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KNOTT BUILDING, DAYTON, 2, OHIO

AI

CONFIDENTIAL

r "SECURITY INFORMATION

CONFIDENTIAL Copy 72RM L52K28a

RESEARCH MEMORANDUIA

AVERAGE SKIN-FRIC7 ION, COEFFICIENTS FROM BOUNDARY-LAYER

MEASUREMENTS ON AI OGIVE-CYLINDER BODY IN

FLIGHT AT SUPERSONIC SPEEDS

By 1. Dan Loposer

Lugley Aeronautical LaboratoryLangley Field, Va.

NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS

WASHINGTON

JanuaryE I

CONFtIDENTIAL

IT NWA RK L52128a L COFD~L

NATIONAL ADVISRY C0QrM E FOR AERNAUTICS

RESEARCH MEMORANDUM

AVERAGE SKIN-PRICTION C0FFICIENTS FROM BOUNDARY-LAUR

t4ASUREMETS ON AN OGIVE-CYLINDER BODY IN

FLIGHT AT SUPRSONIC SPEEDS

By J. Dan Loposer

SuwARY

Boundary-layer measurements on a rocket-powered free-flight modelto determine average skin-friction coefficients have been made on anogive-cylinder body of fineness ratio 15.9. Average skin-frictioncoefficients were obtained for the body area ahead of the fins over arawe of Mach number from 1.3 to 2.5 and over a range of Reynolds num-

ber from 90.3 x 106 to 162.9 x 106 (based on axial body length to themeasurement station). Comparison of the experimental data with a flat-plate skin-friction theory by Van Driest showed good agreement.

INTODUETION

In estimating the total drag of supersonic missile configurationsthe accuracy of the skin-friction drag estimate is significant, sinceskin friction can account for as much as 50 percent of the total drag.Most of the widely known skin-friction theories (refs. 1. 2, and 3) aredeveloped for flow on a flat plate; however, sone calculations (ref. 4)to evaluate the effect of body shape on the turbulent skin frictionindicate an almost negligible effect for bodies of high fineness ratio.The present paper presents average skin-friction coefficients as deter-mined from boundary-layer total-pressure rake measurements using theboundary-layer momentus theorem. Rake measurementa were made at the124-inch station on a fin-stabilized ogive-cylinder body of finenessratio 15.9. The cylindrical section extended approxiately 10 bodyd iaeters ahead of the .easurement station. The model was rocket-powered and the flight test was made at the Pilotless Aircraft ResearchStation at Wallops Island, Va.

Friction coefficients are presented over a Pbch nmber range from

1.3 to 2.5 and over a Reynolds mmber range from 90.3 x io6 to 162.9 x 106

2 COVFIDEUTM NACA RK L52IM8&

(based on axial body length to the measurement station). Results arecowpared with Van Driest's theory (ref. 2) for skin friction on a flatplate with heat transfer.

SYMBOLS

Cf average skin-friction coeffic lent

M Mach number

TV temperature of skin, OF abs

T5 temperature Just outside boundary layer, OF abs

R Reynolds number, based on axial body length

u velocity within the boundary layer, fps

MODELS AND TESTS

The general configuration of the test model is shown in figure 1.The fuselage consisted of an ogival-nose section, a cylindrical centersection, and a boattalled rear section and was made of 0.064-inch-thickduralumin skin with ring stiffeners. The fins were also of duralumtn.The model skin was highly polished prior to flight testing.

The model was boosted with two ABL Deacon rocket motors which pro-v ided a total impulse of about 19,800 pound.seconds each, over a timeof about 3.2 seconds. The sustainer motor within the model was a 65-inch-long UVAR with 7700 pound-seconds impulse.

A photograpb of the model with booster Just prior to launching issbown in fIgure 2.

The model was tracked by a CV Doppler velocimeter to obtain flight-path velocity. An 3CR 584 rlad set was used to obtain the flight path.Freeatram coneditions or static pimsu'e and temperature were obtainedftbhm fli*twp&th a rAltoonle 6*a. The model was equipped with anRACA 10-cm l trr-.p toleaste. A six-tube total-pressure rake(fig. 3) W used to obtsiA the total preUre SMd, hence, the Mch num-bar t th bm= q IqIw. frw trm static pressure was usedas the AMU ' pss~ at tw rolo wtation, elat the neusurement stationW 10 Ue £iate ftm the ame *mm y point. Th. model was also

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ACA IM S120a CCKFrDTnIAL 3

assumed to be flying at zero angle of attack because of the large sta-biltty margin. The skin temperature at the masurement station wasmsured by a resistagce-type temperature pickup (ref. 5) cemented tothe inside surface of the O.Om6-ineb-thick duraluin skin. The sustainerrocket motor near the temperature pickup was covered vith asbestos insu-lation to prevent heat flowing to the skin.

