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AEDC- TR-55-6 ' : ',.,

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AIR TEST

FACILITIES FOR ULTRA-HIGH-SPEED

AERODYNAMICS @

By R. Smelt; 6DF, ARO, Inc. C.," ..', ,-,: I t" ( ; t" '" ,': ....... :

June 1955 ®

ARNOLD ENGINEERING

DEVELOPMENT CENTER

RESEARCH AND DEVELOPMENT

U S ~)~~A F COMMAND

,wo,, ,r a

AF-AEDC

Tullahoma,Tennessee

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TESTFACILITIESFORULTRA-HJGH-SPEEDAERODYNAMICS

By

R.Smelt;GDF>ARO.Inc.

June1955

ContractNo.AF18(600)-1233

CONTENTS

SUMMARY

NOMENCLATURE

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Page ---, I. II.

INTRODUCTION.

ENGINEERINGLIMITATIONSTOHYPERSONIC

WINDTUNNELS.. . . . . . . . . . . .

7 9

III.PHYSICALLIMITATIONSTOHYPERSONIC

WINDTUNNELS.. . . . . . . . . . . .

IV.FACILITIESFORMACHNUMBERSABOVE12

V.SEPARATIONOFINDIVIDUALPHENOMENA.

VI.SHORT-DURATIONHIGHMACHNUMBERFACILITIES.

VII.HEATADDITIONTOASUPERSONICSTREAM

REFERENCES.. . . . . . . . . . . . . . . .

15 19 23
24
30
32

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ILLUSTRATIONS

Figure

1.ApproximateTemperatureRequiredtoAvoidLiquefaction

ofAirinHypersonicWindTunnels.. . . . . . . . . .9 2.

MaximumHeat-TransferRateatHypersonicTunnelThroat;

VariationwithMachNumberandReynoldsNumber. . ..12

3.LimitingMachNumber-ReynoldsNumberRelationinContinuous

HypersonicTunnels,fromCoolingConsiderations.....13 4. 5.

EnthalpyofAiratHighTemperatures

TestArea/ThroatAreaRatioinTemperature

SimulatingHypersonicTunnels. . . . . . .

15 20

6.MaximumHeat-TransferRateatThroatofTemperature

SimulatingTunnel;VariationwithMachNumberand

ReynoldsNumber. . . . . . . . . . . . . . . . .21

7.LimitingMachNumber-ReynoldsNumberinContinuous

Temperature-SimulatingTunnels,fromCooling

Conditions. . . . . . . . . . . . . . . . . .22

8.Operating-TimeLimitationsinIntermittentTemperature

SimulatingTunnelsDuetoOverheating(Steelwalls

assumed;multiplyby20fortungstenwalls).. . . . . .27

9.LimitingMachNumber-ReynoldsNumberinImpulseTunnels,

asDeterminedbyWall-Melting;OperatingTimeOne Millisecond. . . . . . . . . . . . . . . . . . . . . . .27

10.TunnelArea/DriverTubeAreaRatioinNonreflecting

ImpulseTunnels. . . . . . . . . . . . . . . . .28

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SUMMARY

Hypersonicwindtunnelswithtestsectiontemperaturesapproach ingliquefactionareshowntohaveanupperlimitinMachnumberofabout

12withReynoldsnumbersinthegasdynamicflowregime.Thislimit

arisesbothfromtheproblemofcoolingthetunnelwalls,andfromthe requirementforcorrectsimulationofairtemperatureaboveMach number12,toreproducedissociationandionizationphenomena. ThreetypesoffacilitiesforhigherMachnumber,providingcor rectflighttemperatures,arediscussed:

1.Aconventionalwindtunnelwithsufficientlyhighsupplytem

perature.ThisappearsonlypracticableatReynoldsnumbers intheslip-flowregime.

2.Anintermittentfacilityoperatingforafewmilliseconds,using

shocktubetechniques.MaximumReynoldsnumbersareabout

100timesgreaterthanintheprecedingtype,

3.Asupersonictunnelinwhichtheairisheatedafterreaching

highsupersonicspeed.Techniquesforachievingthisaredis cussed. 5

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NOMENCLATURE

ACross-sectionalarea

A*Throatarea

AtCross-sectionalareaofthetestsection

cSpecificheatofthewallmaterial c p

Specificheat,constantpressure

HHeattransferperunitareaofwindtunnelwallpersecond

kThermalconductivityofthewallmaterial khHeattransfercoefficient tv!Machnumber

PoSupplypressure

TTemperature

TmLiquefactiontemperature?fthewallmaterial

ToSupplytemperature

T r

Recoverytemperature

T w

Walltemperature

Time

RReynoldsnumber

rTest-sectionReynoldsnumberperfootofmodellength vVelocity ySpecificheatratio flCoefficientofviscosityatthetestsection

PDensity

6

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I.INTRODUCTION

Itiswellknownthatordinarysupersonicwindtunnels,operatingfromanair supplyatapproximatelyroomtemperature,haveanupperlimitinMachnumber whichisdeterminedbythecommencementofliquefactionoftheairaroundthe modelinthetestsection.Forawindtunnelwithasupplypressureofoneat mosphereandasupplytemperatureof80 o

F,theairinthetestsectionreaches

theliquefactionpointataMachnumberof5.Thisdoesnotnecessarilyimply thatthewindtunnelceasestogiveusefulresultsexactlyataMachnumberof5; theexactlimitisdependentuponthemagnitudeofthelocaladditionalexpansion aroundthetestobject,andtheextenttowhichtemperatureslowerthantheliq uefactiontemperaturearepermissible,eitherbecauseoflocalsupersaturation duringtheextremelyshorttimeatlowertemperature,orbecausetheheatre leaseisnotsignificantwhenthedegreeofliquefactionissmalLThesefactors, primarilydependentuponthetypeandsizeofmodelandtherequiredprecision ofmeasurement,donotchangethelimitMachnumbergreatlyfromthevaluede duceddirectlyfrom"equilibrium"liquefactiondata. Inthehypersonictunnelsnowoperatinginafewlaboratoriesthroughoutthe country(Refs.I,2,3),theonsetofliquefactionhasbeendelayedbyheatingthe supplyair.Bythismeans,anextensionofthemaximumMachnumbertoabout

10or11hasbeenobtainedattheexpenseofaconsiderableincreaseinthecom

plexityofthewindtunneLFurtherextensionoftheMachnumberrangeofhyper sonicwindtunnelsbymeansofheatingispossible,buttherearepracticalengi neeringlimitstothisprocess.Furthermore,thereisalsoaphysicallimitto thesimulationofflightcharacteristicsathighMachnumberinwindtunnelsof thistype. '7

