Experimental Aerodynamic Derivatives of a Sinusoidally Oscillating Airfoil in Two-Dimensional Flow

48 Pages·2014·27.13 MB·English

https://ntrs.nasa.gov/search.jsp?R=19930092144 2019-01-02T22:56:27+00:00Z
NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
REPORT 1108
EXPERIMENTAL AERODYNAMIC DERIVATIVES
OF A SINUSOIDALLY OSCILLATING AIR
FOIL IN TWO-DIMENSIONAL FLOW
By ROBERT L. HALFMAN
1952
For sale by tbe Superintendent or Documents. U. S. Goyernment Prlntinil Office, Wasblnilton 25, D. C. YearlYlIQb.crlptlon, '9.75; rorel.,.. Sll.OG;
Blnllle cOlly price nrl_ aec:ordto, to BiR. - - - - - - - - - Price 40 cente

REPORT 1108
EXPERIMENTAL AERODYNAMIC DERIVATIVES OF A
SINUSOIDALLY OSCILLATING AIRFOIL
IN TWO-DIMENSIONAL FLOW
By ROBERT 1. HALFMAN
Massachusetts Institute of Technology
ational dvi ory Comnlittee for eronautic
Headquarters, 1724 F Street NW., Washington 25, D. C.
Created by act of Congre s approved March 3, 1915, for the supervision and direction of the cientific study
of the problems of flight ( . S. Code, title 50, sec. 151). Its membership was increa ed from 12 to 15 by act
approved March 2, 1929, and to 17 by act approved May 25, 194 The member are appointed by the President,
and erve as uch without compensation.
JEROME C. HUNSAKER, Se. D., Mas achu etts Institute of Technology, Chairman
ALEXANDER ·WETMORE, Sc. D., ecretary, Smithsonian Institution, Vice Chairman
ALLEN V. ASTIN, PH. D., Director, National Bureau of tandard. \VILLIAM LITTLEWOOD, i\I. E., Vice Pre ident, Engineering
DETLEV W. BRONK, PH. D., Pre ident, Johns Hopkins Univer American Airline, Inc.
sity. HON. DONALD W. TYROP, Chairman, Civil Aeronautics Board.
THOMAS S. COMBS, Rear Admiral, United tates Navy, Chief of DONALD L. PUT'!', Major General, nited States Air Force,
Bureau of Aeronautics. Vice Commander, Air Research and Development Command.
LAURENCE C. CRAIGIE, Lieutenant General, United tates Air ARTHUR E. RAYMOND, C. D., Vice Pre ident, Engineering,
Force, Deputy Chief of Staff (Development). Douglas Aircraft Co., Inc.
HON. THOMAS W. . DAVIS, Assistant ecretary of Commerce. FRANCIS IV. REICHELDERFER, C. D., Chief, United tate
JAMES H. DOOLI'lvrLE, Sc. D., Vice Pre ident, hell Oil Co. \Veather Bureau.
MATTHIAS B. GARDNER, Vice Admiral, United States Navy, HON. WALTER G. WHITMAN, Chairman, Research and Develop
Deputy Chief of Naval Operations (Air). ment Board, Department of Defense.
R. 1\1. HAZEN, B. ., Director of Engineering, Allison Division, THEODORE P. WRIGHT, C. D., Vice President for Research,
General i\Iotor- Corp. Cornell Univer ity.
HUGH L. DRYDEN, PH. D, Director JOHN F. VICTORY, LL. D., Executive Secretary
JOHN IV. CROWLEY, JR., B. S., Associate Director for Research E. H. CHAMBERLIN, E:recutive Officer
HE 'RY J. E. REID, D. Eng., Director, Langley Aeronautical Laboratory, Langley Field, Va.
SMITH J. DEFRA 'CE, LL. D., Director Ames Aeronautical Laboratory, Moffett Field, Calif.
