i

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*,●

/(’ CB NOV ● 1942

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS. . ...-. --,,.-.

‘P!!!M!WW \ “

.—— -

WAI,TIME Iuw(w”ORIGINALLY ISSUEDNoveniber1942 as

ConfidentialBulletin

INVESTIGATION OF THE VJ@IATION OF LIFT COEFFICIENT

WITH REYNOLD3 NUMBER AT A MOIERATE ANGLE

OF ATTACK ON A LOW-IRAG AIRFOIL

By Albert E. von Wenhoff and Neal Tetervin

Langley Memorial Aeronautical LaboratoryLangley Field, Va.

~

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%,:; ,,.’ .~?-%lw$ -:+... -,: .,,,,.% w---‘L W.-w ‘!-’, “,” , ,. ,,., F; %;$P:;”:7?..:$$i -“’k.::, ~

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{ .. . ‘“’‘ ‘::”N’&G,*:!{i~’’’’””\ ....’ ,.. .,:,>C,,-,.,.,. . ,>. ~I

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NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of

I

advance research results to an authorized group requiring them for the war effort. They were pre-viously held under a security status but are now unclassified. Some of these reports were not tech-nically edited. All have been reproduced without change in order to expedite general distribution.

L-661

.

,,

.!

EATIOBTALADVISOBY COMMITTEE ~OR AERONAUTICS

COn IDEETIAL EULLWJ!ZE..-. .. .. . .

r-

...-----

3HSTI(+4TIOIJ os TH8 VAEIATION or L131TCOEPFI IEET

. WITH REYITOIJDSliUM2EiAT A MODERATE ANGLE

OF ATTAOH ON A LOW-I)EA”GAI~OIL

By Albert ~. von Doenhoff and Neal Tetervln

SUMMARY

An investigation of the boundary layer about theNACA 66,2-216, a = 0,60 airfoil eaotion has been made In -the MACA two-dimensional low-turbulence tunnel, In an at:tempt to ftnd an explanation for the decreaeed slope ofthe lift curve obeerved for come of the low-drag oeotionsoutside the low-drag range at. low Reynolde numbers. Itwas found that the effect was probably associated with theformation of a small local region of eeparat.edflow nearthe leading edge, which decreased in eize as the EeynoldBnumber inorea~ed.

IMTRODUCTIOH

It has been noticed that the curves of lift coeffi-cient against angle of attack for come of the low-dragsections were not etralght outside the low-drag range,particularly at low Reynolde numbers. At Reynolds numbersIn the flight range the lift ourve beoame more nearlyotraight.

In order to determine the cauae of the variation of“lift coefficient with Reynolde number at moderate angleeof attack, the effect wae investigated for a representa-tive low-drag alrfoll, the IJACA66,2~216, a = 0.6. TheInvetatigatlon, whioh wae oarried out tn the lTACA two-d~mensional ..low~tur-bqlenae tunnel, consisted of boundary-Iayer and lift measurements through a range of Reynoldexmmbere from 0.9 X 10= to 2,6 X 108.

Ohangea In lift and boundary-layer characterietioewere”obtaerved at an angle of attack U of 10.1O. whloh

.

,.2

was chosen in order that a fairly large change of lifteoefflelent with Reynolds number would occur. Thte angleof.attaoks however, was definitely below that for”maximumllft.

APPAEATUS ..

The teptta were made In the HACA two-dimeri~lonal low-turbulence tunnel, which has a test section 3 feet wide,7* feet high, an~ 7* feet long. The tuo-dlmensloqal low-turbulence tunnel has a turbulence level of the order ofa $?ew hundredths of 1 perceat, am Indioated by a hot-wireanemometer.

The lift of the airfoil was meaaured by obBerving thechange in the pressures on the floor and on tha ceillng of “ .the teat section. A correction obtained theoretically 1s “applied to the mea~ured results to take Into account thefinite sise of the test ~eotlon. Lift coefficients ob-tained in this manner are in good agreement with those ob-tained In the ueual” way from pressure-dletribution measure-ments.

The MAOA 66,2-216, a = 0.6, airfoil used In this in-vestigation had a chord of 2 feet and a span of 3 feet andentirely epanned the tunnel. ~he model waa constructed ofwood w$th the grain running in the chordwl.Oe direction tomlnlmixe a~ unf~lrnetas caueed by uneven shrinking andewelllng of”the laminations. The surface of the airfoilwae finished with several ooats of pyro.xylin primer sur=

~ faoer, wet-sand”od ueing”rubber blocks.”

