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U3l-=’
——
FORAERONAUTICS
-ia
CALORIMETRIC
TECHNICALNOTE2838
DETERMINATIONOF CONSTANT-PRESSURE
.—
SPECIFIC
HEATSOF CARBONDIOXIDEAT ELEVATED
PRESSURESANDTEMPERATURES
By Virgil E. Schrock
Universityof Caltiornia
-
WashingtonDecember1952
....-+ .. .._ . ----- . .
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..
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1Cbrl LlnnAn 1n-l--s . ,~,
Iu!ulllllllllll!nllnljUb5132J
NATIONALADVISORYCOMMITTEEFORAERONAUTICS
TECHNICALNOTE2838
CALORIMETRICDETERMINATIONOFCONSTANT-PRESSURESPECIFIC .
HEATSOFCARBONDIOXIDEATELEVATED
PRESSURESANDTmmRmmEsByVirgilE. Schrock
. SUMMARY
Theconstant-pressurespecificheatof carbondioxidehasbeenmeasuredovertherangeofpressures,andtemperaturesfromambientcondi-tionsto1000poundspersquareinchgageand1000°F usinga steady-flowcalorimeteroperatingonanopencycle.Itappearsthattheappa-ratusasusedinthisdeterminationwillyieldvalueswitha probableerrorof0.5percentatthehighesttemperaturelevelconsidered.Theresultsofthesetestscheckthewidelyacceptedspectroscopicdatawithin1 percent.Thevaluesatelevatedpressuresareinreasonableagreementwiththosederivedfromthezero-pressurespectroscopicvaluesand
but
theapplicationoftheBeattie-Brid&maneqyationof st@e.
Onlyverylimitedcalorimetricdataareavailableintheliteraturesubstantialagreementexistswiththoseconsideredreliable.
INTRODUCTION
ThepresentinvestigationwasconductedattheUniversityofCaliforniaunderthesponsorshipandwiththefinancialassistanceoftheNationalAdvisoryCommitteeforAeronautics.
ObjectiveandScopeofInvestigation
Inthepresentresearchprogramtheuseofa steady-flowcalorimeterforthemeasurementof specificheats”ofgasesathightemperaturesandpressureshasbeeninvestigatedto determinethevalidityandlimita-tionsofthemethod.Thepurposeofthisreportistopresenttheresultsoftestsmadeon carbondioxideintherangefromambientconditionsupto1000poundspersquareinchand1000°F. Forthesetestsa calorti-eterbuiltof Inconelandoriginallydesignedtooperatewitha closed
.
.-. ———.—— ———— — --- ———-- — ——...———— --
2 NACATN 283
cyclewasused,butbecauseofdifficultiesinmetering,pumping,andregulatingtheflowitwaselectedto operatewithan opencycle.Certainlya closedcyclewouldhavesomeadvantageinthatitwouldallowlongerrunsata singlecondition.It seemedadvisabletomaketestsusingtheopencyclebeforeexpendinganygreateffortin solvingproblemsconnectedwiththeclosedcyclethatwerenotassociatedwiththeformer.
Of considmableimportancetotheengineersrethespecificheatsoftheconstituentsoftheproductsofcombustion.Becausecarbondioxideisa prominentconstituentinmostcombustiongasesitwasselectedforthesetests.Otherfactorsinfluencingtheselectionofthisgaswere: (a)Itsspecificheatisaffectedto greatextentbypressure,whichappesredtobe desirableforthepurposesoftheinves-tigation,(b)itis quiteinert,and(c)itisavailableatlowcostandhigh
Theas:
(1)
(2)
(3)
(4)
purity.
MethodsforDeterminingSpecificHeats
methodsofobtainingspecificheatsof gasesmaybe classified
Directmeasurement
Determinationofratio 7 = c-p/cv ●
DeterminationofJoule-Thomsoncoefficients ,
Spectroscopicmeasurements
directmeasurementoftheconstant-volumespecificheatofgasesusinga nonflowcalorimeterisimpracticalbecauseofthehighcapacityofthecontainingvesselcomparedwiththegascontained.Thiswasusedonlybyveryearlyexperimenters.Themeasurementoftheconstant-pressurespecificheatusinga flowcalorimetercan,however,bemadewitha highdegreeofprecision.
Themethodsof determiningtheratioof specificheatsby themeasurementofthespeedof soundorthereversibleadiabaticexpansionmethodhavedefiniteshortcomings.E&h requireaccuratepressure,volume, andtemperaturerelationsoranappropriateequationof stateforthegas. ConsiderforandNewtonshowedthatthe
examplethevelocity-of-soundmethod.Maxwelllocalacousticveloci@is
a=E=E(1)
●
NACATN2838 3
where k isthebulkmodulusofthegasand p isthemassdensity.LaplaceandPoissonsuggestedthatthesoundcompressionwaveisisentropic,hence,
pvy= Constant= c
and
k=- <)b~ isentropic
.()=(-v)= =7p~7+1
then
(2)
(3)
andfora perfectgas
a= E7 (4)
Theperfect-gaslawdoesnotapplyfortherealgasexceptatzeropressuresothetrueequationof statemustbe knowninordertoputequation(3) intermsofthetemperature.Thatis, p, v, and T datamustbe availablefromwhich p maybe determinedfrommeasurementsofpressureandtemperature.
Whenthevalueof 7 fromthemeasurementoftheacousticveloci~hasbeenobtained,thespecificheatsmaybe determinedfromthethermo-dynamicidentities,usingtheappropriateequationof state.Forexample,
% 00ap NJ-Cv= ~v--p
andtherefore
(H)apavCV=(7:1)’12%V%P
(5)
(6)
—.—— .—— — _ . _ —-——— .- ——
4 NACATN 2833
Knowingthevalueof 7 thespecificheatsmaybe determinedifthederivatescanbe evaluated.Notehowever,thevalue 7 - 1 willbesmallerthan 7 andthereforethevalueof specificheatwillbe less ~accuratethanthevalueof 7 measured.Sincethespecific-heatdataobtainedinthisindirectmannerrequiretheuseofanequationofstateintwowaysandtheresultsarelessaccuratethanthevalueof 7obtained,itisprobablyoflessimportancethantheothermethods.
