Document
FILE COpy
NO. 1
CA
COpy
NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
REPORT No. 637
DETERMINATION OF BOUNDARY .. LAYER TRANSITION
ON THREE SYMMETRICAL AIRFOILS IN THE
N. A. C. A. FULL-SCALE WIND TUNNEL
By ABE SILVERSTEIN and JOHN V. BECKER THI:i DOCUMlNT ON LOAN FROM THE FILES OF N AT i ONA. L ADVI SO RY COMMITIEE FOR AERONAUTICS l 'W:lf Y AERlJr,,~Ui IC. ~l LABOR./ITORY l ·;~:;l.'{ FIE LD. HAM PTO N, VIRGINIA R~CIJ·~1'S rer; r 'SUCA"ON S SHOULD BE ADOREss m A.:, • ul..LOW S: N ATiCN f\l AD V IS O RY C OM MITTEE FOR _ AERONAUTICS 1724 F ST Rf.tT. N W., W ASHINGTON 2 5. D. C.
For sale by the Superintendent of Documents, Washington, D, C. _ • • • • • • • • • • • Price 10 cents Sub scription pric e, $3 per year AERONAUTIC SYMBOLS 1. FUNDAMENTAL AND DERIVED UNITS Metri c Engli sh Symbol Abbrevia- Abbrevia- Unit U nit tion tion nleter ____________ ______ Length ___ ___ foot ( or mil e) __ __ _____ l m ft . (o r mi.)
se cond ___ ______________ Time _______ _ (or hour) ____ _ __ t s se cond sec. ( or hr. ) Force ___ __ ___ weight of 1 kil ogranl _____ weig ht of 1 pouud _____ F kg lb.
Power _______ hor se power (m etric) _____ horse power _ __ _ __ ___ __ P hp.
--- ------ - miles per hOLlL ____ ___ {kilom e ters p er hOUL _____ k . p.b . m.p .h.
Spe ed ____ __ _ V nl e ter s per se cond _ ______ feet p er se cond ____ ___ _ m . p. s. f.p .s.
2. GENERAL SYMBOLS
w, Weigbt=mg P, Kinematic yiscosity
Standard acceleration of gravity = 9.80665 p, D e nsity (mass per unit volume) g, 2 2 Standard dens ity of dry ai.r, 0.12497 kg -m-(-s2 at m/s or 32.1740 ft ./s ec .
15° C. and 760 mm; or 0.002378 lb.-ft.-4 se c.
nr
m, Mas s= - 3 Specific we ight of " standard" air, 1.2255 kg/m or g 0.07651 lb. /cu. ft.
Mom e nt of inertia = mk • (Indicate axis of I, radius of gyration k by proper subscript .)
Coefficie nt of viscosity iJ., 3. AERODYNAMIC SYMBOLS Angle of se tting of wrngs (relatiye to thrust
s, Area
line) Area of wing S "" Angle of stabilizer setting (rela tive to thrust Gap G, lin e) Span b, Re s ul ta nt moment Chord Q, C, Resultant angular yelocity fl, b Asp ec t ratio S' Vl Reynolds Numb er, where l is a linear dimension
P-'; '
Y, True air speed (e.g., for a model airfoil 3 in. chord, 100 m.p.h. normal pr essure at 15° C., the cor-
Dyn amic pr essure = .!. p P
q, responding numb er is 234,000; or for a model of 10 cm chord, 40 m.p.s., th e corr es ponding
Lift, absolute coefficient GL = :S
L, numb er is 274,000) Center-of-pressure co e ffi c ient ( ratio of distance
D, Dra g, absolute coefficient G = :!s
D of c.p. from leading edge to chord le ngth) Angle of attack
Profile drag, absolute coefficient G = ~S
Do Angle of downwash
Induced drag, absolute coefficient G ;= ~s Angle of attack, infmite aspect ratio
D Angle of attack, induced Para s ite drag, absolute coefficient GD1I=~S Angle of atta ck, absolute (measured from zero- lift position)
0, Cross-wind force, absolute coefficient G = q~ Flight-path ang1e
c R, Resultant force , ,
REPORT No. 637
DETERMINATION OF BOUNDARY-LAYER TRANSITION
ON THREE SYMMETRICAL AIRFOILS IN THE
N. A. C. A. FULL-SCALE WIND TUNNEL
By ABE SILVERSTEIN and JOH N V. BECKER Langley Memorial Aeronautical Laboratory I 0294--39-1 NATIONAL ADVISORY COMM ITTEE FOR AERONAUTICS HEADQUARTERS , NAVY BUILD. G, WASHINGTO , D. C.
LABORATORIES, LANGLEY FIELD , VA.
Created by act of Congress approved March 3, 1915, for the supervision and di re ction of the scie ntific st udy of th e problems of flight (U. S. Code, Title 50, Sec. 15 1). It s membership was incr e as ed to 15 by act approved March 2, 1929. The members are appoint ed by th e P res ide nt, and serve as s uch without compensation.
JOSEPH S. AME , Ph. D., Chairman, YDNEY M. KRA US, Captain , nited States Navy, Ba l timore , Md. Bureau of Aeronautic s, avy D epa rtm e nt .
DAVID W. TAYLOR, D. Eng., Vic e hairman, CHA RL ES A. LI NDBERG H, LL. D., Washington, D. C. N ew York City.
WILL IS RAY GRE GG , Sc. D., Chairman, E xe cuti ve Co mmitt ee, DENIS MULLIGAN, J. S. D ., Chief, nited States W eathe r Bur ea u . Dir ector of Air Commerce, Department of Commerce.
AUGUSTI E W . R OB I S, Brigadier General, United States WILLIAM P . MA CC RA C KE N, J. D. , V ice Chairman, Executive Army, Committee, Ch ief M ater iel Divi ion, Air Corps, Wright Fie ld, Wa sh ington, D. C.
Da yton, Ohio.
C HAR LES G. ABBOT, Sc. D., e cretary, Smithsonian In st it ution. EDWARD P . WARNER, Sc. D., LYMAN J. BRI GGS , Ph. D ., Greenwic h, Conn.
Dire cto r, National Bureau of Standards. OS C AR W ESTOVER, Major General, nited States Army, Chief of Air Corps, W ar D epa rtm ent.
ARTHUR B. COOK, Rear Admiral, United States Na vy, ORVILLE WRIGHT , Sc. D., Chief, Bur e au of Aeronauti cs, Navy D epa rtm ent .
D ayton, Ohio.
H A RRY F. GUGGE HElM, M. A., Port Wa sh ington, Long Isl and, N . Y.
GEORGE W. LEWIS, Di1'ector of Aeronautica l R esearch J OHN F. VI C TORY , Secr e tary HE N RY J. E. REID, Engine e1 '-in -Chw'ge, Langl ey Memo ria l A e ronaut ic al L ab01'atory, La ngley Field, Va.
JOH N J. IDE, T echnical Assistant in Europe, Pa ris, F rance TECH ICAL COMMITTEE AERODYNAMI CS AIRCRAFT ST RUCTURE S POWER PLANTS FOR AIRCRAFT AIRCRAFT ACCIDE TS AIR CRAFT MATER I ALS INV ENTIONS A D DE SI GNS Coor ' dination of R esearch Needs of Mil itcb1'Y and Civil Aviation P 1'e pa1' ation of R esear'ch P1 'ognbms Allocation of P r'ob lems Pre ven tion of D up l ication Con si dM'ation of I nventions LA GLEY MEMORIAL AERONAUTICAL LABORATORY OFFICE OF AERO AUTICAL I TELLIGE CE LANGLEY FIELD, VA. WASHINGTO ,D. C.