EDWARD R. SHARP, C. D., Director, Lewi Flight Propulsion Laboratory, Cleveland Airport, Cleveland, Ohio
LANGLEY AERONAUTICAL LABORATORY, AMES AERONAUTICAL LABORATORY, LEWI FLIGHT PROPULSION LABORATORY,
Langley Field, Va. Moffett Field, Calif. Cleveland Airport, Cleveland, Ohio
Conduct, tinder unified control, for all agencies, of scientific research on the fundamental problems of flight
II
REPORT 1108
EXPERIMENTAL AERODYNAMIC DERIVATIVES OF A SINUSOIDALLY
OSCILLATING AIRFOIL IN TWO-DIMENSIONAL FLOW
1
By ROBERT L. HALFMAN
UMMARY OTOUpS and no known re ume or comparison ha been made,
a portion of th is report is given over to the reproduction and
Experimental mea urements oj the ael'odynamic l'eactions on
comparison of typical data reduced to a common form of
a symmetrical airJoil oscillating harmonically in a two-dimen
presentation. (ee appendLx.)
sional flow are presented ancl analyzed. Harmonic motions
include pure pitch and pure translation, jor several amplitudes This work was onducted at the ~1assachusett Institute
of Technology under the spon or hip and with the financial
and superimposed on an initial angle oj attack, as well as com
as i tance of the ational Advi ory Oommittee for
bined pitch and translation.
Aeronau tic .
The apparatus and te ting program are described briefly and
the neces ary theoretical backg1'ound is presented.
SYMBOLS
In general, the expe1'imental results agree remarkably well
with the theory, especially in the case oj the pure motions. 11 frequency of forced motion
The net work per cycle Jor a motion corresponding to flutter is W angular frequency of forced motion (27rn)
experimentally dete1'mined to be zero. b emichord
Oonsiderable consistent data j01' pure pitch were obtained V air-stream velocity
jrom a search oj available reJerence material, and seve7'al k reduced-frequency parameter (~)
definite Reynolds number effects are evident.
p den ity of air
I TRODUCTION V2)
q lynamic pre. ure (~p
The purpose of the work de cribed in thi report was to
determine experimentally the lift and moment on an 0 cil a pitching angle of wing; po itive in direction of
lating airfoil and compare the results with the prediction tall
of the vortex-sheet theory a de cribed in reference 1. The amplitude of pitch
u e of the theory on aero-ela tic problems such as flutter initial angle of attack
could then be verified or modified. The general plan of the vertical tran lation of wing at 37 percent chord;
program wa to break down the flutter motion into its po itive downward
simplest components so as to examine each one individually ho amplitude of tran lation
before superimposing them to check the flutter condition 8 angle by which pitching motion lead translation
itself. motion
The entire project wa un Im·taken in a ucce lOn of {3 pha e angle between front and rear actuator
pha e by the Aero-Ela tic Re earch Laboratory of the wheel
Massachu ett In titute of Technology over a con iderable a ratio of eli tance of elastic axis behind midchord
period of time and should be con idered a the combined point to emichord
effort of the group wbich worked on each pba e. The x di tance of center of gravity behind miclchord
phases were: m mass of wing per unit pan
(1) The design and construction of the oscillating actuator F real part of Theodorsen's function
mechanism G imaginary part of Theodorsen's function
o
(2) The development of the support of the model on the Tbeodor en's function (F+iG)
actuator and the subsequent installation of the apparatu static moment of wing about ela tic a.."j
a
in the wind tunnel ((x-ab)m)
(3) The development of the force-recording equipment moment of inertia of wing per unit span about
(4) ystematic test with the equipment developed in elasLic axi
pha es (1) to (3) and de ign tudy of equipment for higher natural frequency in bending
frequencie ffective linear pring con tant (mWh2)
(5) The thorough analysis of the test results of pha e (4) natural frequency in torsion
Since a substantial amount of data for similar tests has effective torsional spring constant CIaWa2)
been compiled independently by various other research work per cycle due to moment
I Supersedes NACA TN 2465, "Expcrimcntal Aerodynamic Derivatives of a Sinusoidally Oscillating Airfoil in Two·Dimensional Flow" by Robert L. Halfman, 1951.
1
2 REPORT 110 - NATIONAL ADVISORY COMMITTEE FOR AERONAUTIC
work per cycl e due Lo lift
net work pel' cycle (-VT1L-lf"f)
(4 /:;oh.)
