho stagnationenthalpy
H2 enthalpyofthegasattemperatureT2
Hw enthalpyofthegasat tubewalltemperature~
Thustheinstrmnentisusedtodeterminetotalstresmenthalpy,andthetotaltemperaturemaythenbe determinedfromenthal.pytables.
Therelationbetweenenthalwandtemperatureforvariousgasesinequilibriumisgiveninreference6 and,inaddition,references8, 9,and10.
8.Huff,VearlN.,Gordon,Sanford,andMorrell,VirginiaE.: GeneralMethodandThermodynamicTablesforComputationofEquilibriumCom-positionandTemperatureofChemicalReactions.NACARep.1037,1951. (SupersedesNACATN’s2U3 and2161.)
IssuedSeptember12,1960page1 of 2.pages
. .
9.Hall,EldonW.,andWeber,RichardJ.: TablesandChartsforThermo-dynamicCalculationsEmolvingAirsndFuelsContainingBoron,Cs.r-bon,Hydrogen,andOxygen.NACARM E56B27,1956. ,
10.Moeckel,W.E.jandWeston,KennethC.: CompositionandThermodynamicPropertiesofAirinChemicalEquilibrium.NACATN 4265,1958.
IssuedSeptember1.2,1960page2 of 2 pages NASA-LandeyFfdf,Va.
TECHLIBRARYKAFB,NM
“
lmllullMlllllNATIONALADvIsm CmMrmEEI?cRAEROIIMII?ICS ClOb?l&ll
A COOLEZ)-GASFYR(M.ETERF’CRWE II HIm—TEMmWKmGM S2REAMS
ByLloydN.~ause,RobertC.Johnson,
SUMMARY
An immersion-typepyrometerisdescribed
andGeorgeE. Gkwe
thatutilizesthecon-trolledcool= of a continuouslyaspiratedsmzpleof thegaswhosetem-perat~ istobemeasured.Thegasiscooledasitisdrmn througha ttie,afterwhichitsteqeratureismeasuredwitha thezmmcouple.Free-stresmtotsltemperatureisthenobtainedby a relationinvolvinginternelheattransferinthetxibe,gasproperties,endcertainreaddlymeasuredtemperaturesandpressures.A tecbmiqueisdescribedwherebycalibrationconstsntsoblxlnedin siratnearroamtotaltemperatureareusedto computethehigh-temperaturecorrelationsforotiergaseswithknownpropertyvelues.
~rimental cmqmrisonin a high-tqeraturegasstreamw5.thther-mcoqle probesandwitha pneumatic-pzmbepyrometershowedagreemntwithin2 percentof total_rature inthersmge2000°to 400@ R.
Thermocoupleprobesarethemostccmmn Immersion-typesensingelementsusedtomeawrethetemperatureofhigh-velocityg-es. Theselectionoftheproperthermocoupledesignfora givenapplicationpri-marilyinvolvesccmqmomisesbetweenaccuracyendstructuralconsider-tions. As thetqeraturesndvelocityof thegasstresmareincreased,itbecomesnmredifficulttomeetthereqpi~ tsofmeasurementtswiththermocoupleprobes.In fact,msmyqplicationsexceedthelimitsofthermocoupledesigns,evenwheredeliberateuseismadeofcontrolledcoolingof thethermco@e $unction(refs.1 and2). ~erefore,adefiniteneedexistsforothertypesof -don parameters.Twoex-sqplesof suchtypesarethepneumaticprobe(refs.3 and4)andthecooled-tubepyrometer(ref.2).
Thecmled-gaspyzmneterreportedhereinintroducesanotherqproach;namely,thecontrolledcooldmgof thegasbeforetakinga teqera,turemeasurementwitha thermcoqLe. TMs Is accomplishedby draxdngthe .-
2
hotgasthrougha tubewithcooledwalls.Thelossinh reflectedby a dropIngastemperature.~The smuntaturedropsisa functionoftheflowwithinthetube,
NACATN 43834
energyofthegasthatthetemper- ““ “----gaapropertiesj ‘- -
tubegeon&my,endtubeWSXLtemperature.Therefore,”IftheteqeratureofthegasIsmeasuredafterithasbeencooled,endthegastqeraturedropcm be calculated,thenthefree-streamgastotaltemperaturecanbe determined.
Thisreportpresentsthetheoryoftiecooled-gaspyrometerslongwithe~erimentslresultsobtainedinbothrmm- andhigh-temperaturegasstreams.Room-temperaturecorrelationsweremadeina tdsl-pressurerangefrcm0.1to 2.5atmospheres~.High-temperaturemeasure-mentsrangedfrom20000to 4000°R withtotalpressurefrom0.8to1.S -atmmspheres.AllmesaurementswereatmibsoticstremMachnunibers.Thisworkispertoftheresesrchprogrsminhigh-temperaturemeasure:--mentsbeingconductedattheNACALewislaboratory.
Considersketch:
.—.-
.