Collection, classification, compilation , Unified conduct, for all agencies, of scient ific research on the fundamental and dissemination of scientific and tech - nical information on aeronautics.
prob l ems of flight.
REPORT No. 637
DETERMINATION OF BOUNDARY-LAYER TRANSITION ON THREE SYMMETRICAL AIRFOILS IN THE N. A. C. A. FULL- SCA LE WIND TUNNEL By ABE SILVERSTEIN and JODN V. BECKER UMMARY umber, pres ure gradient, curvature, and surface roughness.
For the purpose oj studying the transition jrom laminar Prediction of the transition i necessary in order to to turbulent flow, boundary-laye1' measurements were made predict the drag because the skin friction occurring in the . A. O. A. jull-scale wind tunnel on three sym- with a laminar boundary layer is less than with a tur- metrical airjoils oj N. A. O. A. 0009, 0012, and 0018 bulent one. 0 reliable extrapolation of wind-tunnel sections . The effec ts oj variations in lift coefficient, drag results to flight may be made until the effect of Reynolds Number, and airjoil thickn ess on tmns ition all the factor upon which transi tion depends may bo were investigated. Air peed in the boundary lay er was explicitly tated.
mea ured by total-head tub es and by hot wi1'es; a compari- Owing to the effects of air-stream turbulence, tbe son oj transition as indicated by the two techniques was in terpretation of "vind-tunnel transit io n data for appli- obtained.
cat ion to flight conditions ha been difficult. The po ss i- The results indicate no unique value oj R eynolds bility of a direct comparison between .vind-tunnel and Number for the transition, whether the R eynolds Numbel' fli ght results is provided by the equipment of the is bas ed upon the distance along the chord or upon the N. A. C. A. full- cale wind tunnel. Tbe turbulence in thickness of the boundal'Y lay e?' at the tmn sition point.
the full-scale tunnel as indicated by sphere tests (refer- In genem l, the transition is not abrupt and occurs in a ence 5) is 0.3 percent. The present investigation, which region that varies in l eng th as a function oj the te t concli- was made in the full- cale tunnel, is the first part of a tions. lrit h increasing lijt, the transition on the upper program planned to correl ate the flight and tunnel surface moves towal'd the f01'wal'd stagnation point; re ults.
whereas, on the low er surface, the transition progresses in In the tests, boundary-layer velocities were measured the opposite dir ec tion. This effec t i most mal'ked for on the upper surfaces of airfoils of the N. A. C. A. 0009, the thin airjoils . The total-head tub es and hot wires 0012, and 0018 sections at tunnel velocities from 30 to indicate essentially the same point of tmn sition. Profile- 90 miles per hour (value of the Reynold s umber from drag results are gi ven and a cOl'relation of the dmg and 1,730,000 to 5,020,000) over a lift-coefficient range from the tmnsition mea urements is attempted.
- 0.57 to 0.65. The tests were made with rectangular 6- by 36-foot metal airfoil having aerodynamically INTRODUCTION smooth urface. Measurements of profile drag at Th e effect of skin friction on the air flow over a flat zero lift by mean of forco te ts and the momentum pl ate or an airfoil 11a been hown by many early method were al so obtained.
writers to be restricted to a thin layer of air of reduced In order to aid in the pre entation of the experimental momentum that flows along the surface. The air .flow data and to clarify discu ion, the following arbi trary in this bOlmdary layer is l aminar at low Reynolds definitions have boen adopted for the present paper.
Numbers; transition to a turbulent regime is, however, Th e transition region is the region in which the bound- genera lly observed to occur when the R eynolds umber ary -lay er flow changes from l aminar to turbulen t.
is increased. Extensive investigations have not yet The beginning of thi region will be referred to as tbe provided a means for reliable prediction of the trans i- "trans iti on point" and will be considered to be the point tion, although Burgers (reference 1), van del' Hegge at which the velocity near the urfaee begins to show an Zijnen (reference 2), Dryden (referonce 3), Jonos abnorma l increase. The end of the transition region has (reference 4), and otbers have shown that transition been taken as the point at which the ve lo ci ty near the depends upon initial cream turbulence, Reynolds surface ha reached a maximum.
2 RltiPOR'l' O. 637- ATlO AL ADVISORY COMM I TT J ~ g FOR AERONA UTI, ' SYMBOLS intersect, as shown in figure 1, and no extreme velocity g radi ents are therefore expected.
Th e symbols used herein are defined as follows: CI, section lift coefficient. . /6 OD O , profile-drag coefficient of the wing.
--- r-- - C do, section profile-drag co effici en t.
Or, skin-friction coefficient. . 14 u, local ve loc it y, f. p. s.
U, veloc it y at edge of boundary la yer, I. p. s.
11, tunne l air speed, m . p. h .
1/, distance above airfoil surface.
S s, distance along airfoil surface from forward
f lO
stagnat ion point.
<l2 I
c, wing chord. !
~ OJ t, wing thickness.
I
~ . 0 8 0, boundary-layer thickne s (u"-'0.99 U at 0).
o 0*, displace ment thickness of the boundary layer
~ I /
III U
V
I
§ 06
( o*=b l· (U-U)dy )- -;;"
V
is ~ R., Reynolds Number based on the boundary-
Vi
.04 layer thickness at transition (based on U) .
V
/
R", R eynolds Number based on the chordwise ./' Laminar
/
y distance from the forward stagnation point to .0 2
/
the transition point (based on V). ' Turfu len /
V
/"" p, local pressure.
.--/ ~
V
L---- /'
-
o .4 .6 .8 1.0 q, dynamic pressure, ~P 11 2.
uj U FIGURll l.-'rypi ca llarninar and tnrl.mle nt boundary·layer velocity pro fil es .
ME THOD S AN D A PP ARATUS 1 40 In a paper on boundary - lay er transition in fli g ht, J ones (reference 4) has given an excell ent di cussion of the methods by which the transition on an airfoil may ,- He igh ! abo ve sur ro ce, in .
'- ~ / 6 7 be detected. Bri efly , the transition may be de te rmined ~I either from observations of the velocity at the airfoil ~ ~ \ sur face by means of a single total-head tube or a hot \0 'r!! .50 " ~ , \ ~ wire or from velocity measurements at everal distances "-...
0..........
\ -"--.
from the su rface so that the boundary-layer profile ~ ~
- .'-
80 _ ..
may be defined. Wh en the indicated velocity at the 0,
"i .'
, ,.G. - -<l _ Q.
1"-- 0 airfoil surface shows a marked increase in the transi-
-
<,.: / '<. 'U . "'-- . 033/ tion r eg ion, the ingle-tube or the hot-wire m et hod is - 1-0 - -0 - ;:1 " I 6 0 I~ quite sat isfactory as a transition indicator. If, how- ever, the chord wise velocity g radi ent in the boundar y layer is low, so that the point of minimum velocity i /V ""'-- r-- r--- r0- indeterminate, the more extensive measurements of the 1/ o
velocity profil es are more dependable. "-
, .00 7
d
Cha racteri st ic veloeity profiles for the laminar and tur bule nt boundar y layers are shown in figure 1.