The boundary-layer measurements beh-lnd 2* percent ofthe chord were made with a Wmouaem that consleted of a .group of four total-pressure tubes and one etatia-preseuretube. The tubes were made of. steel hypodermic tubing thathad an outside dlame”ter of 0.040 Inch hnd a wall thicknessof 0.003 Inch. The total-preeeure tubes were flattened atthe ende until the opening at the mouth of the tube was .0.006 inch high. A mouse one-half as large. as the one~uet described was. ueed. for measurements” at: 2* percent .ofthe chord and forward where the boundary layer was espe-cially thin. The arrangement” was aimllar to that da6a%ibedin referenoe 1.

. . ... .

.-. ---

,’

ma. . . . . .

,48A

..-

“ Wlmoll- “.‘“”“..= . . ,.. .

.. J- --- .. &...._ .. :.. ~u . ..-

,- . .. .. .

The MACA 66,2.-216, a = djg”~%~-fo~.l aea-t.ton“w&s setat an angle of attaak;.of 10.l O.antl:the lift wke meheuredat Reynolds numbers of 0,9; .106; 2,29..206; and 2*6 X 10e.Valuee of the lift were oorreetefi for tunnel wall effect.

:“... .. . .The velocity .diet~ibution”; in the b’oundary layer. ~er.e

obtained by meae~r$ng the static pressure. at a point .Qu~-●ide the boundary layer’ and the total pressure at eeveralpositions wit~ln’th.e boundary la~er~ The total preowreouttaide the boundary layer waa need 46 the ‘refetience pr.qs=oure. Prom these measuramente, the rat~o “of the velacityIn the boundary lay~r to the free-stream velocity wascalculated ae - . .. . . .

. .u. veloc$ty Iie”ide boundary layer

U. free-etream velocity

P local ete.tic pressure

. . .

. . . .

. . ..m.

. . . . . .

h total pressure inside boundary layer. . ...

qo free-etream dynamic pressure

.The.heighte cf the total-pressure tubee above the eurface,. were measured with a micrometer microscope. .

. . . .The p.~essure dtstributiona were ~cbteiinad’.at the same

time the boundary-layer meaaurementa were taken by.uelngthe meaeured “value# “of the local static .prefasur.e..

. . . . -.●

✎ ✎✌

✎✎

❞ ;V—= (~-P\=l.f&A : .“““ ‘.(UJ .“. . q. , \qo.,. ,:”. .,, .+“-.

..+ . ..-. . . . . . .

whexe . . .. . ~.... .. .

.- ...-H“ . free~stream total pte~surg which is constant through- “...

dut teat section.~except.in bou~dai$ ilefer and wake.. . . ... ,..’ .

, . .

..,

-1

.

4 . .

.:.

u 100al Telooity ou$eide boundary layer

A; d“ifferbnoe .bet”w~-l”ocal atgiblcpressure and free-etream tatatiep~”~seure

.,. L, ,..

The distances of thw boundaries of tha region- of- lam- -Znar separation from mthe wing eurface were determitied bynoting the speed at which each total-pressure tube in theboundary layar ftret showed a total prmeomre gr-eater thanthe local static predsure. Plots were then made of,theheight of the region of laminar separation at a particular “chord position against tapeed. ~rom these plots, the’:bound-ar5ga 0$ the region tif lami.nar separation for. the etandardReynolds numbers were determined. . . . “ . “

The thickness of.th? boundary layer 5 I* dbl’~hed as

●the distance y perpend~cular to the surface for which

. . .

(I&.,.

d = 0.707(}

.u_ The thickness 5 Is determined fromU() Uo

the boundary-layer velocity profile for the particular sta-tion un~er consideration. The angle.of attack was ~lxedat 10.1 in the tunnel. This particular angle was chosenbecause a fairl~ large change-in lift coefftc~ent throughthe Reynolds number range was observed. The angle; how- ..ever, was not so high as to cause the flow.to..be on: theverge of complete breakdown.

.,

RESULTS MD”DISCUSSION ., , ,. ..

The”phenohenon under investlga.tion .is.illustrated in... . .figure 1, which showe the variation in the shape”of the..“ lift curve with ReynoldB number. The” variation of section

lift coefficient with Reynolds number at. a constant angle .of attack of 10.1° is shown In figure 20 :It \s ssen thatthe results of the tests in the two=dlmensional low-turbulence pressure tunnel (designated TDT) and in thetwo-dimensional l’ow-turbulence tunnel (designated LTT) are “In good agreement, The slope of the curve decreases withIncreasing Reynolds number, an indication that the effectunder investigation becomes less pronounced as the Reynoldsnumber increas?~. . . .

....+ .. .