('Wr_ coefficient of work due to lift
)
coe fficl·C nt 0 ( wor1~ 1(u e to moment (- ~4qbfcx l/:;,
o
OWN coC'ffi cien t of net work (4 :~Y;ohJ
average drag-amplitude coefficient
t::,.('D(a,)
C steady-state or static lift coefficient
LS
steady-state moment coefficient about elastic
('.\{S8A
aXIS
Re Reynold number based on airfoil chord
The following symbols arc usually combined with subscripts:
L lift pel' unit span; positiYe downward
j\;1 moment per unit pan; po itive in direction of
stall
R real part of complex quanLity
R' dimensionless real part of complex quantity
I imaginary part of complex quantity
l' dimensionless lmagmary part of complex
quantity
,IR2+J2 magnitude
A,B,D,E componeD ts of lift or momen t
i)
phase angle (tan
-1
ubscripts:
p due to pitching motion
T clue to translational motion
R clue to combination of translational ancl pitching
motion
"
L lift L-77889
M moment
FIGURE l.-Test-section arrangement viewed from upstream.
DESCRIPTIO OF APPARATUS
The mechanical apparatu is designed to oscillate an The oscillator mechanism consists primarily of an actuator
airfoil in pure pitch, pure translation, and combinations unit located just below the test section and two identical
of the two at various frequencies ancl amplitudes. The linkage extending up through the vertical fairing on each
in tallation in the test ection of the tunnel is hown in side of Lhe airfoil. As may be seen in figure 2, the actuator
figure 1 and the entire oscillator mechani m is illu trated J has two pairs of circular crank wheels on each side. The
chematically in figure 2. The range of motions obtainable rotational motion of each pau' i transformed into inu
is shown in figure 3. soidal vertical motion by means of a connecting rod sliding
The airfoil which was constructed for these tests is on a member constrained to move vertically. This vertical
rectangular in plan form with a I-foot chord, 2-foot pan, motion is tran mitted up into the te t section by thin teel
and NACA 0012 profile. An eXLremely rigid and light bands D which terminate at the "dumbbell" cams I. Ad
magnesium two-spar stressed-skin construction was neces ditional bands continue from the cams to the adj ustable
sary to minimize inertia load and prevent appreciable de overhead springs C which maintain tension Ul the band at
flection during oscillation. The te ts were performed in the all times. The 1"e ultant, motion of the cam i transmitted
M. 1. T. 5- by 7;~-foot flutter tunnel which wa modified by to the wing through the linkage H. Each pau' of crank
the installation of two vertical fairings as shown in figure 1. wheels can be set to produce either 1-, 2-, or 3-inch-amplitude
The presence of these fairings insured essentially two vertical motion and the front pairs can be et and pha ed
dimensional flow over the aU'foil while any deviations from independently of the rear pairs. Thu with the rear pairs
the usual flow could be detected by the pitot-tube rake exactly 1 0° out of phase with respect to the front, the
installation also hown in figure 1. cam I is rocked about it center in pure pitch.
3
AERODYNAMIC DERIVATIYES OF A SINUSOIDALLY OSCILLATING AIRFOIL IN TWO-DIMENSIONAL FLOW
F to produce signals equal to the inertia reactions of the air
foil which could be electrically subtracted from the total
force signal . This difference, then, represents aerodynamic
forces only. The inertia cancellation proces is necessary
only for the lift and moment signals since there is no inertia
.......... ··8
force in the drag direction. The ignals are amplified and
A····
recorded with Consolidated Engineering Corporation 1000-
cycle-per-second carrier equipment. The correct attenuator
settings for the accelerometer ignals are determined ex
perimentally by ubstituting a "dummy winO''' for the airfoiL
c'- .....- 0 Thi wing is of open con truction to minimize aerodynamic
reactions but ha mas and moment-of-inertia propertie
identical with tho e of the airfoil. Because of the relatively
large range of forces to be covereel elUTing the tests it was
necessary to design and use two complete et of force
.. _. .. ····F
measuring elements, a "soft" set for low frequencies and
_ ·······G amplitudes and a "stiff" set to handle the higher forces at
hio-her frequencie and amplitudes.
__ - ·---H A reference-po ition signal wa at first obtained from. an
-----.. -~ undamped accelerometer mounted on the rear crossbar K
and later from a Kollsman rotatable transformer 0 attached
to the rear crank wheel.