R epresentat iv e data howing the ve locity changes that occur at transition for several heig ht s in the bound ary layer are shown in figure 2 to illu st r ate th e f act that o /0 .20 . 30 40 5 0 . 60 s/c no sharp indication of transition is given for some F I GU RE 2 .- Varia li on in the velocity of tbe boundary layer of the N. A. O. A. 0012 heights in the botmdary la yer . It will be noted (fig . 2) aI rfo il at several heig ht s above the sllrfac e.
that the transition point is shown to occur at s/c= 0.26 for all the heights except 0.050 inch; this height j Ho t-wire method,- Th e velocities in the boundary about that at which the laminar and turbulent profiles layer 0.01 inch above the wing surface were measured, - --- - - - - - -- -- - ~ - - - - - .- - -
j
DETERMINATION OF BOU t DARY-LAYER TRANSITIO ON THREE SYMMETRICAL AIRFOIL' 3 as suO'ge ted by Dr. H. L. Dryden, by means of plati- In onler to obtain satisfactory velocity readings, it
I
num hot wire 0.001 inch in diameter and 1 inch long wa necessary to calibrate the hot wire on a flat plate ( fig. 3). The platinum wires were soldered across the against a total-head tube at the same effective height, ends of forks of B . & . gage 26 (0.0159 inch) enameled Velocity indications based on a calibration in a free copper wire. The end of the forks were filed to thick- tream in which the beat-loss and interference effects nes es of 0.010 inch and prun g to keep the hot wire are neglected give completely erroneous results.
Total-head-tube method,- The ,elocities at four heights above the urface were measured by a bank of four sma ll tota l-head tubes and a single static tube (figs. 5 and 6) . (The static pressure in the boundary layer has been hown to be constant.) The tubes are of stainles steel, 0.040-inch outside diameter, with a 0.003-inch wall thiclrnes . The measuring ends of the total-head tubes were flattened to an out ide thickness of 0.012 inch for a length of 1 inch from the opening.
A hemi pherieal plug wa inserted in the end of the stat ic-pressure tube and four 0.005-inch holes, equally s paced, were drilled around the circumference. TIle
tubes were 3Y inches long and were soldered into }fG -
i nch copper tubes, which extended back along the chord of the airfoil to rubber tubing that was led along the trailing edgo of the airfoil to manometers. Required he ight adj u st ment was secm'ed by placing a ~~ -inch Central portion of winq of 36 - ft. span-, 1<-- -- 6 '- · - - -->I FIGURE 3. - not wire mounted on the airfoil. The pl atin um wire is 0.001 inch in diameter, 1 incb Ion::. and 0.01 inch above the surface.
1 2' taut at all temperatures. The enameled wires were cemented together "vith an in ulating glue at the base of the forks. In order to reduce the time required for obtaining the data, 12 hot-wire units were arranged on the wing at 0.05e intervals between the 0.10e and the 0.70e position, as shown in figure 4. The wires were spaced at sufficient distances along the span 0 that the wake of one wire did not pass over another. T hey could be witched into the measuring cinmit one at a time.
A vVbeatstone br idge circuit, with a hot wire as one fl . rll1 of tb e bridge, wa u e 1 to maio tain the 1'e istance
or L he wire at a con. tant value (fi g. 4). The re i sta n es
AB and Be wer made lar ge so !i ll a!i Lbc current L the h oL wire would be a bout equal that in the baLtel'Y (' i rcuiL . A 5-ohm rheo tat was u eel to balance tbe bridge fo r the initial till-ail' condition; an initial current of 0.15 ampere in the battery circuit corresponded to a F Mu iliple swtfc h wire temperature of 150 O. Th e X-ohm rheo tat in G. galvan ometer A, ammeler series with each hot wire was u ed to adjust the re ist- FIGURE 4.-Location of 12 hot-wire units on the 6- by 36-foot airfoil, and wiring ances of the 12 circuits to precisely the same value after diagram of Whe at tone bridge circuit .
insta llation on the , ing. Adj ustment of a 50-ohm rheostat in the battery circuit was used to increase the bridge 3 X inches back from the tube ends and bending current through the hot wire as the airspeed was the tubes at this bridge to conform to an accurate increased. During the tests, the procedure was to templet-type gage. The tubes showed no tendency to switch in a hot wire by means of the multiple switcb, to lose adjustment during a run and observations during adjust resistance A E until the galvanometer read zero, the tests indicated that no vibration of the tubes and then to observe the reading of the ammeter.
occurred.
4 R E PORT O. 63 7 -NA TIONAL ADVI S ORY C OMMITT EE FOR AE RONA U TI C Oalib rat ion of the ba nk of stat ic a nd tota l-head above the wing surface were mea m ed for lift coe ffi- t ubes in a uniform st r eam aga in st a sta nd a rd pitot- cien ts of - 0 .5 7, 0, a nd 0. 65 a nd at t unn el pee el s of stat ic t ube indi cated th at they were acc ur ate to wi thin a bout 60 a nd 90 mil es per hour. Th e measurem ents 1 per ce n t . we re t ak en a t 0.05 c in ter vals f rom the 0.10 c to tl lC Wh en the res ul ts ob ta i ned with the t ta l-head 0. 70 c position .
tub es were pl otte d, i t was nece sary to co rr ect the Profile-drag meas uremen ts were ob ta in ed at ze ro lift geometric hei ght of the tub e ce n ters to an e ff ect ive for all the airfoils over a ra nge of test vel oc ities.
Addi tio nal te ts were made on the . A. O. A. 0 01 2 airfoil to dete nnin e the e ff ec t on tra n ition and el rao- of a small pro t ub erance acros the span near the leading edge. Ja now g umm ed ta pe 0.00 3, 0.00 6, a nd 0. 00 9 in ch thick were at tached one at a time acro s th e span of th e airfoil at tbe 0.0 5c position on t he upp er ur face .
Th e vel oc itie were mea ured by the ho t-wire met h od at an angle of a ttac k of 0° a nd a tlmnel speed of 75 mile per bour. Dra g meas uremen ts were al 0 made for t ll ese tbl'ee r uns.
RESULTS A D DISCUS ION Th e bo undary-layer mea m ements o bt a in ed by tbe ho t-wire m et hod arc shown in fi g ure 7, 8, a nd 9 for the N . A. O. A. 0008, the N . A. . A. 0012, a nd the N. A. O. A. 001 airfoils, r es p ec tively, at everal section lift coe ffi cie nt s. Fi gures 10, 11, a nd 12 how co rr e- FIO UR E 5.- Ba nk of to ta J-h ead tubes and static tube mounted on the airfoil.
spondin o- res ult s ob ta in ed wi th the tota l-head t ube on th e wing surface. Th e forw ard stag n at ion point, from heigh t to take in to acco un t the vel oc i ty gradien t in which s was meas ur eu, was ob ta in ed from th eo reti ca l the bou nda ry layer . Th e e ff ective dyna mic pr ess ur e pr e s ur e- 11. tribution calcula ti on . Th e section lift co- over the tube opening is greater than th e pr es ur e at e ffi cien ts Cl were com pu ted from th e c ur ves of th eo reti- the ce n ter of the t ub e. Th e e ff ective height was al span load di tribu tion and from t he mea ur ed lif t ob ta ined on th e ass umption of a linea l' veloc it y gradie nt .
Airfoils.- Th e t 11l' ee m eta l airfoils used in the tests were co n str ucted with the utmost pr ecision so that the ection pro fil es a nd the surfaces were as fair and mooth as po sible. After th e m eta l surface h ad been fil ed to te mpl et di me nsion , th ey were a lt e rn ate ly fill ed with a sta ndard m et al prim er a nd rubb ed wi th fine-grade w ate r and paper until they were consider ed to be aerodynamically smo ot h ; they were then wax t and polished. Aerodynamic smo ot hn ess is here in de fin ed as the s lll oot bn ess afte r which fur ther impro ve - ment do n ot decrease th e skin fri ct ion . Inf o rm a ti on on wing sll1 00 thn e ob ta in ed in pr eviou inves ti gat ions in th e J . A. O. A. 8-f oo t hi g h- peed wind tunn el served a a guid e. Th e a ir fo il were carefully du sted before each se ri e of tests .
