_+-,

J RM E57G24

~—. —-,—.-A—

—FzN.ACA.——- -———.. _ —.- .,_____ .-_— ~

RESEARCHMEMORANDUM”-

PRESSURE DWG OF AXISYMMETRIC COWLS HAVING LARGE

LIP ANGLES AT MACH NUMBERS FROM 1.90TO 3.88

By NickE. Samanich

Lewis FlightPropulsionLaboratory

INITLAL

ormatbn aKec udtedstateswithinb L’ceq

mammr b amnunutbariced-U Sspmbithd * lw.

NATIONALADVISORY COMMITTEEFOR AERONAUTICS

WASHi NGTONOctober21,1957

— — —

NACARM E57G24

‘ ~ fi~ml~j~-~ nl144nllli

NATIONALADVISORYCOMMITTEEFORAERONAUTICS

PRESSUREDRAGOF

LIPANGLES

RESEARCHMEMORANDUM

AXISYMMETRICCOWLSHAVING

AT MACHNUMBERSFROM1.90

By NickE. Ssmanich

SUMMARY

LARGEIIKTIAL

to 3.88,

Theresultsof experimentalandtheoreticaldataon ninecowlssrepresentedto determinetheeffectof initiallip angleandprojectedfrontalareaon thecowlpressuredragcoefficientatMachnumbersfrom1.90to 3.88. Thetrendsin cowlpressuredragcoefficientwereapprox-imatedwellwithtwo-dimensionalshock-expansiontheoryat thelowercowlprojectedsreasjbut thedigressionfromthedatabecameincreasinglygreateras thecowlarearatiowas increasedandshockdetachmentat thecowllipswas approached.An empiricalchartis presentedwhichcanbeusedto estimatethecowlpressuredragcoefficientof cowlsapproachingan eK1.ipticcontour.

of a

lNTRODUCTION

Evaluationof cowldesignsforhigh-speedflightis a necessarypartpreliminaryperformanceanalysis.Severaltheoreticalapproaches

areavailablewhichgivesatisfactoryagreementwithexperimentalpres-suredragdataon unity-mass-flowenginecowlsin certainisolatedre-gions. Thelinearizedsourcedistributionmethodgivessatisfactoryre-sultsexceptfor caseswheretheMachnumberor thebodyslopesarelsrge(refs.1 and2). VanDyke’ssecond-ordersupersonicflowcalculationsarelimitedto msximumslopescorrespmdingto anglesof approximately28°,18°,and13°at Machnumbersof 2, 3, and4, respectively(ref.3).Theshock-expansionmethod(refs.4, 5, and6) neglectsreflectionofdisturbancesoriginatingat thesurfaceas wellas thethree-dimensionaleffect.Thedegreeto whichthelocaldisturbancesarereflectedis smalJexceptat largelipangles{nearshockdetachmentvalues).It is inthisarea,lipanglesnearshockdetachmentvaluesin therangefromMach2.0to 4.0,thatexperimentaldataareneeded,becausemostof theapproximatemethodsof estimatingpressuresdeviateappreciablyfromtheexactvalues.

2 NACARM E57G24

Somerecentempiricaldragmeasurementshavebeenreportedin ref-erence7 on a familyof ductedbiconicbodiesatMachnumbersof 2.00, .2.50,and2.77,but no attemptwasmadeto comparetheresultswiththeory.Theonlysatisfactorymethodof predictingcowldragstheoreti- ‘“ ‘“jcsllyin thisareaappesrsto be withtheWe of rotationalcharacteris-tics. Thismethodof solutionis quitetediousandtime-consumingevenwhencomputedwithautomaticcomputingequipment.

.-In viewof theitems

discussedandthelackof sufficientsystematicexperimentaltestinginthisarea,theprogramreportedhereinwas initiatedat theNACALewis

;

laboratory. 4

MODELSANDAJ?PARATUS

An investigationof existingcowldesignsindicatedthatan ellipticcontourcloselyapproximatedthemajorityof shapesexamined.A familyofnineellipticallycontouredcowlswas desigpedwhichincorporatedlargeinitiallipanglesnearthedetachmentvalueat MachnumbersfrOm2.0to4.0. Thecontourfromthe11Pto theconstant-6-inch-diametersection(see .;.fig.1 andtableI) on thesteelmodelswas definedby theellipticequa-tion Y.= 0.441~~ where X.