High-pressurespecificheatsmaybe determinedfromJoule-Thomsonmeasurementsifthezero-pressuredataareavailable.Thepressure-temperaturerelationshipisdeterminedby allowingthegasto expandadiabaticallywithoutdoingworkandwithnochangeinkineticenergy.Dataobtainedarelinesofconstantenthalpyona temperature-presmreplot. Theconstant-pressurespecificheatisgivenby
Cp = ()&@p
orfora smalltemperatureinterval
fromwhichitisevidentthatthespecificheatsatvariouspressuresareproportionalto the AT spacingoftheconstantenthalpylinesandmaybe calculatedfrom AT betweenthesametwoenthalpylinesandtheknow valuesof Cp atzeroPressure.
.Thedifficultiesinvolvedinthismeasurementarethemaintenance
ofadiabaticconditionsandprecisemeasurementofthetemperature.Ityieldsthepressureeffectbutisnotdirectlya measureofthespecificheat.A numberofauthors(references1 to 3) haveusedthismethodwithsuccess.
Thevaluesobtainedspectroscopicallyarethezero-pressureconstant-volumespecificheats.Sincegasesobeytheperfect-gaslawatzeropres-suretheconstant-pressurevaluescanbe obtainedby addingthegascon-stant.Specificheatscalculatedfromspectroscopicdataassumingasimpleoscillatorarespecificheatsmaybedynamicidentitiesas
consideredaccurateto0.5 percent.High-pressureobtainedfromthespectroscopicdataandthethermo-follows(reference4):
(7)
—.———.
NACATN 2838
and
whereagainthe
Cp-cv=
equationof stateGay(reference5)havecalculated
(8)
mustbe known.Ellenwood,Kulik,andthehigh-pressurevaluesof specific
heatsforeightcomon gasesu8ingthespectroscopicdataofJohnston(reference6) andtheBeattie-Bridgemanequationof state(reference7).
At presenttheBeattie-Bridgemanequationisbeingusedinan extra-polatedform(references5 and8). Theconstantsgivenby theauthorsofreference7 wereevaluatedfromtheavailabledataon carbondioxideinthetemperaturerangefrom-lm” to 430° F. All ofthesedataweredeterminedintheperiodfrom1869to 1903exceptthoseatlessthan1 atmospherewhichwereobtainedimx6. The equationtiththecon-stantspresentedby theauthorschecksthedatawithanaveragedevia-tionof0.2percent.Themaximumdeviationforcarbondioxidefo&d intheirtableofcomparisonvalue~was1.3 percentwhichoccursnearthecriticalpoint.
Useofthesecondderivativesofthe13eattie-Bridgemanequationprobablyplacesconsiderablestrainonitsaccuracy,andcertainlyitsextrapolationtotemperaturesof 4000°F is somewhatquestionable.Crown(reference8) statesthatthechiefjustificationof sucha pro-cedure,apartfromtheabsenceof a betterone)iSthegood%mementexistingintherangewhereexperimentaldatadoexistfora largenwnberofgasesevenapproachingthecriticalcon~tionsorliquefaction.Thereisan obviousneedformoreextensivepressure,volumejandtemperaturedata.
An abundanceofempiricalequationsareavailableintheliterature(referencesgto 14). Theseequationsarebaseduponthespectroscopicdata.Heckgivestabularthermodmc properties,inengineeringunits,fromthespectroscopicdata(reference15).
Thedirectmeasurementofspecificheats’has,inthepast,beenseriouslylimitedinrangebecauseoftheinabilityofavailablemate-rialsofconstruction.tosustainhighstressat”hightemperatures.Inrecentyearsmetallurgicaladvanceshavebeenmadeto a pointwheresustainedstressesup toabout10,~0poundspersquareincharenowpossibleat2000°F,makinga high-temperaturehigh-pressurecalorimeterfeasible.Sincetheonlyextensivespecific-heatvaluesavailableintherecentliterature,thespectroscopicvalues,areessentiallyindi-rectlymeasured,thereseemsa needforconfirmationby directmeasurement.
_.— .—...— —.——_.— —— —.—
Y
R
a
k
P
P’
v
T
Tm
P
c
w
v
Q
Qnet
t
A
specificheat
meanvslueof
specificheat
specificheat
gasconstant,
\
SYMBOLS
atconstantpressure,Btu/(lb)(%)
~, Btu/(lb)(%)
atconstantvolume,Btu/(lb)(%)
ratio,%/%
ft-lb/(lb)(%)
NACATN2838
speedof sound,ft/8ec
hulkmodulus,lb/sqft
massdensity;lbsec2/ftk
weightdensi@,lb/cuft
gravitationalacceleration,ft/sec2
specificvolume,I/pr,CU ft/lb
absolutetemperature,‘R
meantemperature,OF
pressure,lb/sqft
constant,pv7
weightrateofflow,lb/hr
volumetricrateofflow,cuft/min
rateofheataddition,Btu/hr
netheataddedto gas
time,min
precedinganysymboldenotesa changeinthatquantity
heat-tramfercoefficientforradiation,Btu/(hr)(sqft)(%)
enthal~,Btu/lb
.- —
- NACATN2838 7
G emissivity
M molecularweight
%? heatduetoradiation,Btu/br
Fe emissivityfactor
Fa geometricshapefactor
D1,D2 diametersofflowtubeandradiationshield,respectively,ft
DESCRIPTIONOFAPPARATUSANDTESTPROCEDURE
Theprimarycomponentsofthesystemusedinthisinvestigationare(fig.1)thegassupply,theheaterstobringthetemperatureofthegastothetestlevel,thecalorimeter,theaftercooler,andthemeter.Schematicdiagramsandsectionaldrawingsappearinfiguree1 to4.
.
Calorimeter
Thecalorimeterconsistsofa shieldedInconeltubewithl-inchinsidediameterhousinganelectricalheateranddifferentialthermo-coupleswhichareshieldedfromtheheater.Oneradiationshield,madeof sheetInconel,surroundsthetesttubeoveritsentirelength,andacoiloffourZ/k-inchInconeltubessurroundstheshield..Thegasentersthroughthecoiledtubingandpassesbackthroughthetesttube.Thisentireassemblyiscontainedinanevacuatedcasingmadeofa l-footlengthof8-inchInconeltubing.Thecasingvacuumwasproducedby aHy-Vacvacuumpumpratedat0.10micron,thuseliminatingconvectionwithinthecalorimetercasing.A sectionaldrawingofthecalorimeterisshowninfigure2. Detailofthetesttubeisalsoshowninthisdrawing.