!l?maRY .-J
ConvectiveHeatTremferina TUbe #-
an element oflengthof a lnibbe,s8*.pwninthefol&whg ~=
1 t-’ .-
Gas flOW ~
tTw
(All syibolsaredefinedinappendixA.) ..- ._
Sincetheheatlostby thegas is eq@l to the heattransferredtothewall,
..----.——
h(% - ~)dx = - + Gcp~ (1)
If (Tb- ~) isrepresentedby theexpressionK(T- ~), where K and~ areas-d Constsmt,then @i!b= K ~-, ande~UL3tiOn(1) csn be ‘
..—-a
statedasfoUows:b
EACATH4563t
.
ItSkrto?l
;&=.*
wlllbeLwmluawet,overaMlulted Reymld8mnberrange,theMmiberc-be ~eed 88MJ-oWO:
me vlacoal*
f%ledaa(~+
()-’4’’=’+In Ref tibaaedon filmtempamtureT#. ThePm3ndtlDlmiberi.aassuuwd
(3)
Tf,WinchIsda-tobecomtantmer
thefihn-tempaz+urerangewltldnthetd3e.Sinceboththecross-sectionalemisaoftheinibeemdthemass-flowratewltldnthetaibemConatarlt, theRaymldanul?txmWlthlnthetlibeVarleaonlybecal16eoftalewlacosi~. &e ~ mdber Ref wlthlnth tr&canbeex-presseaaa
M
39
q - theI!31ibecdpt& ()factorf Ref= ~
IntheStantonnumberbeceaseof--d flowmd theeffectoftubecurvature.
c refemtothelocetdoll
equehlon(3)is imtmduced
ofto
Itwillbe aasmedthat
(4)
(5)
andifequatlom(3),(4),and(5)aremibstltutadInegpation(2),theresultla
Since
T.TO at x= o
T.TC at X=2
(6)
WA TN 43834
endaSS_
theintegrelformof eqyation(6)becomes
(7)
with ~=a - e where161ismuchsmellerthanla].Sincethe~andtlnmbervariesonlyslightlyformostgases,itisdifficultto estsb-lishthepowerof thePrandtlnmber ineqp.ation(7)by anycalibrationtechnique.Reference5 ina similarsituationsuggestsa valueof 2/3for b. Thisvslueof b wLllbe assaed-,forthisinvestigation.
---
In eqpationaturesInvolve&,
where ~ isenviscosityof airiousgasesfora800°to 2300°R.
(7)itwillbe assuredthatovertherangeoftemper-theviscosi@ IL canbe expressedas
(8)
arbitrsryreferenceviscositythatischosenastheat1000°R. Figure1 giyesthevalueof a forvar-rengeofveluesof ~ overa teqeraturerange*Themaximumabsoluteerrorinthevalueof (v/&)al
betwe~t tabibztedinreference6 end._&atc~culatedby ~ &e-cedlngequationis3 percent.
Theuseofthisrelationtoetim &/Kc)al ~ equation(7)yields
—.——
NACA!l?R4303c
5
.
u.)
3
Thesolutionof equation(9)is
()
‘o-%‘T=-%=
.ej /+ln(l+~)=$ c
~23 R+JJ#
wherethe approximationassumesI~[muchlessthan1, end
E+ @(e* - 1) -(+@)@@-‘)=
+ )-$ @e*
+E (lo)
.
ApplicationofTheorytoProbeDesign
Theterm E inequation(lo)accountsfortheeffectsofthevari*tioningsatiscosityalongthetti fortheca8e ~ > ~. This term
cm be controlledto someextentbyprobedesign,becauseitsmsgnitudeisinfluencedby geomtry. It canslsobe seenthat,forthecssewhereTo approaches~, theviscosityvariationisnegligibleand E becomeszero.In my case E mqybe treatedsaa comectionfactor,andthe-r~ com~ationpm=ters em relatedby
O
%-% c‘i~-a23 ~1
(U)Rec
Figure2 isa schematicdisgramof a cooled-gaspyrwleter.Thegasis&awn intotheprobeat station1 andIscooledwhilepassingthroughtheinsidetubewhosewall.temperatureIsessentiallyconstant.At sta-tion2 thegashasbeencooledsufficientlytoobtsdna messUrementoftemperature(T2)witha [email protected] taperedbodyisattachedto thethermocoupleshaftendactsasa flownozzlewhosemintiwareaistheflowpasssgebetweenthebodyandthetubewsU at station3. Thepressuredownstreamof thissection(meas-uredby pressuretap P4) must be sufficientlylowtomaintaincriticalflowthroughthenozzle.
——
...—
6 WA TN45631
Thecorrelation equation shows that It is mmessary to evalude
Reynoldsnmher Rec titlletubeandgas-rature KC=etalm?asur- .
ingstationx = Z. Sttiion2 (fig.2)rerpssents-s measq stktion in the probe. The Reynoldsmmibercsnbe
where D2 istbhside dlemteroftheinmr
expressed as.:
(12)
tub, W2 is thetiscos- !eityof gas at T2,end & 1st@mass-flow-~teofth6gastithetube. .B!