~he”pressure” distribution over tke ~ppor sur~ace of. the airfoil for several Reynolds numbers” is given in fig-

ure 3. The flat region near the trailing edge Indicates

.— —

F

6

jthat separation has ocaurred. It .IJJto be noted that theL.,.

-pressure in the separated reglea-ramains. constant.. $ndoQead-ont of the Reynolds number; whereas the pressures over the

I remainder of the upper surface decrease with Increasingi+ Reynolds number.

v

Preaaures were also meaaured at a ahord-wise position x/o of 0.30 on the lower surface and the

M“value of

()J&a was found to vary from 0.83 at RU.

“= 0.9 x loe .to 0..79at E = 2“.6 X 10e. The increase Inllft of the eectlon with inorea~ing Reynolds number IS -therefore .seen to be conneoted directly with a decrease

● .“ In pressure over the upper surface and an increase iQ.preeeure over the lower eurface.

Velooity distributions In the boundary layer for va-rious ehordwlse positions x/e are given in flgureO 4 to6. “The variation of the boundary-layer thickness withohordwlse position is shown in figure 7. Figure 8 showe .the relative’thfcknega of the boundary leyer nt a = 10.10as compared with the airfoil dimensions hnd the large in-”.cre~ee in thlckneee naeeociatied with eeparatioa. The ve-looity profiles near the leading edge indioate the exl6t-ence of a local region of eeparated flow. !Che extent ofthie region and the preeeure distrtbutlon near the lead-ing edge are shown “In figure 9.

In order to. obtain’more information regarding the”eeparated region near the leading e~ge, a euspenslon oflampblack in kerosene”waO painted on the wing in eachcatae before the tunnel waO etarted. (See fig. 10(a).)When the air Etream wae started, the fluid collected inthe separated region. The flow patterns were photographed .while the tunnel.wae running. It ie tae?n from figuree10(b) to 10(e) that the extent of the separated regton de-creased as the Reynolds number Increased. This reeult i6in agreement with the conclusion~ drawn from the boundary-layer eurveye.

A qualitative picture of the rneohanism that broughtabout the observed variat~on of lift coefflo.ient withReynolds number In this oaee is eugges”ted by the experi-mental results obta-lned.in this investig~t,ion. When par-

tial stalltng of the-flow. near the .traillng ed%e”ocktirs,there le no reason to suppose that the elroulation andhence the lift ooefficlent” Is determined by the. Kutt?- .Joukovskl eonditlon. It was found in this ease that thepressure in the sepdrated region remained substantiallyconstant, Independent of the Re”ynolds-number, at a value

I — -

6

sltghtly below that of .free-etream stat~c pressure. “Exam=ination of numerous pressure-d iatrlbution data shows that “ .the pressure in a region of.permanent separation III.Ml&= “..”tlvely Insensitive to ohangem In flow-about the airfoil “. .and usually has a valve similar to that observed In thlta - “ .ease. The oondltlon that the pressure In the separated.. “ ~.region remains oubstantlally constant is not in itself boufflelent to determine the circulation, because. the point .“ “along the airfoil surface at which thle pressure is at-tained 16 rrot yet determined. If in addition to the pres- ~nure in the ❑eparated reglonm however, the amount of pres-sure recovery from the leading edge is known, then thecirculation and.the poettion of the final separation point18 determined. ..

Conetderatlon of the effect on the pressure. dlatribu- “ .tion of varsatlon in the circulation shows thatI;h;:ea;on- .ditions are euffieient to determine the flow. . . -sumed that the amgle of attack IEIfixed and that separationoocurs at a fixed value of the preesure ooeffioient oorre-eponding to a preesure a little less than free-etreampressure. If the elrculatlon la then inoreased, the pres-sures on.the upper surface near the leadingtedge must de- . ““ .oreaed. Consequently, the amount of preseuro secovery

‘.

which occurs before the flQw separatee Inoreases with In- . ...

crease in the ciroulatlon; that is, the pressure reoovery -1s a function of the circulation. Eor a given airfoil ata g~ven angle of “attack, therefore, the circulation is de-termined if the amount. of prestaure. recovery Is speoified. .in addition to the preesure in the eeparated region. “ .

. .Tho pressure retiovery from the leading edge .takee -

plaoe almo~t entirely In a region oovered by the turbulentboundary layer. The amount of pressure which can be re-covered with a turbulent boundary layer Is mainly a,funu- .tion” of its initial thickness: that is, the thinner the .initial thickness of the “turbulent boundary la?er, thegreater the pressure difference between the point where .the boundary layer begins and the point where It separates..Hence”i a, decreaee In the boundary-layer thickness near theleadlng edge must correspond to an increaee tn the liftcoefficient when the $1OW over the airfoil is partiallyetalled. ..