TESTS ~ ' I G RF. 5.- Bound ary -l ayer sur vey t ub es in frout view. Th e e ffe ct ive heights of the opellings above th e sur lace are 0. 007 inch. 0.033 inch. 0.0 50 inch. a nd O.ISi inch.
Th e h ot wires were no rm ally paced at 0.05 c i nte r- · 'I ' hc height of t be sta tic tuhe is 0. 1 is iuch.
vals from the 0. 10 c to the 0 .7 0 c tat io n. F or some of on th e wings. Th e b oundary -layer ve l oci ty pr o fil es, the tests, mea uremen ts were al so ob ta ined at the 0.05 c meas ur ed wi th th e ba nk of tota l-h ead t ub es, are shown position . Th e air-flow ve lo ci tie at 0. 010 in ch above in fl gure 13, 1 4, a nd 15 for the t hr ee airfoils at seve ral the airfoil ur face were meas ur ed at lif t coe ffi cients ection lift coe ffi cie nt s and p os itions along the airfoil of - 0 .5 7, 0, 0.33, and 0.65 a nd at tun ne l speed of urface. Bo un da ry-la ye r ve loci ty pr o fil es for the tran- about 30 ,45,6 0, 75, a nd 90 miles pe l' hour.
sition r eg ion are plo tted in a nondimensional form in In the tests us in g the tota l-h ead tub e, tbe ve lo c iti es fi g ur es 16, 17, and 18.
a t effective heigh ts of 0. 00 7, 0.0 33,0. 050, a nd 0. 16 7 in ch
!
I
J
D E TE RMI A TlO OF BO N DAR Y-LAYE R TR ANS ITION ON THR EE SYMM ET R ICAL AIR F OILS 5 Comparison of me t hods for detecting t ransi tion.- po in t a nd co ntinu e 1 th.rough th e tr an ition r eg ion, An anal ys is of t he re ul ts in fig ur 7 to 12 sh ow th at r ac hin g m axim um in te n it y at abo ut the tr ansition the s Ul'f ace tota l-h ead tu be or the h ot w ir e i adequ a te po int . Owing to th e h ea vy da mpin g in th e long pr e - to indi cate th e tra nsi tion p o in t exce pt for ca e in which s ur e le ad s to th e tota l-h ea d tu bes, the ac t ual violence the do wn st r ea m ve loci ty gra di ent at th e airfoil s urf ace of these flu ct ua tions was not obser ve d ; however, th ere is 0 m ail th at t he p oint of m inimum ve loci ty is n ot wa a dis tinct i ndi ca tion of un st ea lin e s in th e r ea dings clea rl y defined . Thi condition occ ur on th e u pp er at the tran ition point .
s urf ace of the airfoils at n egat ive lift coefficie nt (c or- Th e ho t-wire m et hod as u ed in th e pr ese nt te ts wa responding to th e low r urface of th e airfoils a t po itive co n id e rab ly faster th an th e tot al -h e ad m e thod , ina - lift coe ffi cien t ), in which case tb t ran ition point i mu h as it wa pos ible to obtain res ult s from each of th e indi cated a far back a 50 to 60 pe rcen t of th chord .
12 wire on the wing without a ch ange in the set -up .
Th e n ondi men ion al bound ary-l ay er pr of il e for th e Th e r ea dings were also obt a in ed mu ch m ore rapid ly 030 x 45 0 6 0 t> 75 + 90 V. m.p.h.
1 00
1 \
1 \ t--
6\
rt---- ~ ~ ./' r-
\\ II
+ + I}- ~V
\ \ i--
I \ I' ~ . ......-
/ /t;;--
" V r- l--- V Ia-
h-. "- I /~ 1.---
f--- i'--
V \~ L If
~ .
!-- f--" + I'-- I V K~ 0
-
l ~ /~ L Lx rr,... V ;0-....
J> 1 t;- V
pc:: V
""r---- "x, ~
V V
X ~ X _ x--+x _ 'x - X _ )( F--to- ;------ rx- 10- / I"--- j.--:" (aJ (bJ I, i
\
10 0 1-+-- ~
II ~ ~
&
II 1 9' ~ ~ ~ f'-.-
,""" "
., ~ ~ r---.
" ~~ "'I'--
v---
~ '- ;::---t:-- ,+ r--
r-- f:-
/ f'-..- ~ f'---.
.........
+ ~ r---- II f---
'''11<-- Wo
"" I t%-
i"-- '" ~ X 1'--.
-%- ro- Ix-- ./!........
f&--... ~ X
r--- "0-
- X / fa.. X r-:-"",
............ -
iO-- i'>-- a
... Jl
/
( c ) ~ (d) o .10 ,20 .30 .40 .5060 .70 .8 0 0 10 .2 0 . .3 0 . 40 .50 . 60 70 ,80 s/ c (a) c, =-0 . 57. (b) c, =O .
(c) c,=0.33.
(d ) c, =0 . 65.
F ' GUI! E 7.- TI ot -wire measuremenls of the boundary-layer vel oc iti es 0.010 inch above tho surface of the N , A. C. A. 0009 ai rfoil.
neo-ative lift coe ffi cien ts ( fi gs. 16 (a), 17 (a), an d 1 (a) ) becau e from 3 to 4 minut es were r e quir ed for the r ea d- axc of co nsid era ble a id in in ve ti gat ion of th e tra n ition ings from th e pr es ur e tub ing to reach eq uili br i um.
for th ese ca e. Th e h ape of tb e pr o fil es in the tra n- Th e ob er va tions obt ained with th e to ta l-h ead tub e ition r eo- ion i a pp ar ent ly a f u nct ion of the len gt h of eemed omewh at mor e co n i ten t , howeve l' , a nd a th e re gion and, at negat i ve l ift coe 1Ii cien ts, til }4 - WL~ :lI m ailer scat ter of th e experime nt al poin ts occ un ed .
power t urbulen t pro fil e d id n ot occ ur un til 20 to 30 Effect of lift on transition.- Th e e ff ect of vari ation percen t of the eho l' d b e hin d th e tra nsition poin t.
in th e section lift coe ffi cie nt on th e t ransitio n poi nt for Th e tra nsi tion a i ndi cated by the h ot wi re a nd t be va ri ous R eyn old Numb ers i shown in fi o- ure 1 9, 20, surface tu be how a r eason able agreemen t wi th th e a nd 21. Th e 1' e ult s from th e urface t ota l-h ea d t ube max imu m va ri ation of th e in dicat ions u unily n ot in a nd th e hot wire for zero and positive lift coe ffi cie nt s ex e of 3 percen t of tb e chord . Th e b ot -wire m eas ur e- are includ ed. T he tra nsition poi nt s were estim a ted m e nt s indi cated th e tra n iti on region by large flu ct ua- tions in the c urr en t r eq uir ed to b al an ce tbe brid ge. for C l= - 0. 57 from th e bound ar y- layer profiles of Th ese fluc tu at ions beg an sligh tly before th e trans ition fi g ur e 16 (a ), 17 (a ), a nd 1 (a).
REPORT O. 637-NATIONAL ADVI ORY COMMITTEE FOR AERO! AUTIC 0 3 0 x 4S 060 t:. 7S +90 V m.p.h.
- t--- ..........
\ L..+--.
t
~ + ,/ ~ '>-....
.~ ..
L + - - "- 0
V
\
k
- 0"- " ",,- r-- ~
7'
'-... /
'\.. -
""
---
~ ~ ...0- -£..
!-.Q.. ~
1'-. " - 0
>
x x x x x
---
(a) (b) 0 o
I
/ ~ ~ +
I 1\
I \ .
1"--.
K-- k
----
vi 60 Q..
~
\ Ii ~
L f
"'--
....: ."