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Inthefollowingparagraphstheseengineeringandphysicallimitationswhich preventfurtherincreaseinMachnumberofhypersonicwindtunnelsaredis cussedinaroughquantitativemanner.ExtensionoftheMachnumberrangeof testfacilitiesbeyondtheselimitscallsforthedevelopmentofnoveltypesof equipment,capableofhandlingtemperaturesandpressureswellbeyondcurrent wind-tunnelexperience.Someoftheproposalswhichhavebeenmadefortest facilitlesofthistypearediscussedlaterinthereport. 8

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II.ENGINEERINGLIMITATIONSTOHYPERSONICWINDTUNNELS

Asstatedabove,thetemperaturerequiredtoavoidsignificanteffectsofli- quefactioninahypersonicwindtunnelisdependentupontheintendedapplication ofthewindtunnel,i.e.,uponthetypeofmodelbeingtestedandtherequired precisionofthetestresults.Afairlyrepresentativepictureisobtainedbyas- sumingthattheairatambientpressureinthetestareashouldbeatatempera- tureequaltotheequilibriumdewpoint.Thisimpliesthatthesupplytemperature ToshouldincreasewithincreasingMachnumberM,andalsowithincreasing supplypressurePo,inaccordancewiththefollowingrelation:':< (1+=4.7+3.5log,o(1+-log,oPo (1)

Therelationofsupplytempera-

turewithMachnumberandsupply pressureisshowngraphicallyinFig. evidentthattheupperlimitofMach engineeringabilitytohandlehigh temperaturewithincreasingMach

1.Therapidityoftheriseinsupply

numbershowninthefiguremakesit numberwillbedependentuponthe temperaturegases,i.e.,uponthe

I,OOOI---------:H777"----------I

4 6 81012 1416 1820

MACHNUMBER

5'0001--------------f--1--+1

13 w ffi4'0001--------,---,-,--------,,==-:c-:=----+---f--.f----f---T--j wSUPPLYPRESSURE o1,000ATM l ~~~~~~J 10 wI QIII

I-::3,000

w a.. :E w f--2,oool------------:hLA.£-r'-------I a..a.. :::l (f)

Fig.LApproximateTemperatureRequiredtoAvoid

LiquefactionofAirinHypersonicWind

Tunnels

effectivenessofthecoolingarrange- mentswhichcanbemadeinwind expressioncombinesanapproximateClausius-Clapyronrelationbetween liquefactiontemperatureandpressure,basedontheexperimentsofDodgeand Dunbar(Ref.4),withexpansioncharacteristicsforaperfectgaswiththe specific-heatratioY=1.4.Thissecondassumptionisofcourseincreasingly inaccuratewithincreasingsupplytemperature. 9

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tunnelsofthistype. Thereisnogreatengineeringdifficultyinobtainingtherequiredsupplytem perature.Whentherequiredtemperatureexceedsthemaximumwhichcanbe achievedbyconventionalconvectiveheating,additionaltemperaturerisecanbe obtainedbysuchmethodsasadiabaticcompressionorarcheating.Thereisalso noseriousengineeringdifficultyinobtainingtherequiredsupplypressuresfor hypersonicwindtunnels;commercialequipmentandtechniquesareavailablefor pressurestentimesgreaterthanthemaximumnowbeingemployedinsuch tunnels.Theengineeringlimitisdefinedbytheproblemofcoolingthewallsof thewindtunnelexposedtohigh-velocityairstreamsatthesehightemperatures andpressures. Toexaminethisupperlimitmoreclosely,itisnecessarytoobtainarough measureofthecoolingrequirementsasafunctionofMachnumber.Theheat transferliperunitareaofthewindtunnelwallpersecondmaybewritteninthe form: (2)

InthisexpressionthequantitieskhandT

r varysomewhatwiththelocalMach numberandReynoldsnumberoftheair,Le.,withpositionalongthetunnel;but theirvariationisnotsignificantcomparedwiththechangesinPandv.Inprac tice,therefore,thecoolingprobleminahypersonicwindtunnelisatitsworst inareasnearwhichthequantityP•visamaximum,i.e.,nearthethroatofthe wind-tunnelnozzle.Theheat-transferrateisinfactroughlyinverselypropor tionaltothecross-sectionalareaofthewindtunnelateverypoint. Themagnitudeofthecoolingproblemisevidentlyincreasedwithincreasing supplypressure,andtherewouldinfactbenodifficultyinoperatingatunnelat extremelyhighMachnumberifitwerepermissibletouseasufficientlylow 10

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supplypressure.Thereareseveralreasonswhythisisnotpossible.Oneob- viousproblemwouldbetoobserveormeasureaerodynamiccharacteristicsin thetestareaatextremelylowdensity. Afurtherrequirementforhighsupplypressureisinherentintheaerody namicapplicationsofhypersonicwindtunnels.Veryfewproblemsathypersonic speedsareassociatedwithperfect-gasaer0dynamics;themostimportantques tionsrelatetotherateofheatingorthedragofahypersonicvehicle,andthese requireclosesimulationofboundary-layercharacteristicsonatestmodel.In otherwords,itwillalwaysbeimportantinahypersonictunneltoobtainReynolds numbersasclosetoflightvaluesaspossible.Inpractice,ofcourse,asin lower-speedwindtunnels,exactsimulationofflightReynoldsnumberswillfre quentlybeimpracticable,andtherequirementwillbereducedtoaneedforsim ulationofthegeneralcharacteroftheboundary-layerflow.Asexamples,a turbulentboundarylayerinaflightshouldofcoursebesimulatedbyaturbulent layeronthetestobject,andflightinthegasdynamicsregionwillnotbeade quatelyrepresentedifwindtunnelReynoldsnumbersareintheslip-flowregion (definedasR<10 4 M 2 ). Anapproximateassessmentofthecoolingproblemasinfluencedbytest Reynoldsnumbercanbemadeverysimply.Ifthetest-sectionReynoldsnumber perfootofmodellengthisdenotedbyr,then: r'"pV/flattestsection.