SYSTEMATIC TESTS
The fom general types of test included in the te ting pro-
gram are:
(1) Pme pitching motion
(2) Pme tran lation
(3) Pure motions uperimpo ed on an initial angle of
_____ ·0 attack
(4) Combined pitching and translation with pecial em
phasi in the neighborhood of a motion corresponding to
flutter
In order to obtain the best 1'e ults throughout the te ting
program, the least difficult tests were performed fu'st and
the experience thus gained was applied to the remaining tests
as they were encountered. Thus the pure motions were
examined fir t at the two amplitude corresponding to the
1- and 2-inch crank-wheel settings on the actuator u ing the
soft force-measuring elements. N ext the turnbuckles, J in
figure 2, were adjusted to produce an initial angle of attack
A Supporting structure I Cams of 6.1° and the lower-amplitude pure motions were super
B Tension adjustment J Turnbuckl s
C Overhead springs K Rear cross bar imposed on this initial angle.
1) Steel bands L Drive shalt Since there are so many po sible combined motions it was
E Tunnel wall M Motion phase scale
F Accelerometers N Actuator necessary to restrict the testing to a survey of the field.
a Vertical guide 0 Transformer Thus tests were made at a constant reduced frequency k of
R Linkage
FWURE 2.- Diagrammatic layout ol oscillator. 0.3 for phasings between the pme motions of 0°, 90°, 180°,
and 270°. Ideally the ratio of tran lation amplitude to
Two sockets in each end rib of the airfoil receive the ball pitch amplitude should also have been kept constant to
ends of short cantilever beams supported by the linkage H permit simple and accurate comparisons of the foW' condi
with the forward sockets located on the center-of-gravity tions; but this was not pos ible, unfortunately, be ause of
aJ':is of the wing at 37 percent chord. Re istance wire the limitation of the oscillator. Another serie of tests at
strain gages mounted on these cantilevers meaSUTe the forces constant reduced frequency was made in the neighborhood
required to oscillate the airfoil in a given motion. Since of a case corresponding to flutter. The derivation of the
these forces include inertia reaction as well as aerodynamic correct motion for the flutter condition i described in the
forces it was necessary to design the "multiple accelerometers" next section.
4 REPORT 110 --NATIONAL ADVISORY COMMITTEE FOR AERO A TIC
_____ .-------,
~.O~~~-'---3---3 --,------,-------.- 24~----~----~------'-----~------r-____~
2.5
3-2,2-3 20
3-3
2.0 16 3-2,2-3
.S. "<0l>.>
~ d" 3-1,1-3
1.5
2-2
I.O«-~=::t:=---t---+--~<;;:-+-~,.--j.--===~ 2-1, 1-2
I-I
I-I
.5r----r--~r_----_r----~~----~~~~
o 30 60 /39, 0de g 120 150 ISO /39. 0de g 120 150 ISO
a
o Test points
100
_\
70
\
ISOr------,------~----~~----.-----_.------~
\ 1-1,2-2,3-3
50
3-2,2-3\ 1-3
~ 1-2
1\
30 120r------r------+------+----~i:~-~2~-3~~~--_J
co ~ ~ 1,1,2-2,3-3
~ 20
'- 3-1 1-3 3-2
s ~ ~ 60~----~------+_----_+-----~~~2~-~1~:::~~-~
" ~ 3-1
~
~ IO "
o~----~------_+------~------~----_+------~
7 ~
~--......
~ ~ ............... 3-1 1-3 3-1
5
~~ ~ 2-1
~2- 300r---~~--3-2--~~---+-------r------+-----~
~
3 \ I-I, 2-2, 3-~
~,2-3
1\ 2-3
2
1-1,2-2,3-3
~
30 60 90 120 150 IS(3 10 240 300 360
/3, deg E. deg
FIGUIlE 3.- 0scillator properties (or various crank-wheel-amplitude and pbase-angle settings.