\ ..:
/ K t-----. 1 \
I'---- ;: l40 --- ....... .
\ l-{ .
"'-.
: 1 t--- ~ ~ .
---:::: )
~ J ~ ---
"'"
~ '0-- ........ 10--..
OJ .-9 "0- <~
/ /
t---= -
-0- -;; --0.
~ k ~ ~ V (d) (el o
\
1\
+ \ Vr--- 1 00
/ +
'-...
'"
I
\ i'...
""
+ + .........
""
• -.......
r I+-
~ I'...
\ + a
""
/ + "",- '-- :---:. I, +
'" r ~ "'--I'-"
I'---
.........
~ .
r-----
,/ II' "I'h. '\.~ °
I'--.. ~ r--- ~ .c-
.
"
+'- + ~ r--- ~ -..z..: • -.......
........
I / ~ r--- k ./ X ~
~ ~ --0- 40 r--- ___
""'"
x --- ...
1-"---= ~ ~ i"- ~ r-- \ I I r--- :::::: ~ ::-- ~ ~ ~ X X I'" -.......
r----
JI !I' r-;;:: h:>- 0
1 I' fT k r--
---
9-
~
~ ~ X r- -0- -.......
\ /, 0
h>- 0
>
-...:::
---- (f)
( el -u- ""0- ~
o .10 . 20 . 30 .40 . 50 . 60 . 70 . 80 0 ./0 . 20 .3 0 .40 .5 0 . 60 .70 . 80
s/ c (6 ) CI = -0.5 7. (iJ) CI = - 0. 1 6.
(c) CI = O. (d) cl=0.J6.
(e) CI=U.33. ( I) C/ =0.6 5.
FIG UR E S.-Hot·wi re measurements of the bounda ry ·layer ve locities 0.010 inch above the surface of tbe N. A. C. A. 0012 airf oi l.
nWrERi\ lI NATION OF 80VNDARY- L AY I ~ R TRAN.'ITION 0 1 THR ] ~ I:': SYM n : TR l AL AIRFOILfl 7 x 45 060 6 75 V. m.p.h.
I 1
(b c,=c.
(d) c' =0.65.
FIGURE D.-not-wire meas urement s of the boundary-layer velocities 0.010 ineb above Ihe surface of the N. A. C. A. 001 airfoil.
SO:l94-39-~ REPORT NO . 637- J ATlO AL ADVI 'O RY COM IJ.ITTEE FOR AERO J AUTICS o 60 + 90 V. mph.
/00
I±.-
- , - , - -1- --1 t-- t--
+1
- +~
-r-
yY
+ 40 f- I-"" + + - V ----' I r----.
/" r-...
r- (a)
o
~ ./ , / + "'"-- I+-- h,.- I j I +/ ./ ""--
::J 40 --
- fo...
/ ~ ~ r-(b) o + /00 \ ~ a t--t- __ J"t--
"" I+-
.........
~
r--
" t-.-. +
1'-0.
. """"-.
t-u- +-0.
"""0- t-o-..
20 2 01--+--+--+-+--1- --l--l---1-+- - -t-- r-(c) f-- (C) -+-+--+----+
!j
I 1 .70 .2 0 . 30 40 .50 . 60 70 o ./0 .20 .30 .4 0 .50 .60 o ./0 s/ c s/ c (a) CI= -0.57.
( a) C I= -0.57.
(b) ,,=0. (b) CI=O.
(e ) cl=O. 65 . (c) CI=O . 65 .
FIGURE ll. - Tot al-head-tube measurements of boundary-layer velociti es on the FIGURE 1O.-Totnl-bead-tube measurements of boundary-layer 'Velorities on the surface of the N . A. c. A. 0009 airfoil. surface of tbe N . A. C. A. 0012 >li rfoll.
DETERMINATION OF BOU DARY-LAYER TRAN ITIO ON THREE SYMMETRICAL AIRFOILS 9 - ,--- The results show that the transition point on the o 60 + 90 V ,m.p.h.
.- -,--- - upper surface moves toward the forward stagnation _.
point with increasing lift coefficient, the rate of forward mot ion increasing with decreasing wing thickness.
I-- - - -1- -l- 80 r-- - T his phenomenon may be correlated with pressure- 1--- -- I-- t- - distr i bution measurements, which are shown in figures +- +- + f-- f-,.--.
22, 23, and 24, for the airfoils tested; it will be noted + - that the adverse pressure gradient over the forward part I--- i-t- ~ 1- of the airfoil varies in the arne manner. The pre sure 0 V
r---
f-- L- distr i bution for zero lift, as measured with the static
f 0
fo- 0
-
tube at the surface and the theoretically predicted pressure distribution are in good agreement (figs. 22, r- (a) 23, and 24).
o Effect of Reynolds Number on t ransi tion .-The effect of variat ion in the Reynolds Number on the position of ,/+ 1--.
80 .....
the trans ition point and the end of the transition region 1-,
/
+.
is shown in figure 25 for section lift coefficients CI of 0 t--+- I---- i--+ -
/
and 0.33. The variation in the transition point for _.c' + -1---- r ot h er lift, coeffici ents may be noted by a visual cross plot -0- ~ of figures 19, 20, and 21. The transition point moves I--<>- ~ forward with increasing Reynolds Number at a rate that
I
-0- y' ..0...
is not greatly different for the 9, 12, or 18 percent thick ~ wing. Transition occurred at no unique value of Rx - (b) but varied n.t CI = O from approximately 500,000 to 1,100,000. At cl =- 0.57, a value of Rx of over o 2,500,000 wa reached before transition. The transi- + r tion Reynolds Number increases with increasing wing R eynolds Number. T he R o values at the transition
\
/00 poi nt (Reynolds Numbers based on the boundary -l ayer i" thickness at transition) vary from about 3,000 to 6,000 ~ at zero l ift and show no consistent change with wing t----- I~ ~ R eynolds umber.
------.
,,'-...
r---!
T he considerable scatter in the experimentally 60 ~+ ....
i'-- measured positions of the end of the transition region
r---
>--, 1\ (fig. 25) prevents definite conclusions from being drawn --..., ~ \.V
a to the effect of Reynolds N umber on the width of th e r---
transition region. In general, however, the width did not appear to vary markedly with the Reynolds um-
- (i)
ber for any of the wing lift coefficients investigated.
Effeet of airfoil thickness: on transition .-The effecL .20 .30 .40 .50 .60 .70 ./0
o
s/ c of variation in the wing thiclmess on the location of the transition point is summarized in figure 26. The points (8) c/= -0 . 57.
were obtained from cross-plotting the faired curves of (b) c/=O.
(c) c/ = 0.65.
figures 19, 20, and 21. Results are given for two tunnel speeds corresponding to Reynolds Numbers of about FIGURE 12. - 'l'oial-iJead·tube measurements 01 boundary-layer ve lo cities on the 3,350,000 and 5,020,000. sur face of the N. A. C. A. 0018 airfoil.
10 REPORT O. 637 - NAT IO NA L A DV I BORY CO MMITT EE FOR AERONAUTICi-l o .2 .4. .6 .8 /.0 0 .2 .4 .6 .8 1.0 0 .2 .4 .6 .8 /0 I.e' Il / U (a) c,= -0 .5 7. (c) c,=0.65.
(h) ",= 0.
F, GU RE J3.- nolln da r y- laycr v eloci t y pro fil es at several chord posit ion s 0 " t he N . A. C. A ()() O\) airfoil. ' runn el air speed, 60 m. p. h .