FromEquation(2)above:

H'"khc

p r/l-(T r -T w)( 3) ThisequationhasbeenemployedtoconstructFig.2,whichshowsthevari ationinmaximumheat-transferrateatthethroatwithMachnumberandReyn oldsnumberperfoot,assumingthatT r isequaltothesupplytemperatureas 11

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showninFig.1.andthatanacceptablewalltemperatureatthethroatis1000 0 R (540 0 F).Thereisconsiderableuncertaintyinassessingavalueofkhappro- priatetoboundary-layerconditionsatthethroat.inviewofthehighpressure gradientinthisregion.theundefinedReynoldsnumber.andthelackofknowledge oftransitionphenomenainsucharegion.Basedonhypersonictunneldesignex- perience.aconstantvalueof0.0014hasbeenchosen;thisisequivalenttoan assumptionthattransitiontoturbulentflowtakesplaceinthevicinityofthe throat.andisprobablysomewhatconservative.Amoreexactvaluecouldbe obtainedbymakingastep-by-stepcalculationofthegrowthoftheboundarylayer fromthesubsonicsectionofthenozzlethroughthethroat;aconsiderableamount ofanalysisofthistype.asyetunpublished.hasbeenmadebyProfessorPaulA. LibbyofPolytechnicInstituteofBrooklyn.Fortheverygeneralpurposeofthe presentsurvey.thesimplerapproachofassumingaconstantheat-transferco- efficientisadequate. ~ a: :::> (f) lJ. o t:: CJ (f) " a: :::> a: lJJ a.. :::> f- l1J a: a: lJJ lJ. (f) Z f- lJJ I o a: I f-

REYNOLDSNUMBER

PERFT:

107
10 6

J-----------jL--f-+---L--+--------i

o24'6 810121416 1820

MACHNUMBER

Thethroatheat-transferrate

showninFig.2isgivenoverarange ofReynoldsnumberfrom5millionsto

0.1millionperfoot.whichcoversthe

rangeoftypicalhypersonictunnels.

TheReynoldsnumberboundarybelow

whichslip-flowphenomenabeginto appearisshowninthefigureforamo- dellengthof5ft.;equivalentcurves forotherlengthsareeasilydeter- mined.

Theheat-transferratehasbeen

Fig.2.MaximumHeat-TransferRateatHypersonic

TunnelThroat;VariationwithMachNum

berandReynoldsNumber 12 expressedinBtuperhourpersquare

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footofsurface,sincethisistheformmostfamiliartoheatengineers.Forcom- parison,typicalheat-transferratesinhigh-capacity,high-temperaturesteam boilersareintherangefrom45,000to80,000Btu/hr/sqft,>:Thehighestheat-transferrates knowledgeoftheauthor,areencoun- incurrentengineeringpractice,tothe teredinrocketmotors;andthecooling nelproblem.Itisreasonabletoas- isverysimilartothehypersonictun- problematthethroatofsuchmotors

SLIPFLOW

10'1--------"---

2:<10 6

MAXIMUMHEAT

TRANSFERRATE/SOFT:-

2xI0 5

1------------------".___-

5 0: g; 0: 5:<10 5 ::;: => z If) o <5 z )0- w 0: 5:<10 6

1-------'<----'--------------1

IOxI061-----\----':---------------1

sumethereforethatifalltherocket

101214161820

MACHNUMBER

Fig.3.LimitingMachNumber-ReynoldsNumber

RelationinContinuousHypersonicTunnels,

fromCoolingConsiderations developmentsinliquidjacketcooling, boilingfluidcooling,orfilmcooling areadoptedforuseinhypersonictunnels,similarmaximumheat-flowrates,of theorderof10 7 Btu/hr/sqft,shouldbepossible.Thecorrespondingmaximum Machnumber,asafunctionofReynoldsnumberperfoot,isshownasthefull curveinFig.3.Thisfigurealsoincludesasimilarcurve,showndotted,il- lustratingtheeffectofdoublingthemaximumheat-transferrate.Itisevident thatsuchadevelopment,ifpossible,wouldonlypermitthelimitMachnumberto beincreasedbyabout1.O. Thisassumptionthatheat-transferratesequaltothoseofrocketmotors shouldbeattainableinhypersonictunnelpracticeisanoptimisticone,sincethe hypersonictunnelthroatpresentsanadditionalproblem,inaccuracyofprofile, Kent'sMechanicalEngineersIHandbook,Power,12thEdition,Section7, p.16. 13

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notpresentinrocketmotors.Toillustratethisproblem,considerahypersonic tunnelwithatestsection1-ftsquare,utilizingatwo-dimensionalnozzletoobtain aMachnumberof10.Theordinateatthethroatisthenonly0.022in.,anda changeofonly0.001in.inthisordinatewillchangethetest-sectionMachnumber by0.1andthetest···sectionstaticpressureby7percent.Anidenticalchangea crossthewholewidthofthisthroatcanofcoursebecorrected;butifthelarge heatflowproducesuneventemperaturesanddistortioninthethroatwall,there sultingtransversenonuniformitiesintheflowcannotbeeliminated. Itisevidentthatahypersonictunnelaimedatreachinglimitheat-transfer conditionsatthethroatshouldpreferablyhaveanaxiallysymmetricalnozzle, notonlytoreducedistortionbutalsotominimizethesurfaceareainthevicinity ofthethroat.Theaxiallysymmetricalnozzlehasnotbeenadoptedgenerallyin hypersonicwindtunnelshowever,fortworeasons:(1)afearthattheaxialpres suredistributionmaybenonuniformbecauseoffocussingofwalldisturbances, and(2)arequirementforvariationinMachnumberofthenozzle,whichismore difficulttoachieveinanaxiallysymmetricaldesign. 14

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III.PHYSICALLIMITATIONSTOHYPERSONICWINDTUNNELS

Hypersonicwindtunnelsofthetypeconsideredinthelastparagraphdonot simulatethetemperatureswhichexistaroundanobjectinflight,butoperateat ambienttemperaturesclosetotheliquefactiontemperatureofair.Ifairwerea perfectgaswithconstantspecificheats,overthewholetemperaturerangeex- periencedintunnelandflight,alltemperatureswouldbeproportional,andanac- curatepictureofflighttemperaturedistributionswouldbeobtainedfromtunnel testsprovidedthatsurfacetemperaturesweresimulated.Unfortunatelyairis notaperfectgas,anditsdeviationsbecomesignificantatthehightemperatures generatedinveryhighspeedflight. i= a:: r--IN "1.6f----------+---+----j'-----j-----j c. u g

I-1.51---------+-+-_+_-{-----j

a:: lJ.J a-

LLlitI----------,---+-+-+-+-{------j

o ....I "

1.3f---------/--/t--cH7----------j

z lJ.J ....I 1.2f--------fh~--------; I z lJ.J

1.11------,£----1---------\

1.0o!:-..L--;2::-:,obo:::::

o --'I;;:::jO,oOO

TEMPERATURE(DEGREESR)

Fig.4.EnthalpyofAiratHighTemperatures

Thesedeviationsarepresentedin

Fig.4,inwhichtheenthalpyathigh

temperaturesiscomparedwiththe valuewhichwouldbeexpectedifthe specificheatremainedconstantatthe lowtemperaturevalue.Thisfigure hasbeenconstructedfromthetables ofRef.5.Itshowshowtheenthalpy increaseswithincreasingtempera- ture,astheadditionalenergyisfirst absorbedinexcitingthevibrational degreeoffreedomofthemolecule,and thenindissociationofthemolecule.