5
AERODYNAMIC DERIVATIVES OF A SINUSOIDALLY OSCILLATING AIRFOIL I TWO-DIMENSIO AL FLOW
Becau e of strength limi Lation , tests using the oft clements a check on the previous run corre ponding to a condition
could not be run in the high-freq ucnc)-range for the larger- ncar flutter. Thi econd flutter serie wa made with a
amplitude motion. Thu , in order to extend the frequency con tant phasing betwcen the pure motion, with a constant
ranO'c already covered in the pme motion te ts, the tiff amplitude ratio, and at a constant airspeed. The only
set of elemcnts was in taIled and high-frequency te t at variable wa the frequency of the motion which produced a
the larger amplitudes were made. It wa also decided to corresponding variation in reduced frequency k.
run anothcr scrie of tests ncar the flu ttCI' condition partly as
r
I I 1 IT IT
IIIII
l~LI IU6 II l ,k7
I 1
0
I II I II I I I
1 I
I I
p,,;,;o~ I II
I
I I
I I '" '" l'" .Drog 'f IIU v- 'vlIv'I\ , I III
if'
"~~V~
i I,
k~~ ""rr~~~
I
~~~ I ~~(
Il iil,l,
I ~~"T ~u~,
f ' II II ' ,
I
II II I I II I I
I
I IIIII I I I I II II I
I
II II I III III II I II II
I
lUu
I
llJ ~ ~111111,Jj
1)
,
I I oo=±13I.5 ° I I
I ll-rrl I I I I I I I I I rTTlT'i
I I 1
iI Time I II II I Ii lTime~ I 1 II !III I: II 31478 1111/3U,1 I
2028 2032 III II
II1II1 I II I I1I11
I
I ,Position I I II I IIIIII I
. I
II I~~I vi I
l~r~~1 f A v~ I
~!
I V KC'i'io IHI,
'(I. nlA~ ~ ~rIN~ I iI:~ ~;~::~j "J'~} W II 1i\1~~ III I III / { 1\ I
IV ~~~ ~ '1! I~ V II wi
rm I
t~
'''r I
~ ~~~w~r)~1 IT I 'I II II I
1
rvll ,~,,~ t ~ /I Yllfrntnr ITItII
' -Lift I mIo oI ' rvv." "'- I 'M} I It "\ I
I I I I II I 1/ . h1t r1 , I
hf~V I
I' IIIII I~~
I
,
I I ~iv '\i-\ I~tW t 1~ft 1\,\ ~~Irv V-I,.;
(r)
II
inch inches
ho = I ho = 2
(a) Pure pitch.
(b) Pure translation.
FIOURE 4.-Typical records or pure pitch and pure translation.
6
REPORT 110 - 'ATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
For all but the combined-motion tests, either two or three Imown forces di.J:ectly to the wing and noting the COl"
airspeeds were used, averaging about 95 miles per hour, re ponding galvanometer deflections in the recording 0 cil
and the frequency range was covered for each air peed in lograph. Typical records are shown in figmes 4 and 5 and
half-cycle per second steps. The combined-motion te t include traces of lift, moment, reference position, and in some
were run at onl)-one airspeed and for each test the frequency case drag, as well as zero traces. Despite the relatively
was varied slowly and moothly over a range from slightly high-frequency "hash" on mo t of the record , consistent
above to slightly below the frequency corresponding to the values of amplitudes and pha e angle were mea ured and
desired value k= O.3. are plotted in figures 6 to 17 and recorded in table I through
The over-all instrument system ,,-a calibraLed by applying X.
-I I I I II r II II I I II I III II
I I Lf.lI
Time I ~~915 ~i9~ f.. Ime ~215~ ~2~1 3I2I6I0
Position
f\ 1\ II 1\ II Positionk- V t--I\ /
V
II 1\
rvl\~ ~I/'(I,I~ II
h ~ IA ~~IA IN ~, 1\ li:l 1\
fJ IV r- [\. I
-0 Drog • Oro
I
I
~
IVIVIV \II~M 1~~N~I~ ~~ I t-.J 1\- Moment! P f'/IAr. f\ !J-.. 1t\V,f.r , N
1 I~ IV I krr-..~)A 1-11.\
Moment
1\
'jJ ~ ~ f"vIf-\ h~ 1\
• 'Lift ~ 1I 1\I~Hr II
JJ V
(~) (?)
_ 'Posi tion
1\ 1\ '/ 1\
II
\ 1\
1/ II
\
n 1&
~V~ ~ M ~ lIyv ~~ ~"
IV1\ If -Drag
I) ~~IVIVI"
VfVIVIV IV II! IAI~
Moment
o
(a) Com bined motions.
(b) Pure pitch with initial anglc.
(c) Pure translation with initial angle.
FIGURE 5.-Typical records of combined motions, pure pitch with initial angle, and pure translation with initial angle.