./6 () _ __ S {~ 'I. --iI U - S; ~-i rln - -lll .'s/J Tiff.' i'
1--1-- "7 -- --.55 ~. "7 --- -. 57 I--!LL. , : 1--- 'l - - - - .58 r / '! I I' I
f x - -- --- .45 I , x - -- -· -.47 , I! ~ x - - ·- -- .48, , . 141-1- + ------- .35 I Ii -I- + ------- 3 7 J I : _. + ---- - --- 38 - '"1 ! j ,
c:: 1--1-- 6 --- .25I--h - 6 - - - 27 f-' 1-: -6 - - - .28 i I / I
0 18
· ~./21--I--oO --- ·O /'5 51--11 !! 0 --- '0 71--1, 1-_- - - -'0 8 l'~/1 I
.2 1- 1- . F~ ~ -'-- 0 ':'1-1-- . I . ! h! j' I
~/O :- j -- I- _ jli I:', i l
~ , ; i: ' I . , , I HI: 1./-1 ' +cHi. -+--+-
0. /1/ 'ii 'i: / Iii!
~
" 1 / " ~Il ;' L -H :.' I i
~ . 06 /" ., i / 'rI-J :-1-. 1--- -I-- !!f11l He- ~ § .f " V ..;, '/ I . . ;(.'<'-t-J-p-' +--t-9i ~ . 04 y~;~I~ ~~t/ -j -- -I--~ I--~ ~~ j!-r Ve-:
~ ~_i/ / /~~ / ~.~/H/
.02 ---:-~~V..--./ L.L"-::::::-/ .:t~v:/" - ;.. .y -e-,'
( a) .., -- - (b) 11'f -: t:"" W' :;; .,., - r- (e) """ _ - ~- ~ -, o .2 .4 .6 .8 /. 0 0 .2 .4 .6 .8 1.0 0 .2 .4 .6 .8 1.0 1.2 u/ U (c) , ,= 0.65.
(a ) CI= -0 . 57. (b) c,= O .
FIGURE l4.- Boundary-l ay er velocity profiles al. several chord p os itions on the N . A. C. A. 00 12 airfoil. Tunn el air speed, 60 m. p. h.
DETERMINATIO OF BOV DARY-LAY E R TRANSITION ON THREE SYMMETRICAL AIRFOILS 11 t 'I ..
si c lif ~ si c ?Iri' s ic X .16 , , 0---.65 0---.68 0---.7 0 ! ! : I' I-- !-- "7 ----.56 "7----.5 8 '7----60 Ii!
!-- x------.46 x------.4B I I , I!
x------.50 - . 14 , + ---- ---- . 36 +--------- .38 : , +--------.40 : / i: I I I/ / I
s -
I-- 6--.26 , , 6--.28 6--.30 , , , , ,
! I-- 0 ----.16 i ll o---- . IB I
ll! 0----.20
- , ~ .12 o .06 0 .08 0 . /0 ; I Ii I
o i III
L 'I. I
"-- : I : Ii: ; i.
~ 10 , \I)' , I{ : I
',I
i I , , ! , ~ , II I! !
! i
Cl . OB , , , I ,
il.- Ii! II
{' I " '8 , , /V! I .' /
L
J
c/- ~ .06
,i. l
.' :j c: ' /£:.' '/ i 4-
<-
t !2 r: , .If, , II " ~ .04 r6-.
~<J ;/ (/r!
19" 'I' .P ~.f ct' J f.-/ ~' ~/ ~ ./ / / /
I rf /I
:f ~ .02 y f/" :--- j!
.......... jj; . ~ ~~ ..k V-" 'J: Ha) , Ib) Ie) .,.Q
~ ----
/
o .2 .4 .6 .8 1.0 0
-' .2 .4 .6 .B 1.0 0 .2 .4 .6 .8 J.O 1.2
u/ U (a) CI= -0.57.
(b ) CI = O. (c) CI=0.65.
FIGUR E 1 5.-Boundary- layer ve lo cit,y profiles at several chord positions on the N. A. C. A. 001 airf oi l. Tunne l air speed, 60 ill. p. h.
I si c s ic s ic .35 ./6 --.07 --.21 .12 - - . 40 ----- .26 -- --- .4 5 -.50 -- . 3/ - - .55 ---. 36 !--
~-I
/ // ,1 I, / Ii ' n!
I, .',!!
' I J )' 1/)
/J !/
,< V J I
:1
If ",; A~ .......... /' d / II' '/ (a) (b) (c) , ..... ,/' ~ .:.--:: 1-:-.:.- J..
~ - k -
==
----
2 .4 .6 .8 .2 .4 .6 .8 /.0 0 .2 .4 .6 .8 !.O 0 10 1.2 o u/ U (a) C,= -0. 07. (c) c.=O.65.
FIGURE If.- Nondimens!onal bo u ndary- I ~yer velocity profil es in the l r an~ition region f or tbe N. A. C. A. 0009 ai rf oi l. Tunne! air speed, 60 m. p . h.
- 7 -- -
I- i- - - - - - - -L L
1-11
sic
llJ
_.- ...
- - - - .0- --.17 - - DB --.1 3 --.55 - ---.22 r- -----60 I - ----.27 ----- ./~ - - 1- - r- - r- - 5 , ---.70 - -- .32- , , --- .37- 1- - - I- - - 1--, , : I .. - , , ;' / .' ~ A !, I
f
I ~/ I / I~/i ~/ :; it! / !: V' ~' V , j'P f ~/ !-- - I--
-1- ,/
V ~~ ,/ .--?'v' k - (aJ (b) (e) ~- , , , i-""" k-- , ---- ~ ? :;.;.,...
~ -::::::
-- -+= - -
o .2 .4 6 .8 /.0 0 .2 .4 .6 .B 1.0 0 .2 .4 .6 .8 1.0 1.2 u/U (a) c.= -0.57.
(b) C/=O. (c) c.=0 .. 65 FIGURE 17.-No ndimensional boundary-layer velocity profiles in the tr ansition region [or the N. A. C . A. 0012 airfoil. Tunnel air speed, 60 m. p. h.
12 REPORT O. 63 7- NATIONAL ADVISORY COMMITTEE FOR AERONAUTIC At c! = O and 0.33 , the transition point occurred at the ahnost at the airfoil nose. Th e e results arc in agree- same cho rd po ition for the 0.12c and the 0.1 c thick ment with previous tudie howing the e fI ect of rivets wing; however, it occurred con id era bly clo er to the and surface irregulariti and reemphasi ze the impor- tagnation point for the 0.09c airfoil . At c! = 0.65, the tance of mooth wing urfaces for low drag.
transition point moved rearw a rd with increasina thick- Correlation of profile drag and t ransi tion p oi nt.- ne s in an almost lin ear manner. Th e l ater tran ition Th e ection proiile-draa mea mement for the ym- for he thicker airfoils i directly related to the more metrical airfoil at zero lift are gi ven in figme 2 for th e favorable pre sure distribution over the urface, a range of te t R eynold N umbers. Th e proiile-dnw pI' viously mentioned. coefficients were obtained by both force and momentum \ ;: It is of intere t to no te th at the pre sure grad i ent measurement that were in exce ll ent agreement ( 1' fer-
I
over the symmetrical airfoils are not 0 fa vora ble to lat e ence 6). Ina much a the knowledge of the tran ition point is of particular in terest a an aid in the estimation transitions a tho e over co n vent ional cambered ai r- of the proiile drag, an attempt ha been made to corre- foil , and it may be ex pected that the tran ition will l ate the transition mea m e ments with the observed occur farth er ba ck along the chord for a cambered air- foil. The l ate r transition indicated in :fli g ht in refe r- proiile-drag measurements for the re pr esentat ive case en ce 4 may be due in part to the more favorable pressure of the N. A. . A. 0009 airfoil at zero lift. Th e thinnest g radi ents, as is shown by a com pari on of the pre me- airfoil wa chosen to avo id a large pre sure drag. At a di tribution curve of reference 4 with tho e for the R eyno ld s Number of 3,350,000, the tran ition point symmetr ical airfoils ( fi g. 22, 23, a nd 24). occurs at s/ c= 0.23 and the transit ion region extends s/ c s/c s/ c . 46 .23 ./0 - - - '--.28 -- ./ 5 - - 5/ -. - --- .56 - - - - - .20 -- .33 I - .38 - .6 / -.25 , , 1:1 I , , , ':; - I- I l, I
' i' /
I,'Ij
/A J J
"
.1,'; V, 1,' l(
V
W' A,y :/ t';'/ ~t;l "",V /' ~/ Y ,y ./ I--"' ~ ~
k
t-- (a) (b) <- :- V F"-" -/ "",- 1--- :-:-:: .-- ;;If'! ~ ~ .- ~
~
o .2 .4 .8 .8 1.0 0 .2 .4 .8 . 8 1.0 o .2 .4 . 6 .8 10 /2 ti ll!