.=●

and YO aretherectangularco- ,.

ordinatesandthe constanta was variedto-giveinitialnominellipanglesof 20°,28°,and34°andprojectedcowlareasof 20,35, and50 .percentof themaximumfrontalarea. Static-pressureorificeswerelo-

—.

catedexternallyon thecowlsat axisldistancesfrom0.060inchtitof,=

thelipto theconstant-dismetersection.Theinternalcontourof thecowlswas a straightdivergingtaperfromthecowllipto thecowlexit.Allthecowlshad sharplipswitha maximumradiusof 0.0025inch.Scsleddrawingsof theexternslcontoursareshownin figure1, Wd pho-tographsof threetypicalmodelsarepresent~d.infiWe._2. Themodelg . –werestrut-supportedandtestedin severalof theLewissmallsupersonicwindtunnelsat zeroangleof attack.The~eymoldsnumberwasheldrel- —

ativelyconstantduringthefixedMachnumberrunsandhadvaluesof5.2x106,6.1x106,4.9x106,andI.1x106per hot at therespectivetest

—.—

free-streamMachnumbersof 1.98,2.47,2.94,end3.88.—

RESULTSANDDISCUSSION

Theexperimentalsurfacepressurecoefficientsezelistedas a fu~c-,, ,,_,tionof,axial.distancefromthelipin tableII. Figure3 is a repre-sentativeplotshowingthelongitudinalpre?s~e ~s~ributiw for both.

theexperimental.andtheoreticalresultsof the34°initiallip angle.—

cowlsat a Machnumberof 3.88. Thetrendsarecloselyapproximatedwithmtheoryat thesmallerprojectedareasbut de@ate progressivelyas theprojectd..cowlareasareincreased.

.

.&NACARM E57G24

.~ 3

.

.

Theexperimentalpressureswereintegratedoverthecowlsurfacesandtheresultantdragcoefficients,basedon a maximumcross-sectionalareaof 0.787squarefoot,werecomparedwithvsluescalculatedusingtwo-dimensionalshock-expansiontheoryin sllcaseswhereattachedshockwavesexisted.No attemptwasmadeto cslculatetheoreticaldragcoef-ficientswhendetachedwavesexistedat the COW1 lips,but estimatescmbe madewiththeaidof reference8.

Figure4 showstheeffectof lipangle,projectedcowlsrea,andMachnumberon thecowlpressuredragcoefficients.Thetheoreticalre-sultssreshownonlyforattachedshockconditionsat thelip. Whilethetrendsareapproximatedratherwellwithshock-expansiontheoryatthelowerprojectedcowlsreas,thedeviationbetweentheorysndexperi-mentbecomesincreasinglygreateras thearearatiois increased.Thisdeviationtithincreasingarearatiocanbe attributedto thegreatervariationin radius(alsrgerthree-dimensionaleffect).In mostcases,thetheoreticalresultsindicateda rathersharprisein dragas theshockdetachmentvaluewasapproachedat thelip. Theexperimentaldata,in general,revealedno abruptchangeswhentheoreticalshockde-tachmenthadbeenattainedat thelip. In theschlierenphotographsinfigure5, shockdetachmentat thelipwasnotapparentuntilMachnum-berssubstantiallylowerthantheoreticallypredictedhadbeenreached.Thiswasprobablydueto thefactthatthe initiallipanglewasnotmaintainedforanyappreciableaxialdistance.

Althoughno dataarepresented,severalof thecowlswererun attwoReynoldsnumbersat Mach2.94. A smalleffectwas notedwhichre-sultedin dragcoefficients3 to 5 percenthigherforthe cowlstestedat a Reyuoldsnumberof 2.5x106as cornpsredwiththosetestedat 4.9x106perfoot.

