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TECHNICALNOTE2117

.DESIGNAND APPLICATIONSOF HOT-WIRE ANEMOMETERS

FOR STEADY-STATE MEASUREMENTS AT TRANSONIC

AND SUPERSONICAIRSPEEDS

By HermanH.Lowell

LewisFlightPropulsionLaboratoryCleveland,Ohio

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13WRODUCTION. . . . . . . . . . . . . . . . . . . . . .

ELSICCOEUIZRATION3.. . . . . . . . . . . . . . . . .ksic~strment . . . . . , . . . . . . . . . . . . .Natureofdevice. . ... . . . . . . . . . . . . .’IiondinensiomlcorrelationofheatlossesfromwiresExposureatobliqueincidenoe. . . . . . . . .Edmtiorofexposedunheatedwire. . . . . . .Radiatimlosses. . . . . . . . . . . . . . .

PossibleArrayConfigurationsandUses . . . . .Usesandproceduresidenticalforallarzays,Single-wirearray. . . . . . . . . . . . .T-axmy. . . . . . . . . . . . .* ***.Pa=llel-wirearray.o. . . . . . . . . .Combinationarray. . . . . . . . . . . . .-i~l -y . . . . . . . . . . . . . .

INSTHM3NTDEEIGNPROBLEMS... . . . . . . .Endlosses. . . . . . . ~. . . . . . . .Aerodynamicstresseffects. . . . . . . .Irqpcteffects....,.. . . . . . . .Vibrationeffects. . . . . . . . . . . . .Oxidation. . . . . . . . . . . . . . . . .Electricstability. . . . . . . . . . . .Reconciliationofconflictingreqtiements

,REAUzEDDESIGNSANDCONSTRUCTION. . . . . . .I%MuationofMterlals. . . . . . . . . . .Wiremateriak. . . . . . . . . . . . . .Supportmsterials. . . . . , . . . . . . .

Momt DetailsandAssembly. . . . . . . . .Mountdetails,. . . . . . . . . . . . . .Wiremountimg.. . . . . . . ,. . . . . .Typesinuse. . . . . . . . . . . . . . .

AFPARATUS.. . . ● *. ● ● * . . . ● . ● ** .TestTunnel.. . . . . . ; . . . . . . . . .hid.ge.. . . . . . . . . . . . . . . . . . .Uhiform-Temperature2aths. . . . . . . . . .

PROCEDURES● ,. . . . , . ..*. . . . . . .Mass-Flowor E3at-LossMeasurement. . . . .Angleeta . . . . . . . . . . . . . . . . .TemperatureMeasurement. . . . . . . . . . .

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CAICUI#EIOIiSANDCORRECTIONS. . , .Evalwtiond fluidOondmts ●

Endloaeea. . . . . . . . . . .Stresscorrections. . . . . . .

~ RESULTSANDDISCUSSION

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CalibrationandMass-FlowDeterm&tion. . .Calibrationof~inglewirenormaltostremCorrel.ati,onequaticms. . . . . , . , . , .

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Limitationti R& method. . . . .yawChaxmcteristicsofAn@e-sensitiv-ev-array...*.....Fmmllel-wire array ...

TemperatureRecoveryRatio.

OONOLUSIONS. . . . . . . . .

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AH’ENDIXC- WIRESTRESSAMDSUPPORTAero-c Stres~. . . . . . . .Deflectiond WireSupport. . . .

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TECHLIBRARYKAFB,NM

C10b5437UONAL ADVISORYCWWi?TEEF’OR~ICS

TECHNICALKWE 2117

DESIGJYANDAPPLICATIONSOFHCH’-WIX3lmmmMETERs

FORE?I!EWY+TATE~s ATTRANSOmc

ANDSUPERSONIC!KETEEDS

ByHermanH.Lowe~

An investigationwasmadeofthedesignrequirementsandheat-transfercharacteristicsofexposed-wireinstrumentstobeusedforsteady-statemeasurmmsntsattransonicandsu~ersonicspseds.Designcriteriom,oonstruction~details,andty-pioalresponsebehaviorarepresented.

Severalty_pesofinstrumentwereevolvedthat,inadditiontoexhibitingtherequiredhighstability,areoapahleofprovidingstea@-ste$emass-flow,flow-angle,andtemperatureinformationofengineeringacouraoyattotaltemperaturesatleastashighas275°C,Machnumbersatleastasgreatas2.4,andairtotaldensi-tiesatleastasgreatastwioeatmospheric.Heat-transferdatafora oircularcylinderoveratleasttheMaohnumberrangefromO to2.4maylecOrrdatedbyadditiontotheconventionalrelationamongIiusselt,Pzmdtl,andReynoldsnumbersofa faotorthatisa funotionofMachnumberonly.Finally,itisshownthatthecombinationof= air-temmmkredatum(obtaf.=dtitha ~) ja tie heat-1OSSdatum,and-a pressurebymorethanabout20a steady-stateflow.

dati.mlimitedtopressurf%notexceedingstatioperoentofthevelocityheaduniquelyspeoifies

INTRODUCTIOIi.-

Inconnectionwiththeinvestigationofthebehaviaofexist-ingcompressorsandturbines(turbanachines)orofproposedimprOwdcomponents,itisoftennecessarytoobtaina detailedpiotnreoftheairflowoomrringthroughoutinterbladeohannels,%etweenstatorandrotoroascades,withinMade ors~oudboundarylayers~immediatelybehindtrailingedgesoftheM_ades,ortithinengineducts.

. . .. —.. —. . ....—- ..— —-— ---- .-. ..—.-. —..——.—-— —. —— —

2 NACATN2117

Dema&lsuponflowinstrumentationaresevere;evenwhena deviceofthepressure-tubeorthermocoupletypeprovidesaccuratedataconcerningonemiable,itisincapableofprovidingalltherequiresinformationconcerninglocalflowcharacteristics.

Inprinciple,thefinewireusedasa resistancethermometeremcmeterissuperiorinseveralrespectstoeitherorhot-wirean

thepressuretu%eorthethemmcouple.A wireorwirearraymayhaveverysmalldimensionsandtheresponsetimeismeasured,atmost,inmilliseconds;moreover,wiresareequallyuseful(atlowairspeeds)fortemperature,angle,andmass-flowdeterminations.Itappeaed~ohablethatwiredata(atb3ghairspeeds),ifsupple-mented%ypressureinfornmtion(whichcould,whennecessaqL@ whenspaceImitationsaianotprohibit,hePrOviaeabyaninte~ pres-suretube),oonld%emadetoyielaMachnumiberinformationaswelJasotherinformationdespitetheunavailabilityofanyadditionaltitsconcerninga compressible-flowsituation.

Yreviouseffortsinthefield(priortoabout1940)were”-Q confinedtothespeedregionlelow104centimeterspersecond.Somesuccesswasachievedwiththeideaofusingwirestomeasure%othflowratesandangles(references1 and2). Morerecently,investigateore,havingtransferredtheireffortsfrmplat- totungstenwires,have‘obtitida few=ss-fl~@*a attransodcspeeds(reference3)anda veryfewinthesupersonicregion;thesupersonicdatawereobtainedbyDr.GalenB.SchubaueroftheNationalBweauofStandards(unpublishedresults).Noneofthedata,however,haveexhibitedtherequiredsusceptibilitytocorrelation.Noinvestigationseemstohavebeenmadeofthepos-sibilityofusingexposedwiresasresistancethermometersathighMachnuuibers,norhasinformationbeenpublishedconcerningtheuseofwiresattemperaturessubstantiallyaboveroomvalues.

Theprobleminthecaseofthegasturbineistodesignan-rumnt ofhighstabili~.Itisnecessm?ythatthewirehavehighstrengbh,befYeeofanytendenqytowariiinternalstructuralalteration,beinerttoanofidizingatmosphere,andbeelectricallystable.Theentiredeviceisrequiredtoexhibitfreedomfrcmaerodynamicallyinducedvibrations.

Aninvestigationhastherefore%eenmadeatthellACALewislaboratoryofthedesignrequirementsandheat-transfercharacter-isticsofwireinstrumentstobeusedattxzmsonicandsuprsonicspeeds.Thisinquirywaslimitedtothedevelopmentofdevicesthatwouldbeusefulundersubstantiallysteady-flowconditionsandatmoderate(below275°C)anibienttotaltempemtures.The

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NACATN2117 3

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heat-transfercorrelationsareneverthelessapplicabletounste@-stateconditions,andthebasiodesignsanddesi~proceduresevol~edareapplicabletoanemmnetqathightempem~s andatmass-flowrateshigherthanthoseatwhichdatawereoltained.

Thereportconsistsoftwomaingroupsofsubjects.Theffistgroupcomprisesmattersofa generalnature;itisintendedchieflyforpossibleusersofhot-wireinstrumen-tswhohavehadnoexper-iencewithsuchdevioes.Dimensionlessheat-transferrepresentation(asapplyingtoanemometry),wire(resistance)ihermome~,and~os-siblearrayconfigurateionsandusesaredisoussed.Inaddition,asection on instrument~esignpro%lemsbasedprincipallyuponworkPerfo-dattheNAOALewislaboratoryispresented.I’hlssection,aswellasthesectionsofthesecondgroup,oontainsmaterialnotpreviouslypublishes●

Thesubjectsofthesecondgroupare,forthemost@,restrictedtos~cificworkpsrformedatthislaboratoq.!rheyincluderealizedinstrumentdesignsandconstruction,descriptionsofayparatus~~a andofinvestigationprocedures,almiefais-oussionoftheoaloulationsmadeandcorrections~Oyea intheevaluationofdata,anda aiS0~t3i~oftheexperimentalresultsObtainea●

Theheat-transferc~oteristicsofseveralinst~nts aregivenatmass-flowratesuptoabout24@arespersquarecenttiterpersecond(1.5slugs/(sqft)(see)),atitotaltemperaturesofapprox-imately36°C,wiretemperaturesUTtoabout300°C,andMachtiersuptoabout2.4atairtotaldensitiesatleastasgreatastwioeatmospheric.Theflowlimitsantitneairtem~ratnrewereestab-lishedbytheoharaoteristicsofthetesttunnelratherthan%ythebehavicmoftheinstruments.

Applicationofthegeneralizedheat-losscorrelationoltainedtoflowsituationssuchthattheMachnunherUstributionisunlmowniSaisc~sea.Inpxrtioular,itisshownthatthecombinationofapressuredatum(withincertatnMnits)andwiredatauniquelyspec-ifiesthe(steady-state)localflowcharacteristics.

BASICCONSlllEREl?IONS

BasicInstrument

Theknownheat-tr&sferrelationsdisoussedinthefollowingsections.

relevanttoanemametryare

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4

Natureofdevice.offluidlosesheatat

.

- A heatedobjeotplacedinaa rated.e~nrlentuponseverel

NACATN2117

movingstreammiables!

identity,pressure,andtemperatureofthefluid;nature,orienta-. tioii,andtemperatureoftheobject;endmass-flowrateofthefluid.Itisokaythatbyproperlyf~ allothervariablesatpredeterminedorascertainablevalues,themass-flowratewi3Jbecomethesolefactordeterminingtheheat-lossrate.

Aocomlin@_y,theinvestigatorwhodeterminestherateofheatlossfromtheexperimentalobjectunderproperlychosenconditionsneedmerelyrefertothepredeterminedrelationbetweenheat-lossrateandmss-flowratetodeterminethemass-flowrate.Undersuchcircumstancestheobjeptbecomesananemometer.

Theconventionalanwmmetermeasures‘windspeed{andoftendirectionaswell)ratherthanmass-flowrate.Bystipleextension,however,thedesignation“anemometer”mayberetainedforhigh-speedmeasurementsbemuseundercaurpressible-flowconditionsthepraluctofdensityandspeedgenem3Uytakestheplaoeofspeed.

Electricallyheatedfinewireshavebeenusedasheat-loss(hence,hot-) anemometersformanypars. Thelistofrefer-encesgivenhereinincludesonlya fmctionofthemorethan100reportsnowavailableonhut-wireanemometry.

Oneofthe4mportan~variablesinoonneotionwithheat-lossanemometryis,as~eviouslystated,thetemperatureoftheobject.Thevariationofwireresistancewithtemperatureprovidessuchinformation.Althoughin~ecisionresistancethemometmccmplexrelationsbetweenresistanceandtempe=turemustbeemployed,itisusuallyfoundthat,foram+mometricpurposes,thesim@elaw

(1)

i8 adeqmte.

(All symbolsusedinthisreportaredefinedinappendixA.)

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NACATN2117 5

“.

Pm)02cc

.

Nondimensionalcorrelationofheatlossesfrcmwires.-TheolasslcInvestigation’ofheatlosses~cmwireswasmadebyKing(reference4)in1913-14.HeevolvedthefoU-icalrelation:

wh~- theokt-.

0.2389izr= (~ + ~cP,epVD)(ew~e”) (2)

#Twoimportantconceptionsareembcdiedinequation(2).The

heat-lossmte isdepemientuponthesquarerootofmass-flowrateand.uponthesim@edifferenceoftemperaturebetweenwireandati(Newton’slawofcoolingasap~iedtothissituation).Inthiscaae,ee equalsthestaticambienttemperaturebeoauseKingassumedtheexistenoeofIncompressibleflow.

WhenlHngattem&edtooonfirmhistheoreticalresultexper-imentally,hewasabletoconfirmthebasiostructureoftherela-tionbutfounditnecessarytointroducea numberofcorrectionfaot~ prinoipillydependentuponwiretemperature.

King’slaw(equation(2))whenwrittenintheform .

i2r= (Cl+ C2@) (ew~e) (3j

isneverthelessadequateoverlimitedrangesoftemperatureandpres-sureyrovidedCl and C2 areexperimentallydetermined.Manyusersofhot-vimanemometershavethereforeemployedequation(,3)asthebasicrelationofsuchinstrumentation.

Theinherentlaokofgeneralityoftherelationand,inpartic-ular,itslaokofprecisionwhentheconstantsCl and C2 areevaluatedunderonesetofconditions(airpm3ure andtemperatureandwiretempmvture)andthewireisusedunderanothersethaveledtoattemptstowritea relationthatwouldbevalidunderwidely-U! ctim=ces.

Nusselt(modemCliscussioninJakob,reference5)haspreviouslyshown(1909-15)thatthemostgene- correlationofheat-transferdataforflowofanincompressiblefluidis

Nu=U(Gr,RrjRe,temperaturefunction) (4)

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6 NACATN2117

.inwhichU representssoresfunction(ofthevariablestithinWrent@ses)andthetempe=turefunctionistheratiooftheabsolutetemperatureoftheobject(surface)tothatoftheunilis-turbedstrean.

Inequation(4),theseveraldimensionlessgrou~s,withtheexceptionofthetemperaturefunction,areunderstoodtobeeval-uatedatthefree-streamstatiotemperature,pressure,andspeed.Thepresenceofthetemperatifunctiontheoreticallyensurescorrelationdespitethevariationofgasproperties(w,cp,andk)withtemperatm.

In1934,Dryden(reference6)indicated(withoutprovidi??

thederivation”oftheresult)thatanadditionalparameterkAe/@ isdemanded,ingeneral,bydtiensionslconsiderationsintheeaseofcompressibleflow(Ae isthedifferenceoftemperaturebetweenstreamandobject).A resultequivalenttohisisobtainedinreferen:e7,whereitisshownthatthegroupV2/c# isofsignif-icance;T istheabsoluteairtemperatureinthisinstanoe.Ineverygeneralizedheat-transfercorrelation,a functionofI?randtlnumbernecessarilyappears.BecauseDryden’sparameterismerelythereciprocaloftheprcxiuct

(*) (%)inwhichthesecondfactoristhePrandtlnruiber,itis-evident$hattheDrydenp?ameterand #/cfl provideessentf~Ythes= f~or-mationifthetemperaturefunctionisunderstoodtobepresentwhenrequired.

l?romthefactthat

it followsthat

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(5)

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NACATN2117

WhenthevirtuallyconstantthatthestreamMachnuniberina2JygivenbyI?usselt.

Ingeneral,therefore,

F1 factormustbeadded

isto

ignored,itistheparameters

7

patentorig-

theNusseltnum%erisanunspecifiedfunctionofGmashof,Prandtl,Reynolds,andMachtiers‘andofthetem~raturefunction.Ithasbeentacitlyassumedthatgeomet-rioallysimiltibcdiesshilarlyorientedwithrespecttothestreamarebeingconsidered.Additionaltermsorfactorsarerequiredwhenthosetwocoalitionsarenotfulfilled;thegointissubsequentlydiscussedinconnectionwithobliqueflowincidencetithrespecttoa oylitier,

Therelativesimplicityofthecircularcylinderwitha reason-ablylargelength-to~ameterratioandnormallyexposedtoa streamhasleda nmiberofinvestigatorstoobtainheat-transferdataInvolvingsuchobjectsandtoattempttocorrelatetheirowndataandthoseofothersbyusingtwoormoreofthedimensionlessgroupsalreadymentioned.

ThespecificresultsofsuohworkarediscussedinthesectionCorrelationequations.Itissufficientheretomentionthefollow-ingpoints:

(1)Asindicatedinconnectionwithfairlycomprehensivedis-cussionsbyMc&iams(reference8)audJakob(reference5)ofthemechanismandthepeculiarities,ofheattransferfromsuchcylinders,suchstudieshavenotcompletelyclarifiedthesignificanceofthelfusseltnuniberitself.Themostfruitfulconceyt,particularlyatReynoldsnumbersbelowabout1000,isthatoftheenvelopingbournlayer,themeanthicknessofwhichdecreaseswithincreasingmass-flowrate.TheNusseltnuniberisthereforea measureofthediminn-tianofrelativethicknessandhenceofthethermalresistanceofthemeanlayer.

(2)LittleinformationhasbeenpublishedconcerningtheinfluenceofMachnumberontheNusseltmmhr.

(3) Nopurelyforced-convectiveprocesscanexist;freecon-vectionmustalwaysaccoq forcedconvection.Accordingly,theG-shofnumber,whichisa measureoftheintensityofthefreeconvection,must,intheory,affectevenhigh-speedheat-tmnsferGorrelati-.Beyondsomeminkl mass-flowrate,however,theinfluenceofGrashofnumberchangeshecmesnegligibleandcorrela-tionscanbedevisedinwhichtheGrashofnumberisreplacedbya

— ..—— ._. —-... ___ —-——.. .. .—.. ..— ..—— ..-— _.. .._ _. ________ . ..... . . ___

8 NACATN2117

suitableoonstmt.In.gene?xd-,itisimpossibletopredicttheminimalmass-flowxateabovewhichsucha procedureispermissible.J&ob (refe~noe5,pp.492-493)presentsa discussiondemonstratingthatthesquarerootoftheGrashofnuniberoanbeconsideredaspecislcaseoftheReynoldsnuuiber;theobservationcouldheusedtoformdatea ruleprovidingtheorderofmagnitudeofthe~minimalmass-flowrateina givencase.Inthepresentwork,Grashofnum-berohangesareofnegligibleimportanceandarethereforeignored.

(4)A singlepsmameter,thediameter,issufficienttochar-acterizethegeometriopropertiesofa long,smooth,roundcylindernomsJ.lyexposedtoa stresn.Undersuohconditions,thel?usseltnumberhas_beengivenbysomecorrelationofthefollmnlngkind:

(6)

Oneinvestigator(referenoe5,pp.559-561)intrcxhmed,inaddition,a temperaturefunctiunbywhiohtherightexpressionismultiplied.

(5)Thetemperatureatwhichtheseveralgaspropertiesareevaluatedisarbitraryunlessexperimentclearlyrestrictsthechoice.Theusualpracticeistoevaluatev, k, and Pr atsomemeanfti temperature.Thefilmtempera- adoptedhen?inisthearith-mtiomeanofthewiretemperature.andthetemperaturethatthewirewouldattainifunheated.Sucha choiceisentirelyarbitraryunlessitisshownthatthe‘lest”correlationsresultframitsemployment.

Exposureatobliqueincidence.-Intheforegoingdiscussion,theassumptionwasmadethatthewireisnormallyorientedtotheflowvector.llanyapplicationsrequireorientationatobliqueinci-dence.ThequestionthereforearisesaatotheeffectofsuchobliqueincidenceontheNusseltnumber.

lhuuerousinvestigators(references1,3,4,and9 to13,in@icular) haveattemptedtoarriveata generalized,quantitativedescriptionoft@ veriationofheat-transferratewithanglesub-tendedbywireandstream.SuchstudieshavebeenmadeatMachnunibersbelowabout0.4;theresultsthereforeapplyonlyinthecaseofessentiallykcomp~ssiblefluw. !

Agree~ntexists‘~ongtheinvestigatorsforwire-flowvectoranglesbetween90°andabout25°.Withinthatrange,theNusselt

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— ——

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“1!