Thermocoupleswereattachedto thetesttubeandthecalorimetercasinginorderto determinesteady-stateconditionsandestimateradia-tionlosses.Thecasingofthecalorimeterandtubingleadingto itwerewrappedwithasbestoscloth.Guardheaterswerewrappedasuniformlyaspossibleontheasbestosclothtoeliminateheatlossfromthecalorim-eter.Twolayersofpipeinsulationconsistingof2 inchesofhigh-temperatureand5 inchesof standardinsulationwerethenapplied.
.
—---- ——-——.--——---- -. .———— ---———
,NACATN 2838
TestGas.
Gassupply.-Commercialcarbondioxidewasobtainedin~-pound wcylindersfromthePureCarbonicCo. Purityoftheliguefiedcarbondioxideisclaimedtobe 99.5percentorbetter.Threecylindersweremanifoldedtogethertoconstitutethesupplyreservoir.Eachcylinderwaswrappedwithanelectricalheaterofl-kilowattcapacityandinsulatedwithasbestoscloth.Heatingofthecylinderswasnecessarytoobtainpressuresabove950poundspersquareinchabsolute,.thevaporpressureatroomtemperature,andtomaintainthepressureasthegaswasboiledoff. Tobe effective,theheatingmustbe donemostlyatthelowerportionofthecylinder.
Controlofthegaspressurein thecalorimeterwasaccomplishedbyGrovepressureregulators.Thelinestoandfromtheregulatoraswellasitsbodywerewrappedwitha resistanceheatertopreventtheregulatotmm icing.Theflowwascontrolledbya high-pressurestainless-steelneedlevalve.
Heatingofgas.-Inadditiontotheheatingat therese~oirjthegaswaspassedthrougha 3-inch-diametercoilof20turnsofheavy-wallMoneltubing.Heatingwasprovidedby a forcedprimaryairgasburner.
-
Close-fittingguidesdirectedthehotfluegasesoverthecoiledtubing.Finalheatingandclosecontrolofthegastesttemperaturewereprovidedby a seriesofeightcross-wireelectricalheatershavinga totalcapac-ityof 4 Hlowattsat110volts.Thedesignwaschosensoasto givethemaximumheatingina minimumof space.Theseheaterswerecontrolledby a variableautotransformer.
Thetest-gasheatinginthecalorimet=wasprovidedby an elec- .tricalheater(fig.3)ofthesametypeasthosejustdescribed.
Meteringofgas.-Therateofgasflowwasmeasuredbymeansofa10-cubic-footmeterprover.A watermanometerconnectedto theinlet. tothetankindicatedtheincreaseinpressurenecessaryto overcomethefrictioninthebalanceassemblywasonly0.2to0.3inchofwater.Thiswasconsitiednegligible.
ThehotgaS leavingthecalorimeterwascooledandh~~fied beforebeingpassed.to thevolumetricmeter.Coolingwasaccomplishedby a two-passshellandtube@at exchangercontainingninety-sixl/4-inch-diameterbrasstubes.Watersurroundingthetubeswasusedto coolthegasflowingthroughthetubes.
Humidificationwasnecessarytopreventtheevaporationofthewater.inthevolumetrictank.Thegaswaspassedthroughtwobottlescontainingceramic-beadcolumnpacldng.Onlybubblesofappro-tely 1 centimeter
2B
..
NACATN 2838
indiameteror smallerwereobserved,withno channelingoftheflow.Thegasleavingthehumidifyingbottleswasassumedsaturatedwithwatervapor.
9
Applyingthevolumetricmeasurementtothedeterminationoftheweightrateofflow,thedensityusedwasobtainedfromreference16at1 atmosphereand32°F, thisvaluebeingcorrectedfortemperatureandpressureby theperfect-gaslaw. Thecorrectionis quitesuitableinviewofthesmalldeviationofthemetercon~tionsfromthestandard.Thecalculationisgivenin appendixA.
Instrumentation
Temperaturedetermination.-Theinstrumentationfortemperaturedeterminationwasasfollows:
(a)Thetemperatureriseusedinthecalculationofthespecificheatwasmeasuredby differentialiron-constant-anthermocouplestogetherwitha Whitedoublepotentiometer.Leeds&I?orthrupthermocouplewireandcalibrationslopes(fig.5) wereused.Allthermocoupleswerecheckedatthemeltingpointofpureleadandattheicepoint.ThemaximumvsriationoftheelectromotiveforceofthevariouscoupleswasO.O3Omillivoltatthemeltingpoint,621.6°F. To obtainthetempera-turedifference,thedifferenceinelectromotiveforcewasrecordedwiththetwojunctionsatthesametemperature(fig.6) andagainaftertheadditionofheat.Netelectromotiveforceswerethenusedto calculatethetemperaturedifferential.A Leeds&NorthruptypeR galvanometerswasusedwiththeWhitedoublepotentiometer.Thiscombinationallowedobservationoftheelectromotiveforcewitha precisionof0.5 microvolt.IntermsoftemperaturethisrepresentsapproximatelyO.OIPF. Inorderto insureaccuratemeasurementsofelectromotiveforcetheEppleystandardcell,usedto standardizethepotentiometercurrent,waskeptina thermostaticallycontrolledbathwitha differentialof0.5° F.
Thedifferentialthermocoupleswerearrangedsothattheupstresmthermocouplecouldbe usedto determinethetemperatureofthegasenteringthetestsection.Thesethermocouplesweremountedindouble-boreceramicinsulatorsandcenteredinthetesttube.
(b)Othertemperatfiemeasurementsweremadeusingiron-constantanthermocoupleswitha Leeds&NorthrupModel8662potentimneter.Acommoncoldjunctionwasused;thethermocoupleswereconnectedthrougha selectorswitch.
(c)Thermocoupleleadswerebroughtoutofthehigh-pressurecalorim-eterthrougha sealassembly(fig.4). Eightwireswerebroughtthrougha singleseal.Theleadswerestrungthrougha 2-footlengthof
- .—. ——— ———-— .— -—
10 NACATN2838
l/4-inch-diameterstainless-steeltubinginorderto getthesealaway ‘fromthehigh-temperatureregion.Theinnerlayerof glassinsulationwasleftonthewiresas’theywerepassedthroughtheseal.ThesealwasmadewithSauereisenLiquidPorcelaincement.
Pressuredetermination.-Test-gaspressurewasmeasuredwitha@ad-weightgagetester.A Bourdontypepressuregagewasusedforvisualobservationofthepressurelevel.