Theream-flowrate~ is determinedbythefallowingrelationforCriticalflowtbrou@e mmle :
c#3P2imB—
T T2
where yend Mmevduatedhum flowareaofthemzsle.
Forthemke ofs~ theReyml@ miberComQation,itcmbe assmedthatthetotal-pressuredI’OPb * tllbeis - (p2“ po)Jd -~tk of Cd is* mcess~ s-e Cd is b t~ a -t-ofReynolds*r. [email protected],ezdCombhingegpations(n),(12),end(US),the%orking”equsrtiomoftheprobe
where
b
h
. -
--
.-. .
(see ncmgrsm, *. 3) with ~ the arbitr=y reference viscosity,tekenasviscosityof-r atlCXXl”R, endwith RJ ~J M, end T evaluatedatT2.
.
Fora givenprobedesign,theconstantendthequtity ~ meybe wevel.uatedby calibratingtheprobewithair* nearrum teqperalmreif .—
HACATH4383* 7
9
.
log
IE@xnst
thecurvelrllldetenujmetha
theterm(cxP#). Thec~-Ofthevskeof B?txttezuper-- aeteminedfora gh?nprobe,
vaheof q sadtheinterceptwllllbeStsntisthencalculatedWithlmowledgeatureT2. After ~ sultheconstamttheprobecanthenbe usedforhigh-tcqwraturemsamrementsofothergasesifthegasproper@valuesm -.
a factorgssesin
Correctim tenu g is Ueflned in equation (lo)emufncluaesa whichisdefinedinequation(8) tad evsil.wtedforcertdnfigure1. Ibr a probeqpllcation,
pal‘2-%%
()
V2
T
()
%-%Y“b ~
ThecorrectiontemE ispresent&lasafbctiOnof a,p,~ * infigure4.
Otherfactorsthathavenotbeencqlicltl.yincludedineqwtion(14)andthatwillintroducedeviationsfor the case (~ * TJ m:
(1) Critical-flov areaofthenozzle~ willdecreaseasthe&peredinsertisheated.
.-
(2)fmm gas
(3)
l!?AcAm4365?
The Tz tem onthe~t side& -@-gpdiau(14)wIU deviatebulktesqperaturebecmueofa teqe~a@reprofYle. m-
._ .- =
TheIndicatedteqerature K(!2
tlon error.
(4)TheViscoeity~ lldJJ.notbeerrorIn T2.
villbelowbecaueeofaradle+
equalto p= because of the.:
Hawmsr,forthepro’kdesignhereinrepmte@eudfortherqngeoftests,thesefactorswereofsmallmagnitudeorof.8cencdlingnature,60thatequation(14)representeda goodqpmdmski_m.Fm@mmre ~thesede-viations~ oftenineignificentc~d to_theunceriSntiesh the --ledge ofgaspropertiesforhigh-teqerature~icat~. .“
AppendixB presentsan endlyeisof thesedeviationsendincludestams thatcan& -led toeqmtim (14)@_ correctfor them, and as-e cekul.ation IS pm’esexltedh 4W* ..- I .
KEmRATm
A detaileddrawingofthecooled-gas~ter is shown in figure
5. Thepyrtxweterconsistsof-e concent~c-8, thelargesttubehavingenoutside‘dimeter ofl/2inch.Thehotgaspassesthro@ th6-l/4-inchtube;cooldngwaterpassesthroughthetwoannull.Wt waterispassednexttothel/4-inchtzibetominiiEzetheeffectof extei5u31heat received by the outside Wbe. Spacing -@, sham In section A-A,twelocsrtedintheennulitaensureunifomcrosssectionsintheregionofthebend.Theinletnozzleismachinedfrm Inconelendhelierc.weldedinplace;Thethermcowpleinserth~d centers~ Junctionaswellasaervlngasa flm mzzle. !l%ecritical.-flousectionisa 13qu&inscribedina circle,chosen.becauseoftheeeaeincantroUlnndimn-SIOEM. A pressure tep locatiddownptreemOXthe*IIIKJCOUPI.8mnibrs.the presameatthedownetremu.sideofthec_fitical-flowsectionandaho actbasa total-pressuretq whenthee@m3tim isshutoff.!lkeeprobeswerebuiltandtestedtodet~ thereprodwibilityof thisdeBign.
High-temperatureevaluationtestswem perfomed- thehlgh-teqerat~ water-cooledtunneldescribedh reference2. Twotypekof-the”mcoupleprobesendonepnematicteqeratureprobewereused,8sCoaupariscm@dmumedt3“ OneprobeQpe was-aham--, croisflaw,-platinm-rhodims,@atimnuthemmmuplewithawater-cooled~.Radlatim,conduction,[email protected] US* met@@saudvaluesfmm referencesI&r&d intibibliographyof reference2.‘-~.o~r [email protected] eonic-aspimtedplatimm-rhodlm-@at* t- ~ describedinreference7..-
i.<
. --..—
..—...- -,-
--.-
● ✍✎
-T.