NACATN2117 9

numbersobse~edarevirtuallythesameasthosethatwould.heobservedweretheactuslflowvectorsreplaced%ytheocmponentsnomaltothewire.Atanglessmallerthanabout25°,theheatlossisgreaterthanthat~eaictedbythisrule;thediscrapa~yandthedisagreementamongobsemersincreasesastheangledecreases.Finally,attheconditionofparallelismofwireandflow,theNus-seltnumberisinthevicinityof50to60Tekcexrtofthenormal-incidencevalue.

Whenwim behavioronlyatwire-flowvectoranglesgreatertk 25°iSconsidered,itiSe~aentthat~ allsuchrelatio~asequations(2),(3),(4),and(6)theairspeedV should%ere@acedby V’= V cosg, inwhichT istheanglebetweentheflowvectorandthenormsltothewireinthewire-vectorplane.ThequantityV coscp is,ofcourse,theeffectiveairspeed.ThevalidityofthissubstitutionatMachnunibers~ater than0.4isassumedinaH discussionshereinexceptwhereotherwisestated;thesoundnessofthisassumptionisunknown.

Behaviorofexposedunheatedwire.-Thetemperatureassuredbyanunheatedciroularcylinderofhighthermalconductivityexposedtoa fluidflowisslw&ysgreatert% thestatictempera~-butlessthanthetotal.Theactualtemperatureattainedunderthestatedconditionsisusuallydesignatedthe”effectivetemperatureandissodesignatedherein.

Investigations(references14andI-5)~ve beenmadeofthevariationoftheratioofeffectivetemperaturetototalorstatictemperaturewithMachandRemoldsnumbers.Theratiohasbeenfoundtobeprincipallya functionofMaohnuniber;Reynoldsnuniberchanges

, haveanahostnegligibleeffect.IRzmericalvaluesaredisoussedinthesectionTemperatureRecoveryRatio.

Itissufficienttonotethat,ifMachnumberisknownorcalculable,staticandtotsltemperaturesmy beoltained%yusingthewireasa resistancethermometerinviewofthepossibilityofexpertientalestablishmentoftherelationbetweenst~ticandindioated(thatis,effective)tempemturefora giveninstrument.

Variationof’theeffectivetemperaturewithQ ocours(refer-enoe14),butsuohvariationisnot-treatedindetailinthereport.AnadditionaldiscussionofthematterisTresentedseotionTemperatureReoovergRatio.

presentinthe

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10 NACATN2117

Radiationlosses.-Nomentionhasbeenmadeofradiationeffects.Ingeneral,heat-transferratesassociatedwiththeexpo-sureofheatedfinewirestoairstreamshavingspeedsgreaterthanabout1500centimeterspsrsecondarefarhigherthananypossiblyresultingfromradiativetransfer.Atveryhightemperaturelevels(eW>800°C), smallradiationcorrectionsaresometimesrequired.;,,suohoorrectionsareas-d negligibleherein.

PossibleArrayConfigurationsandUses

Theterm‘array”asusedhereinmeansonewireoratwoormorewiresarrangedina definitespatialpatternheldbya suitableseriesofsuppotis.

8Thefollowingdiscussi~ofarrayt~s andusesis

groupofandrigidly

limitedtosteady-statemeasursments.A fatilycomprehensivediscussionofthesamesu%jectinthecaseofturbulencemeasurementsisgiveninreference16.

Usesandp oceduresidenticalforallarrays. -Thethreeprin-oipalusesofarraysarethedeterminationoftemperatureandthemeasurementcfmass-flowrateandofflowdirection.Measurementsoftemperatureandofmass-flowzatearemadeacconiingtoessen-tiallyfixedTrocedumesregardlessofthearrayt=.

Inallcases,theqwmtitiesR. - ~ o-ctefistioofeacharraywireordesiredcczibinationarep?edeterm.ined.ThevariableTa/keisthendeterminedasa functionof M byaero-mo cdibmtion.Theorientationofthestreamwithres~ctto .thearrayshould%ethatwhichistobeconsideredinaXlsubse@entuseofthearraytheprincipalormeanorientation(generaJJ-y,normaltoa singlewireorcoincidentwithanaxisofs-try ofa multiple-%dr earray).

A stream-temprsbumdeterminationrequiresa lumwledgeof M.Thetemperatureofoneormoreunlptedwires~ofthearrayisdeter-mi~a. Thestreamstaticandtotaltemperaturesarethencalculatedusingtheappro~ia~eexpxbnental-valueof Ta/Te. Thearrayori-en-tationmat beabomkthesameasthatwhiohexistedduringthecal-ibration.

Thefollowingconsiderationofmass-flow-ra’%emeasurementassumestheuseofanidealized~ consistingofinelasticwiresofzerothermloonductitityexposedtotheflowofanincompressiblefluid.

,A

.

—— ..- ——

NACATN2117 i.

,.

gmco

TheneuessaryIlld.ifications oftheourmmtstm@.ifiedtreahentarepresentedin-severalsubsequentseotionsofttireyort.

Therequiresinitialheat-lossoalibratim.ofthearrayis~0qif3heabyexposureattheprinoipalorientationtoa successionofknownflowso~c!terlzed.bya Mae rangeofmass-flmrates.Inthisinvestigation,constant-temperatureoperationofthearrayis~ as-a. A fa~toroft~ wer input(thatis,ourrent)isvarieaeithermanuallyorautomaticallysoastothedesirestemperature.

Theexperimentaldataareusedtodetermineand C2 of-equation(6),whiohisfOm:

mf 0.2389i2R—= = c1~f0.3 llkfPrf0“S(ew-ee)%

. llofaotorCos”●5 Q hashere

restate’dhere

+ ~2Ref0.5=

bring-the _ to

the Uonstantsc1ina moreexplicit

c1+ 02

(7)

beenassooiateawith Go“5.Infact,ifcalibrationad subsequentdataareobtainedatthesamerelativeorientationofwireandflow,sucha fixedfactoroanproperlybeoonsiaereatobeimplicitin C2. Iftheorientationohanges,however,itisneoessarytoretaintheexplicitfaotmuos~ withintheparentheses.Whenanarrayoftwoormorewiresisoonsiderd,theanglewillnolongerbe p, butratherwill.bethean@ebetweentheflowvectorandtheprinoipaldirectionofthearzay.

Thefaotor~ ise~ioitlyretainedinequation(7)inordertoUlm?ifythefollowingyoint: The--tea valuesof 01 and C2wKU beinverselyproportionaltothevalueof ~ usedinoonneotiontitha pmtioularwire.Theobservationis@st.astrue,however,ofthevalueof I?uf.Theuseofanerrone-% inthecaseofanidealwirewiU thereforeleadtonoerrorinthevalueof G.

Thenextrequirementinthedeterminationofthemass-flowrateofanunknownfluwisthemeasurementofgastemp=tum. BeoauseInoqssible flowhasbeenassumea,ee equalsthestatiotem~=-ture.Asbefore,thepowerinputrequiredtobringthe~ toa

-.. -.-——. . ..— .- .._ ____ ___ _______ ———— .—____ _. _..._ ___ . . .... . . - _ .

12

convenientfixedWiretempemturetion.

NACATN2117

temp~t~ ew isthendetemined.Ideally,theneednotbethesameasthatuseda~hg calibra-

All&antitiesappearinginequation(7)arenowlmownwiththeexceflionof G, whichistherefcmeeasilycalculable.(Thegas

eeeepropertiesaresupposedevaluatedat ‘f )=—0

2

.

Discussionsofflow~irectionmeasurementaresubsequentlypresentedinconnectionwithdiscussionsoftherespectivearrayty-pe8. .

Single-wirearmy.-Thesingle-wiremountcmnsidm,ofmurse,ofa singlewire,twowiresupports,anda suitable&mntingforthesupports.Sucha devicehasthemeritsofextremesimplicity,easeofoonstmction,andPresentationofa minimaldragcrosssectiontothestream.Thew5reisusuallyeitherparallelorperpendiculartotheaxisofthemountingtube.Thearraysu~ortsareattachedtothattube.Ifthemount~ isconsideredverticalintheo%servertsreferenceframe,referenoetoa wirep.rdleltotheaxisasa verticalwireisconvenient;thewireperpendiculartotheaxisisrefereedtoasa “horizontalwire.” Simikrly,a hor-izontal@ane isdefinedasonenomaltothemounkaxis,whereasa verticalplaneisoneparalleltoit.

Theyowerinputrequiredtomaintaina fixedtemperaturevariesapproximatelyas Cosq, ashasbeenstated;consequently,thevaria-tionofinputatsmallangles(nomslincidence)willbenearlynegligible.Forexample,a changeof q from0°to3.6°causesonlya O.1-percentdecreaseinrequiredinput.Thesinglewireatornearnormslincidenceisthereforeveryinsensitivetofluw-directionchanges,asisdesirableformass-flowdeterminations.Inthecaseofa horizontalwire,ohangesofflowdirectionwithina verticalplanenormaltothewirewilJ-causenoheat-lossrateohange;thesameobservationappliestotheverticalwireanddirec-tionchangesinthehorizontalplane.

A singleverticalwireisthereforeuselessasfarasMrec-tiondeterminationsereconcerned.Itcan,ofoourse;beused-todetezminetemperaturesandmass-floyratesinfreestreams,withinboundarykyersadjacenttosurfacesnearlyparalleltothewire,andtithinwakesbehind%lades,thetrailingedgesofwhichareroughlyparalleltothetireorlieina vertical@anecontainingthemountaxis.

.

——- ..— — .—. .—.— -———— —.. . . . .—

.- NACATN2117 13

. .

KCDco

.

..

,,

A horizontalwiremay,however,herotatedaboutthetiountaxis.Inconsequence,itmu beusedtodeteminetheverticelplaneinwmoh theflowveotorlies.Theapproximateflowangleisassumedknown.Thewireisrotateduntilitandthevertioalplaneinques-tionsubtendh angleoffrm 40°to600.A ~a~~nt ofp~rinputismadeaspreviouslydescribedandthemountthenrotateduntil,ata Tointroughly,90°fromthefirstposition,thesamein~tisre@red tobringthewiretothefixedo~ratingtempera-ture.Thevertioal@laneoftheflowthenbiseotsthehorizontalanglesubtendedbythetwg~ positions.

Thehorizontalwireoanbeusedtoadvantageina fceestreamortithina boundarylayeradjaoenttoa surfaoeroughlyyerpendic-ulartothemouqtaxis.Themethodofmeasuringflow-planeangledescribedinthepreoedingparagzqhcannotbeemfloyed,however,unlessthesurfaceispeciselyperpmifoulartothemountaxis.

v-array.-A V-OODibinatiOn00nSiStSoftWOWireS(OfaSnear=equal~nsions aspotioalle)generdllyinterseutin.gatanangleofbetween30°and90°.

Theplaneofthe_ isusuallyeitherhorizontal(fig.1)orvertioal.The~ferred.constructionisthatwhichplaoestheoenterofgravityoftheaxrayonthemountaxis.Inmostcases,thebiseotoroftheanglesubtendedbythewiresisnozmaltotheaxis.

Sucharrays,aswefiasa pxdal array,werefirstsuggestedandusedinreferenoe1. Windspeedanddirectionweremeasuredinconnectionwitha meteorologicalinvestigation.

A T+wraymaybeusedasa singlewirebyplaoingthetwowiresinseries;thepairoompriseonearmofa bridge.Soo-oteit,thearrayiSwelladaptedtothemakingofmass-flcmmeasurements.Alter-nately,thetwowirescompris~twoadjaoentarmsofa bridge,whiohisthe~ferredmnneotioninthe“caseofyaw-angledeterminationswhena horizontalarrayisused.A verticalarrayis,usefulfor.eithermass-flowrateoryaw-angledeterminativewhenoonneotedinseries.Thevertioalarrayisnotordinarilyconnectedotherwise;thepointissubsequentlydisousseii,asem thevariousmethcdsofuseandthelimitationsofbotharraytypes.

Whenconnectedinseriesasformass-flowdeterminatim,V-arraybehavior,asfarastheflowoomponentintheerray@Laneiscon-oerned,isne=lythesameasthatofa singlewirerunningthrough

Q

-----—- .... .... .. .-. -.. -.— .- —.— — .. ..-— ——-_ .._ _ _ .—_ ,_____ _________ _____

14 I?ACATN2117 ..\

thecenterofgravityofthearrayparalleltothelmseoftheerraytriangle.Thesensitivitytoyaw(undesiredinmass-flowmeasure-~ts )ofa horizontalarray(ortopitchof’a vertioal)oonneoteainseriesmy beshowntoincreaseapproximatelyas cot25/2.Thesensitivityinquestionremainssmll,however,unless6/2< = 300.A mass-flowdeterminationwiXLthereforenotbeinaqouratebeoauseofrelativeinclinationoftheflowvectorandthearraybisectoriftheveotorliesinthearrayplaneuntilsuahinclinationisgreaterthanseveraldegrees. .

Theoonslderationofyossibleerrorcausedbythe~senoe ofanout-ofqil.anecmponentofflowisnecess~ina determinationofmass-flowrate.A s~e anelysismaybebaseaontheobserva-tionthatthearrayresponsetosucha mnpmentisthesamsasthatofeaohwireactingindependently.Ifa horizontalarrayisuonsiaemd,thepowerinputrequiredtomaintaina givenmeantem-xti ofthewiresmnnectedinseriesmayaccord

Yy beshown

tovaryapproximatelyas (sin2S2+ cos2~ sin25/2)1 Provide&theyawangle~ issmeJ3..

Thepowerinputrequirmitomaintaina series-oonneoteilV-arrayata f-a temperaturevariesacoordingtoa correspondinglawwhenthepitohangle~ ismKllandtheflowisinolineaatanangle -.* totheem’ayplane.Inthisinstanoe,however,itispossibletoali~thearrayplanewiththeflowvectorby~utatingthemountabouttheaxis.T&able,asisshownby

ByX’@~C@ ~o tion

coniiitionofalinementiseleotrioellydeteot- .thefollowingConsideration:

by ~ inthepreoedinge~ssion, thefuno-

isdefha.

Itis”fullnathat

(9) ‘

(8)

. .

● ✌✌

-—.. _.-.

HACATN2117 15

Therelationisnotoormctwhenthe ocs~ lawisnotobeyed.

Theinputpowerreaohesa mininuzmat ~ . 0. Theminimumpoint,andhencetheflowyawangle,canbeelectricallydetermined.Analternativepmce~ istomaintaina fixedbridgecurrent;at$ = O thevoltageaorossthearrayreachesa madmm. Ineitherease,thesharpnessofthereversalpointincreasesa8 8 decreases.Thesensitivityoftheverticalerraytopitoh-an@echangesalsoinoreaeesas 6 deoreases,however,ashasbeennoted.

Whentheflowvectorliesintheplaneofa V-army,itispos-sibletodetermine~ (whensmall)approximatelybycamparingtheinputpowersrequiredbythewireswhenaotingindependently.Thetheoryisnotpresentedbeoausetheinformationavailableisinsuf-ficientfor’applicationofthetechniqueattransonicorhigherspeeds(wherevalidityofthestipleoos~elawisquestionable).

Thehorizontalarmy isusedtomeasureyawangleinanalto-getherdifferentman&r. Forsimplicityandolarity,itwillbem-smnedthatthetwowireshavelikedi.mensionsandelectriccharac-teristicsandthattheresistancesofthewiresupportsandthenec-essaryconnectingleads=~enegligible.Ifeachwirebecomesoneoftwoadjacentarmsofa simplebridgeofwhiohtheremaininganusareequalresistances,thebridgewi.13bebalancedwhen,andonlywhen,thetwoarraywireshavetheseineresistance,thatis,=e atthesametemperature.Ifthebridgeissoconnectedthatthe-currentflowsthroughboth-s (strictlyspeaking,atthebalance-ootitiononly),thatcondition(equal-resistance)iseasilydeteotedby‘anyofa numberofconventionalinstruments.

Becausethetwowires- nuwatthesametempsratumandhavethesameinputpowers,theanglebetweeneaohwireandtheflowvectormustbethesameforboth,thatis,therelativeflowyawangleiszero.Asa firstapproximation,itcanbeshuwnthatwhen-thisocnditionisnotquitemetthebridgeoutputcurrentispropor-tionaltothe~duot * cot5/2.Inthisinstance,theeffectiEquitelinearanda reversalofsignofoutputoucursat ~ = O.Accordin@y,themethcdisbasicallysuperiortothatpreviouslydescribedfora verticalarray.Ingeneral,sensitivityiseff-icientlyhightopemittheuseofanyvertexanglelessthanabout120°andotherwiseacceptable.

TheresponseofanyV-arrayisaboutthesamewhetherthevertexliesattheupstreamora~tre~ endofthearmy. Inflowsituationsinwhicha lateralflowgradientexists,itoften

.

. . .. —.—. —. .. . . . . -e—. ——. ..—. .. —— -.. . . ..— — -----— — —..— ..— — -.— .—. . .—— -

16 NACATN2117 .

becomesdesirabletooheckthemeasumdflowangle,providedaHorizontalarrayisbeingused,hyrotatingthearraythrough

.

apprazhately180°andredeterminingtheyawangle.Ifthetwoso-determinedapprentyawanglesdifferbymorethanabout1°,asignificantlateralgradientexistsandthetruedirectionisveryclosetothemeanof.theapparentdireotiom.Anx-arrayissupe-riorinsuchsituations,butisusuallyprohibitivelylsrge;foursupportsarerequired.

A V-arraymaybeplacedwithin0.01inohofa surfacecloselyparalleltothearray@anewithoutseriouslossofmeasurementacoumcy;however,forbcundary-layerwork,a singlewireisgen-eraJJypreferable.Thechiefreaaonforthispreferenceisthatlesslossofaocuraoyresultsfrcmforwmxi-supportwakeeffect;asecondconsideraticmisthatitiemoredifficulttomtittwowiresina desiredplanethantomounta singlewireparalleltoa given-.

A singlewirenomaltothemountaxiscanberotatedtoaTositioninwhiohitis‘paralleltoa givensurface.Ingeneral,theflowveotorwillnothenormaltothewireinsucha case.Thatprcmedure,ofcoux%e,oannotusuallybeenqiloyedintheeaseofaV-array.

.,

Finally,the.prinoipaldirectionofa V~ isthevertex-”anglebisector.Ingeneml,temperatureandmass-flowratemeasure-mentsaxemadewhentheanglebisectorandflowvectorhavebeenmadetoooincideasnearlyasispracticableinthegivensituation.

.“

.

l?arau.el-wb=array.-A verticalV-arraymaybeusedtomeasureyawangle,ashasbeennoted,buttheacouracyisusuallynotsohighasisdesirable.A horizontalV-arrayisunusablewhen,forexample>a largelateralgradientofflowexistsorwhenwake-e measure-~fis = aestia.

Theparallel-wirearraywasdevisedtooveroomethesediffioul--ties.Itconsistsoftwowiresmcuntedinthevetiioalplanecon-tainingthemountaxisandheldinspatialandelectricparallelismbytwoSUppOtiS. Thewiresareusuallya few(about5)diametersapart.

Thebasiu prinoipleisthewell-lamwnoneoftheheatedwake;earlierformsofthearrangementaredisoussedinreferences2and17to3.9.Themeantemperat-(hencethewrrayresistance)isa ~ whenonewireliesdirectlyintheleeoftheother,thatis,whenthelooslizedflowveotorliesintheplaneofthearray.

..— . -- _____

NACATN2117 17

Thewtresmaybeparalleltothemountaxisormountedatsaneacuteangletoit. Ineitlieroasejtheoenterofgravityofthearmy is@ace&ontheaxis.

A yaw-angledeterminationisusuellytie byrotatingthemountabouttheaxisuntilelectrioindicationhasbeenobtainea%hattheresistanceofthearrayisatsomemeximelvalue.Thebridgecurrentiskeptconstant.Theyawangleatwhiohtheresistancepeaksi~S-Y aefinea.

Tempmatureandmass-flowdeterminationsaremadeinthemannerpreviouslydescribed.Asbefore,the-y isfirstrotateauntilcoincidenceofflowvectorandarrayplanehasbeenachievea.Theinitial‘zeroing”isof-at importanceinthiseasebeoauseoftheh@h yawsensitivity.Mass-flowdeterminationsareaccuratewhentheflow~ituhangleiseitherknown,inwhichcasea suitablecor-rectiontozeropitchmm beappliea,orissmall.

Ccmibinationarray.-Certainadvantageswillsubsequentlybeshowntobeassociatedwiththeinclinationofa wireawayfromthepositionofnomalinoidence.Onthosegrounds,mountingthewiresofa pwallel-wirearrayatabout45°tothemmnt axisisdesirable.

