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1. AMJ UM W& (LM AW 2.3906 DATI "7 3.3906 Typt Asia oATU COVEUDIJan_10-13.__1983 I____________UNSTEADY FLOW SEPARATION AND ATTACHMENT INDUCED BY_____ (iA;)@UL UOW "

A l! PITCHING AIRFOILS

M.C. RobinsonM.W. Luttges7. PWW A 0 OZ~ATMO NAMES) AND ADU6ES(MS)6 PtWOA 0 4MMU. RT

University of ColoradoBoulder, CO AFOSR

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OTICS IELECTED

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Michael C. Robinson*and

Marvin W. Luttges**

University of ColoradoBoulder, Colorado 80309

Abstract ing edge, and appears to be linked to passage ofthe leading edge vortex. The overall contribution

The dynamics of induced, separated vortices to the dynamic stall process from trailing edge vor-generated from sinusoidal airfoil oscillations were tical development has not been well defined.4,5examined across a range of unsteady flow parameters. Similarly, the effects of the leading edge-trailingLeading edge vortical initiation, development, and edge vortical interaction are still being quanti-interaction with trailing edge vorticity were sum- fied, again stressing the need for all types of un-marized via stroboscopic flow visualization and steady flow data.6

hotwire anemometry. Results indicate the sensitiv-ity of vortical development at both leading and The exact mechanisms underlying the formationtrailing edges to reduced frequency parameter and of dynamic stall vortices have been a topic ofmagnitude of oscillation angle. Certain optimal study for much of the 20th century.l The complex-parametric conditions resulted in dramatic interac- ity of the unsteady forces has slowed the emergencetions of leading and trailing edge vorticity. At of numerical prediction methods. Theoretical stud-diminished oscillation angles, separated flow at- ies of unsteady airfoil phenomena revolve aroundtachment was evident in the absence of the large attempts to relax assumptions postulated in steadyinduced vortical structures characteristic of large thin airfoil theory, but significant progress hasoscillation amplitudes. been elusive. Experimental studies are similarly

complicated, involving various airfoil types andNomenclature modifications designed to enhance vorticity produc-

tion over a broad range of both static and dynamicc airfoil chord flow parameters. 7.8 The general thrust of experi-K reduced frequency, .c/2V mental research has been to reduce the undesirableRe Reynolds number, V c/v effects associated with dynamic stall. Normally,T time tests were done with airfoils driven through large,V. freestream velocity slow oscillations in angle of attack. In contrast,a angle of incidence, a in + a. cos (,T) small amplitude and relatively high speed oscilla-am mean angle of incidence tions in angle of attack may be more consistent witha oscillation amplitude practical applications and technical feasibility../1 kinematic viscosity- rotational frequency, rad/sec The unsteady effects of dynamic stall are char-

acterized by turbulent separated flow and vorticalIntroduction structures. Two prevalent theories have been for-

mulated regarding the occurrence of vortices duringUnsteady aerodvnanic effects enerated by dy- dynamic stall. -,ne suggests that the transient

namically oscillating airfoils represent a %aiar bursting f laminar separation bubbles leads to vor-area of research in mocern fluid echjnics.1 'hen tices.9 The l.nimnar Separation bubble is forneda lifting surface oscillates about i mean in.le of during trinsiti-ns from laminar tz an attacheditri. lk in excess of its static stall inzle, laree. turbulent flcw. ,hen the separation roint oroaress-uns~e_:." aerodynamic forces are produced. The un- es to the base of the bubble, the bubble bursts andicea': lift, drag, and =c7en: coefficients can induces a vortical structure. The seconu aprcaih; ireatiy exceed the expectec static counterparts. .nvisions an ibruvt :uroulent separation iyer :.eThese forces are directly related to the stall front porticn )f the airfoil; this : rbulent sezsra-causea by transient separation of the flow from an tion is thouzht :o be responsible f:r the procuc-airroil dynamically oscillating in pitch. Stall of tion of dynamIc stall vortices.' he boundarv _av-