Electricalheaterinput.-Heataddedto causea riseintemperatureofthetestgaswasdoneelectricallyby theheateralreadydescribed.Theinputtotheheaterwasmeasuredwitha WestonstandardwattmeterNo.326,havinga precisionof1/750ofthefull-scaledeflection,uniformoverthescalerange.Accuracyis claimedby themanufacturertobe betterthan0.1percentofthefull-scalereading.Supplyvoltagewasregulatedby a voltagestabilizertoeliminatevsriationoftheheating.
#
ExperimentalProcedure
Preparationof systemandpreliminarytests.-As thecalorimeterwasassembledallpartswerecleanedaswellaspossibleusingcarbontetra-chlorideinordertoremoveoiland.dirtleftafterthemachiningopera-tions.Thebindingmaterialontheglassthermocouplewireinsulationwasremovedfromallleadswithinthecalorimeterbyburningitawaywitha smalloxidizingflame.Carewastakentoavoidfusingtheglassinsulation.Thisprocedureleftthewiresinsulatedwithclean,white,andflexibleglassinsulation.
Allsealswerepressure-testedwitha soapsolutionpriortoinsulatingthecalorimeter.A negligibleleakagecouldbe detectedfromthetest-gasheaterleadsealsbutnoneco~d be detectedfromthethermocouplesealsoranyfittingsonthecalorimeterordownstreamfromit.
Thesystemwaspressurizedto1000poundspersqusreinchgageandallowedto standfor24 hours.A lossofonlySOpoundspersquareinch “occurredduringthistime.This’rateofleakageisnegligiblefortheflowsusedandintiewoftestsmentionedabuveitappearsthatthemajorportionofthisoccurredupstreamfromthecalorimeterattheelectricalheaters,wherethegreatestdifficultyineffectinga sealwasencountered.Onlyleakagefromthecalorimeterandpartsdownstreamwouldaffecttheresults.
Preparationfortests.-Theguardcontinuedbringingthecalorimeterand
heaterswereturnedonandheatingtubingleadingto ittothedesired
.
.— .—
..
NACATN 2838
testtemperaturelevelandthensupplyingthemaintainthattemperaturelevel.A periodof
I-1
heatlossnecesssryto24hourswasallowedfor
thisoperation,ontheaverage.Heatingofthereservoircylinderswas
begunabout~ hoursbeforethe”establislunentofthegasflowandwas
continueduntil.apressureof18OOto2000poundspersquareinchgagewasreached.Heatwasthensuppliedtoafterestablistientofflow.
Tests.- Whenthetemperaturelevelthedesiredconditionsthegasflowwas1000poundspersquareinchgagein theadjusteduntilthegasenteredthetest
maintainthereservoirpressure
andresenroirpressurewereatestablishedata pressureofcalorimeter.Heatingwassectionatthetemperatureof
thecalorimeter.Afterobservingthereadingofthedifferentialthermo-coupleforisothermalconditionsatthattemperaturelevelthetest-gasheatingwasstartedandadjustedtoproduceatemperatureriseofthegasof20°to 35° F.
DatawererecordeduntiltheconditionsremainedunchangedforaTeriodofabout20minutes;thusa valueof specificheatwasobtainedata particularteweratureandat1000poundspersqusreinchgage.
. Thepressurewasthenreducedbuttheweightrateofflowmaintainedconstant.Followingthisprocedurethesteady-stateconditionswereaffectedonlyby theinfluenceofpressureuponthespecificheatanda newsteady-statecontitioncouldbe reachedmuchmorerapidlythanthefirst.Inthiswaya seriesofmeasurementswasmadeateachtempera-turelevelandvariouspressures.Inmostcasesdatawereobtainedatfourpressurelevelsateachtemperature.
DISCUSSION
ValidityofResults
Specificheatsobtainedhereinaremeanvaluesfora temperaturerangeof20°to 35° F andwereobtainedfrom
~ _%etP WAT
Thenetheataddedwasobtainedfromthewattagesuppliedandthecalculatedheatlossfromthetestsection.Intwocasesthelossincludeda smallcorrectionduetoa slighttransientcondition.Ithasbeenpointedoutthattheveloci~of soundandspectroscopicmethodshavetheadvantageofyieldinginstantaneousvalues,whereastheflow
..——.— —— —-. —. —
12 NACATN 2833
calorimetergivesa meanovera temperaturerange.Thevaluesobtainedinthisinvestigationarereportedatthearithmeticmeantemperature,whichisequivalenttoassumingthatthespecificheatisa linearfunc-tionofthetemperatureinthatrange.Therateof changeofthespecificheatwithtemperatureovera 20°to 35°F rangeissufficientlyconstantsothatno seriouserrorwilJ-resultfromthisassumption.
An analysisoferror(appendixB) indicatesa maximumerrorof0.42percentanda probableerrorof0.25percent.InviewofotheruncertaintiessuchastheaccuracyofthecorrectionappliedtoheatinputtheresultsareconsideredaccuratetoonlyO.~percent.Themaximumcorrectionappliedwas4.3percentandwasatthemaximumtem-perature,950°F. At the685°F levelthecorrectionwasonly2.0per-cent.Becauseofthedependenceofradiationuponthefourthpoweroftheabsolutetemperaturetheheat-lossuncertaintywouldbecomesignif-icantabove1000°F. Additional.shielding,theuseofa higherflowrate,anda lowertemperaturedifferentialshouldmentsupto2000°F.
PresentationofResults
allowaccuratemeasure-
Theexperimentalvaluesofthespecificheatsareplottedinfig-ures7 to 12asa functionofpressureat eachtemperaturelevelemployedduringthetests.In eachcasethedatahavebeenshownin comparison .
withthoseofEllenwood,Kulik,andGaysincetheirdataarethemostextensiveandprobablythemostreliableto tite.Otherlow-pressure‘data(references17 and18) areinagreementwiththoseofJohnstonetalii(reference6).
Figures13 to 18 sh~ thespecificheatsasa functionoftempera-tureforconstantpressuresandwereobtainedby interpolationbetweenpointsandextrapolationto zeropressure.Pointswereshownonthecurvesofexperimentaldatainorderto indicatethemagnitudeofthedeviationfromthemeanlines.Experimentalcurvesfromfigures13to 17have beenplottedtogetherinfigure18 to showtheeffectsoftempera-tureandpressuresimultaneously.TheresultsaretabulatedintableI.