.._ . 4
..- .-
----—
. --- _
. . . ---. ..-
—-=
—
,...._
* *— . .:_
“-●
.
NAC!ATN 4363●
Thepneumaticprobes erat~ intherangeexclusivelyinthersage
9
wasprimsri3yof Importanceinobtsiningtotal._ thatofthethermocouples.Itwasusedfrom36000to4W0°R. ThisprobeutiUzedthe
designsadoperationcriteriaandn&hodsofcomputationpresentedinreferente 4.
In operatingrangeswheresllthreecomparisonprobescouldbe usedtoobtaintotaltemperature,agreemmttowithin1.5percentof themeantemperatureof thethreeinstrumentswaaobtained.
Todeterminetheconstantsintheworkingequation(eq.(14)],room-temperaturetestswereperfomd in a ~-inch-diametervariable-density
tunnel.Becauseof therelativelysmalldlfferencesbetweentotal,in-dicated,andwater-coolsnttemperaturesintheroan-temperaturetests,differentialtemperaturemeasurementsinsteadof *solutemeasurementsweremade. Thetemperature-differenceterms(T.- Tw)~ (T2- ~)appearinginthetemperaturecorrelationwerethusobt~ed d3rectly.
HmCEmRE Am REmLls
PreuminaxyTests
In theprocessof &velophg thecooled-gaapyrometer,severalpre-liminarytestswereperformedtoverifyassumptionsandb fhd theeffectsofvsryingdesignandoperattonslfactors.Thesetestsandtheresultsobtainederadiscussedinthissection.
Axial.locationof thermocouple.- ConsiderationsoftherelationbetweenT2 andgeepropertiesindicatedthatitisdesirdblethat T2be large,sothektheuncertaintyinknowledgeofpropertyveluesbe--comeslessimportant.However,atlargevaluesof T2,radiationerrorsassociatedwiththethermocouplemustbe considered.Therefore,a ccm-pramisemustbemadein selectingthedistancef?xmtheinletto station2. Fortherangeof conditionsandprobedesign(fig.5)hereinreported,a fixedlocationof ~ tfiedimetersfromtheinletwaschosenas acompromise.Theaxialtemperatureprofilealongthecenterl.lneofthetubewasmeasuredby movingthethermocoupleinsert.FY.guxe6(a)showstheresultof a *ical testofthistypeendinMcatesthesensitivityto Sxielpositioning.
Radisllocationof thernmcouple.- At emaxislpositionof 60diam-etersfromtheinlet,thethermocoupleJunctionwasdisplacedradiallyfromthecenterline.Theresultsntradisltemperatureprofileinthetubeisshowninfigure6(b).
10 MUX TN 4383
Choiceof temperat~measurementt torepresent~ in correlation~arqueter.-As presentedintheory,~ isthetemperitmreoftheInnerwallofthecenterl/4-inch-diemetertube..Assumingthatthetentper---aturedropecrossthewdl ofthettieisWgligible,itIsreaaoneblethat ~ cenbe representedbymeasurementof coolenttemperature.Aseriesoftestswasthereforeperformdinthehigh-temperaturerange,andmeasurementsweremadeof cooling-waterinletandoutlettemperatureandoftenqeratureriseintheironerandoutercoollngannuli.Thesetestsindicatidthatthecoolsnt_rature riseintheinnerpassegewassmallandcouldbe neglectedforcorrelationpurposes;thus,coolant-inlettemperature~ couldbe usedtorepresent~.
Inoneoftheabove-nentionedteststhenomml coolant-flowratewasdecreasedasmuchaspossiblewithoutdameghgtheprobe.Thecool=tinletteqeratqreweafixed,andthecoolanttemperaturerisethroughtheprobeincreasedby a factorofthree.Duringthistimethetberm-coupleinsertmeasurementT2 remainedcozistent,thu establishingthefactthat,evenunderthemostmarginalcoolsntflaws,Tw wm.zldrepre-sent ~ asa correlationparemeter. --
Effectof aspirationrate.- & pretiazsl.yindicated,thisprobedepenti_onsapirationforitsoperation@ Includesa critical-flowsectionatstation3 (fig.2). ~is designfeaturewas~orporated“forconvenienceindetermidngthemass-flawrateandtheReynoldsnuniberintheInnertaibe.It alsoconvenientlycontrolstheflowinthethe sothatthecorrelationisindependentof ~-stresm Machnumber.Thisisadwantsgeousbecauseinmany@cations onlyapproximatevsluesof-flowconditions- 3mowm.
Theresultpof a testto establish@e effectof aspirationrateonthethermocoupleinsertIndicationarepresentedinfigure6(c).Apressureratioof srpproxhately0.5isrequiredtomahrktncriticalfluwatthenozzleportionofthethermocouplei~ert. It is seenfromthef@e thatatleastthiscriticalpre~s,ureratioshouldbemain-”tained-acrosstheprobeto ensurea constantprobeindication.