Theabsorptionofenergyinvibration

15

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isnotgreatlyaffectedbypressure,butdissociationproceedsmuchmorerap- idlyatlowerpressures. Intheflowaroundamodelinahypersonicwindtunnel,theairisatlow temperatureandbehavesessentiallyasaperfectgas,withenthalpycorresponding tothevalueof1.0onFig.4.Figure4thusexpressestheratiobetweenthe actualenthalpyinflightandthevaluesimulatedinthewindtunnel,asafunction offlighttemperature.Theexactextenttowhichthisdifferencechangestheaero dynamicparametersofcoursedependsuponthedetailsoftheflow;atpresent comparisonscanonlybemadeinafewcaseswheretheflowoftherealgaswith vibrationanddissociationhasbeencomputedtheoretically.Thecharacteristics ofanormalshockinarealgashavebeencalculatedbyBetheandTeller(Ref.6) andlatercalculationsarealsogiveninRef.5.Thelaminarflowintheboundary layerhasbeencomputedbyMoore(Ref.7),Crown(Ref.8)andothers.Gen eralizingthesecalculations,itappearsthatchangesinthetemperatureandden sityofthesameorderasthechangeinenthalpyshowninFig.4maybeexpected, althoughthepressuresarenotgenerallymodifiedtothesameextent. Withthisbackground,Fig.4canbeusedtoestimateroughlythemaximum Machnumberatwhichhypersonicwind-tunneltestresultscanbeappliedtoflight conditions.ThereisevidentlyaMachnumberrangeoverwhichthechangesin airpropertiesinflightaresosmallthattheycanbeneglectedcompletely.The pointwheretheenthalpyhaschangedbyonepercenthasbeenarbitrarilyselected asdefiningtheupperlimitinthisrange.Thereisasecondregimeinwhich significantbutsmalldifferencesbetweenwindtunnelandflightcharacteristics aretobeexpected;thesedifferencesmightbetreatedassmallcorrectionstothe wind-tunneltestresults,thecorrectionsbeingbasedlargelyupontheoretical treatmentoftheconsequencesofairimperfection.Fromthepointofviewof 16

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simplificationofthetheoreticaltreatment,itappearsadvantageoustodefinethe upperlimitofthisregimeasthepointatwhichdissociationbecomessignificant, therebyconfiningthecorrectionstovibrationaleffectsonly.Inthethirdand highestrangeofMachnumber,vibrationaleffectsarelargeandappreciable dissociationisalsopresent.Theoreticaltreatmentisthenmorecomplex,the differencesbetweentunnelandflightcharacteristicsarelarge,anditappears thatthehypersonicwindtunnelhaslostmuchofitsutility. Thetemperaturesdefiningthelimitsoftheseregimescanbeobtaineddi rectlyfromFig.4.Atfirstsight,thelimitMachnumbercouldbeobtainedby equatingthesetemperaturestothestagnationorrecoverytemperatureinflight, sincethesetemperaturesareattainedbehindanormalshockorattheinneredge oftheboundarylayeronaninsulatedwall.Fromthepracticalpointofview,this wouldbeover-conservative;avehicleflyingatveryhighMachnumbersisnot likelytohaveanyextensiveareasofstagnationconditions,anditswalltempera turemustbewellbelowtherecoverytemperature.Undertheseconditions,the maximumtemperatureoccursintheboundarylayerawayfromthewall;the temperatureriseisaboutone-fourthofthefullstagnationvalue(Ref.9).The Machnumberlimitsforthethreeregimesundertheseconditionsaregivenin Table1below.InpreparingthistablethedissociationcurveofFig.4fora pressureofO.01atmospherehasbeenused,sincethiscorrespondsapproxi matelytoboundarylayerconditionsatthetopofthestratosphere. 17

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TableI.RangesofApplicationofHypersonicWindTunnels

RangeIRangeIIRangeIII

ResultsApplicableCorrectionsforLargeDifferences

toFlightwithoutVibrationEffectsbetweenTunnels

CorrectionRequiredandFlight

Maximumlocal

temperature(0R)Upto10001000-3400Above3400

Corresponding

Stagnationtem-

perature(0R)Upto28002800-12,400Above12,400

FlightMachnum-

berinstratosphere (T=400 0

R)Upto5.55.5-12Above12

Fromthistableitisevidentthatthehypersonictunnellosesmuchofitsvalue attheupperlimitofRangeII,i.e.,ataMachnumberofabout12.Itisinter- estingtocomparethisconclusionwiththecurveofFig.3,whichshowsthatthe practicalcoolingproblematthetunnelthroatbringstheReynoldsnumberalmost downtoslip-flowvaluesataMachnumberof12. ItwillbeobservedfromTableIthatcorrectionsforthevibrationaleffects inflightarerequiredoverquiteawiderangeofhypersonictunnelMachnumber, i.e.,aboveaMachnumberof5.5.Thereisatpresentverylittleexperimental ortheoreticaldatauponwhichtobasecorrectionsofthistype.Probablythe greatestneedatpresentisforanadequatetreatmentoftheturbulentboundary layerinarealgas,topermittheinterpretationofhypersonictunnelmeasure- mentsofheat-transferrateandskinfriction.Theproblemiscomplicatedby therelaxationtimeofthevibrationaldegreeoffreedom,butevenanequilibrium theorywouldbeofconsiderableassistance.ThenewfacilityattheFreeport LaboratoryofthePolytechnicInstituteofBrooklyn,withitsabilitytoduplicate flighttemperaturesatmoderatelyhighMachnumbers,shouldgivemuch-needed informationinthisarea. 18

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IV.FACILITIESFORMACHNUMBERSABOVE12