Data were obtained only during the powered part of the flightbecause of the failure of the model just prior to sustainer burnout.

RESULTS AMD DISCUSSIC9

The skin-friction coefficients were obtained from boundary-layertotal-pressure surveys and skin-temperature measurements. The Machnumber distribution through the boundary layer was obtained from thetotal-pressure measurements and the local static pressure on the bodywhich was assumed equal to measured free-stream static pressure. TheMach number distribution and temperature measurements were used withthe Crocco temperature equation (ref. 6) to obtain a velocity and tem-perature variation through the boundary layer. The Crocco temperatureequation was modified by a recovery factor of 0.89 to give a realisticvalue of adiabatic wall temperature at the skin rather than stagnationtemperature. In reference 7 and in other references the value of 0.89for the recovery factor has been found to be representative for turbu-lent flow. Shown in figure 4 are typical boundary-layer velocity pro-files obtained for two of the test conditions. From the velocity andtemperature distribution, the average skin-friction coefficient vanobtained by use of the boundary-layer momentum theorem. The procedurefor obtaining skin-friction coefficients from rake measurements isdescribed In reference 8.

Time histories of the measured, average skin-friction coefficientsfor the area ahead of the mea urement station and the average skin-friction coefficients predicted by the Van Driest theory are shown infigure 5 for the test Reynolds numabers, Mach mmbers, and heating con-ditions. Also shown In figure 5 are time histories of Mach nmer,-Reynolds nuaber, Tv, and Tv/Vb. Also shown on the plot of Tv/T are

the values which would have existed for an insulated wall condition.Although the cooling condition tend to raise the skin friction, thehigh Mach numbers of the test bring the measured friction values belowthoee for incoupressible flow at comparable Reynolds numbers.

The maximm difference between the experimental pointe and theVan Driest theor is about 8 percent, with excellent ageement shownover mout of the range of test data.

CKl AL

4 CO*FIDEWrIAL MACA 1R4 L52K28a

CONCUDING REMARKS

Average skin-friction coefficients have been measured on an ogive-cylinder body over a Mach number range from 1.3 to 2.5 and a Reynoldsnumber range from 90.3 x i06 to 162.9 x 1 0 6. The experimental skin-friction coefficients were in good agreement with a flat-plate skin-friction theory by Van Driest.

lazngley Aeronautical Laboratory,National Advisory Comittee for Aeronautics,

Langley Field, Va.

COMM-VTIAL

I

MACA IN( L5BBS CONIDEfAL S

1. Von Kkinm, Th.: The Problem of Resistance in Compressible Fluids.R. Acead. d'Italia, Cl. Sci. Fin., Mat. e Mat., vol. XIV, 1936.(Fifth Volta Congress held in Rome, Sept. 3o - Oct. 6, 1935.)

2. Van Driest, E. R.: The Turbulent Bounary Layer for CcmpressibleFluids on a Flat Plate With Beat Transfer. Rep. No. AL-997,North American Aviation, Inc., Jan. 27, 1950.

3. Frankl., F., and Voishel, V. : Turbulent Friction in the BoundaryLayer of a Flat Plate in a Two-Dimensional Compressible Flow atHigh Speeds. NACA Th 1053, 1i3.

4. Blasel, Lowell E., Sinclair, Archibald R., and Hamilton, Clyde V.:Preliminary Investigation of the Drag Characteristics of theMA RM-1O Missile at Mach Numbers of 1.40 and 1.59 in theLangley 4- by 4-Foot Supersonic Tunnel. XCA RK L52A1, 1952.

5. Fricke, Clifford L., and Smith, Francis B.: Skin-TemperatureTelemeter for Determining Boundary-Layer Heat-Tranafer Coefficients.MACA RM LSOJ17, 1951.

6. Crocco, Luigi: Transmission of Heat From a Flat Plate to a FluidFlowing at a High Velocity. NACA T 690, 1932.

7. Chauvin, Leo T., and deMorses, Carlos A.: Correlation of SupersonicConvective Heat-Transfer Coefficients From Measurements of theSkin Temperature of a Parabolic Bo&y of Revolution (NACA RM-IO).NACA RM LSIA18, 1951.

8. Auswey, Charles B., and Loposer, J. Dan: Average Skin-FrictionCoefficients From Boundary-Layer Measurements in Flight on aParabolic Body of Revolution (MACA RM-I0) at Supersonic Speeds andat Large Reynolds Numbers. MACA R( L51BI2, 1951.

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