An interestingresultisthatwiththeaspirationshutoff,thethermocoupleT2 wiU indicate‘+. Thisleadsto a simplenmdeofoperation when using the probe in a hot gaa; that is) with the aspira-tionoff,thethemnocouplein8ertwillyieldcooltng-watertemperature~ endthe p4 tapwillmeasuretotalpressurePo. Then,tithaspira-tionon,a measurementof T2 ~ completethemeasurementsrequiredtoobtaintotaltemperature.No independentmeasurementsof cooling-watertemperatureo;[email protected] probeb thismanner.These@larksendsupersonicstreams,whereforthesu@isonictotalpressurebehindthenormalshockformedby
if time isavsilzbleb~= tibothsubsonicca8e P
Lwouldbe the
thepro .
n
*
l!cm-- .—
-.:e-
,.—.. .
—
-..—
. ...—. .._
——
..._*--—b
NACATN 4383 u●
Pressuredropin Inibe. - To verifytheassumptionofnegligiblepressuredropwithinthel/4-inchtube,testswereperfomedatbothambient-sadhigh-temperaturecondttlonswitha total-pressuretubere-placingtheth~couple insert.Withthesensingendofthetotal-pressuretnibelocatedetthenormelaxialposition of the thermocouplejunction, a constant total-pressme loss of 4 percent of strem totalpI’eSSUr&WSS obtained. Because of the fact that the percentage pressure&rop was constsnt, a correlation Reynoldsnuniber evshated at station 2(fig.2)wasbasedon PO insteadof P2. Thissimplifiedtheprobedesign and operation in that it was not necessq to have an internaltotal-pressure measurementt at station2.
cooling-water flow rate. - Figure7 presentsvariationofwater-flowratewithvsrlationofwaterpressuredropacrosstheprobe.About1.6 gallons per minute are passed ktth a pressuredropof 50 poundsperSquexeinch.
Final~StS
Usingtheresultsobt&ned- theprelimtrm?ytests,a cooled-gaspyrometerwaetestedatbothsmbkntendhigh-eratures withthethermocouple@nctionlocated80taibediam=tersdownstreamoftheprobeentrance.Room-taqeraturemeaaurementsweremadela a totel-pressurersagefrom0.1to 2.5atmospheres.High-temperaturemeasurementsrsngedfrcm200@ to 400@ R withthetoteLpressurerangingfrom0.8to1.5atmospheres.Free-streamMachnumbersforallmessuz%mentsweresub-sonicandrangedfrom0.1to1.0.
Thecorrelationfortheffialprobeconfigurationis shwwnInfig-ure8,withtheabscissaplottedbothintermsofReynoldstier andintermsofparametersInworkingequation(14)thatareproportionaltoReynoldsnuniber.
Bothroom-andhigh-temperaturetestsareincludedin figure8,with 35percentofthe118data@nts inthe200@ to 400@ R range. .Forconvenience,twostrmt lines,computedby themethodof leastsquares,havebeendrawnthroughthedata,withequslweightassignedtobothroom-andhigh-temperaturepoints.Thedatafedlwithina bandof& percentin (To- ~), theprobableerrorof a singleobservationbeingQ percent.Theslopeof tiemdn portionof thecurveis -O.348;~ove a Reynoldsmmiberof 27,000theslopeis -0.160.ThersmgeofReynoldsnwnberscovered- test- thecooled-gas”pyrometerisnotccau-pleteenoughto establishtheslapeatluwerReynoldsnuuibers,butitisresaondbleto assumethattheslope~ chmgewhenflowinsidethet*e iscaurpletdylsmi.nsr.Therefore,theextrapolationof figure8 tolowerReynoldsnumbersis questionablebecauseof theuncertaintyof thetrsmsitiontolminarflow.
.—
12 NACATN 4383●
Twootherpyrometers,madefromthessmedrawingasthatof figure5,wereslsotested.Theresultssxepresentedasthedashedlinesof .
figure8. Althoughthecorrelationcurvesofthethreeprobessresti-ihr inshapead intheirprobableerrors,theslows areslightlydif-ferentandthecurvessredisplacedby amoUntsup to15percentof(TO- TW). Geometryfactorsthatmayproducethesedifferencesare~
—
follows.:
(1)Differencesintubedfameterj
(2)Variationintubedismetersndcross-sectionalshape
(3)Differencesinsizeandshapeofnozzleportionof thermocoupleinsert
(4)VaryingsurfaceroughnessinsideLube .—
Fromtheseconsiderationsitwouldbe&ifficultifnot@racticslto controlthefabricationto thepointwherebe obtainedbetweenprobes.Therefore,itiscorrelationcurveby individualcalibration.