InthehighestrangeofTable1,aboveaMachnumberof12,itappearsnec essarythatthetestconditionsshouldsimulatetheactualtemperatureoftheair inflight,sincethechangesinairpropertiesathightemperaturewillhaveapre dominanteffectuponthewholeaerodynamicpicture. Tobestrictlycorrect,italsoappearsnecessarytohavecorrectsimulation ofpressuresaroundthetestobject,sincethedegreeofdissociationischanged quiteappreciablybychangeinpressure.ItisevidentfromFig.4howeverthat theeffectofareducedtestpressurecouldbecompensatedapproximatelybya reductioninthestagnationtemperature,atleastoveramoderaterangeinpressure. Theinfluenceofpressureontherelaxationeffectsassociatedwithdissociation andvibrationpresentsmoredifficultproblems.Iftheseeffectsareimportant inflight,theirsimulationonthemodelrequiresanequalnumberofmolecular collisionsinacomparablelengthoftestobject,andthisresolvesitselfintoa requirementforequalReynoldsnumbersinmodelandflight.Ofcourse,ifthe flightReynoldsnumberissohighthatrelaxationeffectsarenegligible,there quirementforequalmodelReynoldsnumberisreplacedbyarequirementthat themodelReynoldsnumbershouldbehighenoughtoavoidsignificantrelaxation distancesinthiscasealso. Itisevidentfromtheearlierexaminationofthecoolingproblemsofhyper sonicwindtunnels(SectionII)thatMachnumbersabove12willnotbeattainable exceptatverylowReynoldsnumbers.Therequirementforcorrecttest-section temperatureofcourseconsiderablyenlargesthecoolingproblem;thetest-section temperatureisincreasedbyafactorofabout4comparedwiththatofanordinary 19

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hypersonictunnel,sothattheheattransferatallpointsismultipliedbyabout thesamefactorfromthiscausealone.Thereare,however,twootherstrong effectswhichfurtherincreasetheheatingrateatthethroatofsuchatunnel:

100,000r--.......,--,-----,----r---,.---r--,----,-,.,-...---;

Throughoutmostoftheexpansion

processinthenozzleofatem perature-simulatingtunn e1,the vibrationalmodeoftheairisal mostfullyexcited,andthereis appreciabledissociation.Under theseconditionsthespecificheat isgreatlyincreasedandthespe cificheatratioYhasfallentoa valuebetween1.2and1.3.This considerablyincreasestheratio oftest-sectionareatothroatarea foragivenMachnumber;anap proximateestimateofthiseffect hasbeenmade,andisshownin

Fig.5.Boththisratioandthe

specificheatenterintotheex pression(Equation3)fortheheat transferrateatthethroat,with theresultthatvery1a r g ein creasesinthisheatratecanbe expectedwhentheimperfections oftheairaretakenintoaccount. 2.

20181614

.........IDEALGAS "1'.1.4 6 I Ia I / I / D. ;'/ Ia D./ I 4 ,'6 I 10 I I Theincreasedtest-sectiontemperatureincreasestheviscosity,andre ducestheReynoldsnumber.ToobtainthesameReynoldsnumberper footasinthehypersonictunnel consideredinearliersections,it isnecessarytomultiplytheden sitybyafactorofalmost4.This ofcourseincreas e stheheat transferrateatthethroatbythe samefactor. 2 1. o Il // ,

IDEALGAS..........Ii

7=1.29//'AIR

10,000'-----:'-------;r<---J

/ a // 1/ // D.a I / 1,000 " UJ a: " !;:( 0 a: :I: " " UJ 100a:
" z 0 i= u UJ en en UJ 10

81012.

MACHNUMBER

Fig.5.TestArea/ThroatAreaRatioinTemperature

SimulatingHypersonicTunnels

ThecurvesshowninFigs.6and7havebeenconstructedtoprovidearough illustrationofthethroat-coolingproblemwhenallthesefactorsaretakeninto account.TheyshouldbecontrastedwiththesimilarcurvesshowninFigs.2 and3fortheheat-transferconditionsinaconventionalhypersonictunnel.It shouldbeemphasizedthattheheat-transferphenomenaatthethroataresocom- plexunderthehightemperatureconditionsnowbeingconsidered,andthedataon 20

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Q) u .E .... :::> I/) -

REYNOLDS0

"'"'

NUMBER

-

PERFT:

r:i- I/) ...... .... 10" :::> 0 .<= .... a> a. :::> I- ID LiJ t: a:: a:: LiJ lJ.. 10 7 CJ) Z <{ a:: l- t: LiJ J: t: 0 a:: J: I- 10"0 24
airpropertiesaresosparse.thatFig.

6mustberegardedonlyasanorder-

of-magnitudeestimateoftheprobable heat-transferrateandisprobablyan underestimateofthetotalheatflow inthisarea.sinceimportanteffects suchasradiationhavebeencompletely neglected.Itservesthepurposehow- everofdemonstratingthatawindtun- nelsimulatingcorrectflighttemp- eraturesandReynoldsnumbersinthe gasdynamicregimeisquiteimprac-

161820

ticaLItappearspossibletomake

Fig.6.MaximumHeat-TransferRateatThroatof

Temperature-Simulating

Tunnel;Variation

withMachNumberandReynoldsNumber suchawindtunneltogivelowslip- flowReynoldsnumbersatMachnum- bersaround20.andtoextendoutoftheslip-flowregionatthelowerMach numbersaround10.Whileafacilityofthistypewouldclearlyhavesomeutil- ity.thepracticaldesignerofvehiclesforflightattheseextremeMachnumbers willundoubtedlybemoreconcernedwithaerodynamicproblemsatthehigher Reynoldsnumberswhichcorrespondtoflightconditionsatloweraltitudes.Fig- ures6and7invitespeculationontheextenttowhichitmaybepossibleinthe futuretoimprovecoolingconditionsatthethroatofahigh-temperaturetunnel bydevelopmentofnewcoolingtechniques.Thereisnodoubtthatsomeimprove- mentwilloccur;intheopinionoftheauthor.thefullgaintobeofferedbythe useofcoldairinjectionaheadofthethroathasnotbeenrealizeduptothe 21

AEDC·TR·55·6

10' present.Theremayalsobedevel- \GASDYNAMICFLOW \ _SLIPFLOWLIMIT,5FTMODEL (R:I0 4M2) opedhigh-temperaturematerialsca- pableofprovidingsufficientstrength 10' \ 5\ i!''\ ffiMAXIMUMHEAT\.SLIPFLOW a..TRANSFERRATE/SQFT:\ 10 4

1--------->.;,-----\-'--------------1

10MILLIONBTU/HR/\..

z

20MILLIONBTU/HR'"

"\ '" tocontainthethroatpressureattem- peraturesofseveralthousandde- greesRankine.Butinfact,suchim- provementsincoolingsurfacetem- peraturebecomeinsignificantincom- ratesshowninFig.6areseveral ordersofmagnitudehigherthanthe temperature;andtheheattransfer parisonwiththerequiredair-supply presentpracticalmaximum,sothata

20181614

MACHNUMBER

1210
10'