(8) CI =- 0.57. (c) CI= O.55.
( b) CI = O.
FI GU RE 1 . -Nondim ensional boundar y· l aye r veloc it y pr om in the tr a nsition region for the N. A. C. A. 001 airfo il. Tunn el a ir speed , 60 m . p. h.
\ Effect of protuberances on t ransi tion.- Th e effect of from s/c= 0.23 to 0.40 (fig. 10(b)). Th e section profiIe- a protub e ran ce near the leading edge on tran ition and drag coefficie nt Cdo co rr e ponding to these te t conditions
I
tbe in crea e in tbe drag above that of the aerodynami- is 0.0(l61 ( fig. 2 ).
ca lly smooth wing is hmvn in figure 27. Th gummed J?or the lamin ar a nd transition r eg ion , it wa pos i-
I
tape 0.003 inch thick placed at the 0.0 5c stat ion bad a ble, ina much a the complete boundary-l ayer proiiles s light tendency to move the transition point fo rward had been mea ured , to determine the dra g by in tegra- and increased tbe dra g about 2.3 perce nt. Th e 0.006- tion of the loss in mome ntum by mean of the von inch-thick ta pe mov d Lhe tran ition point forward K arma n mom ent um eq u at ion, taking int o acco unt the pres ur e distribution over t Il e urface. 1 i'1'om this cal- only abou t 1 per ce nt ; llOwever, it bor tened the transition culation it wa fOUl) 1 tL at the average kin-friction r gion to abo ut 10 per cen t and added 3.7 per cent drag.
coeffici ent 0, over the lam in ar and tran ition region Th e 0.009-inch-tbick ta pe moved the transition point was 0.0026.
ahead of the 10-per en t-chord tation and added 7.5 per- Thi s kin-friction co llicien t i bas ed on an area. of cent drag. Th e transitionl'egion in the case of the 0.009- only 40 percent of the surface on one ide of the airfoi l.
inch tape wa very long and extended to the 0. 35c station.
In or le I' to conve rt 0, in to the u ual coellic ient for111 o r at ional e;-,:p lan at ion of the efrects ob er ved when c ao , the va lu e is doubled and multiplied by 0.40 so that tbe tapes were used can be ofIel'ed. It should be noted, the cont ribution to ClIO of the la minar and transition however, that a protub eran ce with a h e ight of less than reglOn is 0.0021.
0.01 inch was ufficie nt to cause transition to occur DETERMI rATIO OF BOUNDARY-LAYER TRANSITIO ON THREE SYMMETRICAL AIRFOILS 13 Reynolds Number From hot-w i re dala-> 0 1,730.000 x 2,680,000 0 3,350,000 II 4 ,1 80,000 + 5,020,000 From fofol-head-Iube dofa-> o 3 , 350,000 'Cl 5,020,000 1\ '\ ~~ \~ ~ .6 \ ~\ , ~
~ ~
\ \~\
~I"- \\
,,~
'\ t'\\
1 \\\ ~ ~:
j\
~\
~ \ 1 \'\ 1 \\ \
"~
1 \)' j
"-~ ~\
l': 1 \ \
~ l~ LL\
"- t).."'" ~ _ \ 1 \
~ \\\ l\l~ .1
, \
1 \ \
f"-'
~ r0 ~\I'
\ 1 \
"
\
i ~ \
~ ~
"
"-
"-
~ f"- 1 \
1 "-
"- "-
I'.. ~ i"..
-.4 '\ I'..
" ~
"-
~
i'--
"- '\ ~ i'-- "'" I'---- r-.,.
---- r-----r-
-.6 '( '( ( .50 .10 . 20 .30 .40 ./0 . 20 .30 .40 . 50 .10 .20 .30 .40 . 6~
'"
s/ c s/ c / c FIGURE 19. -N . A . C . A . 0009.
F I GU RE 20 .- N. A. C. A . 0012. FIGURE 21. - N . A. C. A. 001 .
Variation of the transition point with section lift coe ffi cient for tbe N. A. C. A. 0009 , 0012 , and oo lS aIrfoil •.
- -- -- --- --- - Theoretical pressure d i stributIOn for c, - 0
~ \
-1.6
\ \
\
-f-- - 1-- -
-1.2 -\
"
1 \
"- ""\
\
-.8 "- c, ~ 0.65 c, = 0.65 c, ~ 0.65 1 r-:::< ~ p/ q
""
? c, ~ 0 ~ 'b. ~ I ~ ~ -
-.4 '" r-
"'- ~ I I?
~ lc,~O~ ~ ~ ~ ~ t---, i-o-.
~ ~ l- ~ """ ~ [-0-, I --0-, ~ i"--- I , ~ I c' ,= 0
--
I i' 1 """'--
~ o "-
-
~ I \
/' " 11 "
~ \ - \ : j c, ~ -0.57
I c, ~ -057 c, = -0.57
\ / ~ - -- -- I- I - .4 ?
I f-- - -1-- f--
r
I-- -I--f- - I- .8 10 0 ( 100 i 20 40 60 80 /00 20 40 60 80 20 40 60 80
l' Perc ent chord
Percenl chord Percent chord FIG UR E 22 . -N . A. C. A. 0009 . FIGURE 23. - T. A. C . A . 0012. FIGURE 24.- . A. C. A. OOIS .
Pr essure distribution on t he up per surfaco of the N. A. C. A. 0009 , 0012 , and OOIS ai rfoils for throe section Jift coe ffi cients.
14 R E PORT NO . 637 - NATIO AL ADVISORY COMMITTE E FOR AERO AUTIC X 1 0.
o-- N.A . C.A.000 9 o-----NA .C.A. OOlc 6 - -N.A .C.A. 0018 ,\ ~ . ~ \
\ ~\
,
\ \
,~ \ ~\\ ~\ ~ ~ + , I \ + I + \\ '.
\\
\ \
+ t\ ,\! I? , 1'\ ~ ~.
V
\\ ~
\
. 009" Tope v \ ~~ ~C D' 75 percent- \ 1 \ y
I ~ ~ \
I I ~\ \ ~\
\ \
_ ~ ~ '-<In I ~ . ~~< R, o "' .......
E;'"';] of
"I + Endof
an - Tron-:: ~ - - I---
r. - fron- - 80
I- fron - - sdlon ·f· sition '---- sitio.n _ ~ ~
. t_ -r~1 Ion - -p o int to
I--- "-t>-....
n Pl'n r~qi~ n - (a) ( b) rf q' f 1 I I a ./0 .20 .30 .40 .50 o ./0 .30 .40 .006" Tope
.20 /
"' .......