Theoneimportantadverseeffectoftheinclinationistheconsiderableinoreaseofpitohsensitivity.InthediscussionofV+?mrayssuoharrayswerefoundtobeinsensitivetodirectionchangesoccurringintherespectivearray@anes(whenthetwowiresareoonnectedinseries).Combinationoftheparald_el-andvertioal-Vconceptsis,a sim@ematter;theresultisa ver-ticalv ofwirepairs.

Thetwopairsmaybeusesincombinationorseparate-l-y.ThePW angleisobtaineabyrotationofthemount,asina vertioalVora single~ti. Thesensitivi@topitohduringmass-flow-rateaetemninatimnsisabouttheSEUMasthatofa singleverticalwire.

Buththepmallel-~ instrumentsaesoribedare@ioul.arlyusefulforwakesurveysandforfluwmeasurammtsnearsurfaoesessentiallypamUleltotheaxisofthemount.T@ areusuallynotusefulnearsurfacesnormltotheaxis.

- A yyramidalarrayoonsistsoftln%eormorewiresofequallengt;meetingatanapexandsptrimlly aispseaaboutscm axis(usuallyonenormaltothemountaxis).

. . ----- .—_. — ..___ ---—--— -—----—— ---- ———- — .—--— -.— . .——. ——. ___ . .

NACATN2117

.

18

Suoharraysaretoholdaccurately.

veryusefulwheneverthe cos~ lawIsknownForexsa@e,ifthethreewiresareoriented

&longthreeinterjectingedge;ofanIms@narycube,itcanbeshownthatifthewireEIareconneotedinparsdlelthepowerinputwillbevirhdlyindependentofflowdireotionovera substantialsolidanglecenteredabouta cubediagonalthroughtheapex.Ameansofmeasuringthemagnitudeofmass-flowratewithoutregardfordiredtionisthereforeavailableunderthehypotheticalccndi-ticns@osed. Oncethemagnitudeisdetermined,thedirectioncanbemeasuredbyusingtheindividualw3res,ortheyawanglecanbedeterminedbyrotationiftwoofthewiresm symmetricallydisposedabouta verticalplanethroughthep-d apex. .

Ingene=, huwever,thecomplexityandthesizeofthe-dalstructureaswelJ-astheuncertaintiesinthecurrentlamwledgeofoblique-incidenceheat-transferratesatthehigherMachnmibersservedtopostponeinvesti~ticnofsucharmys.

Theprecedingdiscussionshaveassumedtheexistenceofidealanemometers.~icitly, thea8_a imrments =re supposedto . .’consistsolelyofwireshavingunalterableproperties,dimensions}andyositicnswithrespscttooneanotherandtothemounttube.Finally,thewireswereassumedtohavezerothemalocnductivity,sothatnoinputpowerwouldbelosttothesupports.Suchinstru- .ments,ofccuke,cann~betitised. ,

12xmithepossiblemountdetails,theavailablemountandwirematerials,andthealternativemountingtechniques,thedesignermst selecttheoptimmcombinationfora particularap@icaticn.Thecptimmcombinationisthatwhichyieldsthemostaocumteflowinformationaftertheinstrmmnthasbeeninaotiveusefora pro-tractedperioi,fa exsa@e,20hours.

Althougha whollyquantitativetreatmentofthedesign~oblemisclesrly@ossible,thefoIlowingdiscuss@nrepresentsanappr~chtothatideal.Reconciliationoftheocnfl.iotsamongthevariuusfindingsisdiscussedaftertreatmentsofendlosses,aerodynamicstress,impactandvibrationeffects,oorrosicn,andelectricstability.

Endlosses.-Inthealmenoeoferrorduetovariationwithtime~f thedhensicnsorofthephysicalpropertiesofthewire,.thechiefsourceoferroristheconductiveflowtothe . .

. .

_.—. —. — .. _____

NACATN2117 19

su~ortsofa substantialfractionoftheheatreleasedinthewire.Themagnitudeofthatf%actionmustbeknownina giv6nsituationtomakepossibleinteroomparisonsamongaerodynamicheat-lossdatatakenunderdifferingsetsofconditions.

Thefractionalendloss,representedbythes@bol ~, isdefinedastheratiooftheheatlostbymnductiontothatlostdireotlytothestream.Thisratiodepmiisuponthephysicalprop-ertiesofthewireandthesupportmaterials,thedimensionsofthewireandthesupport,theprevailing100aleffectivemass-flowrate,andtheeffectiveembienttemperatureand.themeantemperatiatwhichthewireismaintained.

Tabulationofa fairlyprecisevalueof ~ issubsequentlydisoussedinthesectionCALCUMTIONSANDCORRECTIONS;however,theequationsgiventherearesuohthatthedegreeandthemannerofdependencyof ~ onthevaluesoftheseveralparamete~deter-miningitarenotapparent.Ana~a3dmateexpressionthatclearlyexhibitstherelationssoughtisdevelopedinappend5xB andgivenherejthisexpressionwKllbefoundusefulinthemakingofpre-limi~ estimates:

(lo)

Thevalueoftheexpressioninbracketsdiffersfrom1 bylessthan10pe~entinalmostdl oases.Thevalueoftheexpression

. (%pJ) usuallyisnearly1 when ~S O.1 (atnicslvalue)..

Variationoftheprduotofthesetwoexpressionsisaccordinglyamatterofseoondaryimportance;theprcductmayoftenbetakenas1withlittleerror.

—-——. ————..—- –—..

—.——. . . . .. . — . ____ ______

.

20

Minimizationof ~equation(10)indioates,

NACATN2117.

maylestbeaccom@ished,asinspectionofbyIWdJlliZi73$the ~/Dw ratioEmd”usiIlg

wireoflowthermalconductivity.InMew ofthepresenceofthefactor(Reff,&)-1/4,anincreaseoflengthata comtant~~ratiowillcausea smalldeo~aseof ~, sothatoftwogecmetri-- S~ -S theMger will-loserelativelylessheattothesupports●

.

Decreaseofthesupporttipdiameteranddecreaseofthesup-portthezmuilconductivitywillresultin~~ decreasesof ~.throughchangesintheratio~;::y. O@rationatli@er

meanwiretemperatums,throughde&easeofthequantity(1-t)1/2,willsimilar

7affect~; thisquantityvariesapproximatelyas

(1+ saw)-l2. Forexample,anincreaseofmeanoperatingtempera-turefrom200°to400°C reduces[ undernormalconditicmsbyabut 6peroentfor20-percentiridium-jlatinum(asthewirematerial)orbyalout20percentfornickel.Thephysioalreasonforthedecreaseisthatwiththeriseinresistanceofthecenttiportionofthewirea higherf’mctionofthetotal.powerisreleasedwithinthatportion. .’

Ingeneral,errorsinthecalculationof !-leadtoerrorsincomputedflowcharacteristicsthat”aresmallbutnotnecessarily

*-

negligible.It isimportant,however,thata distinctionbedrawnbetwaenaninc-ct velueof ! consistentwitha valuecalculatedonthebasisofcalibrationdata(andusedtooomectsuchdata)andanincorrectvalueof ! inconsistenttitha calibrationvalue.If,totakeauextremesituation,thecalibrationsituationandtheexperimentalsitqationarethesame,thefact‘thattheaculatedvalueof ~ islowby50prcentineachcase(becauseofuseofaninoorrect~, forexm@e)hasnohearingontheresultantflowtiasurements.Close@milarityofcalibrationandexpertientalsit-uationsisa guaranteethatnegligibleetiorwillresultfromuncer-taintiesin ~. ASthetwodiffermorewidely,greatercareisrequireilinthecehulationoftheend.leases.A t~icelcase,involvinga fourfoldchangeofflowratefromcalilmaticntoexper-Mente3situaticm,wasanaly%iodlyinvestigated;sucha situationcouldariseasa consequenceoflimitationsoftestfacilities.InordertoavoidanerrorgreaterthanO.5percentinthecalculateReynoldsnumber,ascausedbyanerrorintheassumedvalueofanysingle~ter, itwouldbenecessarythatthemagnitudesofthe

.4

.-

—.- ——_.

NAC!ATN2117

followingparametersbeaoouratetoatleast~, 5.5percent;~, l-l~roent;Dn, 60

21

thestatedpercentages:percent;~ and k+,

each110peroent;‘eftb 2} 200pero~nt.If,however,‘sucherr&sexistedsinm.ltaqeously,jtieerrorintheReynoldsnumberuouldbeas-at as3 peroetisothatthepermissibledeviationsare,ingeneml,correspondinglysmaller,

Asrdynamicstresseffeots.-Whenthewirestressisoftheorderof3X 10@dynecentimeter-2orgreater,theeffectsupontheaw~i&9 andthepropertiesOfthewirearesigdfic~tti ~tibequantitativelymnsidered.

Whenthewireisnotexposed,‘thestresshas,bydefinition,thevalue01. Uponexposure,thestressisinoreased;theinduoedstressisaesignatea(72● Theresultantstress,called03, isnotsimplythesumof 01 and 02. There-ktionamongthethreestressesd anexpessionmeldingthevalueof 02 follow;thederivationsaregiveninappendixC. TheerrorsinvolvedintheuseoftheserelationsaredisoussedinthesectionCALCULMTON8ANDCORRECTIONS●

033+J32o@23 = o.

.

(U)

(12)

ThequantityF inequation(12)istheoombinedflexibilityOfbothSUppOtiS. Inthesituationofleastoomplexity,thatis,thatofa single-wiremount,thewiresuppotisofwhichconsistoffrustumsofconesrigidlyattachedtothemounttube,therela-tion(appendixC)

128$3F= (13)

~ % %,13%,2’

applies.

—-— ...— —. -- —— -- -.—-———-. —- —— .— —_____ —.--- .. —--. —_ .. —- . . .

..— . .. ..— _ ..-— .——. —.. —

22 NACATN2117

A knowledge&fthewiredimensions,dragoc-efficient,mass-flowrateperunitarea(takenata rightangletothewire),flowspeed(alsotakenata rightangletothewire),andsuy-portflexibilityisre~ueafora determinationof 03.

A @ot of 03, thestressinthewireduringopsration,asafunotionof 02 forseveralvaluesof’theititislstress01 is~sentedinfigure2. Athighvaluesof 01, 03 isnearlyinde~ndentof 02 atthelowervaluesof 02; theiiepmdenoybeoomesstrongeryithincreasing~2. Thissignificantcircumstancewillbereferredtoagain.

Thevalueof 03 mayhemin3mizedbydecreasingthe L@wratio,bydemeasingtherigidityofthesupports,andbyincliningthewiretothestream(equations(Xl.)and(12)).Inconnectionwiththefirstmethodofminimization,itshouldbeconsideredthatoneofthefm factors~ inthedenominatorofequa-tion(12)isassociatedwithF. Whenequations(12)and(13)arecombined,theexpression

‘23=*(93(83(!+‘CDG’V’)2%’14)

.

isobtained.ASthemuurksizevarie~,theratios~~, ~,1~,and ~,2&- wi31remainf-a ifgeometricsimilarityismain-tainedforthearrayandthesupports.Theratio~,2~ ispresentbeoausetherelativerigidityofwtresandsupptisaffeotsthedisplaoemetiofthew3re(fromthestraightcondition)perunitaerodymmicloading.Ithasalreadybeennoted,ineffeet(equa-tion(u) andfig.2),that03 decreasesS1OW1Ytithdecre=~al●

Theeffeotsofthesteadystress03 ontheacouracyofmea-uzwnentsare: (1) Highstress,byoausingslowirreversibledefama-tion,leadstoirreversibleandunoertainohangesinthemagnitudeoftheheat-transfersurfaceandintheelectriocharacteristicsofthewhe oreventocumpletefailure;(2)thewireismademorevulner-abletoimpactandVib”mtionalstresses(subsequentlydiscussed);and(3)a reversibleresistanceohangeocoursthatiserroneouslyconsideredbytheobsenertobe~sed bya temperaturechange(thestrain-gageeffect). .-

f-

_.— .—— –———-.. ——.

-.

NACATN2117 23

Theailverseeffeotsmaybeavoidedtosomeextentbyproperseleotionofmaterials.Thewirematerialshouldhavethehighestyossibleyieldpointintensionatthedesiredoperatingtempera-ture.Itisimprobablethatanymaterialhavinga roomtemperaturelong-time@eldTointbelowabout6.2x 109dynecentheter-2(90,000lb/sqin.)willbesatisfactoryforhigh-speeda@ica-tions;thefigurecitedisbaseduponexperienceattheNACALewislabontory.

Thestrainincrementaccompanyingtheohangefromal to &isgivenby

(15)

IntermsoftheresistanceChmgeis

strain-resistancefactorS, thefractionalthengivenby

AR s (03-al)—=R %

(16)

.

Seleotionofa materielhavinga lowvalueofthestress-resistancec=fficient%-1 isthereforedesirable.unfortu-nately,thevaluefor20-percentiridiumqil.atinumis2.87x 10-12centimete#dyne’1(1.98x 10-7olm/olug/(lb/sqfn.));thematerialservesverywellinstrain-gageapplications.

%stenissuperior

inthisres~ot,exhibitinga valueof0.44x 10- Ohmp ohmyerdynecentimeter-2.Ontheotherhand,tungstenwire,usedathigher~~ ratios,isusua21ymm highlystressedthanisiriaitnn-@SHTlum.

Minimization(byincreaseof Ul) ofthequantity(03-ul)ofequation(15)istheonlymethcdotherthanmaterialseleotionofminimizingresistanceohangescausedbystressohange.

Impaoteffcots.-A quantitativetreatmentofinstantaneousstressescausedbyimpactsofstream-honesolidp,rticlesisunavailable.Anoversimplifiedanalysis@eldstheexem@aryresultthata partiolehavingapproximatelythedensityofwater

. —.. .—. . ._____ ___ ._. _ ————. -. —- ..—.-— ~—. — —— _ ___

—-—- .. —--

24 ~CA TN2117

anda diameteraboutthe‘seasasthatofa 0.0038-centimeterwirecancausea tensilestressofatleast1.4X ld” dynecentimeter-2(200,000lb/sqin.)insuoha w5rewhenthep.rtioleissuddenlybroughttorestfromaninitialspeedof45,000centimeterspersecond.Nowireusedforanemometriopurposeshasa dismetergreaterthan0.0038cerdzlmeter.

%’

--

The&obabilityofa “hit”maybereducedbythereductionofwirelength(normaUyprojettedtothestream)anddiamter.‘Reduc-tionofw3rediametermch belowthemeaneffeotivkparticlediamterwillnotgreatlydeoreasetheprobability,however,becausethesumofthetwodiametersisthecontrolJAngfigureinthisconneo-tion.Themosteffectivewaytoavoidimpacts,ofcourse,isto “adequatelyfilterthestream.

Thereductionofimpactstressesmy beaccom~istidbyincreasingthewire.diamsterbeoausethedevelopedstressvariesinverselywiththesquareofthewirediameter.Lengthohangeshavea relativelyminorinfluenoeonthedevelo@3(tipact)stress,whereastheeffeotofohangesoftensionisunlamwn.ImpactstresseswSllnotexceedthosemusedbyparticlesofthe~ size(hence,generallymass)permittedtopassthroughthefilter.Inclinationofthew3retotheflow,whennotcotiraindioated,isaneffeotivemethmiofstressrduotionbeoausethedevelopedstressvsries

.“

approximately~-thesquareofthe‘ccnnponentofparticlespeednormaltothewire. . --

Theselectionofmaterialshavinghighyieldpointsintensionwillminimize_ oausedbyimpacts.Althoughcompressiveandshearstrengthsareequally@portant,allthreestrengthsaresufficientlywellco-1-atedto’obviatethenecessityofseparateconsiderationofeaoh.

Vibrationeffects.-Noattem~haqbeenmadetodevelopquan-titativetheorywherebypredictionscouldbemadeoftheamplitudesandfrequemiesofvibrationsoftheseverslcomponentsofa hot-wiremount.Instead,theapproachhasbeena whollyqualitativeoneoonsistiugprincipallyofreco@itionofthefaotthata veryrigidstnotur&isunlikelytodevelopsignificantvibration.Ingeneral,then,themcuntandsuppotismustbetie asrigidaspraotioablewithinlimitationsimposedbyotherconsiderations.Thewireratio~~ mustlx?minimizedandthewiretensionu1maximized.Hightensionvirtd2yelimimteswirevibration,afaotthathasbeenconfixmwlbyaotualobservation.

. .

.

——

.

NACATN2117 $ 25

.

Becauseoscillatorys%res~eBas~ocia%edwithanyrenanentvibra-tionnotpreventedbythestncturalrigidityaresuperimposedonthesteadyaerodynamicstresses(asmll asuponoccasionalImpmtstresses),itisdesirabletominimizetheaerodynamicstressesandtousematerialshavinghighfatigue-limitedyieldpaints.

oxidation.-Thesensitivity(toflowchanges) ofananemometerincreaseswiththetemperaturedifferencebetweenwireandfluid.Furthermae,a givenabsdhrtechangeinthefluidtemperaturewillcauseanundesiredchangeintheinptpowerrequiredformain-tenanceofa givenwiretemperaturethatisinverselyproportionaltothemeantemperaturediffennoe.Otherwisee~ssed, operationata high- tempera- minhizesreadingchangesmoasionedbyrandamorotherair-temperaturechanges.High-temperatureopera-tionhasalreadyteenfoundtodeorease~. Finally,theairtempera-turewilloftenbeabove200°0,which,apartfromtheprecedingconsiderations,requireswizeopsrationata minimmofabout3500c.

Corrosion(usuallyo@dation)ratesmaybeminimized,primarilybyoperationatwiretemperaturesthatareminimalwithrespecttotheconsiderationsmentioned.Noblemetalsoralloysuponwhich“layersformthatarerelativelyimgerzneabletooxygenmayleemployed.Alternatively,suitablebarriersoflmpemeahle,nonoxidizingmater-ialsmaybedepositedo-qthesurfaceofthewire.FinaUy,theuseofmetalsmaybeavoidedaltogether;oxidesexisthavingresistivi-tiesfailingwithinauseful-e whensuffioientimpuritycontentispresent.

Theonlymethcdwherebytheeffectofa givenoorrosionratemaybeminimizedistheuseofwirehavinga maximuma310wablediameter-a quantitythatvarieswithmanycircumstances.

Electricstability.-Aninwiantcorrespondenceof-resistanceandwiretemperatureisclearlyofbasioimp*ce.Intermsofthequantitiesusuallydealtwith,the0°C resistanceandthetemperaturecoefficientofresistanceshouldbeknowntoabout*o.05Prcentandshti re~inf~d ~t~n *O●1 wroe~orbetk-rovera peritiduringwhiohrecalibmtionistoleavoided.

Materialshavinghighmeltingpointsandhighstrengths(intheannealedstate)wi12almostinvariablyexhibithigheleotricstability.lngeneral,allOYSareless=ce@ible toc=st~inegrowthandotherinternalohanges.Eleotricohangesmaylereducedbysuitableannealingorpartialannealing(normalization).The

.

i

——. ..— -.—- —.—....- ————

.— —

26 NACATN2117

-t@es of*~ val-uesofmsistivityandtemperaturecoefficientofresistanceneednotusuallybeconsideredbecause,whensuita%lebridgesandgalvanmwtersaree@ OyedjvirtuallyE&I.materialsotherwiseacceptablewillyefuundtoexhibit”ausefullylargeohangeofresistivityperunittemperature.Itisinadvisable,however,toattempttousea materialhavinga temperaturecoeffi-cientbelowabout0.0006per% becauseinsuohcasesa givenuncertaintyofwireresistancechangeacmmpanyinga particulartemperaturedmngeisususXlya prohibitivelyIxmgefractionofthemallresistancechangeitself.

Reconciliationofconflictingrequirements.-Thewtcehasbeenchieflyconsideredasananemmeter-a devicethatfunotionsbecauseitste-ture israisedabovetheeffeotivemibient.Thesamewireservesverywellasa resistarmethermometer,however,sndthetwofunctionsaOnotrequiredistinotdesignconsiderations.

The ~~ ratioshouldbewmhizedtodecreaseendlossesandminimizedtodecreaseaerodynamicstresses,~creasevibrationalem@itudes,andincreasefrequenciesofresidualvibration.Ithasalsobeenfoundthat~ shouldbemin3mizedtodecreasetheprob-abflityofa partiolehit,andt~t ~ shouldbemaximizedtoreduceimpaotstressesandcorrosioneffectsandminhizedGOdecreasetheprobabilityofpartioleimpact.

Althoughestablishmentofa singlequantitativerelationthatwill~rmitcalculationofopt5mnmvshesof ~ and ~ inthe“absenceofquantitativetreatmentsofimpmtandvibrationeffectsishpossi%le,typicalexampleswillbegivenofproceduresthroughwhichtheseveticonflicti~~quti~ntsw ~ey inS= de~e yreconoflea. .