CONCLUDINGREMARKB
A pyrometerwhoseprincipleof operation
reproducibleres~tswouldadvisabletoobtainthe —
h
isbasedonmeasurements —ofthe;ontroUedcooli~of abeendescribedandevsluated.locsltemperaturemeasurementsthermocouples.
continuouslyaspiratedssmpleofgashasSuchaninstrumentisofuseinmskhgabovethem:uslrsngeattributedto
—
Probecorrelationcurvesobtainedfrombothroom-temperatureandhigh-temperatureevaluationsshowedagreemEntwithink2percent,whichwasthessmeastheorderof accuracyofthehigh-temperaturecomparisoninstrumentsusedtoestablishstresmtotsLtemperature.
Theoperationoftheprobeisrelativ_+lys~le, andthecorrela-tionisindependentoffree-stresmMachnu@er. However,theaccuracy
—
dependsdtrectlyontheknowledgeof gasproperties,andtheprobemustinitiallybe calibrated.In applicationswherethegaspropertiesarenotknownaccuratelyenoughto establishaccepts.bleabsolutemeasure-ments,theinstrumentsmaystiIlbe usedfortemperatureprofilemeasurements.
LewisFlightPropulsionLaboratoryNationslAdtisoryCommitteefor
Clevelsmd,Ohio,August8,Aeronsut$cs1958
x
.
NACATN 4383*
A
c!
D
G
h
z4
M
Ii
P
B
P
R
Re
Rec
Ref
St
T
Tb
. Tc
. Tf
APPENDIXA
SYMBOLS
cross-sectionslflowarea
a constant
dischargecoefficient
specificheatatconstantpressure
insidedismeterof aspiratedtube
mass-flowrateperunitarea
convectiveheat-transfer
axialdistsmcefromtube
molecularweight
mass-flowrate
totslpressure
Prsmdtlnumber
staticpressure
universalgasconstant
Reynoldsnumber
internslReynoldsnumber
internal.Reynoldsnumber
Stantonnumber
totalgastemperatureM
coefficient
inlettomeasuringstation
withviscosityevaluatedat T=
tithviscosityevaluatedat Tf
centerof tubeat anyaxislpositionx
gasbulktemperatureintube
gastemperatureticenterof
T+TWgasfh temperature,2
tubeatmeasuringstationx = Z
14
TW
%
TO
7?~
x
T
w
Pc
IJf
&
P2
NACATN 4383
temperatureof inletcoolingwater
temperatureof insidetubewall
totslgastemperatureoffreestrewn
gastemperatureincenteroftubeasindicatedby thermocoupleinsertedatmeasuringstation2
axialdistancefromtubeentrance
ratioof specificheats
viscosity
viscosityevaluatedat Tc
viscosityevslluatedat Tf
referenceviscosity(airatlWX1°R)
viscosityevsluatedat T2
Probestationnotation:
o freestresm
1 ttieentr=ce
2 Lnternalmeasuringstation
3 critice3-flowsection
4 pressure-tapposition
—.
——
.,-1+
-E
8
.
.
15% NACATN 4383
APPENDIXB
A
In
FACTORSCONTRIBUTINGTODEVINFIONSNOT
EXPLICITJ21WORKINGEQUATION
morerigorousstatementofequation(14)wouldbe
The
Tc whenjunction
RadiationEffect
indicatedthermocoupletemperatureT2 willnotbe equsltoT2 > ~ becauseof a radiationlossfranthethermocoupletothecoldwsll.s.A radiationcorrectionfactoren canbe
definedsuchthatJ.L
Tc = T,(1+ ~) (B2)
ViscosityEffect
TheviscosityKc atthemeasuringstationshouldbe evshatedatthecorrectedtemperatureTc fiste~of at T,. me visco~itYcomec-tionfactore~ willbe definedsothat
v== I@ + Q (B3)
Temperature-ProfileEffect
ThetemperatureTc willnotrepresentbulktemperature~ whena temperatureprofileexistsinthetube;therefore,a relationforthesetwotermsmustbe established.~US, =b wX12.be definedsothat
Whenthetaperedbodythecriticsl-flowarea,hot
~ = Tc(l- @ (,A)
Nozzle-AreaEffect
thatformsthecriticsl-flowareaisheated,~ wil.lbe lessthanthecritical-flow
area cold
% canbeA3C;therelationdefinedsothat
NACATN 4383
between=eas andthiscorrectionfactor
A3C—=1+6=‘m
Total Corrections
(B5)
Iftheprecedingcorrectionsaresubstitutedinequation(M), snd—the msgnifmd&Of ~, Ev) Gb> ~d en are assumedtobemuch-lessthan1,theresultis
In()
‘o-% .Cxpr‘2 - ‘w
-2/3[f,M,,j-~(*~ x
EvaluationofCorrectionFactors
(B6)
Radiation.- Theradiationcorrectionfora spike-typethermocoupleisapproxtiatelyone-third greater thanthatfor a bare-wire crossflowprobe:
wherethegasis air.
Fortheprobedesignhereinreported,theMachrnnnberNM inthettieisabout0.2,thewiredismeterd is0.020inch,andtheaveragee?nittsnce~/IA oftheChromel-Alumelwirecanbe takenas0.75. b-bn
troducingthesevsluesintoequation(B?),
()2.82~0.0087 ‘2—.