10'L-__L-_----JL-_----"__-----l__....J.__.-I

Fig.7.LimitingMachNumber-ReynoldsNumberin

ContinuousTemperature-SimulatingTunnels,

fromCoolingConditions verymajorengineeringdevelopment mustbepostulatedtomakefacilitiesofthistypepossible.Researchworkersin thefieldhaverealizedthislimitation,andhavesoughtalternativeapproachesto obtainaerodynamicdataatveryhighMachnumbers.Someoftheseapproaches aredescribedinthefollowingthreesections. 22

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V.SEPARATIONOFINDIVIDUALPHENOMENA

Intheprecedingsections,theaimhasbeentoprovideameansofsimu latingalltheparameterswhichenterintotheaerodynamicbehaviorofairin highMachnumberflight,includingMachnumberitself,viscosity,vibration, anddissociation.Thisisveryevidentlyadifficultobjectivetoattain,andsome ofthepresentapproachestotheproblemhaveconfinedthemselvestothesimpler problemofsimulationofonlyafewoftheparameters.Assoonasthissimpli ficationisaccepted,itisnolongernecessarytouseairastheworkingfluid, andothergaseswhichpermitthepracticalvaluesofthecriticalparametersto beobtainedmorereadilycanbeemployed. Forexample,apartialsolutionoftheprobleminvolvingonlytheeffectsof Machnumberandviscosity,andneglectingthevariationinairpropertiesdueto vibrationanddissociation,canbeobtainedbytheuseofagaswithalowlique factionpointsuchashelium.TheworkofProfessorBogdonoffofPrinceton University(Ref.10)isagoodexampleofthisapproach.Thelowtemperatures towhichgaseousheliumcanbereducedinthetestsectionpermitsratherhigh Reynoldsnumberstobeobtained,sothathypersonicviscousproblemsinthe gasdynamicregimecanbestudied.Thespecificheatratioyisnotcorrectly simulated,butitisevidentthatinsistenceoncorrectsimulationwouldleadtoa requirementforsimulationofthevariationwhichoccursinairinflight,andto thesamepracticalproblemasdiscussedinthelastsection. Anexperimentalapproachtotheeffectsofdissociationontheaerodynamic characteristicsisalsopossiblebychangeoftheworkingfluid.Thisapproach hasbeeninvestigatedattheNavalOrdnanceLaboratorybyDr0Slawskyandhis associates.Theyemploygasessuchasbromineandchlorinewhichdissociate 23

AEDC·TR·55·6

atverylowtemperatures;thispermitsthephenomenaassociatedwithdissocia- tiontobeexaminedwithoutseriouscoolingproblems.Atpresenttheworkin thisareahasbeenlargelyamatteroffree-flightinvestigationsusingballistic rangetechniques;thepossibilityofawindtunnelemployingreadily-dissociating gasesshouldalsobeexplored.

VI.SHORT-DURATIONHIGHMACHNUMBERFACILITIES

Ifairistobeusedastheworkingfluid,itisevidentthatsomemeansmust befoundtocircumventthecoolingproblematthetunnelthroat.Onepossibility istoreducethetimeofoperationofthehigh-temperatureflowtosuchanextent thattheheattransfertothecriticalpartsofthewallisnotlargeenoughtodo damage.Thelimitingdurationofafacilityofthistypeisquitedifficulttoesti- matebecausetheextremelyhighheat-transferrate,operatingforaveryshort time,canproducetwotypesoffailure.Itnecessarilyresultsinextremedif- ferencesintemperaturebetweendifferentportionsofthetunnelwalls,giving risetothermalstresseswhichmaybeexcessive;oralternatively,themaximum temperatureontheinnerwallmaybesufficienttoliquefythesurfaceatthepoints ofmaximumheat-transferrate.Aquantitativepictureofthistransientheating processcanbeobtainedbyapplicationofclassicalheat-conductiontheory.The temperatureTatadistancexfromtheairsurfaceinthemetalaftertimet,is givenby: where n=k/cp xerfc(_x)] 2yni (4) Thetimetakenforthetemperatureatthesurface(x0)toreachthelique- factionvalueTmisthengivenby 24
t=ITkpc 4 (5)

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Ifthewallismadeofsteel,insertionofnumericalvaluesleadstotherough resultt=whereHismeasuredinBtuperhourpersquarefoot.However, steelisnotthebestmaterialforthisapplication;evidentlythelongestoperating timeisobtainedwithamaterialgivingthemaximumvalueofkpcT m 2; thissug geststheuseoftungstenoraceramicmaterial.Tungsten,forexample,gives twentytimesthedurationofsteel,beforeitsmeltingpointisreached. Itappearsatfirstsightthattheconditionoftheinnersurfaceofthewall reachingitsmeltingpointmightberegardedasanupperlimittotheoperating timeinintermittentfacilities.Thereishowevernostructuralproblempre sentedbythiscondition;thehightemperaturesareconfinedtoonlyafewthou sandthsofaninchindepthsothatthemajorityofthewallstillmaintainsitsorig inalstrength.Furthermore,thequantityofwallmaterialwhichismeltedis notverylarge.Inpointoffact,someoftheexperimentalfacilitiesnowinoper ationutilizingtheshocktubeprinciple,describedinRef.11,alreadyoperatefor adurationsufficienttoproducemeltingandevenevaporation.Themainproblem undertheseconditionsisthepollutionoftheair,andeventuallyofthewallsof theshocktubeandtunnel,whichmakesitnecessarytoprovideforfrequent cleaningandreplacementofcriticalareas. Wecanassume,however,thattheupperlimitinoperatingtimewillbear somerelationtotheliquefactiontimeasobtainedfromEquation5.Thisequa tionhasthereforebeenemployed,inconjunctionwiththemaximumheat-flow ratesfromFig.6,toestimatethetimerequiredtoliquefythesurfaceinan intermittenthypersonicfacility.Theresultsofthisestimate,assumingasteel wall,aregiveninFig.8(seepage27).Itisevidentfromthisfigurethata reasonableReynoldsnumbercanonlybeobtainedifsurfacemeltingafterafew millisecondsisaccepted. 25

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Thisresultleadsnaturallytotheuseofashocktubeasthedrivingelement ofahypersonicwindtunnel.Thecurrentpositionofdevelopmentof"impulse" windtunnelsofthistypehasbeensummarizedinRef.11.Itisthereforesuf- ficientinthepresentpapertopointoutsomeoftheadvantagesoftheshocktube astheyrelatetotheproblemsdiscussedhere:

1.Theshocktubeisprobablythesimplestequipmentpermittinghigh

pressure,high-temperatureflowstobegeneratedandterminatedwithin afewmilliseconds.Iteliminatesthepracticalproblemsofrapidly operatingvalves.