!-

,.

Letitbeinitiallyassumedthat”thefiltrationisperfect;hqactsarenonexistent.Itisfurthersupposed,inthisfirstexam@e,that‘kllmationhasbeenlargelycl-ted bytheselectionofanappropriatelyhighvalueof 01. Thewirelengthandtheorientationwithrespecttothestreamareassumedfixed.A valueof F inequation(12)isas8umed;thesu~ortshavebeenmadeasrigidastherequirementsofaer~c “cleanness~permit.Finslly,thewireistobeusedata temperaturesuchthatoxida-tionwillnotoccur.Underthesecircumstances,thewirematerialthatshouldbeusedandthediameterthatismostdesirablemustbeseleoted.

●

. .

--!

..—. ..— .— -.. —.—z. —. — -.——

NACATN2117 27

. .

,

,-

Inequation(10),thequantity

(!%’3’)[’-2(0.’%JI$T$Tmaybeassumedequalto1 forthepresentpurpose.Uponsoltingthemodifiedequation(10)for ~, thefollowingequationisobtainea:

I)w.80.4752/3~t4/3@}/3~-)2/3 (Ref,J1/3

(17)

Asanexample,a solutionbaseauyonthefolJmwingfiguresisgiven:~ = 0.254oentheter;~ = 0.12(aratherhighvalue,butgotexoe

Fi&al);filmtemperature,125°C;meanwiretemperature

~, 250 C;effeotiveambienttempera- ee, 0°C;and Re‘f,L,3000(correspondingtoanairspeedof2072cm/seoor68ft/see)atstandardpressureand0°C.

Initially,theuseof20-percentiridium-@atinumisassumetl;a is0.00085pr % and

%is0.042(cal/(sec)(cm)(°C))

(2.82x 10-3Btu/(see)(ft)( )). Incomperis~withthevalueof ~, ~ = 0.0000807(cal/(see)(cm)(°C)).

It5.Bfoundthat~ = 0.0023centimeter(O.00091+in.).Thedesignerwouldselectthenearestavaila@lesize.Theminimum~~ ratiowouldbe310.

Thediameterintheeaseofa differen%’materieliseasily

()l+c+ysoabulatea;the figcreal varytith

%. Forexample,

thediameterinthecaseoftungstenwoulabeabout0.00084centjme-ter(0.00033in.).TheminimumL@w woulabe303.

-———— ~—. —____ ___ ..______—- —z. —-- _ ———— . ..—. . . . .

______ .__. . —. ___

28 NACATN2117

~ Afterthew3rediametemfor-wmiousmaterialshavebeendeter-ti~a,thewiresmnstbeO~a onthebasisofexpectetistressesw ~da potits.TheinformationthatisEquireaisthemaximmlflowvelooitytowhicheachwiremay%esubjecteawithoutexceedinga certainfractionofthelong-the~da pointofthematerial.

Themaximumsteadystressshouldprobablybelimitedtoone-halftheknownlong-timeyieldpointofa givenmaterialattheoper-at~ temperature.A safemarginisaffordeabyobse’rvanoeofthatrule.

Bydesignatingthemaximumdhwablestresson (seleote&byanysuchrule),ignoring01 incmpwtsonwithus, andnotingthatG’= p~’,thefollowingequationisobtainedfrcmequa-tions(U) aria-(14):

Equations(17)and(18)areoaibineatoyield

—

!

“(18)

(19)

inwhioh

Forthepresentpurpose,thequantity(P~) ‘1/2‘isconside~dfixes.

3/4(k)

l+a5w2/3T@ quantityam

wconditionsofthea~fi~ti-&a “figure

naybeconsideredunderthe

ofmerit”ofthewirematerial.

.

.

-.

.“

--,.

. .

-.,b

.

—— . —

NACATN2117

. Byusing3.55asthentio oftheYielatungstenandof20-peroentiri!iium-@atinum,ofmeritofthetwomaterialsisfoundtobe

!$ cedingbasis,thenoblealloywtlltithstand

29

pointsintensionoftheratioofthefiguresabout1.05.onthep.re-airspeedsslightlyin

8? excessofthosetowhiohtungstenmaybesubjecteii,.

Impact stresseshavebeenignoresinthe~ceaingdiscussion.Suohstressestithetungstenwirewoulabeover13timesasgreatasthoseinthenoble-alloywirebeoausethesquareofeaohdiameterisinvolves.Clearly,ifspatialresolutionaemand.spermit,thelarger(alloy)~ woulabeemplo~a.

Asanadditionalexam@e,= outlineoftheanalysisreguireabyoneothert~ioalsituationisconsiaerea;,nonumericalresultisgivenasitwoulanothavethegeneralsi~fimnoeoftheresultobtainmlinthePvious case.

.

Itissu~oseathata wireofspecifiesmaximumdiameteristobeusestosurveya boundarylayer.Thestreamisnot-freeofpar-ticles;themaximmallowablediameteristhereforetheonechosen.Thecmqonentofwirelengthinthedirectionofflqwislimitedby,thema@tudeofthegradientinthatdireotion.toa givenfigure(~). Tk lateral-gradientisaullandthew&e-lengthomnponentinthelateral.directionisunspecified.Theanglebetweenthestmesmandthenozmltothewire9 shoulabelessthanabout60°topreventthdwirefromlying,insubstantialpart,inthewakeoftheforwardsuppti.ASpti-lY$ t~ madmumallowableend10SSiSapecifieii.

Theangle~ iseither60°,aea maximum,orisf-a atsome● lesservaluebytherelation(f%ome~ti~ (17))

(

Thelastquantitythetrueatis~ed

.-

.

04’’$2Y’’E=Y(!’20)~inparenthesesandthelength

. .

istheReynoldsnumber@se&upon%1”

—.-— . ..----- - -.— . ..-- —-———-—.—— --- ——- —.. . ----- .—- - --- –.—

.— -.. -.— ____ _--_a

.

30

Folhwingthedetermination,of ~eachofthexmterialsbeingconsideredofmaterialsismadefromthe~ointofequations(n) and(1.2);theprecedingaswellas V’=Vooscp. Itisfoumi

NACATN2117

andof ~=~osoCp forina givencase,a comparisonviewofsteadystressusingexpressionfor ~ isusedthat

(21)

Inthiscaseitistipossibletostatea simplerelationthattillserveasa figureofmerit.ThestressesC3 wouldbecaqmtedforsomegivenhighveloci~withinthedesiredworkingrange.Thesevetimatiridsofinterestwouldthenbeassessedonthebasisofcomparisonsamongtheseveralratios03/Om.

Theconsiderationsgoverningselectionofmaterialsaredis-0u8sed.The~sentationofthesalientconstmzctionfeaturesofmountsisfO~~Ted3Ya discussionoftiremountingtechniques.

●

EvaluationofMaterials

Wirematerials.-References20to24andotheryullicaticmswereconsultedtoobtaininformationconcerning~oys andelementalmtalsofpcmsihleuseintheexprimntalprogram.Unfo*tely,manymatetids(manychromium-bearQ3alloys,forexamyle)thatwere~omisingonthebasisofstrengthandcorrosionresistancecouldnotYeconsidered“beoauseneitherthermalcondnctivity noreleotricdatawerefoundinthelitera~. Itwasconsideredinfeasibletomakethethermal-conductivitydeterminationsrequiredtoevaluatesuchmaterisls.Electricaldatawereeasilyobtainable,ofoourse,ifa givenmaterialwasavailable.

. . .

--

-.

-.

-.

-“

.

NACATN2117 31

Thematerialsfinallyconside~dinsomed&ailweretungsten,noble-metal-platedtungsten,andthenoble-metalalloys.

Itwasknownthattungstenoxidizesfairlyreadily;dataontheincreaseofresistancecausedbyotidationarepresentedinfigure3.Thecurvesrepresenttheincreasewithtimeoftheroan-tenpratureresistanceofthreetyyicaltungstenwiresSuspetiedwithina heat-ingjacketandexposedtotheatmosphere.Evenatthemode~tetemperatureof482°C,thente ofincreaseofresistanceofthebarewireisabout1 percentperhour.Themaximumpermissiblevariationisabuut0.005percent.~erhouriffrequentrecalibration- tobeavoided.Theremainingcurvesrepresenttheincreaseofresistanceoftwotungstenwiresplatedwithplatinumbysputteringandbyelectroplating.!Chemte ofoxygendiffusionthroughtheplatingineachcasewassuchthattheplatedwiresoxidizedaboutasra~idlyasbarewire. “

Belowabout375°C,tungstenresistsoxidation(atnomnalpres-sure)sothata tungstenwireoperatingata meantemperatureof300°C wouldprobablynotfail.bycorrosion.A temperatureof300°c isthemaximumallowablebecausethetemperatureatthecenterofa tungstenwirehavingan ~~ ratioof250willexceedthemeanvaluebymorethan60°C. Inpracticea wirecannotbesafelyO~~tea atthemaximmallowabletemperature,foranysub-stantialelectricoverload‘willinevitablyoausea changeinchar-acteristics.

Tungstenwirecommerciallyelectro@atedwithgoldorplatinumisavailable.Suchmaterialcaneasilybefaptenedtosuitablesupportsbyroutinesilversoldering,buttheplatingservesnootherpurpose.

Severalnoble-metalcmbi~tions(gold-platinure,silver-platinmnjpalladium-@atinum)wereexcludedfromconsiderationbecauseoftherelativelylargerateofdecreaseofstrengthwithincreaseoftemperature.Rhciiium-@atinumalloyshaveinsuffi-cientstrengthevenatlowtemperatures.Alloyscontainingmorethanabout10~rcentofeitherosmiumorrutheniumcouldnotbeusedbecauseofsusceptibilitytooxidation.Noinformationwasorisavailableconcerningbinaryrhodium-fiidiumalloys;suchalloys,aswellasternaryalloysbasedoneitherrhodiumoriridiumorboth,should%eexperi&nta21yinvestigatedastheircharacteristicsshouldbeoutstanding.OnebinaryaIloy(20-percentiridimn- 80-percent@atinmn)andoneternary(5-percentruthenium-15-percentrhodium- 80-psrcentplatinum)appwmedto

.

— —--—.—.- —....+ ..—..-. —- . . . ._ .._,. ___ ________ _ ._ -———. - --—..——._____

.——.- ..—_— .—— ——-—.—

32

havedesirableelectric,mechanical,andteristios,onthebasisofthepublishedfromcammrcialsources.

NACATN2117

.

aorrosion-msistantcharao-data,and& available

.

.

2ublisheddata(withtheexceptionofthermalconductivity)concerni~bothalloyswerecheckedatthislaboratory.Thetwomaterialswerefoundtohavevirtuallythesameelectricpropertiesandcorrosionresistances;however,thestrengthoftheternaryalloywasfoundtobeabuut20percentlowerthanthatofthebinary.Theternaryalloywasnotconsideredafteritwasfoundthatthermalconductivitydatawereunavailable;itwasfeltveryunlikelythatthethermsloonductivity wouldprovetobesufficientlylowerthanthatofthebinaryalJ_oytocompensateforthestrengthdifference.Thermal+mnduotivitydatawereavailable(referenoe25)fortheiridium-platinumalloy.

Theresultsreportedhereinwereobtainedwith20-percentiridium- 80-percentplatinum.Oftheavailablealloysorelem=ntalmetalspossessingpropertiesthathavebeenevaluated,nomaterialisbelievedsuperiorinsofaraesteady-stateanemmetricworkisconcerned.

. .

.

. .

— -.

NACATN2117 33

Therelevantcharacteristics,insofarastheycanbeassignednumbers,arelistedinthefollowingtable:

Property Value mts . RemarksResistivity 32.9X 10-6 .

ohm-cm Dependentuponhistory-ofmaterial

Strain- 6.1 dimensionlessIndependentofhistoryresistance ofmaterialcoefficient

Temperature 750 Oc Valuecorrectonlyabovewhich forairatnormaloxidationis pressured.eteotable

Temperature 0.00085 Oc-1 Dependentuponhistorycoefficient ofmaterialofresist-ance

Thermalcon- 0.042 ml cm-lOc-1 Nomeasurementmadeatauctivity thisla%oratory;

valuecorrectat8 both0°and100°C

Yieldpointin 0.723X 1010 dynecm-2 Nomeasurementmadeatfullyan- (105,000) “ (lb/sqin.) thislaboratoryonnealedcon- fullyannealedaitlon material

Yieldyointin 1.00x 1010 dynecm-z Conservativevalueas-drawn (145,000) (lb/sqin.)Conaition

Young’smd- 212x 1010 dynecm-2 CalculatedfromUlusof (30,800,000)(lb/sqin.)elasticity

measuredstrain-resistanceandstress-resistancecoefficients

.

Thewireisusuallyannealedatthislaboratorybybei~broughtinopenairtoa temperatureofabout800°C andheldthereforseveralminutes.Thepericdisnotoriticsl.Suohananne~if3nota fuKlannealbutdoesnormalizethematerial.A decreasein~sietanceofabout5 percentoccurswithinthefirst3minutes.Aslightchangeoftemperaturecoefficientalsooocurs.changesof

.

--..——._.__. -

34

anykinaOcourringison.Therateofpractiaalpm-posesannealing.

Thelinearity

beyondthe3-minuteoxidationat800°C

NACATN2117

periodaresmallincompar-issolowthatforall

thewtrecompositionisunslte~dduringthe

ofresistancechangewithtemperature●isshowninfigure4. The-threespecimenshad-beensubje&edtoa 1/2-hourannealak820°C. Dataatthesevemaltempera-sw&e takenatbothincreasinganddecreasingtem~ra~s. A fewpointsweretakeninanentirelyrandomfashion;nevertheless,littlesoatterandnoapparenthysteresisocour.Becausestraightlinesoanbedrawnthroughtheyoints,theconclusioniswarrantedthat,totheorderofprecisionrequiredinthepresentapplications,therela-tionbetweenresistanceand.temperatureislinear.

Thestress-resistanceco&ffioient(2.87x 10-7(ohm)(ohm-l)(~2)(~-1) )~s fou~ inthema ~=r; t~ re~i~~e _measuredwhilea successionofstandardweightswas@acedonaloadingpansupportedbythetestw5x’e.Excellextreproducibility@ linearitywereobtaineduptothemximm stresstowhioheachspeohenwaasubjetted,namely,0.430x loo @e centimeter-2(62,400lb/sqin.).Thestress-resistancecoefficientwasthe. sam withinexperimentalerror(+3~rcent)forboththeas-drownandtheannealed(at800°C wires.OnthebasisofanassumedYoung’sldlulus07212x 1d 0 @ centimeter-2,a stcmin-resistancecoefficientof6.1wasTredicted.Thevaluewsslaterconfirmedbyexperimentsmadetodeterminethegagefactor(6.O)ofstraingagesmadewiththematerial.Asthegagefactorisinvariablyslightlylessthanthestrain-resistancecoefficientofthematerialitself,theassumedvalueofthemodulusmustbenearlyoo~ot.

Supportmaterials.-Thesupportwasrequiredtohavehighstrength,acoeptsaversolderreuyj ex~bithighelectficstability,havea lowprduotofresistivityandtempera- coef~ficientofresistance,oxidizetith’clifficulty,besufficientlyhazdtomakerepeatedoleanlngpracticable,andbeoapableofbeingmaohinedorfO~a. Inaddition,itwastiesira%lethatthethermalconductivitybelow.

Theocmmercialnickel-chromiumalloyInconelintheformofweldingrodwasselectea,foritmetallofthesespecifications.

Occasionallyitisaesirabletohavesupports,which,althoughexhibitingrigiil~tygreaterthanthatofInconelthesameorevenlessoppositiontoloodflow..

.

tipports,offerTheYmmg’smcilulus

--

--

.

.

NACATN2117 ‘ 35

.

ofInconelisabout214x lp” dynecentimeter-z(31.,000,000lb/sqin.);apparelltlyj nomaterialthatisatleastequallyacceptableinotherrespectshasa higherYoung’sIucdulusthanalloysintheniokel-chromiumseries.

Oneexper&nentalmountwasneverthelessconstructed.usingwiresupportsof(ground)tungstencarbide(6-p=ercentcobalt-bound.)oones.TbesupportswereconsiderablymorerigidthantheusualInconelsupportsdespitethe~smallercrosssections.TheelectriccharacteristicswereslightlyinferiortothoseofInoonel,how-ever,foralthoughtheresistivityisslightlylowerthanthatof@W3sten,thete~ra~ Ooeffioientisverymgh (ahOutO.006/%).Suohsupportsshouldthereforebewea onlywheneitherconditionsofseverevibrationprevailatthemeasuringstationorthechannelisofsuohsizethat suppoz%sofminimalorossseotionareessen-tial. Ingeneral,thesupportresistancewillnotthenbeknownaspreciselyaswhena niokel-chromium-alloysupportisemployed(forwhichthetemperatbcoefficientisusuaUyabout0.00016/°C).Tungstencabideaooeptsqilversolderrgadily;furthermore,itsetiremehardness&es possibleanindefinitesupportlife.

MountDetailsandAssenibly

. Therealizedmountscarryingaifferentarraysaresimilartooneanotherwithrespottonmterials,constructionaldetails,andadherencewithinpracticallimitations.tothedesignprinci@espreviouslydisoussed.

Mountdetails.-Typica2.oonstructionalaetailsareillustrated-infigure5. ThemounttubesofstainlesssteelorInoonelarethick-walledwhereverthepermissibleouterdiameterisabout D0.48oentim?terorgreater;thelimitationisthesubstantialfractionofthecrossseotionoccupiesbytheleadwires.Theportidnattheinst~nt endisgivenanapproxhatelystream-linedcrossseotionwhenever~cticable;oonsiaeredasanapprox-imateellipse,theminoram majoraxesoftheseOtionhavebeenassmallas0.20and0.35cent-ter,respectively,whenthesup-portscodaheplacedina planecontainingtheflowvector.Thesmall-sectionedportionisfairedintoa largertube;thetubeultimaix?lybeoomesa round,thiok-walled,l/4-inch-diametertubethatcanbeaccommodatedbya standafi.instrumentaotuatorofIVACAdesign.

.

.-— . .__ ...+__ .——.——-.—..— —-—. -.--..— —.———-—— .- —-. -.—.

36.“

NACATN2117

Thesuppotis,usuallyofInoonel,mnsistmostotiinationofoiroularrd andfrustumofa crone.pqrtion,almut1.9oentmterslong,hasa diamster0.064to0.15centheter.forthedifferentmounts.yortionistaperedfromthe~.ointofemergenoefrom

-.frequentlydfa‘lhecylindricalvaryingfromTheconical mala commercial ~

yorcelain-typoementinsulationtoa tipMameteroffrom0.01to0.023centimeter;thelengthvariesfrom0.76to1.9oetiimeters.Thesuppo%.isusuaXlybentatornearthebase(exitpoint)toplacethetipnearthedesfidlooation.Inaddition,thetipisoftenourvedinsuitablefashion.Irisomeinstanoes,a solidsupportisre@aoedbya suitableomibinationoftubes,makingpossibletheincorporationofa pressureta . Thequantit

‘~(007ti.lb-$)~ori~~~i~%%elof4.0x 10-7centimeterdynesupport. Thesamesupport,iffab&ted oftungsten-bide,whiohoannotbeinelastioellydeformed,wouldhavea flexibilityofabout1.48x 10-7centimeterdyne-l(0.026in.lb-l).

Theleadsareofglass-mated.copper.Theminhunnumberisfourasa Kelvinbridgerequiringtwole- Wr &upportisused..Eachleadissilver-solderedtothesupportbasepriortomountassembly.BytheexpedientofsilversolderingonesupportintoaslotintheendofthemounttubeandtherebyusuaUygroundingthatportionoftheoirmiit,itispossibletoreducethennmberoflead

. wiresoarriedwithinthetubebyone.Insucha ease,theadditionalleadconnectionIsmadetothebaseofthemount;thetwomaincurrent-supplyleadsalonecanbehandledinthismnner.

Itisessential.thata12leads(otherthanthetwofurnishingcurrenttotheentirebridge)be joinedtotherespectivesupportsatpointswithina smallfraotionofa cent~terofoneanothertoavoidtheprcduotionofdifferentialthermoelectricelectromotiveforoea.

StandardAN-seriesoonnectorplugs~ used;mmmeroialflex-iblecablearmorconnectsplugandmount.Whena pressure-p ispresent,a smll-diametertube.isbroughttothe@lugehngtheinsideofthesrmorwiththew3res;itleavestheplugthroughaholedrilledata convenientpoint(fig.5). Thisconstmzotionmakesitpossibletodisconnectandtoremoveplugandarmora!ndtherebytoreducetheover+lldiameteroftheinstrumentto0.637centimeterforimertionintoorremovelfromanaotudorwithoutpossibledamagetotheworkingend.