% & 10004.()]Tw
1- % (B8)
.
%8;
.-
—
where ‘o is in atmospheres.
NACATN 4383 17b
- ForfulLydevelopedturbulentflow,reference8. =%”~”expressionfortherelationbetweenbulktenmer-
simre C% sadthetemperatureinthecenterofthetabe Tc: “
(B9)
Substitutingthisequationintoequation(B4)ad solvingfor ~ give
%- Tw=om18T 2-%eb = 0.18~c ‘2
(B1O)
whenwhen
Nozzleexpansion.- Therelationforthecriticsl-flowarea A=thetaperedplugis atelevatedtemperatureT2 andthearea A=theplugis atthecold-wallt~erature ~ isgivenby
A==A4-25@-)(T2-Tw~ (Bll)
where b isthecoefficientoflinearexpansionOrtheplugmaterisl.Substitutingequation(B1l.)into
(A2% ‘26 G-
equation(B5)yields
)1 (T2- q) (B12)
viscosity.- Sincetheviscositiesofmostgasesarefunctionsofthegastemperatureto qproximatelythe0.7 power,EW msybe expressedas
= 0.7‘P % (B13)
.
NACATN 4383
JwPENmxc
SAMEILECALCULATIONS
As anexample,assumethata temperaturein a flowsystemusinghigh-temperaturetir.
measurementistobe madeThecorrelationcurvefor
theprobetobe usedwi.11be representedby thelowercurveof figure8.Thiscurvecsmbe identifiedby twostraightlines,overtherangeofReynoldsnurbersshown,sothat
—
—RangeI Range11 k
Re2 6,000-27,00027,000-60,030
% 0.348 0.160
Intercept 1.57 1.045
Constat 1.24 ().825
wherethevalueof theconstant(eq.(14))isfoundfrom d
c = Interceptx Pr2/3
withthecorrelationgasPrandtlnuniberbeing0.7.
Theprimarymeasurementstskenwiththeprobewillbe assumedtobeasfollows:
P.= 1.5atm
% = 520°R
T2= 1620°R
ThepropertyvaluesofthegasattemperatureT2 are
T = 1.34
Pr= 0.70
M=29
P2= 0.815X10-6lb-sec/sqft
MACATN 4383 19+
Thefollowingcorrelationparameterssrethenevaluated:.
f(M,y)fromnomogrm(fi$.3).. . . . . . . . . . . . . . . . . . 3.6I.@r.... o........ . . . . . . . . . . . . . . . . .. 1.36
where Vr is a referenceviscosity(tirat1000°R). Therefore,
Thisquantityisthewhichcorrespondstothat
= 3.13
vslueoftheabscissaforthecurve(fig.8)rangeof thecurvewhere
% = 0.348
c = 1.24
slopeisequalto ~, andtheconstantC istheprobecon-theworkingequation(14)sothat
()‘o - ‘w [1‘2/3x f(,,r)-al
‘~=cxfi
-%
% (1.24)(0.7)-2/3(3.6)-0”3&(,.3;%i’’0”3*
= 1.055
Therefore,
()TO-TW =287r% “To- 2.87(1620- 520)+ 520
= 3680°R.A morerigorousrelationforcalculatingTO appearsin appendix
. B, inwhichseverslfactorssreaddedtoequation(14)andappearascorrectionfactorsineqution(B6).
20 NACATN 43834
Evaluationofthesetermsasappliedtothesamplecaseis ssfol-lows: Fromequation(B8), L
= 0.0277
From(B1O),
‘b-0*’8t’2:~:20)
= 0.122
From(B12),
en = 2(7.0KIO-’)(2.75- 1)(1620- 520)
= 0.027
From(B13),
- 0.7‘v %
s (().7)(0.()277)
Fromfigure1,
By definition,
a= 1.69KL0-4
_ 1620- 520
(1.36)0”3&
* I.loo1.113
NACATK 4383+
Therefore,.
c@= o.m7
g= 1.055
previouslyevsluatedfromthegeneralworkingfromfigure4,
equation(14).Therefore,
E= -0.024
Substitutingthecalculatedvaluesinequation(B6)~elds
.
. Therefore,
()‘o-%ln~= L055{1.00}+0.041- 0.024
= 1.072
To-% 292
— =.
‘2 - ‘w
To= 2.92(1620- 520)+ 520
= 3730°R
Therefore,forthegivenssmplecomputationthedifferencebetweena solutionusingequation(14)sndoneusingequation(I?6)wouldbe 1.3percent.Thisdifferenceof1.3percent,hawever,shouldnotbe tskento implya smsllmsgnitudeinthetotslcorrectionforsll.cases.Ingeneral,thesignificanttermsinthecorrectionfactirswillbe thelasttwotermsinequation(B6).
1.Matton,G.,sndFou&, C.: ThermoelectricProbesforMeasuringHighTemperaturesin(MsStreams:Theirapplicationto theStudyofFlamesStabilizedbyObstacles.SixthSymposium(International)onCodmstion,ReinholdPub.Corp.,1956,pp.757-763.