The experimentaldatasrecombinedin figure6 as an empiricalchsrtforuse in estimatingthecowlpressuredragcoefficientfor cowlsap-proximatingor havingsn ellipticexternalcontour.The constant-arearatiolineswerelocatedarbitrarilyin a mannersuchthattheexperi-mentaldataforgiveninitiallip anglesresultedin definitetrends.Thesymbolsin figure6 sretheactualexperimentaldataobtained.Asw exsmpleof theuseof thechart,thecowlpressuredragcoefficientat Mach3 of an ellipticallycontouredcowl,havinga cowlproJectedarea25 percentof thetotalfrontalareaandm initiallip @e of 30°,wouldbe foundby followingthearrowsas shownin figure6, resultinginan approximatedragcoefficientof 0.10.

.

●

v

4 .. NACARM ES7G24.

CONCLUDINGREMARKS-.

.Theresultsrevealedthatthetrendsin cowlpressuredragcoef-

ficientcouldbe approximatedratherwellwithtwo-dimensionalshock-expansiontheoryat thelowerprojectedcowlareas>but thedeviationbetweentheoryand experimentbecomesincreasinglygreateras thepro-jectedcowlarearatiois increasedandshockdetachmentat thecowllipsis approached.An empiricalchartwas developedfromtheexperi-mentaldataenablingtheestimationof cowlpressuredxagsforcowlshavh.gor approximatingellipticexternaltiontours. ~-

4

LewisFlightPropulsionLaboratoryNationalAdvisoryCommitteeforAeronautics

Cleveland,Ohio,July25,1957

1.

2.

3.

4.

5.

6.

REFERENCES—

BrownjClintonE., andParker,HermonM.: A MethodfortheCalculat-ion of ExternalLift,Moment,andI?ressureDragof SlenderOpen- W

NoseBodiesof Revolutionat SupersonicSpeeds.NACARep.808,1945. (SupersedesNACAWR L-720.) .

Jack,JohnR.: TheoreticalWaveDragsendPressureDistributionsforAxiallySymmetricOpen-NoseEdies. NACATN 2115,1950.

VanDyke,MiltonD.: PracticalCalculationof Second-Or~erSupersonic __FlowPastNonliftingBodiesof Revolution.NACATN 2744,1952.

Eggers,A. J.,Jr.,Savin,R. C.,andSyvertson,C. A.: TheGeneral-izedShock-ExpansionMethodandItsApplicationto Wdies Travelingat HighSupersonicAirspeeds.PreprintNo.487,Inst.Aero.Sci.,1954.

Syvertson,ClarenceA., andDennis,DavidH.: A Second-OrderShock-ExpansionMethodApplicableto Bodiesof RevolutionNearZeroLift.NACATN 3527,1956.

Eggers,A. J.,Jr.,andSavin,RaymondC.: ApproximateMethodsforCalculatingtheFlowAboutNonliftingBodiesof Revolutionat HighSupersonicAirspeeds.NACATN 2579,1951.

.

.

.

.

NACARM E57G24 5

7.Wallace,A. R.: A SystematicInvestigationof theExternalPressureDragof a Fsmilyof DuctedIbdies. Paperpresentedat BumblebeeAerodynamicsPanel,Univ.Mich.,Dec.4-5,1956. (APL/JHUTG 14-31,Mu. 1957.)

8. Moeckel,W. E.: EstimationofsonicSpeeds. NACATN 3457,

InletLipForcesat SubsonicandSuper-“1955.

.

.