Thevariable@ug contactresistanceshavenoeffeotonthebridgerelationsbeoauseoftheKelvinconnection.Forthesame

.

. .

NACATN2117 37

reason,a oableofindefinitelygreatlengthmaybeused,providedreasonablyheavycopperisemployed.Noleadresistanceshouldhesignificant(>0.03percent)inoompsrisanwiththeminhalvalueofa bridgearmcontainingoneofthevariableresistances.

wiremounti~. - Itwaspreviouslystatedthata wireshouldbesomountedthata knownminimalstress01 existsinitapartfromotherstresses.Theentiremountingprocedureisdescribedinsomedetailleoausesatisfactoryinstrumentoperationiscriticallydependentuponwirebehavior.

Bycalibratingthesprin&ofa Jigsuchasthatshownalongwitha micromanipulatorinfigure6,thewireMy bemountedata@ownappliedforoe.Itisconvenienttowindsome20or30turnsonthebobbin.Whena mountingistobeperfomed,a lengthisbroughtoverthepulleysandattaohedtothespring-amclamp.Thebobbinmaythenbeturnedina retrogradedirectionuntiltheten-sionreachesabout6.9x 108dynecentheter-2(10,000lb/sqin.),afterwhichthemin clampistightened.Inthecaseofiridium-platinum,anannealingcurrentthatissulfioienttoraisethewiretem~ratumtoabout800°C isemployedwhilethewireisheldinahorizontalposition(bobbin,mainclamp,andbothpulleysareinsulatedfromtheyoke). Anannealingpericdofatleast3minutesisrequ~a forthenoblealloy.

Followingtheanneal,themainclampisreleased,thetensionadjustedtoabout0.414x ld” dynecentimeter-2(60,000lb/sqin.),andtheclampretIghtened.

The~ jigisalwaysattachedtoa micromanipulator.Inmanyoases,a secondjigand~ti~tor arere~md} asform~nti~ aT-wire.OneorbothofthemanipulatorsareadjustedtobringthewiretotheproperyositionwithrelationtotheSUPPOMS.The-shouldjusttouchthesuyports.Intheeaseofa singlewire,amixtureoffluxandfinelyground650°C silversolderisappliedunderthestereoscopicmicroscopetothejunctionfartherfromtheJigspring.Atthispoint,eitheranelectricora torohmethcdofheatingtheprongtipmaybeused.Thealcoholtorch,fins-tipPeaIandfedbyo~genunderseveralpoundspressure,isexcdlentforthework.Theflameshouldbeperhaps3 centimetersinlength;itcanhardlybetoofine.

Theflametipisdirectedatthewiresupportbetweenthemountandthe~unction.Undernocircumstancescanitbeallowedtoplay“‘onthewireorthejointitself.Whenthesupporthasbecomelocally

. .

.

. _ .. ..-—.—-. .—. . . . . . .-—. —— — —- —-— --- ——~ . . . . .. ..

. -—

38 NACATN2117

heatedtoa moderateredheat,theflametipis~roughtnearerthejointuntilthe~oint-by conductiononly-hasbeenbroughttoamoderatered..Itisnearlytipossibletomeltthesoldertooquickly.Severalseconds’useoftheflameisadequate.Thewireonthejointsideshouldnowbemeltedthronghata distanceofabout0.5cen-timeterfromthejoint.ThisPoceduretransfersthespringloadtoonesupport.Next,thejointatthesupportnearerthespringshouldreceivesolderandthe- flametreatment.Thewire@nthenbemeltedthroughonthatside;thes~ingarmshouldbecaughtbytheoperatorora rubberstoptopreventdamage.Alternately,thespringam maybepushedtowardthe@ley ad themeltingaccomplishedor,inthiscase,a pairofscissorscanbeuses.Thejigisthenremovedfromtheworkarea.

Underthemicroscopeeachfreewireendisseized,preferablybya reverse-actionpairoftweezers.Intheprocessofengagement,the@r oftweezersisadvancedtuwardthepropersupportsothatthefreeendisneverundertension.Finally,a half-loopismadeofthefreewireandthepieceismovedbackandforth(trans-versetothetie axis)untilthefreeendbreaksoff.

Ifthis~ocedureisfollowed,thewirewillberigidlyfastenedtothesupportsundera stressaboutone-halfthatorfg-.inallypr

$8cedbythespringactionofthejig.A stressofabout

0.212x 1 dynecentimeter-2,(30,000lb/sqin.)canthereforebeachievedinthisfashion;bytheuseofmoreelaborateschemes,thisfigurecanbedoubledifnecesssry.Theclifficultyofwiremountingincieases,however,morerapidlythandoesthefinalstress.Inthecaseoftungsten,higherstressesareeasilyachievableandaredesirable.

Inthe-se ofa parallelpairofwires,whereinbothwiresareattached(inspatialand.electricparallelism)tothesamepatiofsupports,theonlyproblemisthatofholdingthewiresonthejig.Forthispurpose,anauxiliarypulJ-eyisaddedtothespringarm.Whena continuouslengthofwirehasbeenattachedtothejig,thecoursebeingfrmnbobbinthroughclamp,overfirstandsecondpulJ-ey,andthenoverthespring-am@U.eyandbacktotheclamp,theforcesonthetwowireswill,ofnecessity,kemainequal.Ifeachmainpulleyispluralllygroovedtoa depthofabout0.005centhneter,usinga grooveintervalofabout0.013centimeter,thespacingofthewirescanbe~a b O.0~3-.centimeterstew,thetwobeingheldtotrueparal&lism.

Whena mountcarriesmorethanonewireorparallelpair,thewfresorpairsareshiltaneouslypositioned.Theprecisesoldering

--

-“

,.,

.-

NACATN2117‘ ~ 39 ,

procedurevarieswiththeconfiguration.Thebasictechniquesremainthesame,namely,tosolderasquickly&mlwithaslittleheatandsolderaspracticableandtotranEfers~ng forcetothatsupportfartherfromthespringarm~iortoapplicationandheattngofsolderatthere=iningjointofa givenwire.Inmostinstancesinvolvinga wirearray,a supporttowhichistobeattache~apluralityofwlrgmiseitheractuallyoreffectivelymorerigidthaneaohofthosethatcarrya singlewire.Itistherefonbesttoattaohthewirestothesingle-w&esuppotispriortoattachmenttothemulti@e-wiresuppoti,forthroughsucha prooedurethefinalwirestreseesaremoreeasilyestablishedathighvalues.

T= s inuse.-Severalt~icalmountsincurrentuseareshowninfigures7to9. A photographoftheworkingendofa horizontalV-q thatwasuodinedwitha total-pressuretapisshowninfigure7. Uponsuitablecalibration,thetapw beusedtoin-dicatea pressurelessthanstaticbyrotatingtheinstrumentthrough180°abouttheaxis;thecalibrati~willbefollowediftheradial-flowcomponentisnottoogreat.The~nsionsO.0038-centimeterwirearray;theentireworkingforthesmallerwires.

.A parallel-wirearrayisshowninfigure8.

aretypicalofaendissoeleddown

TheO.0020-centimeterwires&e se-ted byabout0.013oentim&er(centertocenter)andareinolinedatabout45°totk horizontalplane.A total-pressuretapisincorporated.

A doubleparallel-earrayisshowninfigure9. Eaoh@rissimilartothearrayoffigure8. Nopressuretaphasbeenpro-vided;thecentralsupportcmuldhavebeendesignedtoservethispurpose.

APPARATUS‘

TestTunnel

A conventionalwoodconverging~ivergingnozzlewasusedfortheinvestigationandcalibrationofthearrays.Thecrossseotionisreotangulsr,thewidthisconstantat7.62centimeters,W thethroatheightis10.16centimeters.

InstrumentbossesarelooatedalongthecenterlineofoneortheotheroftheplanesidewallsatpositionssuchthatflowsateightfixedMachnunibersrangingfrom1 to2.4axeavailablewhen

.

.——. . ..—. —.—— ..-— .—. —.+= ~. _.. _ -—— _—. _ —.. .—. — .-. ._— —..

—-..—_ _—...— —.—— ....— ..——. —.— — .—

40

thetunnelisSubsonicdataratios●

beingoperatedataareobtainedatthe

NACATN2117

sufficientlyhighpressureratio.throatatsubcriticalpressure

Dried, felt-filteredairissuppliedthrougha plenumohaaiberhavinganinsidediameterof91centimeters.Itisshowninrefer-ence26thatlargechangesofrelativehumidityhavesmallbutdetectableeffectsonhot-wireheat-lossmtes. Itwouldhavebeenimpossibleto obtainsubstantiallyshock-freeflowatsupersonicspeedswithoutatleastpartialdesiccation.Aaco?ili@y,therel-ativehumidity,asmeasuredatroomtemperatureandatmospheric ‘Pssure,waskeptbelow5 peroent.

NoevidenceofshockformationatMachnumbersbelow2.2waseverobservedwhenthetotaltempera- exceeded35°C. ObliqueshockfozmationoccasionallybeoameevidentbeyondMachnumbersof2.2.TheReynoldsnumberrangeforMachnumbersbeyond1.5wasrestrictedbylimitedheaterca~city.

Bridge

Theoirouitofthebridgeemployedisgiveninfigure10. Forallfhotionsotherthanthedeterminationoftheratiooftwoarrayresistances(forexample,armsofa V),thecirouitisthatofaI@lvinduublebridge.

Theswitcharrangementsaresuchthatleadandcontactresist-antesareeithercompensatedbytheKelvinconnectionorareinserieswiththehigh-resistancearmsofthebridge.Ineitherease,noap~ciableerrorresults.

A 1.O-ohmfour-terminalresistorisusedastheftiedreferencearm.Thevariablearmsbonsistofcommercial&cadeunitsofhighstability.

Suitablemeansareurovidedwherebytheeffectivegalvanometerssensitivity”maybealteredorremovedfrm thecirouitwhencontactsaresoarrangedthatcirouitonlyafterinitiationdisconnectedfromthecircuitofwirecurrent.

thegalva&eteraswell& thewirenoreadingisbeingtaken.Theswitchthegalvanomterisconnectedtotheofourrentflowinthewireorispriortointermptionoftheflow

.-

.

NACATN2117 4-

Oneuseofthebridgeisthedeterminationoftheresistanceofanunheatedarrayoranarrayheatedbythepassageofa fixedOurrent●

A seoo&useofthebridgeistheconventional’on&ofhot-wireanemomet~;thatis,provisionofa sensitiveandamuratemeansofdeterminingwhethertheresistanceofa heatedarrayagredswithsomefixedpedeteminedvalue.

Thethirduseofthebridgeisthatofdeterminationoftheratiooftheresistancesofmembersofanarray(forexample,thearmsofa V). Suoha determination~beanoriginaloneorasubsequentonere@red tomakeyossiblea deoisionastowhetheraratiohasremainedfixedattheoriginalvalue(asduringrotationofa heatedV exposedtoa stream).

Bridgeoperationsaresubsequentlydiscussedintheseotion~.

Unifonn+TemperatureBaths

Theeleotriocharacteristicsofthesupportsasfabricatedandofthemuunted.wireshavebeendeterminedbytheuseofioebathsanda molten-saltuniform-temperatuebathbasedonNationalBureau -ofStandardspraotices.

Thepurposeofeachbathistheprovisionofa reasonablyextensivezoneoverwhichthetemperatureisvirtuallyconstantandinwhiohthetemperatureisaccurately?mown.Thesupportandwireresistancesat0°C areobtainedbymeasuringthosequantitieswhilethemountisfmmersedinthemelting-icebath.Thetemperaturecoefficientofthew5reorofthesuppoz%sisthenobtainedbynotingtheresistanceofthewireorsupportswhilethemountisimmersedinthesaltbathatanawropriatetempera-,usuallyabout300°C.Ineach

(befo~.anoeto

ease,a closelyZitt-@metallioprotectiontubeisused..

thecaseoftheresistanceofthesupports,itisconvenientwiremounting)toattaoha shortingbarofnegligibleresist-eaohpairof-supports;thepositi6nis

thewire(orpair)thatistoreplacethebar.anoemeasurement,theknownresistance(attheture)ofthesu~rts inserieswiththearraythetotalresistance.

thesameasthatofInanarrayresist-appro~iatetempera-issubtractedfrom

.

.

——._——.p. -. —.. ——————. . — -..=———.-.— _. —.._ —.— -——.

_.. —. ..-

42 NACATN2117.

,.

.Thesalt-bathtemperatureisuniformtowithina deviation

undetectablebyuseofanexploringthermocoupleoverthecentral60or70cubiccentimetersofthebath.A 650°C mercurythermometerreadableto+0.1°C isusedforroutinework;thethermometernmstbeoheckedf%omtimetotim againsta platinum-platinum-rhcxliumthemocou@e.

Thetempez&mreassuredbythewfreineitherbathdiffersnegligibly,aftera suitablewaitingperid,fromthebathtempe=-ture.Thesalt-bathtempe=tumisroutinelydeterminedtobetterthan+0.25°C;theinternalconsistencyofthereadingsishigher.Theover-allaccuracyisthe~foresufficientforthepresentapplication.

heatflow

I$R~

Mass-FldworHeat-LossMeasurement

Theexperimental~oceduresrequiredtomakemeasurementsoflossesfroma wireunderknownflowconditionsandtomakenassvdeterminationsinunknownflowregionsaresimilar.

‘l!otaltempendmreandpressureandexitpressureofthetesttunnelareassumedtohavebeenadjustedtothedesiredvshes. Ingene-, thearraymustbeexposedtoa successionofmass-flowratesateachofa successionofMaohnumbers;thetotaltemperaturemay,scootingtostipletheory,bepermittedtovarywidely,butinpractioemustusuallybeheldwithincertainnarrowlimits(whiohwasthecaseinthepresentwork)iftheamountofcomputationallaborinvolvedinthereduotionofdataandpresentationinnon-dimensionalformisnottobe-y large.

..

,.

Arrayresistances,tempemtumcoefficientsofresistmce,dimensiom,andbehaviorwhenunheatedandexposedtoflowsatvariousMachnumbersmusthavebeenpreviouslydetermined.I&cmthisinformationtheratioTe/Tthastobedeterminedasa funo-tionofMaohntmiber.

Anarraymeanop=rati&tempemture(uptoabout500°C foriritium-platinum)ischosenandtheresistancecalculated.Thebridgevariable~ settingsrequiredtoensurebridgebalance(atthesumoftheresistancesoftheseleotedsrrayandsupports)a&e

‘ rode.

.

-.

. NACATN2117 43

.

.

Thearrayiserposed to thestreamatthedesiredimmersiondepthandorientation.Ourrentisthen~rmittedtOflowthroughthe_ and.them9gnitudeadjusteduntilbridgebalancehas13eenattainea.Themagnitudeofthecurrentisdetermined.

Becausetheflowconditionsareknown,theMaohnumberandthereforetheeffectivetemperaturearelmown.Allquantitiesre@red forthecalculationof TW#?rf0●3 intheidealizedrela-tionequation(7)arethenlmown.Thepraoticdcalculationoftheend-losscorrectionfactorreqma inthecaseofa realwirehavingfiniteratherthemzerothermalconductivityissubsequentlycon-sideredinthesectionCALOUMTIOI?sANDCOI?RECTIOIVS.

Ina mass-flowdetemnination,theheat-lossdeterminationmustbepreoededoraooompamiedbya flow-angledetermination(discussedPviouslyintheseotionPossibleArrayConfigurationsandUsesandsubsequentlyintheseotionAngleData).Knowledgeoftheflowyawanglepmnitsthearraytobeorientedwithrespecttothestreamapprmimatelyasitwasorientedwithrespeottothecalibrationflow. Successivemeasurementsofeffeotivetemperatureandofheatlossata seleotedarraytemperaturearethenmadeasdismissedelsewhere.

.

A pressurereadingismadeatthesametimeiftheinstnmentisequi~d withanappropriatetapandtube.

.

AlthuughtheNusseltnnnibercanbemlculatedatthispoint(theneoessaryend-losscorrectionhavingbeentie),thecalcula-tionofxtws-flowratecannot,ingeneral,becontinuedaccordingtoequation(’7).Therequiredalgebraioproce- is~esentedintheseotionAdaptationofgenetiizeficorrelationformss-flow-detenninationapp.lioations. ,

AngleData

Theyawangleoftheflow(withrespeottosomearbit~airedion)canbemeasurwi,asdiscussedingeneraltermsinthesectionPossibleArrayConfigurationsandUses,bya singlehor-izontalv, orbya verticalxel pair.

Therequiredproced~inthecaseofthesingleWre orhorizontalV hasbeendescribedinsufficientdetail-.

.

.

Inthecaseoftheuseofeithera vertiodV, v’efiica~el pair,orthearrayoffigure9 inthedeterminationof

—....—— ... . ..— _ . — —---- .-. —

_____ ...__ . .. ..__

44

yawangle,the~ooednrehasbeenoutlinedinConfigurations.Anunbwmrtantdiffioullzvin

NACATM2117

.-thesectiononarraymmcticeisthatof

combi&g%hemass-fluw&d angledetermi&tio&.Thebridgearms- setforthedesiredarrayoperatingtemperature.Theamay isthenorientedsothattheprinci~directioncoinoideswiththe :estimatedvertloalplaneoftheflow.Intheeaseofanarrayhavingtwoarms,thearmsam3placedinseries.Thearrayourrentisadjusted%0thevaluerequiredtoImlanoe,approxi~tely,thebri@e.

Themmxitisthenrotatedwhiletheourrentremainsfixeduntilthedirectionofchangeofbridgeoutputvoltage’reverses.Atthatpointthesrmyplaneandthevetiioalplanecontainingtheflowvectorooinoide.Ifa parallel-~irarrayisofthecurrentrequiredforbridgebalanceistheeaseofa vertioalV (ofsinglewires),sarybeoausetheNusseltnumberwillnotvary

TemperatureMeaeurement

beingused,a reoheckoftenreq-d.nosuohcheckisrayi~ywith~W

4

Te&ra~ measurementshavebeenpreviouslyconsidered;

Inneoes-angle.

it.

hasbeenre-ked thateacharrayisusableasa &sistancether-mom4er.Theprocedurein~otice isfirsttoalinethe”arraywith ..theflow(inyaw).A ourrentrangingfrom3 tillismperesfortiesmallestwiresaqdluwestairflowsto15fiiamperesforthelargestwiresandhighestairflom isthenpermittedtoPss

..

throughthewire.ThebridgeisWlanoedbyadjustmentofthevariablearmsandthetotslresistanceofarrayandsums isoeMulated.Afterthedeductionoftheresistanceofthesupports(~ y imiepndentoftemperat-inthecaseofInoonel),thearraytemperatureiscomputedbytheuseofequation(1).Finally,theeffectivetemperatureisconvertedtostatic(ortotal).

Theprecedingdiscussionneglectstwo~ossiblesouroesoferror,namely,strain-gageeffectandtheconductionofheattoorfromsupprtsimmersedinportionsofthestreamflowateffec-tivetemperaturesdifferingframthemeanvaluecharacteristicoftheregioninthevicinityofthewire.Thecorrectionforstrain-gageeffectisdiscussedlaterinthesectionStresscorrections.Theseoond.souroeoferrorhasbeennegligiblesofar.Therequiredtheorymaybeobtainedbya slighttreatmentpresented4ina~endixB;

modificationoftheend-losshowever,itisnotgivenherein.

.

-.

—. —

NACATN2117

CALCULATIONSANDCORRECTIONS

45

.

devaluationoffluidoonstants. -Throughoutthemkulations,thepropertiesofairhavebeengenerallyevaluatedatthemeanfilmtemperatuzw,whichisdefinedasthearithmeticmeanofthe100aleffectivetemperatureandthe‘objecttempemture.A slightde~-tureFromthestatedpzacticeooourredintheevaluationofairpropertiesinconnectionwithheattzmsferfromthesu~ortstothestream.Forreasonsofsimplicity,andwithnosignificantloss‘ofacouraoy,itwasdecidedinthatinstanoetousethetotalratherthanthemeantemperature,aspreviouslydefined.

Theairthermaloonduotiyity,visoosity,qndPrandtlnumberwereevaluatedatthef@ tempera- assodefined.

End.losses.-Theprincipalcorrectionregytredinconnectionwithallwiredevloesistheeliminationoftheeffectsofendlossescmtheabsolutevaluesoftheheat-transfercoefficients.

Thenecessarytheory,whiohessentiallyisa modification.ofearliert~aliments,isgiveninappendtiB. Theapproximationsmade,asstatedinappendixB,donotadverselyinfluencetheexaot-# itudeofthetreatment.