A comparisonoftheexperimentalresultswithdataofGmdenoughandFelbeck(reference19), Partin@onandSchilling(reference20),andJohnston(reference6) is showninfigure19. These dataareforlowpressure.Theeffectofa pressureof1 atmosphereinthistempera-turerangeisverysmall.Twopoints,thedataofSwarm(reference21)at1 atmosphere,wereincludedin-thiscomparisonbecausetheyrepresentaccuratecalortietricmeasurementsandarein goodagreementwiththeresultsofthesetests,especiallyintrend.
— —
NACATN2838 13
ThedataofPartingtonandSchil.lingrepresenttheaverageofalargecollectionof dataobtainedbyvariousmethods,[email protected] comparisonsoftheearlierhigh--pressuremeasurementsinconsistent,showing
Factorsinvolved
havebeenincludedsincethosedatawerefewandonlyqualitativelytheeffectofpressure.
LimitationsofCalorimeter
intheoptiqumcalorimeterdesignconditionsare:
(1)Limitationoftemperaturerisetoallowaccuraterepresentationofthedatabymeanvalues,butlargeenoughto allowaccuratemeasurement
(2)L@Ltationoftheflowveloci~toeliminaterecoveryinte~er-aturemeasurements
(3) A highratio
(4)A largeheat
ofgascapacitytocontainercapacity
inputcomparedwiththelosses
Unfortunatelythesefactorsopposeoneanother,requiringa com-promisecondition.IthasalreadybeenpointedoutthatthetemperaturedifferentialusedwasZ13°to 35°F andthatthissatisfiesthefirstcondition.~hiswasconsideredtobe anindependentrequirementandtheotherconditionsselectedonthisbasis.
Theflowveloci~duringthesetestsvariedwithpressureandtem-peraturesincetheweightrateofflowwasmaintainedconstant,forthereasonspreciouslystated.Themaximumveloci~obviouslyoccurredatthe “ temperatureandminimumpressure.Approximatecalculations,basedontheassumptionofa perfectgas,indicatethatthemaximumllachnumberwas0.026wl$chcorrespondstoa stagnationtemperatureriseofonlyO.O1°F.
Thethirdconditionisnecessarytominimizetheeffectoftransientconditions.A highweightrateofflowandasthina tubeaspossible=e desired.Condition(4)alsorequiresa highwei~t rateofflowandminimizationof theheatlosses.Boththeseconditionsweremetsatis-factorily.However,foranextendedtemperaturerangea higherflowrateandadditionalshieldingseemadvisable.It appearsthata practicallimitofthetemperaturerangewillbe dictatedby theradiationlossbecauseofitsrapidincreasewithtemperature.
—----—— ——. —
14 N/MITli2838
CONCLUSIONS
Thefollowingconclusionsweredrawnfroman investigationofthecalorimetricdeterminationoftheconstant-pressurespecificheatsofcarbondioxideatelevatedpressuresandtemperatures:
1.Theresultsarea reasonableconfirmationofthespecific-heatvaluesof carbondioxideobtainedspectroscopicallyforthezero-pressurestateandovertherangeoftemperaturesfrom100°to700°F. Theexperi-mentaldataareapproximately1 percentlowerthanthespectroscopicdata.Thissmalldifferencemaybe dueto lackof completeequilibrium;thatis,thevibrationalenergymaynotbe fullyactivatedatthepointwherethetemperatureriseisobserwed.
2.Greaterdifferenceexistsbetweenthehigh-pressurevaluesmeasuredandthosecomputedbyEllenwood,Kulik,andGay. Themaximumdeviationisapprod.mately3 percentandoccursata pressureof1000poundspersguareinchabsoluteandwOO F. Theagreementismuchcloseratthispressureforbothhigherandlowertemperatures.Thisdetiationmaybe e~lainedby thestressplacedontheBeattie-Bridgemanequationh obtainingthesecondderivatives.
3. A singlemeasurementat 950°F and1000poundspersquareinch .gageseemsto offerconfirmationofthespectroscopicdataatthishighertemperaturelevel.
4.Theresultsshowthattheeffectofpresswquponthespecificheatbecomeslesssignificantathighertemperatures,aspredictedbythethermodynamicidentitiesandtheBeattie-Bridgemanequat~onofstate.
5. Theeqtipmentshouldbemodifiedtoreducetheradiationlossfurtherwhenusedathighertemperatures.
UniversityofCaliforniaBerkeley,Cslif.,January31,1952
——z. —-
NACAm 2838 15
AH?ENmxA
CALCULATIONS
Thespecificheatsweredeterminedfrom:
CP= (E)p = (Z)p ‘%
Flow
Sincetheflowratewasmetereddeterminationwasnecessary.Itwas
Rate
volumetricallydeterminedfrom
reference16at0°C and1 atmosphereasfollows:
~nsi~ = ~.g769gram/liter
1 wuu = 0.002205lb
1 liter= 0.03531Cuft
fromwhich
and
ThisiE
0.002205P! =1.9769x o 03531.
R=~= 14.6g6X 144P’T 0.1235X 491.6
notthetrueularweight),butitsuseaccurateresultsthan
gasconstant
inaccuratedensi~thevaluegivenin
= 0.1235lb/cuft
= 34.88 ft-lb/(lb)(%)
154-4/M(whereM isthemolec-nearthestandardconditionswillyieldmore-
R = 1544/M= 35.11
——. .——— ——. ..
16
Thethe
useofthevslue34.88smalldeviationofthe
saturationpressureofthe
yACATN2838
foot-poundsperfootperOFis justifiedby.
meterconditionsfromthestandard.Thewatervaporwassubtractedfromthebarometric
toobtainthepartialpressureofthecarbondioxideatthemeter.
TemperatureRise
Readingsoftheelectromotiveforceofthedifferentialthermo-coupleswerecorrectedby subtractingtheelectromotiveforceobservedwiththetwojunctionsatthesame,temperature.A curveoftheisothermaldifferenti~isgiveninfigure$6.Thenetdifferentialwasconvertedtotemp~atureby usingtheLeeds& Northrupcalibrationslopes(forstandardlJ.031thermocouples)giveninfigure5.
Net
Thenetheataddedtothelossesasfollows:
HeatAddition
gaswasfoundby correctingfortheheat
.’(a)Measurementofwalltemperaturesindicatesthatnonetheat
lossoccurredbecauseofconductionalongthetestsection.Apparentlyheatwasconductedbackintothedownstreamendatthesamerateitleft .theupstreamend,withintheaccuracyofexperimentalmeasurements.