m

TMLi31. - COWL CHINATE8

[Alldlmenslom i. in.hea~

TI

6.00 Dia..

i’ l---’ ----+

cowl. 1 cowl 3 cowl 4 Cowl 6 cowl 7 cowl 9cowl2 cowl5 Cowl 8

x

).10.20.40.60

.&l..00.,2U..50!.00

!.47

x ZIEE x x xYp

2.4202.4472.4732.52132.570

2.6i152.6532.7002.7542.631

2.8922.9402.9742.9952.999

3.O(M

x Y~

2.4202,4672.5102.5532.592

2.6642.7352.7652.8302.864

2.9532.9913.000

t

x Yp

o 2.665.10 2.750,20 2.794.30 2.833.40 2.670

Y~

?.685?.712?.74C2.7822.822

?,8592.891?.917?.951?.9B5

5.000

D,10.20.40.60

.ti1.001.201.502.00

2.505.005.50Loob.50

4.56

0 2.124 0.10 2.151 .10.20 2.178 .20.40 2.230 .30.60 2.260 .40

2.6852.7322.7762.8092.643

2.b632.8962.9372.9672.988

2.9963.000

0.10.20.30.40

.60

.801.001.201.50

2.002.5o2,89

0.10,20.40.60

.i301.001.201.502.00

2.503.003.504.004.36

%

2.1242,1712,2172,3002.380

2.4’532,5182.5792.6602.772

2.859,2.9232.9662.9693.000

0.10

.2Q

.30

.40

:“.60.80

1.CM31.201.5Q

2.002.40

2.4202.4882.5422.5982.646

2.72ti2.7922.8432.8902.937

2“.9893.000

0.10.20.40.60

.$Oi1.001.201.502.00

2.503.033.503.63

2.1242.1922.2502.3592.452

2.5342.6062.6702.7522.860

2.9342.9602.9903.0001

1’.60!2.9)24.80 2.862

1.00 2.9651.20 2.9971.3053.0002.001“2.5801 1.20

2.50 2.683 1.503.00 2.738 1.573.50 2.8054.CQ 2.8574.50 2.902

5.00 2.9415.5a 2.9686,00 2.9906.50 2.9996.80 3.000, 1

,,,, .,,,’

NACARM E57G24 7,

TABLEII.- EXPERIMENTALPRESSUREDISTRIBUTIONS

cmrll II L%W12 II ma3 IAxial

dintance.rtor lip,

x,in. !-4xiaLdintance

aft02 lip,x,

.aa ill.

.s12 0.07

.276 .11

.242 .18

.229

.19s :E

Slrfao* mmraOoerrlclant at II-distanceM2uhSamkucsof - titor lip.

SurfaoepramrOoefrlcialt aIkohmnabernc

1.9812.47[2.94

:

8.26

1.325.264.214.251.247

.2s-6

.226

.md

.lsa

.165

.164

.ls9

.1=

.us

.lW

.ms

.Caa

.072

.fx7

.CS?

.027

.021

R

..981241 12.94

T1.5760.4690.398.50s .3Z41.328.462 .3ss .506.4s-3.337 .226.4ss .s40 .509

0.07.11.16.21.28

.s8

.44

.s4

.64

.7s

J.5100.4030.s4:.46a .524 .51!.401 .S2a .267.368 .220 .232.364 .265 .2?4

.3L.5.242 .202

.27S .2$!3.MC

.= .203 .157

.266 .= .164

.224 .130 .1!5?L.172 .38.122 .4a.?sS .80.140 .74.L27 .8s

.114 1.C=S

.105 1.30

.062

.on ;:!

.060 .

.052 2.m

.C96 2.953.5a3.m4.%

.40

.62

:%!.98

.410 .526 .27s

.561 .310 .2S7

.362 .28s .247

.342 .277 .241

.316 .=l .217

.2n .Z?l .1s3

.236 .1s9 .16S

.210 .173 .155

.184 .157 .1s3

.165 .140 .12Q

.L54 .M1 .117

.lU .126 .112

.lu .027 .072

.064 .058 .044

.065 .042 .0s6

1.18

M1.902.2Q

2.502.753.253.754.23

.20

::X1.361.6s

.107 .2.62

.167 .134

.162 .127

.118 .097

.090 .071

.0s4 .030-.OM -.00s

.126

.102

.Dx

.0S4

.032

1.202.40

.02s

.Oaz

4.755.2s6.006.m l-l.034 .036 .026

.022 .Ola .012..014-.01s-.010..055-.050-.024

~

8U

2—L.S8

3.M61.765.676.822.594

.552

.4n

.387

.520

.236

.191

:E.01s-.CKG

cowl5 Cawl6.

.

Lamldistanceft of lip,

x,in.

hidOi#tanaeft of lip,

x.U.

Sm.iaoe W—COefflulerltatEachmndmra of -

hialdlmtmaeStor llp,%in.0.06.12.18

:3

‘ace ],tric!inud~..

1.s86.810.s37

.481

.449

.399

.524

.279

.126

.16s

.I.16

.076

.024

.006

BnaurentatrB Of-

T.24 3.24

.6050.522

.529 .U6

.459 .412

.408 .381

.427 .361

.