Allheat-lossdatapresentedhereinwerecorrectedforendlosswhensuohcorrectionhada signifioanteffeetonthema@itudesofthed@a re~orted.Thefollowingrelationdeterminedthecorrection:

() 1/2Y .+r-t - “(l-t

(l-t) --(+) -t)+ B(*-)=O

(22)

Theseveralparametersaredefinedbythefollowingequationa:

(23)

...-

46 NACATN2117

(24)

mcc2

B O.2389i2R~ (25)

1*= ‘bl’2%1’2% (Re’t,h,2)o”3(% -‘e)

when t haslhzsseltnumberiswhichb’C~S

beenoelculatedhy”theuseofequation(22),thecalculatedaccordingtoa ratifiedequation(7),

0.2389i2~=fik@uf(~w-G=)(1+ ~) (26)

ThequantitiesB, ~~, (Rett,b,~o*3,., Y, aud t aredimensionless.Theconversionfactor-0.2389caloriepersecondperwattthata~ars inthepreviousequationsisyresentbecausetheprcducti2r hasthedimensionswatts~erunitlengthwhereasthethermalconductivities~, ~, %, ~ ~ arenomallyassignedthedimensionscaloriesperunitlength~r second~r ‘C.Thefactor1.54isa purenumber.Thecalculationof ~ .requirescomputationof B, t, and Y.

Whena giveninstrur@ntisbeingcalibratedalltherequiredquantitiesareinnne&iatelyavailable.Inanexperimenidsituation;however,neitherthetotaltemperaturenorthelocalmass-flowrateisini’tiellylamwna- itisthereforetipossillehmediatelytodetermine~ and Re’t~,2.Themagnitudeof g isnotcriticallydependentuponB (whic~essentiallydeterminesthetemperatureattheendsofthewire),however,andbecauseB variesonlyas&/2 (Re’t,b,2)‘o”3itfo13mwsthattheuseofreasonableestimatedvaluesofthesequantitieswillleadtoti~y thefinalvalueof~ uponfirstcalculation.Inthisconnection,thequantities~and We mayhei~tial.lyusedinplaceof ~ and ~, respec-tively.H aesirea,~ and Re‘t~ z ~Y berec~c~ted~er”thefirstapproximationofthelo~-$lowconditionshasbeenobtained.

.

..

.

..

.

.

NACATN2117 47

.

J

)

1

Theover-allerrorinthecalculatedvalueof ~ inanygivencaseisestimatedtobelessthan5 percent.Ontheotherhand,theinternalconsistencyofcalibrationdataandexperimentaldatawillbeofa higherorderthanthatfigureappearstoimply,inasmchaserrorsin ~ areprimarilyofa systematicratherthananaccidentalnature.

Inthepresentend-losstreatment,anassumptionismadethattheratioofeffectivetototaltempemtureisthecameforbothwireandsuyyorts.Otherwiseexpressed,suohanassumptionisequivalenttotheIgnorationofReynoldsnumbereffectsontheratioinques-tion.Theexperimentaldataavailableareinsufficienttoformabasisofdeterminationofthevalidityoftheassmnption.

Intheabsenceofa differenceofeffectivetemperaturebetweenwireandsupport,noendeffectsexistwhentemperaturesarebeingmeasuredandnoend-losscorrectionneedbemade.

stresscorrections. -Despiteallprecautions,hot-wireinstru-mentsarerathersusceptibletodamage.Nodataarepresentedhereinthatwereobtainedwithanywirewhichforanyreasonwhateverexhibitedanirreversbilechangeofresistanceamountingtomorethanabout0.1percentbetweenchecksofthatquantity.Temperature-coefficientchangesasgreatas0.2to0.3percentoccurredbetweenchecksandweretolerated.

Ashasbeenyointedout,reversibledeformationsofthewirecausechangesoftbtalheat-transferratesassociatedwiththecor-respondingchangesoftheexposedsurfacearea.Suchohangesarepatentlynegligible.

Theaccompanyingresistancechange,tothecontrary,isnotnecessarilynegligible.

Inthecaseofthecurrentdatatherequiredcalculatedcorrec-tionswouldhavebeenof-er magnl.tudethanthefigureofpreci-sionofthemsasurements.Suohreversiblestrain-gageeffectswerethereforeignored.

Calculationofthestresschnge(occasionedbyaerodynamicloading)andoftheassociatedresistanceohangehasbeenbrieflydisoussedintheseotion.Aercdynamiostresseffeots.Useoftherelationspresented(equations(I-1),(12),(13),(15),and(16))ina fewtj-picalcasesledto AR/Rvaluessmallenoughtowarrantignoration;however,themagnitudesoftheerrorsinvolvedinsuohcalculationsmustbeconsidered.-.

,

..48 NACATN2117

.Beoauseofthenatureoftheassumptionsmadeinthederivation

ofequation(12)(appendixC)andtheratherlargeuncertaintiesInthevaluesof ~ andof F inanygivencase,itisquesti~hlethatthevalueof 02 isknowntoletterthan4i10peroent.

Thevalueof ~ isactuallyobtainedbymzlti~yingtheina~pressiblevalue(~ n infig.I-1)bythentio ofthec~-pressiblecoefficientto)theincompressible(fig.I-1);thevalueshavebeentakm fromreferences27and28. Theprocedureisnotrigorouslycorrectbutyieldsvaluesof CD probablyCO~Ct tObetterthan&10peroent.Theunderlingassumptionisthatthevariationsof ~ reportedformuxtousMachnuuiberswere,toafirstapproximation,un3tiluenoed%ytherelativelysmallchangesofReynoldsnumberoccurringoverthespeedrangesinquestion.“

Thecalculatedvalueof 03 -ies sl~lY~~th~2 at1~valuesof 02 (andhighvaluesof 01)W approx~telY~ U2atthehighervakesof 02 (thatis,thoseconsiderablygreaterthanUl). Thegreatesterrorin 03 isthereforeabout10per-c-entiftheuncertaintyin al iSiwored.

Thepossibleerrorinthedifference(03-al) isef~eaterimportancethantheerrorin 03, inasmuchaq (03-C@ determinestheohangeofwirecharacteristics.Atourrentlyemployedvaluesof 01 (ab6ut20peroentoftheroom-temperatureyieldpointsofthewirematerialsused),the~cefiaintYof (~ -al) ProbablY

2isusuallylessthanA2.1x 108dynecentimeter-(+3000lb/s in.)atanyabsolutestressUTtoabout3.4x 109dynecentimeter-?(50,000lb/sqin.).Wheneversubstantial(greaterthan0.0025cm)differentialbendingofsupportsoanoccurduetounequalaerodynamicloadingoruseofunmatohedsupportsofinsufficientrigidity,theerrorswillbegreater.

..

Substantiationofequations(n) and(12)shouldbeaooom@.ish-ablebyexposinga wiretoflowscharacterizedbya rangeofRepoldsnumbersatnearlyconstantMachnumberandtotaltem~rature.IftheReypoldsnumberrangeisnotgreatenaightoaffectconceivablytheratioofeffectivetotow tempemm} a~ a-nt v~iatio~ofeffectivetemperaturecanbetentativelyascribedtoresistancechangescausedbyvariationoftensilestress.Recently,a fewdatawereobtainedwitha sta=-mnt~ sitie-~~ c~bi~ti~ inan‘attempttosubstantiatequantitativelythetheoryaswe~ aEtheprecedingconsiderationsconcerningtheover-tiTrecisionofoal-oulationsofstresschanges.

.

..—

NACATM2117 49

Nosignificantchangeofresistanceofaniridium-platinumwireoouldbedetectedwhiletheair-flowcharacteristicswerevariedinthemannerindicated.Thevalueof 01 wasalout1.4x 109dynecentimeter-2(20,000lb/sqin.).Thenegativeresultwasinterpretedassigaif@gthateitherthetrueresist-anceohangewasaspredictedhytheory(inthiscase,notquitedetectable)orwassmallerbysomeunknowndecrement.Suchtestsshouldberepeatedatluw CTlvaluesandhigh~~ ratioa.

Accordingly,resistancechangegivenconditions.

thetheoryprobablysetsanupperbound.totheaswellastotheabsolutesteadystressunder

~AL RESULTSANDDISCUSSION

CalibrationandMass-FlowDetermination

Inthefoll.owingparagraphs,t~icaldataobtainedwithasinglewirenormaltothestreamareconsideredalongwiththeutilizationofsuchinformation.Thebehaviorofa morecomplexarrayissimilarfora fixedorientationwithresTecttothestreamalthoughthevaluesoftheMmensionlessconstantsoftheequationswill,ingeneral,bediffenntfromthoseapplyingtothesingleWixe.

CalibrationofSi@ e wirenomaltostream.-Resultsofaseriesofheat-lossexperimentsmadewiththesame.0.0038-centimeter-diameterwireovera peridofabout1 montham presentedin ofigure12. Theairtemperature-ied between23°and45°C. Thetiretemperaturewasfixedat290°C. A systematicchangeof~uflfifO.3 fith~oh -e-r canbeobserved.

Datatakenatseveralwiretempera~sarepresentedinfU?llre13● Thetotalairtemperaturesvariedletweenabout25°an.iand

for

50°c. Theuncertainties-ofthethe- oonductivity ofatiofviscosityarenotthoughttohesufficientlygreattoacc~nttheincreaseof I?uf/PrfO”3.atdecreasingwiretempemtures.

Thedeviationsareina directionsuchthattheinferenceispossiblethatthemeanwiretemperaturesactusllyarehigherthantheassignedvalues.Forexample,ifallmeanwiretemperaturesaotusllywereabout3°C higherthantheassignedvalues,theseveralourveawouldcoincide.Nosourceofsuchlargeerrorsoouldbefound,however.

.———. -—— -. ._._. _ ..— ___ ..- ____ ——..————. -———.——. . . . .

50

Correlationequations.-\ figures12and13properly,aequation(7)isrequired.In

Inordertocorrelatemorecomplexrelationviewofthechangeof

NACATN2117

thedataofthanthatofNuf/Prfo“3

withMachtier, itisnecessarytointroduceinthemannersub-sequentlyindicateda whollyempiricalfunotiondesignatedflanddependentsole~upm Machnumber.Thevalueof fl isarbitrarilytakentobe1 ataMachnmiberof1.

Thes~ad ofthedataoffigure13withwiretem~raturecanbeelbinatedbytheadoptionofa temperaturefunctionintheman-nerindicatedinthesectionBasicInstrument.Intheabsenceofvariableair-temperaturedata,however,theexponentofanytempera-tureratiosoemployedwouldhequitearbitrary.Whensuchdatabecomavailable,itshoulanotbedifficulttoexhibitheat-lossdataoverwiiierangesofairtempmatmre,tiretemperature,Reynoldsnumber,andMachnuniberasa single-valuedfunctioninviewoftheregularityofchangeofnondimensionalheat-lossratewithc_@ngeofwiretempemture. Becausea &ifferenceoftempe=- (@w~e)ofatleast150°C isrequirdifreasonablyreliableheat-lossdataaretoheobtained,themaximumallowableeffectiveairtexnperatuzwwZU beabout275°C;thisvalueisbaseaontheconservativemax-imum’allowableopenatingwiretemperatureof500°C ~ theusuaJ-ilifference(apprmimtely70°C)betweenew,~ and ev. Thetirtemperatureisunlimitedbyanyfactorotherthanwirebehaviorandtheexistenceof’suitablecalibrationfacilities;themountshavebeensuccessfullySubjecteatohigh-temperatureflows.Forthepresent,however,theairtemperatureisassunmitoremainwithin

o perhaps+50°C ofsomereferencevalueandthewiretempemtuxeisassumitovarybynotmorethan+25percent(intermsofthevalueonthecentigadescale).Undersuchconditions~ofiionofa .temperaturefunctionisunnecessary.

A correlationofthedataoffigure12ofthetype

Nq ().c1+C2Re’fjw0.5fl~fo.3

(27)

isaccordinglyindicatea,fortheseveralcurve~apparentlyoon-vergetoa comonzero-flowinterceTtont~ ~/~fO”3 as”

. ..—.5 —.

NACATN2117 “ . 51

pJcoco

Actua12y,however,itisimpossibletodetermineeitherfromthedataoffi&re12orfromothersimilerdataobtainedatthislaboratoqwhethersucha correlationoroneofthefollowingtyperepresentsa correctdescriptionofthedata:

(28)

Inviewofthefactthatitisunnecessaryaswellas@ossibletodistinguishbetweenthetwoTossiblecorrelationsbeoause: :hesmallnessoftheconstantCl 7incomparisonwith C2 (Re’f,W ●

forReynoldsnumbersgreaterthanabout30,equation(27)hasbeenarbitrarilyadoptedasthedescriptionoftheseandsimilardatabecauseofitsrelativesimpl.ioity.

Accordingtoequation(28),fl oouldbedefinedastheratiooftheI?usseltnuml)erata particularMachnumbertothatata Machnmberof1.0andthesameReynoldsnumber.Suoha definitionalthoughnotrigorouslyap@icableintheeaseofequation(27~,isconvenientasanapproximationtotheprecisedenotation.

Noattempthasbeenmadetoestablisha quantitativetheoretloalbasisfor fl. Qmlitativelyjitappearsreasonablethatt% funo-tion,whateveritsnatureinthesubsonioregime,shouldexhibitroughover41 symmetryabouta pointataMachnuniberof1.0onaplotof fl againstMachnumber(fig.14).Thisobservationstemsfromtheconsiderationthatthefluidflowovera substantialTor-tionofthesurfaoeofa - ata givensupersonicfree-streamspeedisroughlyequivalenttothatatsomesubsoniofree-streamspeedbecauseofthepresenceofa bowwaveatthesupersonicspeed.Theoomespondencerequiresfurtherinvestigationbutis@ly con- .firmedbytheoiroumstancethat fl hasnearlythesamevalueat@rs ofMach@era connectedbythewell-knownnormalshockrela-tion

.

.. . . . -—-— —..-—. —. -—. . . ..-— –.—-—. .._ —,____ .—. _ ... —- _ _ ——

52 NACATN2117

inwhichthesubscripts1 and 2 refertotheconditionspriorandsubsequenttothesh&k,respectively.

Thefunctionfl aswellascertainotherfunctionstobedis-cuseedisshowninfigure14. Althoughthevaluesplottedareprobablynearlycorrect,modificationfl possiblyberequired -aaadditionaldataareobtained.Furthermore,acmeevidence(notpresentedherein)existsthatinticatesthattheshapeofthecurveismaiifiedbyorientationofthewireatanacuteangletothestream.Qualitatively,suchaneffectshouldexistatsuper-sonicspeedsbecauseoftheflow-fieldmodificationsaccompanyingtheshookconfigurationassociatedwiththeforwardsupport(orsup-ports,inthecaseofcertainmultiple-armarrays). Inanycase,fl mat currentlybeexperimentallydeterminedforeacharray.

Ccnnparisonofthedataoffigures12and13withphlished.dataona quantitativebasisisimpossiblebecausenosimilarinformationhasbeenreleased.TheequationofthelineM = 0.375is

Nuf7= 0.16+ 0.468Refoe5‘f .

Theuseof ,

% 0:35+ 0.47Refo”52Frf0.3=

(29)

(30)

isrecommendedinreference8 (equation(4a),p.222)intheReynoldsnuniberrangefromO.1to1000atlowMachnumbers.Becauseequa-tion(30)representsthebestcurvethroughmanydatapointsobtainedbyanwiberofinvestigators,itshouldbereliable.

Thevalue9.80forthevariableN~/Prfo*3atan Ref”*5valueof18isobtainedfromeqyation(30);equation(29)yields8.58+atthesameRefo05value.Thedifferenceispartlyascribabletothefactthatthedataoffigure12donotexkndtotheverylowMach.nnmbersatwhichfl certainlyexceedsthevaluecorrespondingtoM= 0.375.

—— ---—-— .— ———— —. ——- —.— .— -

.

.

NACATN2117 53

Furthermore,noentirelysatisfactorymethdhasbeenemployedatthislaboratoryforthemeasurementofwirediameter.Thediam-eterusedinthecalculationsispossiblyinerrorbyseveralpercent.Accordingly,itisfeltthattheagreementbetweenequations(29)and(30)isfairlygood.

Adaptationofgeneralizedcorrelationformass-flow-deteminationapplications.-Becauseintroductionofa functionofMachnumbertoeffectcorrelationofheat-lossdatao%tainedatdifferentMachnunibershasbeenfoundnecessary,thequestionoftheutiliza-tionofsuchdataarises.Itwi13nowbesh~ thattheconibinationofanIndicatedpressure,aneffectivetempera~, anda heat-loss,datumuniquelys@cifies”thelocaleteady-stateflowchsxacteristics.Theflowdirectionisassuredtobeeitherkn-mrnordeterminable.

Thequantities .

and

.

aredefined.

Then,

Furthermore,

PiP*=W

Ref,w=Re*f,w~P~e

isdefined..

(31)

(32)

(33)

(34)

.. —.—. -. .—— —— — — ——. — ———. -. —-— - - ..- ——— —.- -—- —--—.-—

54 NACATN2117 .

I&omequations(33)-10••(~),

, Ref,w= Re*f,wfz (35)

The_diate significanceisthatseparationhas%eeneffected ‘of fz, thefactorsofwhicharedependentsolelyuyonMachnurher,andof Re*f~, experimentallydeterminablewithoutreferencetotheMachnun&er.

Combinationofequations(27)and(35),permissiblebecauseRe‘f,w= Ref,winthiscase,@eIds

Nuf0.3 ()

= Cl+ C2 Re*f,w‘“5flf20*5~Prf

=c~+cz( ‘)0.5f

Re*f,w 3 (36)

inwhich

‘3= flfzo”s=?

Now f. isa functionof

‘1 3?s

.

..

0.5(37)

1- A

Machnumberalone;itisexperimen-tallydete&&edpriortoanymass-flow=awtint. - .

ACCOfitiY,theMach-er d~ss-flow ~~ ~Y beobt~ned“bythefollm&~”proce&&e:

(a)Tu experimentaldataandtocalculate~ aml Re*f,w.

(b) Equation(36)isusedfor

(c)Theexperimentalrelationsentedbyequation(37),isusedto

equations(26)and(32)areused

thecalculationof f3.

letweenf3 and M, rePlW-detemineM.

.. .

——.._

. mm m 21i7

(d)Equationobtainedvalueof

(34)andthevalueof f2M areusedtocaloulate

correspondingpv●

55

tothe

Limitationof Re* method.-Themethodisclearlyapplicableregahilessofthe valueoftheexponentof Ref,w.,

Inpractioe,theprocedurewillyielda well+iefinedvalueof.f3 onlywhentheindicatedpressurepi exceedsthestaticp~by,atmost,about20percentofthevelocityhead.Infigure14,value~of f5 areplottedforthreecases.Thecaseinwhichtheknownpressureisthestaticpressureisthatforwhichp~/~= 1.0. ,A secondcurveIsgiventhatcorrespondstotheuseofa pressuretaphavingtheconstantrecoverycoeffioientofO.5sothat

l% 1E= ()%1+0.5 —-1

Ps

(38)

Thetotalpressureupstreamofanyshockconfigurationhasbeenusedherebeoausethenatureofthedeviceisunspecifiedd calculationofthetotal-pressurelossacrossanyshockisthereforeimpossible.Thethirdcurvecorres~ondstotheuseofa @otheticaltotal-pressuretubethatindioatestruetotalpressureunderallcondi-tions. ThecorrectionsatMachnumbersbelow1.4,foranyrealtotal-pessuretube,wouldbeW.

It”ispatentthattheprescribedprocedurewillfailcompletelyinthetldrdcase;itwiXlbeunsatisfactoryinthesecond.Thephysioalreasonforthesituationappearstobethat,witha pre-ssurewhichisitselfnearlyinvariantwithMachnuriber$~it~r thechangeofNusseltnumberwithMaohnumbernorthechangeofeffectivetemperaturewithMaohnumberissufficientlygreattodefinethepointontheMmh num~erscaleatwhichtheheatlossisoccurring.otherwisestated,theprinoipal-detemnerof~ch n~er ~st heapressurethatvariessubstantiallywithMachnuniber,thatis,a pres-sureapproachingthetruestaticpressure.ConsideredfromthepointofviewofReynoldsnunibervariations~

*e*f,w

mustbestronglydependentuponMachnumber.

u

56 NACATN2117

Becausetotal-pressuretapshavealreadybeenaddedtotwotypesofmount,statio-pressuretagsmaybeeddedaswell..Theoutlinedprocedureisoneofverygeneralusefulness,asitisnecessaryonlythattheidicatedpressureroughlyapproxirmte.thestaticpressure.