2.Theshocktubeconsiderablysimplifiestheproblemofobtainingthehigh

stagnationtemperaturesrequiredintheoperationofh ypersoni c temperature-simulatingfacilities.Thetemperatureoftheflowbe hindtheshockcanbemanytimesgreaterthanthetemperaturegenerated inthehigh-pressuredrivingchamber.Itshouldbeobserved,however, thatsufficientlyhightemperaturescancertainlybeobtainedbythedirect useofelectricarcheating. Twotypesofimpulsetunnelsutilizingshocktubeshavebeenconsidered.In thereflectingtype,theshockisdrivenalongthetubeandreflectedfromthewall atthefurtherend.Theflowbehindthereflectedshockisstationaryandatex- tremelyhightemperatureandpressure,sothatitcanbeusedastheairsupply forawindtunnel.Thereis,however,analternativeoperationinwhichthe shockisnotreflected,butinwhichtheendofthetubeisexpandeddirectlyinto thetestarea.Thishastheattractionthatthereisnosonicthroat,andthethroat heat-transferproblemthendoesnotexist.Initsplace,themaximumheat-flow rateoccursatthewallbehindthedrivingshock,whichissubjecttoahigh- pressure,high-temperaturestreamataMachnumberofabout2.Themaximum heat-transferrateundertheseconditionsisabout60percentofthethroatvalue. Takingintoaccountthissmallalleviationofthewallheatingproblemwith nonreflectedoperationofashock-tubetunnel,andassuminganoperatingtimeof onemillisecondbeforeliquefaction,thelimitingMachnumber/Reynoldsnumber 26

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201816141210

0.0001L-_--'__..L.L_-'---'-----'-_..!....-__'--'--_---J

8 (ij o z § II) '.J w :E0.11----\--\--------\------\-------1 ...J...J 0.001!----\---T---\------\----___i 8,andisshowninFig.9.Theas- beenderivedfromthecurvesofFig. andthetotaloperatingtimeshouldbe relationforanimpulsetunnelhas pressureshavearesponsetimeofthe

MACHNUMBER

thantheresponsetimeoftheinstru- ments.Thereis,ofcourse,scope

Fig.8.Operating-TimeLimitationsinIntermittent

Temperature-SimulatingTunnelsDueto

Overheating(Steelwallsassumed;multiply

by20for tungstenwalls) shouldbeobservedthatareductionin onlyincreasethemaximumReynolds withshorterresponsetime;butit correspondstoadistance0fonly more,thetimeofonemillisecond operatingtimebyafactorof10will forfuturedevelopmentofinstruments numberbyafactorof10.Further- twentyfeetinflightataMachnum-

STEELWALL

10'!--------------"""""------->,j

(f) o ...J o Z a:: b fr ffi a. ffi 1051---------~-----"---__j ::> z berof20,sothatfurtherreduction 10 3

MACHNUMBER

intimepresumablywillproducein-

Fig.9.LimitingMachNumber-ReynoldsNumberin

Impulse

Tunnels,asDeterminedbyWall

Melting;OperatingTimeOneMillisecond

strumentationproblemscomparable withthoseoffree-flighttechniques. 27

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AlthoughtheseconsiderationsmayindicatethatthecurvesofFig.9are somewhatconservative,itisprobablethatthefigurerepresentsveryapproxi- matelytheupperlimitatthepresenttime.Ifthedataarecomparedwithcorre- spondingdataonFig.7forthecontinuoustemperature-simulatingtunnel,it willbeobservedthatthemaximumReynoldsnumberhasbeenmultipliedbya factorofalmost100bytheuseofshock-tubetechniques. Atthispoint,itisappropriatetodiscussthemeasurementofmodeltemper- ature,whichconstitutesthechiefprobleminintermittenthypersonictunnels. Sinceheatingislikelytobethemostimportantproblemforthedesignerofhigh Machnumbervehicles,itisessentialtobeabletomeasureratesofheatflow intothemodelinanyhigh-speedtestfacility.Itisobviousthatthispresentsa difficultprobleminimpulsetunnelsoperatingonlyfortimesoftheorderofa millisecond.

10,0001--------------j'-----7I

n:: f- e]1,000 > " MACHNUMBER

Fig.10.TunnelArea/DriverTubeAreaRatioin

NonreflectingImpulseTunnels

28

Itisusefultolookatthisprob-

lemquitegenerally,goingbacktothe basicheat-transferrelationofEqua- tion2.Aroughdeductionfromthis equationisthattheheat-transferrate isinverselyproportionedtothecross- sectionalareaoftheairstream,so thattheratiooftheheattransferper unitareaatthethroattotheheat transferperunitareaonatestobject (treatedasaflatp 1atealongthe stream)isgivenroughlybythevalue ofAIA*.Thisratiohasalreadybeen

AEDC.TR·55·6

giveninFig.5.Asimilarrelationholdsbetweentheheattransferatthetest sectionandtheheattransferbehindthedrivingshockinashock-tubetunnel;this isshowninFig.10. ThesefiguresshowthatatMachnumberof19ormoreintheshocktubeor continuoustunnel(asnotedearlier,thenonreflectedshock-tubetunnelisalittle betterbecauseoftheabsenceofasonicthroat)thearearatioreachesavalueof

100,000.Inotherwords,quiteindependentlyoftheoperatingtime,ifthemodel

andthedriverwallareofsimilarconstruction,therateoftemperatureriseat themodelwillbeonly1/100,000ofthatattheworstpointintheairchannel. Duringthetimetakenforthehotspottoreachthemeltingpointofsteel,the modeltemperaturerisewouldbeonlyO.02 0 F. Ofcourse,atypicalmodelwillnothavemerelyflat-plateheat-transfer values.Ontheotherhand,itwillnothavetheverylargeheat-transferrates whichwouldcorrespondtoanisentropicrecompressiontosonicspeed.The casewhenthemodelisprecededbyanormalshockhasbeenconsidered,for comparisonwiththeflat-platecondition.Inthiscase,theworstheat-transfer rateisobtainedwhentheairacceleratestosonicspeedagainbehindtheshock; athighMachnumber,thevalueofpvisaconstantmultiple, 1 (Y+1)liz(Y+1)y-l (Y-1)(2y) ofthevalueintheambientstream.Theheat-transferrateisthenmultipliedby afactorofonly1.66withY=1.4. Topermitmeasurementofheattransferwithreasonableaccuracy,itis necessarytoobtaintemperaturerisesofseveraldegreesonthemodel.This canonlybedonebymakingthemodelsurfacesothinthatthesmallamountof heattransferduringtherunisenoughtogivesignificanttemperaturerise.Itis 29

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estimatedthat,evenwithoperatingtimesufficienttomeltthedriverwallina shock-tubetunnel,themodelwallthicknessatthepointwheretemperatureisto bemeasuredmustbereducedtoonlyafractionofamicron.Thisimpliesthat specialtechniquessuchastheevaporationofaverythinmetalfilmonaninsu latedmaterialmustbeadopted.Thesetechniquesarecurrentlybeingdeveloped, butitisnotpossibleatthisstagetopredicttheirultimatedegreeofsuccess. TheadditionallimitinMachnumberandReynoldsnumberimposedbythisre quirementcanthereforenotbeassessedatpresent.