..62—1.914.610.751.723.716

.673

.619

.566

.504

.414

.s10

.251

.216

.178

.14s

.094

.021.054

t

.47 2.24

.7560.695

.645 .22L

.596 .E61

.822 .5ca

.592 .s7

,.68—,.ss3.498.482.U6.Uo

.416

.405

.377

.335

.277

.224

.163

.152

.129

.107

.076

.037

.007

—

..m 2.47 2.24 .86—.524.536.506.4S2.475

.455

.407

.356

.2S3

:=.194.151.111

,067.065.041.023.a—

}:= 0:74:0.645.6CW

.64s .6m .5a4

.n3 .642 .554

.7S2 .629 .559

O.cm.11.16.21.W

.36

.43

.63

.64

.76

1:&1.m1.ss1.60

0.06.12.16.22.26

.s97 .328

.ss8 .299

.262 .247

.244 .20s

.176 .ls4

.133 .126

.020 .095

.063 .082

.02s .@s

.Cfn .019

.33

.44

.84

.64

.76

.= .6s4

.529 .420

.425 .443

.437 .418

.362 .s4s

.273 .2s8

.220 .207

.201 .193

.160 .124

.lss .lz4

.020 .089

.034 .04’6

.014-ml

:%.74.20

.661II.6EE.515

.525 .630 .461

.464 .456 .391

.324 .m2 .325

.3S6 .Ssl .284

.’zm :;% :2S;

.2M

.172 ;;g .160

.m2 .118

.103 .039:% .W8 .C6a,.012IO& S&.m3..079-.014-.011

1.081.331.661.202.22

::&3.50s.m4.30

A1.201.sS1.54

l.m2.352.20

1 1—

COWL

T 8Udiatanoeft or Up, A

x,h. 1.98

me pr9a-rficiaw,atnumtmw of -

.47i2.941S.88Tx. ‘-in. 1.s8

0.08 1.23C.12 1.L26.16 1.01s.22 .902.26 .82s

.56 .737

.44 .620

.s-4 .534

.64 .482

.76 .410

Mm0.08 1.116.12 .s66.16 .675.22 .713.28 .596

.36 .488

.44 .424

.s4 .343

.64 .278

.76 .194

.1281% .OW1.12 .05s1.26 .0111.40 -.009

.aJ90.2020.773

.877 .723 .349

.762 Al& s;

.633

.5s5 .460 .400

.4S6 .320 :=

.304 .326

.296 .246 .241

.=l .224 .187

.172 .160 .143

.125 .101 .107

.Oal .067 .073

.043 .m6 .066

.027 .028 .055

.Cm2 .014 .C%?s

.659 .613 .ml .36

.5’94.ms .U6 .48

.476 .422 .390 .6JY

.Uo .411 .339 .74

.367 .34s .285 .20

.297 .265 .236 l.m

.253 .203 .192 1.53

.126 .161 .146 1.55

.142 .156 .114 I.m

.022 .063 .024 2.25

.819 .703 .712 .606

.72s .707 .636 .553

.s52 .=7 .4s8 .467

.48s .497 .4m .367

.4CQ .423 .s91 .534

.S27 .549 .506 .262

.232 .276 .241 .231

.2Q2 .258 .213 .186

.126 .166 .164 .L55

.050 .023 .0+37.092

.S241:OT .2541.241.42 :21.62 .Cm

.

.

1.92 .0382.42 -.051

.Ch50.250 .056 2.m -.001 .m4 .CS2 .W3

.007 .032 .010 2.6S -.aB .024 .051 .0ss3.= -.057-.005-ml .0173.sa -.Cal-.016--- .012I I

8 NACARM E5TG24

External lip angle a (Constant usedin cowl eqmtion)

27:51I 4s662.08

3

2

uk,,,,,,,l llJ,ll, !llill,l!4111i Ll,LLLC,4cowl External lip angle a (Constant used

in cowl equation

19°401E

8.60p7043 , 3.B2

-?

.

Icross-secttonalarea.0.35 mm

u

cowl Externallipangle a (Constantusedin COW1 equation)

3 190401 13.006 27°51‘ 5.77

1 3 4 5 6Axial distance aft of lip,x, In.