YawChsxacteristicsofAngle-SensitiveArrays

v-array● -Figure15presentstheyawcharacteristicsofaV-tirehavinga 90°apexangle.Galvanometersdeflectionhasbeenenteredasa funotionofangleofdeviationfromthepointofzerodeflection.Thesedatawereobtainedfora euooessionof M values,thetotalpressureandwireandairtotaltemperaturesremaitingfixedthroughout.Itisapparenkthat:(1)Theplotsarestraightlinesthatwouldallpassthroughthecommonoriginhadtheynotbeen,except’forthelowestone,displacedupwazdtoexhibittheirchmaoteristicsmorecle~l.y;(z)thelineshaveroughlyequalslopes,indicatingconstantsensitivityovertheflowmnge inquestion;and(3)thecha.raoteristicsathighsupersonicspeeds.srethes= asatlowspeeds.

Theover-allaccuracyofa determinationofangleshouldbeconsideredtobeabout+0.5°.ThisvaluewouldbesmallerforaV-wirehaving,forexarqle,anapsxangleof45°.

ThelinearityofresponsehasbeenPredictedinthesectionontheV-mountforthesubsoniccase.Notheoryisavailableforthesu~rsoniccaae,butevidentlythesamerelationholds,thatis,thebridgeout@ currentorvoltageislinearlydependentupontheangleV atsmallangles.

RareJ2.el-wim2array.-Figure16showstheyawcharacteristicsofa typicalprdlel-wiremount;inthiscasethearrayconsistedoftwoO.0025-centimeterAiameterwires0.25centimterlongsep-aratedbyabout0.013centimeterandorientedatabout45°tothestream.

Foryawapplications,a bridgeoutputmeterhavinga smallperiod,forexam@e,lesst- O.1sec~l isvev desi~blebutwasunavailable;thesensitivityrequirementsarehigh..Thegal-vancmeterusedhada peri~of3 seconds;thepointofilefl.ection-mmementreversalwasaccofiin@ylesscertainthantheinherenttolemmceofthearrayandthereisthereforesomescatterintheaatapoints●

beo-ide=dTheover-allacouracyofanangledeterminationshouldasabout+0.5°.

..

.- NACA

tion

Mach

TN21-17 57

Thedeflectionsarepresented.asa functionofangleofdevia-fromdirectionofmaxbmmdeflectionforseveraldifferentnumbers.Again,thecharacteristicsareessentiallyindependent

.ofM, althoughthereisa slightincreaseofsensitivitytithincreaseof M. Supersonicresultsareunavailable,butnoreasonexiststomzpposethatthearraybehaviorwouldbedifferentinthatregion.

Theaccumcywithwhichflowanglesoanbedeterminedisindi-catedinfigure17. Inthefirstcase,theMachnumherwasheldat0.457andthemas8-flowratevariedovera tiderange.Inthesecondcase,theMachnumberwasvariedfroma lowvaluethroughthetran-sonicrangeandthesectionpresaumheldconstant.Thedensityvariedslightly,ofcourse,asthestatictemperaturevariedwithM. Theshiftoftheangularzeropositionwassmallineachcase.Therearereasonsbasedonexperimentforbelievingthatthetest-tunnelair-flowdirectionvariesslightlyanditmustbeconsideredthattheerrorsaretotalvalues,thatis,wire@us tunnel.

TemperatureRecoveryRatio

Infi~ 18,the currentknowledgeof Tt/TeYTefit,~Ta/Teia~esentedforair(Pran&tlnumber% 0.74and Y = 1.4)inthecaseofnormalexposureofa circularcylinder.

TheGermandata(referencel-5)wereobtainedatsamewhathigherReynoldsnmnhersand,althoughofinterest,arenotstrictlycom-parabletothoseobtainedatthislaboratory.Othersubsonicdata(reference14)areinsubstantialagreementwiththesubsonicpor-tionsofthecurvesoffigure18.

Infigure19,prel~narydatapertainingtothequestionofvariationoftheratioTe/Ttwiththeangleletweena supersonicstreemandthenormaltothewirearepresented.Sucheffectsaresignificantandinviewofthesurprisinglackofsymmetryoftheresultsaboutthe0°pointendeffects(expo- topost-shockconeflow)arepronounced.

Theseresultsindicatethatwhenanerrayofwiresnotallofwhicharenomsltothestreamisused,thearraytemperatureratioTefitaS~~ aSthe~at-10ssc~ctefisticsIUUStbedete~ned”

—.—— — .——. —.. . --—,_____ _. ._. . .. ____

58 NACATN2117

colmLusIms

.

.

Aninvestigationwasmadeofthedesignrequirementsandheat-transfercharacteristicsofwireinstrumentstobeusedashot-wireanemometersandresistance-wirethermometersattransonioandsuper-sonicspeeds.Thefollowingoonclusiomweredrawnfra theresults:

●

1. Fine-wireinstrumentsofproperdesignmayheusedtoobtain~curateairtemperature,mass-flowrate,andflow-angledataoveratleastthetotaltempemturemnge from0°to275°C,atMachnmnbemrangingfrm O toatleast2.4,andatairtotal RensitiesatleastasgreatasWoe atmos@eric.Thestabilityofsuchdevioesmy bema@esufficientforengineeri~use.

2. Heat-transferdatafora ciroularcylinderoveratleasttheMaohnumberrangefrcmO to2.4maybecorrelatedbyadditiontotheconventionalrelation~ongNusselt,Yrandtl,~a Reynoldsnum-bersofa factorthatisa functionofMachnumberonly.

3. Thermometricandpwer-in@ datao%tainedwithsuohinstrumentstogethertitha pressuredatumhavingasanuppmlimita pressureexceedingstatiopressurebyabout20psroentofthevelocityheaduniquelys~cifya locelflowsituationregard-lessofthelackofotherinformationooncemngMachnmiber.

. .

kWiS Flight~rO@SiOIlLaboratory,NationalMvisoryCommitteeforAeronautics,

Cleveland,Ohio,January12,1950.

. .

. .

. NACATN2117

APPENDIXA

SYMBOIS

59

and

A

‘b,2

, a

B

SymbolsusedonlyinappndixeeB andC aredefinedwhereused- notlisted.

cro6f3-~ectionalarea,c$

%

%,n

C1,C2,...

c??D

%,1

%,2

E

F

f~

cross-sectionalareaofwiresupportatpointofwireattachment,on?

speedofsound,cmsee-l

0.2389i2~~nondimen-

1.54kbl/2~1/2~Re’t,%,20*3(~w-f3e)’

sional(1.54isa purenumber)

dragcoefficientforciroularcylindernormaltostream

dragmsffioientforcircularcylindernormaltostresmunder,inoom@essible-flowconditions

oonstantsdefinedintext

specificheatofairatconstantpressure,Cal--1 Oc-1

diameter,cm

diameterofwiresuppotiatbase,on

diameterofwiresupportatpointofwireattach-ment,cm

Young’smodulusofelasticity,dynecm-2

flexibilityofw%?esupportorpairofsupports,deflectionpertit force,cmdyne-l

ratioofNusseltnumberatgivenMachnumbertothatatMachnumberofunityatfixedReynoldsnmiber(definitionapproximate;defined@mntitativelybyequation(27))

.

—.-—---—. .—.—— -z . . . . . . . . . _ ___ ._—----- ——- -. -- . . . . . . --- .. —-. . . . . —-

. ——— ._ — —.. .— .. ___ ._

60 NACA‘TN2117 .

.

mUJ2

f2

.

[01T -1/2nflf2n= fl M ~ & inwhichn isusually0.5

pi TfZJ

A

perunit area,gramcm-zi3ec-1G

Gr

H

mass-flowrate

Grashofxmniber

heat-transfercoefficlent,calcm-2see-l‘C-l

%=

i

k

wirecurrent,amperes

calcm-l-sec’1‘C’1(referstoe, f, or t used)

thermalUonauotivity,airwhensubscri@

L

%

length,cm

maximumallowable(projectionof)wirelengthindirec-tionofflow(seeteti),cm

M

Nu

Machmniber

HD/kW3seltnumber

0.2389i2r ideally,ur 0.2389i2~k- ifend

Xkf(a--oe)(1+ C)

lossesoccur

0.2389i2~*Q (%”ee)

.. .

.

/

—

NACATN2117 63.(

Pr

P

R

Re

‘ef,w =

Re*f,w =

‘e‘t,ll,2

Re’f,L

‘gr

Pratitl nuder.

fluia(air)PreSSUZW,~ cm-2

Tressureindicatedbymea~ng device,inherenterrorofwhich(takingeithertruetotalortruestaticasa reference)isfunctionofMachnuderOnly,@e cm-2

wtreresistance,ohms

Reynoldsnumber

~ (whdnprimed,replaceV by V’)

P*ae~

M

Reynoldsnnniberoffluwbaseduponsupporttipdiam-eteratpointofw-heattachment,uponmass-flow=te perunitareacomponentnormltosupporttipatsamepoint,andupontotaltemperature

Reynoldsnumberofflowbaseduponwirelength~,tiponmass-flowmte perunitareacomponentnomaltowire,anduponmeanfilmtemperature

gasconstantforair,erggram-1%-1

wireresistanceperunitlen@h,ohmsem-l

r

%?

%-1 r ~J wherex = &stancealongwireJo

strain-resistance

changeperunit

factorofwirematerial,resistance

%ARresistanceperunitstrain— —Rx

. ——-— --.. —-— ——... -. . .

—-—— .. . .

62 ‘

T

t

u

v

a

e

ew,ll

ew, c

ew,=

P* =

absolutetempera~j ‘% .

NACATM2117

..

i?w-eeFw+a-l

general,fbotion (U$>8 isdefinedbyequation(8)ofthetext) .,

fluidValooity,m See-l

temperatureooeffioientofresistanceofwirematerial,.Oc-l

ratioofspecificheats

auglebetweentwowiresofarray,radians

ratioofheatlost%yconductiontosuypotistothat10stawdlytOfluiast~~

temperature,‘C

temperatureatintersectionof

temperatureatcenterofwire,

wireandsupport,‘COc

temperaturevirtuallyi$enticelwith f3w,~ (seea~psmiixB),‘C

viscoeity,yoise

density,-

W em-3

cm-3

.

.

..

..’

.,

.,

-. .

.

NACA‘TN2117

m.

SubscriptsI

b

a

D

e

f.

i

L

m

n

P

stress,dyneem-2

wirestressprior

63

toaerodynamicloading,dyneem-2

aerdynamioallyinducedwirestm”ss,dyneem-2

wirestressauringaerodynamiclc@ing,dyneOre-z

~ allowableoperatingwirestress(seetext),dyneem-2

anglebetweenflowvectorandnormiltotireinplaneofwireandvector,radians .

.angleinplanenozzwiltomountaxisbetweenprojec-tionofflowvectoronthatplaneandeithervertexanglebiseatorofV-arrayorprojection,onsame@ane,ofwireneitherorthogonalnorparalleltomountaxis,

anglebetween=iS,pitch

wiresupport

center

radians

flowvectorandplanenormaltomountangle,radians

.

effeotive-withrefersnoetotemperatureattainedbyunheatedbodyinfluidstream

meanfil.mvalue,basedonaritljmetiomeanofobject‘ andeffectiwtemperatures.

indicated

wirelength

maximumallowable value “

incompressible-flowrenditions

pressure

-—— - ——-- —,-—-——--—— .———— -- —-- ———. — —- . . . . .

. .. ———.—

64

s

t

w’

o

a

Superscript:.n

(

n

*

NhCATN2117’

static

total

evaluatedat0°C

pertainingtoideal,

conditionofnoendloss

generalexponent.

basedonflow

notcorreoted

oomponentnormltoobjeot

forendloss

reference

TheWr (_) denotesmean

state(asdefineaintext)

vslue...

.

.

. .

..

—.- ._ ..- .—. —- —

NACATN2117 65

. .

.

APPENDIXB

ENDLOSSESOFKIZ@S

Thesteady-statecaseofa one-dimensionalheatflowiselemen-taryandhasbeengivenbynumerouswritersfordifferentsituations.Thechiefpurposeofthetreatmenthereinisthereorganizationofthematerialwiththeah ofexpressingthelossina mannerthatwillfacilitateestimatesandfl expeditethemakingofprecisecomputations.Theresultsareexpressedina generalizedformandthefinitenessofthethermloonductanoeofthesupportiscon-sidered.Initiadly,thetreatmentisthatofreference12.

Thedifferentialequation(Ill)connectingthedirectlosstotheairstream,theconductionfromthevolumeelementinquestion,andthejouleanheatdevelo~dloudlyis

~2gw0.2389i2ro(1+ @w) = (e~r~e)~kfNuf-~ ~ ~ (Bl)

inwhichx isthe

This

and

ro istheresistanceindistancealohgthewire.

equationmaybewritten

L&3.

ohs percentimeterat0°C and

inwhich

YckfNuf-C).2389i2roaP=

%?&

YIqIWqee+ 0.2389i2roPI=

%?%

(B2)

(B3)

(B4)

——.— . — —— -.--..—— .. .-. —.- .—— —— —— .—— -%-. .-—-—- ----- .-— .. —-

_.. ._ _____. .

66

ing

1=

NACATN2117

Theveriationof k N% d- the* iSi~O~a; theretit-errorisnegligible.

Byutilizingthe%undaryconditionsdf3w/dx= O atwirecentertddngtheoriginthere(sothat @ = ~ at x . t, defiti~~/2),thesolutionisfmindtobe “

ew=ev,m-(ew,m-ev,b)cosh91/2Xoosh$1/22

inwhich

.

e $1”w,==—=B + q - 0.2389i2roa

(B5)

practicalaswellastheoreticalInterestItisofconsider&blethd ew.=isequal.totheequilibriumtemperaturethewirewouldassumeiftherewerenoendlosses.l?urthermo=,theclifference%etweenthetemperatureatthecenterofevena shortwireandtheqtiitY ew,aiSS&.

Thus

eW,OJ -ew,c= ‘~* ‘at‘=0) (B6)

Inpraoticalsituations,j31/2z isseldmlessthan6& isusually~ater; hence,cosh$~/22> 200.ItwtllYeshownthat’ew,~s eeandthereforef3w,@a~ f3w,~ differbyatmost2°C.Thedifferenceisusuallynegligible.(Thatfaotwouldbeofgreatimportanceinthecaseofa fine+drethermocouplestretchedbetweentwosupports● Thepresenttreatmentwuuldnotherigorouslycorrectinsucha situationbecauseofthedifferencebetweenthethermalconductivitiesofthetwomaterials.butthebasicobservationwouldstill %evalid.Intheease&fcourse,ee and ew,aarevirtually

a fins-w&ethermocouple,thesameheoausejoulean

of

.

.

.-

. .

-— .—z.

.

.

-.

.

MACATN2117

heatingmaybeneglected.immersionoftheEupports‘e.)

Themeantemperature

67

Thesourceofconductionerroristheinregionshavingtemperaturesotherthan

isnowobtainedasfollows:

Al 1

5..* 1LI (%,cn-ew~) coshFl/2x=— e (ix-2Z w,= 1/2~ &z

cosh~-z -2

tanh~/2 1

-J

(B7)

validforvaluesof~ 6, tanhfi~121 ~ 1, Thisapproximationisp/2 2 assmallas3.5;therefore,

(B8)

justgiven(refer-Simmonsandence12),showed

Beavan,whopresentd_thetheorythatR = RO (1+ a 8W), inwhichR.~ ~ ro;

theidentityfollowsdirectlyfromtheobservationthattheresistanceperunitlengthisa linearfunctionoftemperature.

Upontakingthederivativeoftheexpressionfor f3w,therateofheatlosstoeachsupportisfoundtobe

Therefore,thefollcwlngequationoanbewritten:

(39)

— -——.. —=..—._. ——.——._. .. ——- ______ ___ .—— ... ——____

-...—. —.. —-.—- -

68

Thequantity

NACATN2117

isdefined.Itisportstothatlost

Theratio~

theratioofheatlostbyconductiontothesup-directly%0theairstream.

mayelsolewritten.

(m)

makingonlythepreviousapproxinwtionthattanhj31/22 = 1.OOO.

Itisnotablethatthe~rameter@/2 Z hasthefol.ltingphysioalsignificmce:Itisgivenbythe_mtioofthedifference~m~o~:g~ LO thedifference(6w,@-ew);thereforeitisa

ofthede-e ofdepartureofthewiretempera-turefromtheid

Yconditionofudformity.Utierthepreceding

oirotuns-ce@ 2 Z =m. Sucha situationvirtuallyexistswhen-evertheratio~~ or Nuf isvew lw3e orw~n % is~vsmall.

Itisa sim@emattertotransfomntheearlierexpressionforP insuoha wayastoobtain

Itthenbecomespossibletoconibineequations(Bll).and(B12)toobtain

1/2 ‘c=c3[(l-t)-til (B13)

.

OYal

“

.

,.

--

.. .. .——

. NACATN2117

inwhich

69

.

.

(B14)

Byexpandingthebracketinequation(B13),thefollowingequa-tionisobtained:

~=c3(l-[

t)m 1 ~ tt

1mm-”””

0

(Ills)

F C whereitappearsinthe’right-handexyessionby C3 (1

BYre~~ ,therelation

[ 1t=c3(l-t)l/21- Cst -O**=

(B16)

isdeduoe~.

Inequation(27),thepresenceofthefactorfl complicatestherelationbetweenNusseltandReynolds@era. Forthepresentpurpose,however,fl isconsideredfixedata value suchthatC2flPrf0-3 hasthevalue.O.475,whichisa representativemeanvaluefortheMaohmmiberrangeinvestigated.

Underthatcircumstanceandwith Cl permittedtovatish,

Nuf-~~2= ()0.475-1/2 Rel -1/4f,u (B17)

UponreplacingNuf-1/2 inequation(B14)bytheseoondappra-imateequivdtent,equation(10)isobtained.

- . . . . —.-— —--—- —-—-—— ---—— —-- —-— --—---—— - - ———— -—.—— — .--— --——-—

70 NACAk 2117

Equation(26)followsdirectlyfromtheprecedingsolutionofthedifferentialequationfortheheatflowtoandfroma givenpor-tionofthew5reandfrcmthedefinitionof !. Equation(22)remainstobeobtained;theinitialstepconsistsofa statementofthefollowingrelation:

ew,b= r ew, a+‘er+l

inwhioh

Thequantity1.02isa purennniber.

‘(B18)

(B19) ,

Equation(B18)isderivedbysolvingthedifferentialequationofheatflowforthesupportandtakingthenetheat-flowrateatthesupporttiyaszero;thesolutionissimilartothatforthewirealoneandwillnotbegiven.Theassumptionofa uniformsup-.portdiameterequaltothatatthepointoftireattachmentleadstonegligibleerrorbecausemostofthetemperaturedropirithesup-yortoccurswithina smalldistanceofthatpoint.

Thefollmtingquantitiesaredefined:

Nu”fE 0.2389i2~?tkf(~~-ee)

0%%2(3W-ee)-l‘%%

(B20)

(B21)

(B22)

..

-..

I

71NACATN2117

I

,,

Byuseoftheserelationspreviouslytosubsistamongthe

(B23)

definitions,equations(14)and.(15),andotherestablish@,thefollowingrelationsarefoundseveralquantities:

Nu”f=N~ (l+t) (B25)

~ =nl?uf”l-o(e,,,o-e~,b) , (B26)

Tw= ew,m- (ew,=-ew,~) (B27)c

o =mIWfl/2~-t (1+~)11’2

ew,b=boevo+eebo+l

Ikmmequations(B26)and(B29),itisfoundthat

Therelation

qJ(bo+ 1)-1=:*

(B28)

(B29)

(B30)

(B31)

.

---- ..— —. ._ _____ ——.—..——— .. —- .-.—— —.. _ .—— .—. . .-. .——-——

72 NACATN2117

tisthenobtainedfromequations(B27)and(B29).

or

when

fg=

Combiningequaticms(B30)@ (B31)yields.

~= nNuf-l(ew,a-9W)02

nNuf-l(5W-~e)c2t= C(bc+l)-1

equations(B27),(B29),and(B32)areused.

Ifequations(B28)and(B33)areused.,

(B32)

(B33)

1 -t (1+ !) ‘ ,

[

-11 [ 1

1/2bm?Nunf (1+ c) @ (l+~)-!t -1-t + mNu”f

.

.

..

(B34)

notingthatnm2(3W- f3e)= 1.

BydefiningB s 11~/2bm2Nu”f.and Ys rd?uf itisfounathatB and Y aretheexpressionsgiveninequatio~(25)and(23),respectively,andthat equation(B34)becomesequation(22).

\

.-

-.

_——.— ...— — —-. . -—.-.