22 NACATN 4383
2.Warshawsky,1.: PyrometryofHighVelocityGases.SixthSymposium(International)onCombustion,ReinholdPub.Corp.,1956,pp.739-750.
3.Baker,DwightI.: MixtureRatiosandTemperatureSurveysofAmruonia-OxygenRocketMotorCombustionChsmbers.JetProp., vol.25,no.5,W 1955,>p. 217-226.
4.Simmons,FrederickS.,sndGlawe,GeorgeE.: TheoryandDesignof aPneumaticTemperatureProbemd ExperimentalResultsObtainedin aHigh-TemperatureGasStresm.NACATN 3893,1957.
5.McAdsms,WilliamH.: HeatTrsmstission.Thirded.,McGraw-HillBookCo., Inc., 1954,eqs.9-10b,p. 23-9.
6.Hilsenrath,Joseph,et al.: TablesofThermalPropertiesofGases.Cir.564,NBS,Nov.1, 1955.
7.Glssre,GeorgeE.: AH@h TemperatureCombinationSonicAspiratedThermocoupleandTotslPressureProbe.JetProp.,vol.27,no.5,May1957,~. 543-544.
8.Eckert,E.R. G.: IntroductiontotheTransferofHeatandMass.McGrsw-Hi31BookCo.,Inc.,1950.
.
.:.—
——
——
.
.
.
NACATN 43%3
.
.
. ——. .—
3.2
2.8
2.4C!02.02
2.0 Atc—
g}
1.6 %—
/
1.2“/
d
.8/
.4- f
0 .1 .2 .al
Figure1.- Vmiationof a with al forseveral@ses.
()A&%!+a.AT”
Station
Gas?Gi-
, 1
1
Waterout
Waterh
I2
}
Figure2. - Schematicdiagmm of ccwled-gaspyrometer.
I+
To low-pressureSUp-@y
!3sm’ . *
NACATN 4383
60
50
40
.
.
30
20
15
10
98
7
6
5
4
2
M f(M,T)
6.0
5.0
4.0
3.5
3.0
2.5
$2.0
1.5
-
.9
.8
Figure3.- I’bnogrsmforflmction
——
——
——
—
—
—
—
—
—
—
—
—
— 1.7
—1.6——1.5——1.4
—1.3—
—1.2—
—1.1
—
—1.0
mleculsx weight and ratio of specificheats.
: 0 I I I I 1 I I I 1 1 I
;0.02 I I I.04 I / I I I
.d..02— .1* —. . =!=!=== ~
la“..14
.16
-.c&.1A
.6 .7 .8 .9 1.0 1.1 1.2 1.3EEEEl
1.4 1.5
. I
()-HFl@me 4. - Varktlonofccmwct.lonfactor E with cormktica prmnt..s.
I
14N
l-la)c
Normal LXatlon
1000 of thernmouple\
900
m
700ti 13 14 15 16 17 18 19
Axial distanm of thermocouplefrommet of ttie,h.
1 I I I I I60 65 80 85
Length-%neter m~io, l/D
(a)Variationof axial.locationof thermocouple.Totaltemperature,2730°R; totalpreasm, 1.16atmospheres.
Figure6. - Vmiat ion of probetidicationwith changeh axialorradiallocatIonof thermocoupleor asptiationrate. Watertqer-ature,- R.
.
. , s t
1
NACATN 4383●
m24
.
29
.
Location
800-of“till
I(* — — ~ I- 4
700 I
6oo-“0 .02 .04 .06 .08 .10 .l.zRadialdistanceofthermocouplefromcenteroftube,3n.
(b)Variationofradiallocationofthermocouple.Totaltemperature,28500R; totalpressure,0.94atmosphere.
Figure6. - Continued.Variationofprobeindicationtithchangeinaxialorradiallocationofthermocoupleoras-pirationrate. kktertemperature,5000R.
m~ - - 0- — ~
800 / I/
700 /I I
600 / I/
500
mI !
300 I [
4Criticalpressure
1.0 .9 .8 .7 .6 .5 .4 .3 .2Pressureratioacrossprobe,p~PO
(c)Variationofaspirationrate.Totaltemperature,30700R;totalpressure,1.11atmospheres.
Figure6. - concluded.VariationofprobeindlcationwithchangeinaxialorradialIocationofthermocoupleoraspirationrate.Watertemperature,50@ R. .
.
NAC!ATN4383
1.6
i 1.2>al A.
$f .8 Fg$~
.43
0 10 20 30 40 50Waterpressuredropacrossprobe,lb/sqin.
Figure7. - Variationof water-flowrate withwaterpressuredropacrossprobe.
I.7
.61 2 4 6
..
\\
M lE 20
I I I I I I4 6 e 10 1s
I I I I20 2s so 40 50 6 @
Reymld6 tier, Re2
FiEIZM a. . Correlaklon curve.
* ‘1 r , SsW