(b)Theradiationlos~wascalculatedfromtheasfollows:
Stefan-Boltzmann
wherethesubscriptr referstofactor,and Fa isthegeometrictheform
radiation,Fe istheemissivityshapefactor.Thiscanbewritten
law
in
where ~ istheheat-transfercoefficientforradiationandisa func-tionofthetemperaturelevelandthedifferenceT1 - T2. TheshapefactorFa = 1. Theemissivityfactorforthisgeometryisgivenby
—..—— .—. ——
3B IUCATN283gI ‘.
17
andactud-~ssionlinearvariationof
Theuseoftheshieldcalculation;
inwhich 6 istheemissivityand D1 and D2 arethediametersoftheflowtubeandtheradiationshield,respectively.
Theemissivitywasobtainedfromspectralmeasurementsmadeonanequivalentnickel-chromealloy(fig.20). Totalemissivitieswereobtainedby graphical,integrationofthecurvesofPlankianradiation
atvarioustemperatures.Theresultsindicateatotalemissivitywithtemperature(fig.21).
linearrelationshipforradiationsimplifiesthethatis,
.F=6,-2 1-+($(+)
.,2-3 ‘++ (-($-‘)then
theresultsofthiscalculationaregiveninfigure22.
Values.ofhr werecomputedatvarioustemperaturesusingthemeantemperatedifference(tableII)andthesevaluesusedtocomputetheradiationlossfromthetestsectionperhourperdegreemeantemperaturedifference(fig.23).
(c)Usingheatcapaciwanddensitydatafurnishedby theInternationalNickelCo.,producersofInconel,thecapacityofthetestsectionwas-determinedanda correctionappliedbecauseofa slighttransientcondi-tionduringtwooftheruns.Thiscorrectionwas2.8percentoftheheataddedforrun1 and1.0percentforrun5.
.
-..—- -.—— —..——_ .- -— .—..—— —..—— — -_ __
.
18 NACATN 2838
.
Theerrorsofwhere
APPENDIXB
ANALYSISOFERROROFOBSERVATION
observationinrun16,
Q. 229.3——WAT 30.19X33.55=
whichisusedasanexample,
0.2263Btu/(lb)(%)
aregivenbelow.
Errorin Q (Q= 229.3Btu/hrreadto ii/kwattwithscalefactor1/4):
i~X~X 3.413= *0.21Btu/hr
+“”~ – M0091percent’229.3
Errorin AT (AT= Potentiometerindication/Calibrationslope):
potentiometerindication= 1.2065t 0.0005mv
Calibrationslope= 0.03063* 0.00005mv/OF
, AT = 33.55°F
Errorduetopotentiometertolerance:.
0.0005= 0.000411.=65
Errordueto slopetolerance:
o.moos = 0.00160.0306C,
*
4
NACATN2838
. Maximumerror:
3.44(o.cm6+0.00041)=to.067
T = 33.55 i 0.067° F
Probableerror:
●
(33.44x0.0016)2+ (33.55x0.00041)2=io.0555
AT=33.55* 0.056°F
[6op’vErrorin w W=7=
)30.19lb/hr
P’=&
No errorresultedfrom p or R.
Ap’. p’~=o.1089x~ = 0.000051
v= 9.82 tO.0025 tuft
t = 2.126”t0.oo2min
Maximumerrorin w:
Aw( )
.w~+~+$
(. 30.19~ +3+
w = 30.19 t 0.05
)0.002izzm = 0.05
19
—.— ..—.—..
20 NAC!Am 283a
l%robableerrorin w:
(30.19X 0.0047)2 + (30.19X 0.00025)2+ (30.19 x 0.00094)2
w= 30.19 2 0.032
Maximumerrorin Cp:
[ 1AW+AB.+A~=cyy AT
( 0.056=o.2263&+— )0.21
33.55— = 0.00095. + 229.3
“ ~ .0.2263 t 0.00095Btu/lb/°For tO.@ percent
4Probableerrorin Cp: .
%—= 0.001652+0.001652+ 0.000912= to.oo25or to.25percent‘P
CustomarilyitisfeltthattheprobableerrorascalculatedHereismoreapplicable,butinviewofotheruncertaintiessuchascalculat-ion ofradiantlossesandpossibilityofa slighttransientconditiona morepessimisticviewshouldhe taken.Theresultsarebelievedtobe accurateto0.5percent.
.
,
.
.
.
.—
NACAm 2838
REFERENCES
21
1.
2.
3.
4.
5.
6.
‘7.
8.
9.
10.
Keenan,J.H.: ProgressReportontheDevelopmentofSteamChartsandTablesfromtheHarvardThrottlingExperiments.Mech.Eng.,vol.48,no.2,Feb.26, 1926,Pp.14-4-151.
Roebuck,J.R.: TheJoule-ThomsonEffectinAir. Proc.Am.Acad.Artsanasci.,vol.60,no.13,Dec.1925,Pp.537-596;vol.64jno.9, Aug.1930, PP. ~7-334=
Sage,B.H:,Kennew,E. R.)and~cy~ W“N“: PlymeEquilibriainHydrocarbonSystems.Ind.andEng.Chem.,vol.28,no.5,my 1936, pp. 60L604.
Dodge,BarnettFred: ChemicalEngineeringThermodynamics.Firstcd.,McGraw-HillBookCo.,Inc.,1944.-
Ellenwood,I!YankO.,Kulik,Nicholas,andGay,NormanR.: TheSpecificHeatsofCertainGasesoverWideRangesof~ressuresandTemperatures.Air,CO,C02,CH4,C@2, H2,N2,and02. Bull.No.30,Eng.Exp.Station,CornellUniv.,Oct.1942.
Johnston,H. L.,Davis,C.O.,Chapman,A. T.,Walker,M. K.,andDawsonjD.H.: HeatCapacityCurvesoftheShplerGases.Jour.Am.Chem.SOC.,ser.A, vol.55,no.1,Jan.1933,pp.153-186; no.7,July1933, PP.27W2753; VO1.56j no. 2>Feb.1934>PP.z71.-276;VO1.57sno.4)April1935,PP.@2-684.
BeattiejJ.A.,andBridgeman,O.C.: A NewEquationofState.Proc.Am.Acad.ArtsandSci.,vol.63,no.5,Dec.19~, pp.229-308~
Crown,J.C.: Flowofa GasCharacterizedbytheBeattie-BridgemanEqyationofStateandVariable.SpecificHeats.Memo.No.9619,NavalOral.Lab.,April1949.