VII.HEATADDITIONTOASUPERSONICSTREAM

Thelastfewparagraphshavefocussedattentionuponaquestionwhichis reallythebasicproblemoftestfacilitiesforthehighestspeedrange.Itisgen erallyrealizedthatthemajorproblemofflightatsuchspeedsistoavoidover heatingofthevehiclewalls.Ithasbeendetermined(SectionIV)thatgroundtest facilitiesshouldbeabletoduplicateflighttemperaturesatMachnumbersabove

12;sothatatthesametest-sectiondensityasinflight(whichimpliesReynolds

numberslessthanflightvaluesifthemodelissmaller)theheatingrateperunit areaisjustaslargeasinflight.Butitistheninherent,inthefacilitiesjust discussed,thatcriticalareasexistinwhichtheheatingrateismanythousand timesthealreadylargeflightvalue. Inthesecircumstances,thevalueofgroundtestfacilitiestosupplement flighttesttechniquesisopentoseriousquestion.Groundfacilitiesareonly justifiediftheyshowappreciablegainsineconomy,convenience,andsimplicity comparedwithflighttests;andtheneedtosolveagrosslyenlargedheating problemmayoffsettheusualadvantagesofgroundfacilitiesinthisrespect. Thereisonemethodofapproachwhichappearstoofferthepossibilityof 30

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ofpreventingmostofthemultiplicationoftheheatingproblemwhichoccursin thefacilitiesdiscusseduptonow.Iftheairstreamcouldbefirstexpandedto highsupersonicMachnumberatmoderatetemperatures$andthenheatedtothe temperaturesrequiredforcorrectsimulationofflightconditions$withoutre ducingtheMachnumbersufficientlytoapproachsonicconditions$thenthecritical heatingratesatthethroatwouldbeavoided,andthemaximumrateswouldbeof thesameorderasinflight.Measurabletemperaturerisesonthetestobject wouldthennotbeaccompaniedbyexcessiveheatingelsewhereonthewind-tunnel walls. Itisnotfeasibletoheatairtravelingathighsupersonicspeedsbyconvective orconductionprocesses$butanelectricarcofsufficientintensityacrossthe supersonicstreamcanproducesufficientlyhightemperatures.Thechiefprob lemwithsuchanarcistopreventtheionizedareafrombeingsweptdownstream$ blowingoutthearc.InrecentworkbySmithandEarly(Ref.12)thisblowout wasavoidedbyastrongmagneticfield;itisalsopossibletoutilizearadio frequencypowersupplyforthearc$andthustoarrangeveryrapidre-ignition asameansofstabilizingthearc'sposition.Atfirstsight,itappearsthatthe ionizationproducedbythearcmightbeadeterrenttothistypeoffacility.Atthe lowtemperaturesofthesupersonicstream,however$theionizationdiminishes veryrapidly.AsamatteroffactIionizationoftheairislessofaproblemin thistypeofawindtunnelthaninthefacilitiesdiscussedearlier.Inthesefacili tiesatthehighestMachnumbersthereareregionsofthestreaminwhichthe temperatureexceeds12,000 0

R,whichissufficienttogiveappreciableioniza

tionandradiation.Theadditionallossesfromthiscause$whichhavebeen ignoredinthesimplifiedapproachdescribedabove,areofcourseavoidedwhen theheatingisconfinedtotheareaofhighsupersonicspeed. 31

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Verylittleworkhasbeendoneuptothepresentonfacilitiesofthesupersonic heatingtype;thebestmethodofheataddition,andtheresultingnozzleshape, needconsiderableexperimentalandtheoreticalworkfortheirresolution.Itis evidentfromtheestimatespresentedherethatthisapproachtohighMachnumber testfacilitieshasfarmorepromisethananyofthealternativesatpresentbeing investigated.

REFERENCES

1.Wegener,P.,etal."NOLHyperballisticsTunnelNo.4,ResultsI:Air

Liquefaction."NAVORDReport1742,January1951.

2.Nagamatsu,H.T."GalcitHypersonicResearch."ContributiontoAGARD

Conference,October1954.

3.Allen,H.Julian."DevelopmentofTwoHypersonicTestFacilitiesatthe

NACAAmesAeronauticalLaboratory."ContributiontoAGARDConfer ence,October1954.

4.Dodge,B.F.andDunbar,A.K."InvestigationoftheCo-existingLiquidand

VaporPhasesofSolutionofOxygenandNitrogen."JournalAmerican

ChemicalSociety,VoL49,pp.591-610,1927.

5.AppliedPhysicsLab.,JohnsHopkinsUniversity."HandbookofSupersonic

Aerodynamics."NAVORDReport1488,VoL5,August1953.

6.Bethe,H.A.andTeller,E."DeviationsfromThermalEquilibriuminShock

Waves."BallisticResearchLaboratoriesReportNo.X-117,(alsopub lishedbyEngineeringResearchInstitute,UniversityofMichigan).

7.Moore,L.L."ASolutionoftheLaminarBoundary-LayerEquationsfora

CompressibleFluidwithVariableProperties,IncludingDissociation." JournaloftheAeronauticalSciences,Vol.19,No.8,pp.505-518,1952.

8.Crown,J.C."TheLaminarBoundaryLayeratHypersonicSpeeds."

NAVORDReport2299,1952.

9.Eckert,ErnstR.G."SurveyonHeatTransferatHighSpeeds."WADC

TechnicalReport54-70,April1954.

10.Bogdonoff,S.M.,andHammitt,A.G."ThePrincetonHeliumHypersonic

TunnelandPreliminaryResultsaboveM=11."PrincetonReportR260, July1954(preliminarycopyofWADCTechnicalReportNumber54-124).

11.Dodge,J.A."Ultra-HighTemperatureAerodynamicTestingFacilities."

AEDC-TN-54-61,April1955.

12.Smith,H.L.,andEarly,H.C."InvestigationofHeatingofAirStreamin

aWindTunnelbyMeansofanElectricalDischarge."EngineeringRe searchInstitute,UniversityofMichigan,ReportNo.2154-3-F. 32

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