. . ..In.the oaae under conalderatlon, the. turbulent b.m.tnd- .

ary layer Ita affected “by the ReYn.olds. numbe.r..~n $~o .waYS~” .The firat effect la the normal decrea~.e In.thi,aknepa.of “the turb”ulea~ ”boundary layer aaaociatei! w.lth an Iricre@abIn Reynolds number. The aeoond and more $mport.ant ef~eot ...,

..

? ““

in the-> roeent ease is the “large decrease l’n the Initial .thlcknes~ of”tho’ttiibulbnt “b’ovndar~ layer--.wherltlt. formsjust at the end of theregion of laminar separation.(see ftgi 11. ) The thickness’ of the initial tur’buletitboundary layer ia lirgely determined by the oize of thepreceding region of laminar s“eparat~on wh~oh deoreadesrapidly with increase in Repolds number.

At higher Eeynolds numbers it meem~ iikely that the “regton of loaal reparation near the leading adge will.be-aome insignificant. Or will completely disappear. It ieto be expeoted then that the lift may oentlnue to increaoesomewhat with increaae an Reynolds number, owing to the.normal deorease In boundsry-layer thlekness with lnereae-“ing Reynolds number, but at a considerably lower rate.

Langley Memorial Aeronautical Laboratory,Eatlonal Adv180ry Committee for Aeronaut Ice,

Langley Eseld, Va.

RErmEln?cE

1. Jones, B. Nelvlll: Plight Experiments on the BoundaryLayer. Jour. Aero. Sol., vol. 5, no. 3, Janti 1938,PP ●

81-94.

..

..,.

—-

8

.-

Y3RIIATAON FIGUR3S

The values of section lift coefficient obtainedfrom TDT test 90 (fig’s.1 and 2) should be correctedby the following equation

cl (corrected)= o.964c~ + 0.008.

NACA Fi~s. 1,8*

Cfn

9--.0

., . __

*o

xIn

mII

w

\

\-

&———

-c,

.— 0 Boundary-layer thloknemm—.—. — UsIa where U. dyntio proasura la-id. the boundary layer im ~ual to

2 percent of the dynamic prossuro outmldo the bomda~ layer

—

Wind dtiethn

‘Chord dlrectlo~

.

Flame ~.- Ekmndnry-layer thlcknena on upper surfaoo of liA12A b6,2-216, a = 0.6, airfoil

section. R, 2.6 X 106.

Reynoldm ntiber

Figure 2.- Variation of section llftnumber. NACA b6,2-21b, ● = 0.6,a, 10.1O.

coefflolent ulth Reynoldsairfoil aectlon;

Szl

48

4.4

0 0.9 x 106

40

!

f- 1.5A 2.2

3.6 x

n 2.6.52

2.82

()-t. ~ - I&

Z.a — —

1.6

La

0

+

0+o .20 .40 .60 .ea

Figure ~.-Reynoldaaectlon~

x/o

Upper-aurfaoe preawre diatrlbutlo~for severaln-berm. NACA bb,2-21b, a = 0.6, alrfolla, 10.1O.

.

,,+. . . .. .

<’o;..--

; (P

;!

T& !

I1.2

iE .0125

-. .ol~l -.—A .0171

I o .050

0

2..(

8

,4

1––,___

I1

-----

0

I—

x/c

❑ .0125

A .0171

+ .025

.001 .002 fw3 .any/c

(a-d) (a) R, 0.9X106.y/a

(b) R, 1.5 x 1060T,lgure 4.- Boundary-layer velocity profiles in the region formrd Figure 4=- Continued.~f the 10-percent-chord ~tatlon. NACAb6,2-216, a = 0.6Uairfoil si?ctlcn; a, 10.10.

7G“

0

“Alil-u

.5

.4

2.,4

2.0-/T p ,4-

S /-1

v/.6 1

+

1.2-

!x/c

o 0.0094❑ .o125

I/

/

x .0131

A .0171

v .020 _ -_+ .0250 .050

.001 .002. .003 .004

z.+-

2?0

1.6 I

$w / ‘“,

L?!

/ +$

/ o O*W4,_-.../ x .0131

.8 A .0171v .020

0 .050$

.41

/

.001 .00?., .003 .004

y/c y/t3(c) R, 2.2 X 106. (d) R, 2.5 X 106.

F’lgure4.- Continued. Figure 4.- Coacludsd.