Bryant,W.M. D.: RnpiricalMolecularHeatEquationsfromSpec-troscopicData. IntLandEng.Chem.,VO125,no.7,July1933,pp.8~-823. ~ “
Chipman,J.,andFontana,M. G.: A NewCapacityatHighTemperatures.Jour.no.1,Jan.193>,pp.48-51.
ApproximateEquationforHeatAm.Chem.Sot.,vol.57,
— .. ..—_ ..—
22 2!338
11.
12.
13.
14.
16.
17.
18.
19.
20.
21.
22.
23.
Eastman,E.D.: SpecificHeatsofGasesPaper445,Bur.Mines,Dept.Commercej
NACATN
atHighTemperatures.1929.
Tech. .
Spencer,H.M.,andJustice,J.L.: RnpiricalHeatCapacityEquationsforSimplerGases.Jour.Am.Chem.SOC., vol. ’56, no.~, Nov.1934, pp. 2311-2312.
Smallwood,J. C.: EquationsfortheSpecificHeatsofGases.Ind.andEng:chem.,vol.34,no.7,July194-2,PP.863-864.
Sweigert,R.L.,andBeardsley,M.W.: EmpiricalSpecificHeatEquationsBaseduponSpectroscopicData. Bull.No.2,Eng.Exp.Station,Ga.SchoolofTech.,vol.1,no.8,June1938.
Heck,R. C.E.: TheI?ewSpecificHeats.Mech.Eng.,vol.62,no.1,Jan.1940,PP.9-W.
Washburn,EdwardW. (cd.):InternationalCriticalTables.Vol.III.McGraw-HillBookCo.,Inc.,1928,p. 3.
KAssel,L.S.: ThermodynamicFunctionsofNitrousOxideandCarbonDioxide. Jour.A.m.Chem.SOC.,vol.56,no.9,Sept.1934,pp.1838-1842.
Woolley,HaroldW.: C“arbonDioxide(IdealGasState).NBS-NACATablesofThermalRcopertiesofGases,Table13.10,July1950.
Goodenough,G.A.,andFelbeck,G.T.: An InvestigationoftheMaximumTemperaturesandPressuresAttainableintheCombustionofGaseousandLiquidFuels.Bull.No.139,Eng.Exp.StationjUniv.ofIll.,March17,1924.
Part@ton,J.R.,andSchilling,W. G.: TheSpecificHeatsofGases.ErnestBerm(London),1924.
Swarm,W.F. G.: SpecificHeatsofAirandC02atOneAtmosphere,by a ContinuousElectricalMethod.fioc.Roy.Sot.(Iondon),ser.A, vol.82,no.553,nay6,1909,PP.147-149.
Henry,P. S.H.,Blackett,P.M. S.,andRideal,E. K.: A FlowMethodforComparingtheSpecificHeatsofGases.Proc.Roy.Sot.(London),ser.A, vol.126,no.801,Jan.1,1930,pp.319-333.
Osborne,NathanS.,Stimson,H. F.,andSlight,T.S.,Jr.: A FlowCalorimeterforSpecificHeatsofGases.Sci..PaperNo.503,Bur.Standards,vol.20,April4,1925,pp.498-523.
.
—— ——
NACAm 2838
,
23
Run
B123
:
789
10u.121314151617181920212223242526
Flowrate
(lb/hr)
30.71;;.:;31:4528.7528.1331.2133.4030.4229.1032.7137.5828.1032.6730.3830.1928.0829.9328.9230.1232.7831.1030.0030.4230.6830.23
Netheatinput(Btu/hr)
174.2252.5217.4200.7213.2208.2208.4207.5425.9286.7283.3264.1259.9234.5234.0229.3234.8234.2233.1232.2251.8264.7263.5279.2279.1282.0
TABLEI
TABULATEDRESULTS
Temperaturerise(OF)
21.2331.5725.6827.8328.5028.8226.4025.08“38.1034.3236.8234.5034.4028.4031.8233*5532.u30.6232.0531.4031.5231.2032.6334.7835.1032.70
Meantemperature
(OF)
339.0338.0339.0339.0540.5537.5535.5533.5145.0101.599.599.5
297.0292.0293.0293.0456.o453.0453.0454.0 ‘455
%686687951
%orrectedfora slighttransientcondition.
Pressure(psia)
101571541520
101571541520
101551531520
101571541520
101571541521520
101571541520
1015
Btu/;b)(%
0.2669.2537.2435.2293.26r2.2569.2531.2475.3672.2870.23TL.2038.2687.2530.2420.2263.2605.2555.2514.2457.2435.2727.2691.2683.2589.2853
(SeeappendixA.)
~
.,
—_______ .—. - ———— ——— .—-—— —=. ——
24 NAC!.ATN 2838
TABLEII
VALUESCOMPUTED‘US~GMEAN~ DIFFERENCE
Temperature % % Qg(%) ~AT m
100 1.40 0.0186 0.0260200 2.00 .0210 .0420400 4.40 .0260 .1144600 8.20 .0310 .25ti800 14.0 .0360 .4890
1000 22.0 .0410 .9020
.
.
.
—
0-300 Psl
>cREGULATORS
T
300-1000 Psl
Coz CYLINDERS
—
VOLUMETRIC
DISPLACEMENT
METER
IT6AS HEATER ELECTRIC HEATERS
tzI
f In
— c T@.“’c :; ,=11%2\
I Ill\ \ I
CALORIMETER ~ HEATER :
I
-–HUMIDIFIERS C OLER
Figure1.- Schematic layout of sy8tem. 0
(“73’)o
0 0
0 O*
00oo~fi$o
,.
@ /
Vm AA
--?
L-
F@re 2.- Calorimeter detail.
r , , ,
t
?’”2 ‘n”11PK!F “
I
!]IUDI H!r
Heater Wound With 14.3 ft ofNo.26 Kanthal Wire
@
IiFigure3.-Test-gas electrical heater. Twice full scale.
I
28 NAC!.ATN 2838
.
COMs
FILLEDWITH
ISENCEMENT
1/4 in
.
Figure4.-Thermocoupleleadsealassembly.Twicefullscale.
———— .———— .—
.033C
.0320
,0310
.0”300
.0290
,0280=%%=.
100200300400500600 700~9001000
TEMPERATURE, 0 F
Figure .5.- Slope of calibration curve for Leeds & Northrup standard 11031iron-conatantanthermocouple.