- this nature is classified as dynamic stall. The oc- er may remain totally laminar prior :o seoaration,curronce and severity of dyvnamic stall is directly and this, by definition, precludes :he formaticn orrola:ed to the cype of airfoil, Reynolds number, a laminar separation bubble. Both ech.riss af

oscillation rate, and oscillation amplitude. In- vorticity proauction are associated ..tn the '.'nam-herent in dynamic stall is the formation of leading ic separation of the flow, although icme criticaledge vortices; these vortices can produce .j surge parameters nay "arv in relation to :-e lcminance ofin the lift force as well as unsteady moments on the one or the other -echanism.airfoil.2 It is believed that repetitive generationof dynamic stall vortices might be exploited to de- Vortical structures appear to te important cr-lay stall or energize the flow field to greatl. in- relates of the unsteadv -tallin.; of in airfoil.crease the operating characteristics of an airroil rhere seem to be two favored nethodi by which thcsepast its static stall angle (cf. Ref. 3). important structures na. be experi-entally ennanced:

(I) by continued increments of jirfoil angle pastAnother energized structure generated from air- the turbulunt separation point,' iz (L2) bY arupt-

foil oscillation is the trilling edge vortex. The ly :h.ngin4 the pitch Jirect'on f the iirfoilcirculation of the trailing edge vortex is opposite shortlv itter :ht- turbulent separation of the flowin direction to the vorticity generated at the lead- hah uccurred.'

(raduate kesearch Assistant, Department ofAercspacc [ngineering Sciences. Xember AIAA. In the folluwing studies, jbrupt chances in

**Professor, iep.Artrent of *..rospace Lnziner- pitch direction of the airfoil were achieved v'inein Scicnces. ,mal I os, ill.it ion anrles ( .-5 ' at hiz: spevd (11 iz)

,,,,,fl,,, ,m. , ,,n..., . nd AIR FORCE OFFICE OF SCIMMIFIC RKaS RI (AYq............. IOC... ' ""1 411 ...... d I NOTICE OF TRANSUITTAL TO DTICThis technical report has been reviewed ajniapproved for pu'blic release IAW AYR 190-12.Distribution is unlimited.MATTHEW J. KERPEK

pitch oscillations to elicit repetitive vortical gra;hs highlightcd the repetitiveness of flow fieldstructure. Extensive flow visualization was used i disturbancLs.conjunction with hotwire anemometry to characterizethe initiation, development, and migration of the Velocity measurements were made using a conven-vortex through the oscillatory cycle. The evalua- tional constant temperature 2-needle hotwire probe.tion of independent static and dynamic variable com- constructed of 0.0001-inch Wollaston wire. Usingbinations focused upon those that might maximize ex- various linearizing circuits referenced elsewhere,10

pioitable aerocynanic phenomena from vortex develop- a 0 to 5 volt output was generated proportionally toment. Of principal interes. were the utility of the the mean flow. The hotwire probe was mounted on anreauced frequency para=eter in characterizing flow orthogonally driven traversing mechanism in the air-disturbance from reduced oscillation angles, and the foil test section.formation and development of trailing edge vorticalstructure. Hotwire data acquisition and subsequent reduc-

tion were accomp~ished with a PDP 11/23 microproces-Methods sor. Upon receipt of a 300-usecond pulse from the

phase-lock trigger, the analog hotwire signal wasExperiments were conducted con NACA 0012 and digitized and stored at a sampling frequency of 1000

NACA 0015 airfoils in the low-turbulence 2' - 2' Hz. At each pulse, data were collected over twowind tunnel at the Univ'rsity cf Colorado. Flow complete oscillation cycles representing one datafield measurements were obtained via flow visualiza- run. Ten such successive data runs were averaged totion in conjunction with hotwire anemometry. reduce the signal noise and accent the periodic dis-

turbances generated during the oscillatory cycle.A solid aluminum NACA 0012 with 10-inch cncrd

and a hollow-core NACA 0015 with 6-inch chord, both Resultswith a 2-foot (infinite) span, were used for the ex-periment. The airfoils were driven through pitcning Stall angles for the NACA 0012 airfoil were de-motions with a 1/3-H.P. D.C. otor using a 6-to-1 ter-ined photographically to be approximately a =gear reduction connected to . variable dispiace=cnt IC.9 at a Reynolds num-er of 100,000. In staticscutch yoke. Sinusoida osci-lation rate could oe testing at these angles of attack, the streamlinesneid constant while tne magnitude of angle p:cn was cleariy lifted from the airfoil surface as the flowctianged by adJuscing the raa:a7 bearing on tne fil- neareo the trailing edge. Turbulent flow was ob-wneel of the D.C. motor. The angle arouna whicn trn served in the area from which the streamlines hadoscillatory cycle occurred was determined by initial separated. In most instances, the flow was not at-positioning of the wing in the drive yoke. A rata- tached over the last 2 inches of the 10-inch chordting potentiometer on the fl:-.t eel was used to deter- airfoil. The NACA 0015 airfoil exhibited separatedmine the angular velocity and specific attitu4e of flow at just slightly higher (- 0.50) angles of at-the airfoil during any portion of the rotation cycle. tack. These flow patterns for both airfoils were

used for comparisons with the various dynamic condi-Flow visualization was obtained using a smoke tions reported below.