NACATN2117

io?PENDIxc

Wm3ESTRESSm slIePoRrDEFLECTION

Aerdynamiustress

73

If w istheuniformtransverseloadperunitlengthappliedtoa hingedthinbeamassumedtobebentintoa circulararcofwhichthesagittaz (portionoftiiusnormaltoohordinterceptedbychordandarc) issmallcomparedtiththearclengthL, thefol-lowingrelationsubsistsamongtotaltensileforceT ,amithosevariables:

Foranaer@namioally

Therefore,

T WL2=—82

loadedwire

T=CDPV2V2162

()If 03 ~= ~ isthestressinthewire,then

(cl)

(C2) -

(C3)

(C4)

Thisrelationappearstohavefirstbeenmentionedinrefer-enoe3,exceptthata faotorof2 isomittedinthedenominatoroftheexpression,.

Thequantityz mustbee~ssediablesandofthelmownohsracteristicsSuppotis.

interms oftheothervar-ofthewirematerialand

.__—. —.—. . . . — -. —.. —-- .— - —.-—- —-— — ——— -—— .————

74 NACATN2117.

Let u bethe=diusofthebeamarc;A, theanglesubtendedatthecenterofthecirclebythesemiarc;and L~, thedistancebetweenthewiresupports.

Then

-&=uA2 (C5)

Now,

21/2()zl/2(1+*+...)= ii

.

.

..

(C6),.

Thelastrelationfollowsfromthefactthat

=[?$’’2-+)1’2.-%($’’2-”●]++)3’2-$(%)’’7s)+..]

\. . .

, NACATN2117

T.herefcm3, ,,,,)

()L = 2UAz 2312(uz)l/21 +&

Ontheotherhand,

().2..g.$1’2b

!rherefore,

L-‘s=23’2“’)”2(*‘4()$/2 ~~lz ‘

=—-3U

toa firstapproximation.

now,

.(iiqy?$...)

75

(C7)

(C8)

(Clo)

— .. . . . . . .-. ——— —.—. — ... _ ——.—— —.. —

76

3Xthefirsttezmoftheright-handmemberofinequation(C9),theseoondequationbecomes

tion

8 ~2L- L~=-—3 L~

NACATN2117

equation(C1O)isused,

.(Cll)

Theoriginal wirelength(aftermpunting,butyiar toimposi-afdm9gload)isdesi~ted~.

Thedecreaseh distancebetweenthesu~ortsisgivenby

((m)

inwhiohF inthis&se isthecambinedflexibilityaf’thetwosup-portsand LS,2 isthedistancebetween~b supportsduringaero--iu. l~m” .

Thechangetiwirelengthisgivenby

Therefore,

‘=++%9

(c13)

(C14)

#

..

..

— .—— ——--—— -—

--

-.

.

.

NACATN2117

Whenequation(Cll)isused,

77

By?xmallingequatim(C4)enddroppingtheand L~, therelation

NowM thequsntity

(an“exact”formof

023=~32

distiukionbetweenL

~ (03- 01)2 (C16)

equation(12))isdefined,

(C17)

(C18)

M arbitrzxryunits,if

03-3

.

.—— — ____ —-—. .— —. —-. .— ______

.

78

then

NACATN2117.

.

‘( )q++ -1- 3.3.x10-4

4

()therefore03 ~+ ~“v

‘1C<1 andthesecondtermofequation(C18)

mqybetakenaszero.

Thefinalresultis

033-032-01-023=0 (11).

.

Thepcedingtreatmentneghotsvariable-temperatureeffects.Theseeffectsareusuallyofsecond-ordermagnitude;however,inthecaseofhigh-tempemturework(air),theeffectM a changeofthemodulusd thew3&esupportandaPthethermalexpansion@ themountmaybesubstantialandmustbeconsidered.b theprece~.expressionfor 02, because~ ~>> L, theeffectd a changeofthemodulusaPthewirematerialisnearlyalwaysnegligible.

Thereseemstothedeflectionofaload.

Theassumption

DeflectionofWireSupport

benoexpressiontistructuresliteratureforconicalcantileverbeamundera concentrated

thattheconicalwiresupportisrigidlyheld.atoneendisa goodoneastheamountofmovementatthebaseisverysmllinanycase.Itisobsemedinpnmticethatthecementusesdoesnot de%lopcracksintheaxeaofthesupportinthecourseofordinaryfairlybrittlesubstance.

~ediatelyaroundthebaseusageeventhoughitisa

‘,

.

. .

———

. . NACATN2117 79

Inthefollowingrelationa,M istheconventionalmomentofbeamtheoryand I the(beam)momentofinertiaofthecrosssec-ti(m.Thedeflectionoccursalongthey-cooMinate,takenpositiveintheupmrddirectionfora horizontalbeam.TheloadW isassumedtoactinthedownward~ction ata disknceL fromthepetitofSupprt. Thehorizontalcoordinated anycrossseutionasmeasuredframthepointofsupporttakenastheoriginis x.

A%theorigin,thediameteris Do; itis D1 attheloa&ingpoint●

Then,.

()D=DO 1-$ +Dl$

UJplwriting

anduponrecallingthat

it fOllowsthat

.

Do-%.=bLDO -

M=- W(L -X)

(C19)

(C20)

Y“=&=- 64W(L-X)d

(C21)lmo~Eb (1- X5)-’

.

—.-. ..-. ——. -—- ————... .- .-————— — ..-. -—— ——

.. -=.- . ..- -.——

80

or

N.ACATN2117 .

.

[

—

Y“ =k2 —-—(1-2)4 (1-:)4—

64Wk2s —ltDo4lb

(C22]

Uponintegrationandimpositionoftheconditionthat yt= Oatx=O, equation(C22)becomes

~

Jl= -1 1- Lk2 + ‘2:2m)

252(1-X5)2+ 352(1-X5)336 (1-m)a

@on a secondintegrationand@ositionofy= Oatx=O,

L=. 1 + 1 -J.5:X+Qk2 253(l-m) 653(1-25)2mz =

thecondition

(C23)

that

(C24).

I@cmreoal13ngfinallyobtainedis

2 k2L3y..

6(1-L5)

thedefinitionsof k2 and

(C25)

8, theequation

.

.

.—-— —

NACATN2117

.

81

(C26)

whichisequivalenttoequa’bion(13)H itisreoalledthatequ-tion(13)a@.iesintheeasecdthedefl.eotional?a pairofsup-ports.

R33FERmm

1. Sirumons,L.F.G.,andEailey,A.: Noteona Hot-wireSpeedandDirectionMeter.R.& M.No.1019,BritishA.R.C.,Feb.1926.

2. Bailey,A.: A Db?ectionalHot-wtreAnenmueter.R.& M.No.777,RritishA.R.C.,Jan.1922.

3. Weske,JohnR.: MethodsatWasurementtiHigh- VelocitiesbytheHot-W&eMethod.NACATN880,1943.

4. E@, LouisVessot:OntheConvectionofHeatfr~ -11Cylindersina Streamd?Fluid:DeterminationoftheCon-vectionConstantsof*11 PlattiumWireswithA~Uc-ationstoHot-WireAnemometry.Phil.Trans.Roy.-c. (Londa).vol.214,no.14,ser.Al

5. Jakob,Max:HeatT%ansfer.1949.

6. ~, W.l?.:Aerodynamic

.-1914,pp.373-432.

Vol.I. JohnWiley&Sons,hc.~

Theory.Vol.VI. DurandRepzzlnt-ingc-o, C.I.T.,1943,PP.252-253.

—

7. Boelter,L.M.K.y~ewy V.H.)Jotio% H*A.>~dWrtinelli,R.C.: HeatTmnsferNotes.Uciv.Cal-if.Press(Berkeley),1946,pp.XI-15.-=-19.

8. MoAihs,WilliamH.: HeatCo.,tic.,2dcd.,1942$

~SSiOI1. Mc&x3w-~11Bookpp.210-230,237-246.

-. -.—.—— -...—-—- . —— -——- ——— -—- ..—. —— —..-

— — ._— —.

82 NACATN2117.

9. Burgers,J.M.: Hitzdrahtmesmngen.Handb.a.I@. Phys., ‘-Bd.IV,Teil1,1931,S.656-658.

10.%ylor,C.Fayette:A suggestedMethodforMeasuringTurbu-leme. NACA!l!t?380,1931.

11. Ziegler,M.: OntheDirectionalEffectaftheSingleHotW&e Anemometer.Proc.~jke AlmiemievanWetenschappen(Amstemlam),vol.2GIZV,no.8,1932,pp.1067-1076.

12. S5mmons,L.F.G.,andBeavan,J.A.: Hot-wireTypeofInstrumentforRec_.Gusts. R.& M.No.1615,IkitishA.R.C.,Feb.1934.

X5. I@oblock,F.D.: AHot-W~eAnemometerDevelopedforFull-ScaleAirshipMeasurements.pub.No.2,TheIlanielGuggenheimAirshipwt., 1935,~. 58-61.

14. Eckert,E.,andWeise,W.: The‘lempe=tured Heated Bodiesha High-SpeedGasStream.NACATM1000,1941.

25. Eber:~rtientelleTMersuchungderBremst~peraturunddesWarme~bergangesaneidachen~rpernbeiUeberschall-geschw3nd@ke;t.Teil2: Abbildungen.WVAArchivNr.66/57(Peenemmde),Nov.21,1941.

16. Willis,J.B.: Review& HotWtieAnemometry.Rep.ACA-19,AustralianComcilAero.,Oct.1945.

17. Tkmas,J.S.G.: HotWireAnemometry:ItsPrinciplesandApplications.Jour.Sot.Chem.Ind.(London),Trans.,vol.~, no.11,June15,1948,pp.165T-168T;.discus-sion,pp.169T-170T.

18. Thomas,J.S.G.: TheHot-wireAnemometer:ItsApplicationtothelhvestigationd theVelocityd GasesinPiyes.Phil.l@g.,vol.~Nljno.CC~, 6thiser.,May1920,pp.505-534. .

19. Schubauer,G.B.: A Turbulenceh@icator’UtillzingtheDti-fusionafHeat.I?ACARep.524,1935.

’20.Woldman,NormnE.,andDornblatt,AlbertJ.: lhgineeringAlloys.Am.Sot.Metals(Cleveland),1936.. I

21. Hoyt,EkmuelL.: MetalsandAlloysDatarook.ReinholdPub.Corp.,1943. .

.

,-’

.

“.

,.—

,

NACATN2117 83

:cc

,

.

. .

22. Anon.:MetalsHandbook,1948Edition.Am.Sot.Metals(Cleve-land),1948.

23. lYverhartjJohnL.,Lindliti,W.Earl,Kanegis,James,Weissler,WarlG.,andSiegel,lWieda:MechanicalPro~rties&MetalsandAlloys.CircularC447,IVES,Dec.1,1943.

24. Nemilov,V<A.: Splavyplatinyipalladiai,ikh@menenie.IzvestiiaNo.19,Sektorplatinyi drug~wblagorondnykhmetallov,Inst.obshcheiineorganicheskoilMmii,Akad.naukS.-S.S.R.(tin@@), 1943,pp.21-44.

25. -.: -ternationalcritical!kbles.Vol.V.McGm-HillBookCo.,~., 1929,p.225.

26. Schubauer,GalenB.: EffectofHumidityinHot-WireAnemmetry.,Nat:Bur.StandardsJour.Res,,vol.“~, no.6,WC. 1935,pp.575-578.

27. Prandtl, L.,andTietjens,O.G.: AppliedHydro-andAero-mechaniOs.‘Mc@’aw-~~BookCo.,k., 1934,PP.96-97.

28. titi, Th.:TheProblemofResistanceinCcmpresstbleFluiaE. QuintoConvegno“Volta”,RealeAccademia&tI~~(Ram),Sett.30-Ott.6,1935,pp.3-57.

.

_.—__.-. .—- -.—— ..—— . . ..— -. --.--—-— ..— ----. —-—. ----.———.—. ——— -

84.-,

NACATN 2117

.

,

LooalizedflowVeotor7

Pltohangle

tainingmimntaxisanilccalizedflowveotor

. m Horizontal@anenomsl-tomountaxis

Extensionof pro~eotlonofflwVeotoronh~lzoatal@ane— wires 7

+ u-.-~-=”=”-- ---

biseotor

ti8

,>

I?ignre1. -Gecmetricrelationsemmwmountaxis,wires,h flowveotor;horizontal

F-Jcoco

..

Ny\

v-array.

.

. ..

.— —- ——

I

i

1

IiI(4

I

I

..-

,

c“. ”

15.0 - -12.5

— y/ “

10.0 ~ — - -/ “

—

w5=---, I , , I I

4 6 8 10 20 40 60 80 I 00 2CHAerodynarni C loading, 023

F

h)

gure 2. - Stress in wire as function of initial and aerodynernlc loading. .J33-C132 a,-023 - 0.

Unit of stress qrbltmry.

i

Tine, hrFl@re 3. - Oxldatim of tunostan wire.

,.

.

6821

I

III

.

.

NACATN 2117 87.-

115

T /*

110

I05

I00

95

(nE

% 90.

.a

85

80

) 300 4 )

7a

65 .1 ) 5e~,Oc

1 6

Figure 4. - Variation of resistanceofiridium - 80-percent

three specimensof 20-percentplatinum wire.

. —— . ..—._._ __ __ _ ._ _ _ ___+ _ -. —--.———.—’— .- —z ..——.- .=_ ._ . .

88 NACATN 21[7

End

. .

3SolidInconeltaperedsupportPoroelain-tmoement

TwocopperLea&ssilver-solderedtosolidsupport

If

tubesilver-solderedtotapsredextensionof0.40-in.tube

~Base ofslotoutIntol/4-in.tubetoreceiveo●040-ti.pressuretube;oneaop~rleadattaohedto$lllotion“oftubes

KFlattenedl/8-in.tube

_ Silver-soldered

.

w%.

Airflow

bFermledampedbyAIJenheadsetmmew

.

h-Oneoopper lead attaohedtobaseofl/4-in.tube

-“\\\! Soale: 1 2X

4

m 5.-Constrnottondetailsof.

. .

—— .-. ——.—.- .—— ——.-

NACATN 2117 89

Springandepi-@+m clamp

Figure6.-Mounting$@andmicromanipulator.

.* .,,

——.. . .=. = ..-. .-—_ ——-.—...- .. ——— — __ -.-. — ——— —.— —.___ . . . ____

,

-.I

..

,*

. ●

.,

.

,

———. —

.

--

.

NACATN 2117

mcoNl-l

.-— _

(a)Sideview.

.

-. .

(b) Rmn-tview.

o +I

INCHES

,

,

(0) T.Optiew.

Figure7.-V-arraymountswitht@-preSStWe tip.

91

=s=C-244119-28-49

. . .. ——.. — —.—— ——-—— –———-—

.

.-

—._— —_ .

,

.

“-

.

.

.

NACATN 2117 93

C-2~1083.9-49

(a)-view..

(b)Sidetiev.

Figure8.-I?araUel-wirearraymountwith

=s=C-231093-9-49

total-pressuretap.

— -------- ——-.—..–- ——— . — ———

.

..

,

.

.

.

—

.

.

.

NACATN 2117

—._

(a)

—I

I

—— —. . ... ... ——— — -—-- —

Ikcoutview. (b)Top view. “

.

●

(o)

Figure9.-Dcnzble

iv‘!*’ .

‘: .+-<y -

-.—— .. ..-— —. —.. .

sideview.

parallel-

.—— . ..—

0-i

INCHES

C-2242410.11.48

.,

95.

———. _____ ____ ..-_ .. _____..__. . . ...>.- ___ ____

..

..

.

“.

.

—.—. ..-— — ---— —-—. -- .-— .. ——. .—— .-. ———..— -——-

. NACAiN 2[ 17 97

.

POtentlcuetar Pwer Galvanmeter Plug C’xltdcts

-QQ Q(

Q-Jmeter

I

.

.

II

%S, %Itch, nwtral msltian RI 0.1 or 1.00km,

standard re$lstor

1.0 ohm, stacdard

3.5 Am

Branches of lWO-OtadRMde mtantl~tOrS

450 ohms,matched

lCO-obMhelicalpotent i~ter1.5 ❑wohm

150,0W ohms

15,0m &m

~ Gangs-itch

P.mltlcm: %R3

ff4, 5,6,7

%10

I Opml2 shorted3 T-t4 Wra I

(C00tact6 1-2->4)5 llre 2

(contacts 3-4-5-6)6 tiss flow

(contacts I-2-6-6)7 Dlrattien

(Cootacts 1-2-4-5.-6)~ 381tch

f%

fIII

%2

R13

Figure 10. -Bridge CiKwlt.

_______ .. _.._ _.. —— .—.——... . . . .- ..-. ~——.——. — ------ ———— ...— —

NACATN 21[7

.“

2.

1.

1.

.

0-

6 \

2 \

80 “1 2 3 4

1og Re

(a) Experimental data from reference 28.

2. (II

n/ \/ \/

/\

1.6 /\

\\

\1.2

.

.86●4 .8 1.2

M

(b) Experimental data from reference 29.

Figure !1. - Variation of drag coefficient with Reynoldsand Mach numbers.

.

..

.

. .

.

— ——— —

. NA~ATN 2117 99

.

I

tklf

Prf0”3

10

9 r

u

values)a

❑ .575

7+ 1.5304 1.825 /

x 2.3256 /

//

/5 — — — — — — — — — — , /

//

//

4 ,/

/

3

/

2

I

a>=@=

o 2 4 6 8 10 12 14 16 18 20 z?0.5

‘Of,w

Figure 12. - H.s.at Ioasas frm wirq normal to stream at fixd wire temperature. Mean wire temperature. W C;WI re diameter, O.~ cat Iaeter.

..

.

— .. —-. —._ . .——-. — .. —.—— ... .. .—-. --—-

I0;.

NACATN 2117

,,,v. &

(%) values)72

123

J

176 2.32523[

75125 1178

J

1.Q30 I I I I I I Im

6

5

4

3

2

I

o

..

Ref,.0.5

. .

Figure 13. - tkat IOS5W from wire normal to streanat several *IIW tmmratures.

,

‘.

_-. ._ ——— ———. . ——. ——— .-— -

4

NACATN 2117 . 101

inco2

I

.

,!

2.4

;r

2.2 I#I/

/2.0

/ //

//

1.8/

//

/,

1.6 / {/

,/ /

/1.4 //

// f3——.— khchnumber/

‘m 1.2 //s / Recovery

coefficient( Pi-P~

1.0>1 Pt-P~\ -

\ .5.8 h

— _\

\

.6 \\

\\ \

\.4

\\

\\

\ \ \.2 \

\

=S=4 \

\

01.00 1.04 1.08 1.12 1.16 1.201.24 1.28”fl

Figure 14. - Relations amongMachnumberand heat-loss parameters.

-- -. .. —. —- _____ .. . .. . .. ._

I02 .,.

80

60

40

20

0

-20

-40

(

-60

A 1.350V 1.765 , ‘t I

A‘b

. 1* d

i

A /

-

-8 -4 0 4 8

Angle of deviat i-on from zero deflection, deg

Figure 15. - Yaw characteristics of 90 0 V-wire.

.

.

I

—. —.—

NACATN 2117 I03

.

I

I

E

‘1.co

—“i-0

-0

4

2

0

8

6

4

2

Angle of deviation from maximumdeflection, deg.

Figure 16. - Yaw characteristics of parallel-wire array.

.— .-. —z —. --— —— __ . . .._. —z -—.—— -——

104 NACA TN 2117

.

.

malu

.cdalE

EoL -.+

+c

on -.

8-

4

0

40- ‘

.

n725

0LaN

+“ 40c0 I

+a ,0.->:-.4

-. 8

50 75 100P’ressure at t“est section, cm Hg absolute ,.

[al Constant Mach number of 0.457 ~O. 007.

c~

=S=

.

. 5 .6 . 7 .8 . 9 1.0M at test section

(b] Constant pressure of 22.1 LO.4centi.mete”rs of mercury.

Figure 17. - Angular error of parallel-wire ar;ay.

.

.. .

— ——_—..—.— ——

I

I

1.C$3d

(refe?L%.! 16)1

T~lTe1.04 ~ ~ —

~—“

— — — NACA —------ TeITt / “ . — .

~ / 7 “

Te‘—-—TtiTe- < >“

“z

I.(X2 / ‘

// “,

/ ‘/ .~.

I.00~ * : -=-~.--’* —

\ ~ ->,x \

~ -.’.98 .

.’ .\

. . . =It

NACA-- _. -= ---- -- —- -- -- %< ---

.%3+

-- -- NACA’-. --

+--

-German

.%. I.2 .4 .6 .8 1.0 [.2 1.4 1$6 I.8 2.

M

Figure 18. - Recovery ratios for circular CYI Inder normal to stream.

I.00

o.40

I

97.0

eoo5

m.o

95,5

95.0

04.5

84. 0

w.~,oo-80 -m -40 -20

U

o 1.55❑ 2.10A 2.43

L/D = 74

20 40 m so IAng I a, deg

Figure 19. - Variation of ratio of effective to total temperature with angle between stream and nomal to WI re.

. “. . ,