30
,04
,03
*O2
,01
00
/’
200 4 o E
NACATN 23*
Zj7
‘o 1000
TEMPERATURE, 0F
Figure6.- Isothermaldifferentialfordifferentialthermocouple.
.
.
,— . .
31
ILo
.
..
.360
,340
,320
.300
,280
,260
.24C
.220
.2000
/
ELLENWOOD,KULIK, .4100° Fa GAY
+
/ ELLENWOOD,_
. .
. .. .
III EXP. DATA 145 ‘Fo E)(P, DATA. 100° F.
200 “400 600 ‘ 800 1000PRESSURE,psia ‘ . .
Fi@re 7.- Effectofpressureuponconstant-pressurespecificheatofcar~ondioxideat 100°andlw” F.
———— —.— .—. .._ .
32 NACAm 2838
.
.280
,270
260
,250
,240
,230
0220
ELLENWOOD,KULIK,& GAY
/ - EXPERIMENTALDATA
=@=
—-- ----
.
0 200 400 600 800 1000
PRESSURE,psia
Figure8.- Effectofpressureuponconstant-pressurespecificheatofcarbondioxideat295°F.
.
.
.
5B NACATN2838 33
.280
.270
,260
,250
no
.240
,230
,220
ELLENWOOD,KULIK,
8 “y -L .
- 200 400 t
1 /
4“
- EXPERIMENTALDATA
10 1000
PRESSURE,psia
Figure9.- Effectofpressureuponconstant-pressurespecificheatofcarbondioxideat 3400-F.
.
— —— — ——.— — –———
34. NACA m 2838
,280
.270
.260
,240
ELLENWOOD,KULIK
.2300 200
Figure10.- Effectof
EXPERIMENTAL DATA
400 600 800
PRESSURE,psia
pressureuponconstant-pressurecarbondioxideat455°F.
specific
.
.
—
35
..
.
,290
,280
,270
0260
250
,24C
ELLENWOOD;KULIK8 GAY ~
0 200
Figure11.- Effectof
/
EXPERiMENTA DATA —
400 600 800 1000
PRESSURE,psia
pressureuponconstant-pressurespecificheatofcarbondioxideat535°F.
—-— –——— —
36
.290
NAC!Am 2838
ILo
,280
La)
Q .27031-m
.
0= ,260
,250
,240
I ELLENWOOD,KULIK
‘ ‘“y-=-.-.-,EXPERiMENTAL DATA
o. 200
Figure1$’.- Effectof
400 600 800 1000
PRESSURE,psia
pressureuponconstant-pressurespecificheatofcarbondioxideat 685°F.
.
———
.28C
IL .2600LQJn
uc
s.240
a.
I
3
1- .220m
.Q
0
.200
.180
I ELLENWOOD, KULIK I8 GAY-
\
A
‘o 100 200 300 400 500
~ EXPERIMENTAL DATA I
TEMPERATURE , “F600 700
Figure 13. - Effect of temperatureof csxbon dioxide
upm constant-pressurespecific heatat zero pressure.
800
I
.300
IL0 ,280
=1-a! ,24C
“n
0
.220
.20C
%
ELLENWOOD, KULIK
~ GAY
\
EXPERIMENTAL DATA
/
v
100 200 300 400 500 600 700 800
TEMPERATURE ‘F
Figure 14.- Effect of temperature upon constant-pressme specific heatof carbon dioxide at 100 pounds per square inch absolute.
I
I
1
1
.320
.30C
L0La)n .280~zn
9 .26C?m.a
“ .240
.2200,
.,
?
ELLENWOOD, KULIK8 GAY
\
\ /
100 200 300 400 500 600
EXPERIMENTAL DATA .
T=J==700
TEMPERATURE, “F
Figure 15.- Effectoftemperature u~n constant-pressure specific heatof carbon dioxide at 300 pounds per square inch absolute.
\
Boo
IL0kaln
,340
.320
.300 1
\
280 :
.260
.240
‘ EXPERIMENTAL DATA
T
o 100 200 300 400 - 500 600 700 000TEMPERATURE, 0 F
Figure16.- Effect of temperature upon constant-pressurespecific heatof carbon.dioxide at ~ wunm per square Inch absolute.
I
I
I
I
1,
(
i
I
(
I
Lmn
3!-m
.
on
.360
.340
.320.
.300.
,280.
.260,100 2(
ELLENWOOD, KULIK& GAY
/
3 300 400 500 600 7TEMPERATURE, “F
I I
EXPERIMENTAL DATA .
/
*
10 800 900
Figure 17.- Eflect of tem~rature upon constant-pressurespecific heatof carbon dioxide at 1000 pounds per square Inch absolute.
I
360
340
3?0
\1000
.300 PUIQu.●
,
2)
~~ ~
,280 \, / fg
/
ka
/ / ‘MO
E/ ‘ ZERO-PRESSURE DATA d
JOHNSTON .j
\240 \ /
\ 300 & /
220100pnb
AT
.2000 I(XY 200 300 w 500 600 Too 800 Soo 1000 1100 1200
TEMPERATURE, ‘F
Figure 18.- Specific heat of carbon dioxide from experimentalresults.
-wm
.
I
i
i
I
II
,
140
u50n
“
s
,280
260
JOHNSTON
,240 \y /
SWANN ‘,220 , % GOODENOUGH a FE -BECK
PARTINGTON 8 SCHILLING
,200 EXPERIMENTAL
=s=
.180, “o 100 200 300 400 , 500 600 700 800
.
., TEMPERATURE, “F
Figore 19. - Comparison of low-pressure data for carbon dioxide.
I
F4=
I
I
10090
/ ~80
// ‘
70
/60 )
50
40 ‘
30
2 0
10-=%=-
0 I
0 2 4 6 8 10 12 14 16 18 20
WAVE LENGTH, microns
Figure 20.- S~ctral reflectivity of Inconel.
7B
.
NACATN2838
30
20
10
c)
.05
.04
.03
1-& 4..z .02
,01
0
2
TEMPERATURE, ‘F .
Figure21.- TotalemissivityofInconel.
/
/
/
J__b!ico 200 400 600 800 1000 1200 IL
TEMPERATURE,“F
Figure22.- PlotoftemperatureagainstQr/h#T.
45
00
~—. . ..-—
L20
LOO
0.80
0.60 /
Q40/
020 ‘ /
—o
I
—
—
—
—
—
—
o 100 200
Figure 23.-
300 400 500 600 700 800 900 1000
TEMPERATURE, ‘F
Radiant heat loss fran test section.