NACA ~igs.,5a, b

%/0x 0.70

,. 0 .6o

1.6- -

❑ .50

-e-A ●4O

— + .30/ * .20

/.2 . ,4/ ‘ ~ < / < _ _ _ _ > ,.10

~ —/ ‘ ~ Y

~

.0

L _ _ _ _ _ _ _ _ _

/ ‘/ ‘

h. ‘“/ 2

/ )

o0 .004 .Ooe .012. .0/6 .020 .0%4 .0.28 .032.

(a) R, 0.9 X 106.y/o

Figure ~.- Boundary-layer velocity profiles In the region from the 10-percent-chord to the~0-percent-chord atatlona. NACA 66,2-216, ● = 0.6, airfoil eectlon; a, 1o.1o.

x/cx 0.700 .6o

1.6- n .so

/ y /Jr-A .I,lo

/ / ~ – A i- .30 t

/1,L

—-—,-

J

4

0

(b) R, 1.5 X 1060 7/0

Figure 5.- cantinue~.

,. ... . . . .. . . —.-. ..-.——.

-..

NACA Figs. 5c, d

,,L6

/.2

~

4

f

0,0 flo4 .008 .012, ,016 .020 .024 .0.23 ,032

(c) R, 2.2 X 106. .y/c

Hgure 5.- Continued.

I.z

4

0

/

o .004 ,006 .012. .0/6 .02.0 .02.4 .028

(d) R, 2.5 x lob.7/0

Figure 5.- Concluded.

77

6/0

Figure 6.- Bcnmdary-layer velocity profiles in the region from the 5-percent-ohord to the

z:-$zc:n:zg?rd 8’a’’0n8” ‘ACA’6’2-216’ a=o”b’ airfoil aection; as 1°”lO;

.CM \R

o

+ 1.5.0/6

x 2.5 I Jf❑ 2.6 1

.012/ .(

}

-O*-

/ / /

.004 -+

o Io ./0 . .30 .4 ,s0 .63 .70 .80

Hgure 7.- Variation of boundary-layer thickneaa with chordwise position for various

Reynolds mnnbers. NACA b6,2-216, SP= 0.6, airfoil section; a, 10.1O.

“4.6

4,2,

()12U.

Z3.4

‘3.4

3.0

‘\\\\

‘\ \ \

\\ y.

f.

\ \ f?

\ L/ ‘:,v ~

PI.esstu‘e dil Itrlbt.tion\ \

.

\

BCmmdax~ of separated

reglcnA-

.

\\

p \

Figure9.- Extent of aepsrated region

leading edge of NACA bb,2-216, a =

x/c

Figs.———R

+ 0.9 x id!!!!e 1.5~ 292

\.

\

\

\\\

.62 .03

end pressure dia%ributlon near0.6, airfoil aectlon. d, 10.1O.

* o-

3,11

,0008

y/o

0004

0

.-,-,-.,

NACA

,—

Fig. 10a

(a) Model before tunnel was started,

Figure 10(a to e).- Suspension of lampblack inkerosene painted on upper

surfaoe near leading edge of NACA 66, 2-216,a= 0.6, airfoil section. ~ , 10.1. Directionof flow from bottom to top of photographs.

—

I

(b) Flow patternat R= 0.9 x 106.

i?-igs.10b,o

(o) Flow pattern at R= 1.5 x 106.

Figure 10.- Continued.

1

NACA

.,

(d) Flow pattern at R+ 2.2 x 106.

Figs. 10d,e

(e) Flow pattern at R = 2.5

Figure 10.- Concluded.

x 106.

—

—— ra==' (Bras) .1—-, i~ r.n

CB-L-331 PU3USK3) DY: (Sana)

MOT '43 Unclass. U. 3. BlCT. pec3 ie njtcftq, BTPPSIO

ABSTRACT:

An investigation of boundary layer about an airfoil xma mads in a tuo-dimensicaal. too-turbulence tunnel to find an explanation for Use decreased slope of the lift curve observed for some of the loo-drag sections oulelto the loo-drag range aft loa Reynolds Numbers. It oas fcucd that the effect TTOS probably associated oltb tfce formatter of a small local regloa of separated floa near the leading ed33, wMch decreased in sloe as Use Reynolds dumber Increased.

DISTRIBUTION: Request copies of this report only from Qriglnattna Agency DIVISION: Aerodynamics (3) SECTION: Wings and Airfoils (6)

ATI SHEET NO.: R-2-6-J7

SUBJECT HEADINSS: Boundary layer (18200); Airfoils - Aerodynamics (07710)

flia VECKMSCAl B39BR wrigTi>*Pattcf£ioci Air FGTCO OOOO

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