7

Figure 1. - Scale drawings of cowls defined by the cowl equation

mey. = o.44~ s,

—

.

.

N.ACARM E5TG24 9

(a)COW17.4w-f2

.

E

C-45U73

(b)Cowl8.

.

~

.-. :.,..:

,.b .-—

.F, .+* ----.. ... ...--- ,.-. .. _=.~.-.. .

: .,,:-:-.,--m.

%.

—.—

---,., -..

~.w

-.—...— . .-—

-;,- ..=,+, ..

mlir--(C)cowl9.

,.:-453’4

Figure2.- CowlS7,8,and 9.

-.

1.0

.9

.B

.7

:.2 .8:

z“

~ “5

:k

.42g

. .

.3

.2

.1

0 .5 1.0 1.5

Figmw S. - Compm’imn of e

o .5 1,0 1.5 2.0 2.s o .5 1.0 1.5 2.0 2.5 3.0 3.5 4.0AXIal d18tance aCt Of lip, X, in.

xrm+.mentnl and ttworetiaal cowl premure fliatxfbutlms. ~rnal Up angle, 34°; frea-atrea.m Mach rmbor, 3

,L .,

I

,, ,!

I

i ,!!6s%’~ f..1’”‘, ,,,7 II

NACARM E5TG24

y“g

.

“18 z? 26 30 34External lip angle, deg

(a) External llp .engle.

Figure 4. - Effectso??lip angle, projected 00W1 area, and Mach number on cowl pressuredrag coef~lclents.

11

.—

12 NACARM E5YG24

.

..

1.0 “:“.20 .30 .40 .30 .Ratioorprojected cowl area to maximum cross-aectlonal area —

(b) Projeoted cowl are=.

Fl~e 4. - Continued. Effeuts of lip angle, projected cowl area, end Mach number on .oowl pre5sure drag coefficients.

f. 4597 “, ,

Fine-BmMmMMh -

(c) Maoh number.

Figure 4. - COnolurle~,E.tfecteOf lip mgle, projebted00wIerea,and Mach numberon cowlpressuredragcoerrlclenta.

i

G

14 NACARM E5YG24

.

Free-streamMachnumber,1.98 Free-EtreamI.kchnumberJ2.47 ‘

2-456q

Free-streamMachnumber,3.88

Figure5.- Schlierenphotographsofcowl7.

, ,, 4597 , ,

2 .0ti ““.06 ““” ,10 .14 .la .22 .2aFree-abeam Haoh number Cowl Pressure drag ooe!’fioient, baaed on maxlmm 0P0s.3-

neotional area

Figure .9,- BKIptiloal ohm% for eBtiB!atina elllptioal owl pressure drag OC.OffiOientB. PUI

*

afa.m.lty

Cowm.m Es7&?41- by l-fret-laIlepld.Erm=-b=w~2-h 2-fretw==@~W-Id hnmel

Cca?m.F# 57G241-by l-footVariahhReynolllnmbl-b Jet aufl2- by z-rmtBU~BOlliC

Viral bmnelLxmm.

Ea4m70241- by l-footVa24abla

&+mnnOlmwm.

RM E57a241- w l-fwtvmiablaReYmMO m-ber jut w2- by ~-rmtw=mnic

c1

cl

c1

c1

me-&emKcb

mto

5.B9

E

s%

YET

3%9

1,92ta

S.m

—

Fmynal&-r -sXIn

~to8.72

0.59tu

2,72

0,s9to2.72

0.32ta

8.7’?

JJlg10 ye

LttdOk, w,m ‘@

Znm 2er0

20r0 &m

al’o zero

ZOlm 2am

m

i

i

7

7

It88ta

la*c&-

m~

—

FlmL&me

—

Frot 1.0

w’ 1,0

bwl pmMllrO drag -ura-nntuuetionninc

.Iliwdly ~tmred ewlwith Iars8 initial13P~_-cv=icuB m*~

w,fl gremurn drag wmm-merit.medonnlnael.J.iptiOanYaataura m%’1with large ma MBC.U2MB ad variam moJ_d u-.

~~~w—-mtiaremaaeonld.neellipmcany nmtmrul C-avltii!bkm initinlMpmgleo ma TarionnsuvJ0at4ml arms.