~C D = .3.7 percent- s i c ~
~
~ (a) CI=O. (b) CI=0 .33.
FIGUI(E 25.-E tr ect of Reynolds umber ou the transition point and extent of the transition region .
. 60 ~ :::-- ~ ~C I; O / .00.3" Tope
I-- 1-- - - - - - ,,' = .33 1\
. 50 t. CD = 2..:3 percent- --- "= . 65 e-- - ~ V 0 V = 60m.p.h.
,,=90 " + . 40 o ~30 0) If' .20
7 wing
Bare /' -- --~ - C = 0. 0064 - Do "- I () , '0-- ~ ...0..
I I I
-- 1- -
, . 10 , / f..-'
-'(
, I /' , 6/ 1/ o .1 0 ~/ .20 .30 40 .50 I 'Ie .I .c o Wlnq thickness , t / c FIGURE 27.-Etrect in the tran ition and drag of the N. A. C. A. 0012 airfoil
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of mall protuberan ces at the O.05c point on the upper surface. Reynold s FIGURE 26.-Etreet of airf oi l thickness on the location of the transition point.
Numbe r =4.1 0.000 .
.: .010 (.J Theoreticol flat-p l ate . - I- turbull?nt boundary laYffTi - .- .-
- 1=
i- - - i- i- - (\).00 8 r-.
- - NA·FA.OOl S - -- I- - -
8 -
l- - i-- I-- 8'. 007 I- NA.C.A.00.12 {:; I
-
~ - ~.00 6 NA.C.A. 000:-1 ~ c: .0
t . 005
2 .5 3 4 5 6 7 8 3 x 1 0' 1 2 QJ I/) R&!vnn/ds Number FIGunE 28.-Seetion profile·drag coe ffi cients at zero lift for the N. A_ C_ A. 0009, 0012, aDd 001 airf oi l s.
DET ERMI ATJON OF DO NDARY - .LAYER TIlA 'l TLON 0 T HR EE ,'YMMETRICAL A1RFOJU"; ]5 Complete tm bul ent profiles were not measmed; the to predict the drag of an airfoil even when the transition determination of the drag for the tmbulent region there- is known.
fore required the appli cat ion of the empirical kin- Th e wind-tunnel measmements of the transition fr iction law derived for flat plates, uit ably corrected point are at an advantage over flight measurements in by the method of Dr yden and Ku et he (reference 7) th at it is po ss ible to determine sep arate ly the effects of for the pre ss ure gradient on the airfoil. Th e crux of R eynolds umber and lift coeffici ent; however, there the whole calc ul ation lie , however, in the assumption are serious disadvantages owing to the initial wind- made regarding the state of development of the tmbu- tunne l tmb ulence. Th e conclusions of these te ts are lent layer at the end of the trans ition region. If the t her efore restricted until projected flight tests for com- drag for the tmbulcnt region i computed according to parison with the full-seale-tunnel measureme nt s hav e the mo t obvious assumption, that the developed been made.
tmbulent layer begins with a momentum loss equal to that at the end of the tran ition r eg ion, the va lue of the drag is much too hi gh so that, when it is added to the drag for the laminar a nd transition regions, a nega- LANGLE Y M E MORIAL AERONA UTICA L L ABORATORY, tive press me drag on the airfoil is indicated . ATIONA L ADVI SORY COMMITT EE FOR A ERONAUTI S It is believed that fmther study of the local skin- L ANGLEY FIELD , VA., Niay 26, 1938.
friction coefficients in the boundary layer will be re- quired in order to predict the wing profile drag, even when the trans ition point is known. REFERENCES 1. Burg ers, J. M.: The Motio n of a Fluid in the Bound ary CO CLUDING REMARKS L ayer along a Plan e Smooth Surface. Pr oc. First I nt.
Congress for Appl. Mech., D elft , 1924, C. B. Biezeno, J . M .
Th e results of this investigation are consi stent with Burg ers, ed., J . Waltman (Delf t), 1925, pp . 113- 128.
tho e of previous studies in showing that transition 2. van der H egge Zij nen, B. G.: Meas ur ements of the Veloc it y does not occur at a particular va lue of R x or R o. Th e Di st ri bution in the Bound ar y L ayer along a Pl ane Surface.
tests show that a later tran ition occur on t hi cker Repo rt 6, Aero. Lab. T ech. H. S. Delft, 19 24..
airfoil s, which partly explains the relatively low va lues 3. Dr yden, Hugh L .: Air Fl ow in th e Boundar y L ayer near a Pl ate . T. R. No. 562, N. A. C. A., 1936.
of Cdo obtained with the . A. C. A. 0018 airfoil at zero 4. Jone s, B . Melvill: Flight Experiments on the Bo undar y lift. With increasing lift coefficient and Re ynolds Layer. J our. Aero. ci., vol. 5, no. 3, J an . 1938, pp. 81-94.
umber, the tran ition point on the upper smface moves 5. Platt, R obe rt C.: Turbul ence Factors of N. A. C. A. Wind toward the stagnation point . Th e width of t he transi- Tunn els as D eterm i ned by Sphe re Te sts . T . R. No. 55 , tion region hows no large var i at ion with R eynolds N . A. C. A., 1936.
6. Goett, H a rr y J. , and Bullivant, W. Kenn eth: Tests of . A.
umber.
C. A. 0009, 0012, and 001 Airfoils in the Full-Scale Tun- An attempt to correl ate the transition data with nel. T. R. I o. 647, N. A. C. A. , 19 38.
profile-drag measmements with th e a id of existing d ata 7. Dryden, H . L ., and Kuethe , A. M.: Effect of Turbul ence in on the skin-fri ct ion drag of fl at plates proved unsuccess- Wind Tunn el Measurements. T . R. No. 342, N. A. C. A" ful, indicating th at fmther study is required in order 1930.
U. S . GO VERNMENT P RI NTIN G OFF1CE : 19 39 y
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I I I I
"-
"-
"
z
Positive directions of axes and angles (forces and moments) are shown by arrows Axis Mom ent about axis Angle Velocities - Force (pa rallel Linear
I
(compo- Sym- to axis) Sym- Positive Designa- Sym- Designation Angular Designation neat along bol symbol 001 direction tion bol axis) Rolling _____ Ro lL ____ LongitudinaL __ __ X X L Y----->Z u 4> P LateraL ________ _ y y Pitching ____ Pitch ____ (J q M Z ----->X v NormaL _______ __ yaw _____ y a"' ing ____ Z Z N x-----> y w r
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Absolute coefficients of moment Angle of set of control surface (relative to ne utr al N position), O. (Indicate surface by proper subscript.)
G=~ 0 =M 0,,= qbS I qbS '" qcS (rolling) (pitching) (yawing) 4. PROPELLER SYMBOLS D, Diamet er
Power, abso lu te coefficient Op= ~nIi
P, Geometric pitch pn J.F p, 5/ pV Pitch ratio p/ D, G., Speed-power coefficient= -y Pn 11', Inflow velo city Efficiency "1), Slipstream velo city 11" n, Revolutions per second, r .p.s.
T, Thru st, absolute coefficient OT= r 4
D pn <P, gle Effective helix an =tan- {2!n) Q, Torqu e, absolute coefficient OQ=pn9 D5 5. NUMERICAL RELATIONS 1 hp.=76.04 kg-m/s=550 it-lb./sec. 1 lb . =0.4536 kg.
1 metric horsepower = 1.0132 hp. 1 kg=2.2046 lb.
1 m.p.h.=0.4470 m.p.s.
1 mi.=1,609.35 m=5 ,2 80 ft.
1 m.p.s.=2.2369 m.p .h.
1 m=3.2S0S ft.