rake constructed of a NACA 0015 airfoil with 1/8-inch diameter tubes inserted in the trailing edge. Depending on test parameters, a number of re-The smoke rake was located in the settling chamber producible flow perturbations were characteristic ofof the 2' x 2' wind tunnel in order to minimize dis- the airfoils during oscillation. Many of these per-turbances to the test section. The rake could be turbations have been described previously for dif-moved vertically to optimize the position of the ferent test parameters (cf. Ref. 11). The mostsmoke lines. Dense smoke was generated from heated prominent flow disturbances were the formation of aRosco fog juice stored in a 55-gallon drum and de- leading edge vortex, the movement of the vortexlivered to the rake. at modest pressure. The pres- along the'airfoil surface, changes in vortex struc-sure and ensuing flow rates were adjusted to prevent ture, interactions between the vortex and the air-smoke from being emitted as a turbulent jet. foil, interactions between the vortex and the free-

stream flow, interaction of the vortex with theSynchronization of data acquisition with the trailing edge of the airfoil, formation of a trail-

airfoil angle during an oscillation was accomplished ing edge vortex, and interactions between leadingusing the rotating potentiometer which produced a 0 and trailing edge vortices, both at the trailingto 5 volt ramp output corresponding with the 0 to 2r edge and in the airfoil wake. Most of these dis-oscillation of the airfoil attitude. Voltage dis- turbances were stable enough during each portion ofcrinination levels from 0 to 5 volts could be preset the oscillatory cycle to permit repeated strobosccp-on the electronic trigger. When the selected volt- ic (z 7 useconds) illumination for multiple (z 20)-age was reached during an oscillation, a 300-usecond exposure photographs.pulse was generated to trigger both the strobe forflow visualization and PDP 11/23 microprocessor for When a leading edge vortex is generated, thevelocity reasurements. In this manner, all angle- growth characteristics of the vortex during the re-dependent data collection could be synchronized with maining portions of the oscillatory cycle and acrossthe proper phase angle of the airfoil. All angle- time appear quite constant. A small vortex is Iden-dependent synchronization signals were checked regu- tifiable near the leading edge as the airfoillarly by stroboscopic examination of airfoil posi- pitches toward the maximum angle of attack (Fig. 1,tion relative to " fixed micrcmecer scale. 0 1 cycle). The vortex increases in physical mag-

nitude as it moves across the airfoil surface to-Single and multiple phase-locked strob'scopic ward the trailing edge (Fig. 1, 25 :. cycle). In the

(7 asecond duration, point-source flashes) pictures presence of large vortices, flow separation occurswere taken of the flcw field, using a 35 c7. SL' car- over the entire airfoil chord as the vortex inter-era with ;SA 400 film. The still photograp:is rvner- acts with the trailing edge and sheds into the wake.ated exact details of the vortical flow s:ru:ture, Shedding occurs as the airfoil approaches the bottomwhereas the piase-lucked multipte-exposure pnvto- of the duuistrcke (r. nium angUe). Flow reattaches

2

Octl n>

-346.

25%' 25- C W

A' t

,b 7 50c

.. ,. -IM

4,~. .

7~ 5.c75c~t

-'7

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Fig. 1. Vria eeomn nLifi uIIV i.2 osnh1u tcldvlpetaat~~~~~ ~ ~ ~ in ru .%I. per od in th i--lrIU:,;ag e

cycle. ~ ~ ~ PC:- 60005K 0.5 a 1.9

Re-10,O .;u 1 . !5..: -

3, 4 .---k'aZ'

k-

L .7

7- .4 -.

-Y i777 -. 4.

K~~. 0.75 Loe iht 5 yle .5

7 7I

~~'71

Fig hotFograhnetwt raigrdcdfeunis. Re 100,000 -0.; a - 13.90 00 * 5et0edngeg.Rgh:taln

(rig. 1 75 cyle a 25e pcyce Kieto ch025 nges le tal vrcyce; K, no 1.5a pp ert (Figh. 2.075%) cyceKo th 0.75.ok Loter reaigt 7dge cycle; cyli p a 1.25.l lwfil itubne aemr

flow ~ ~ ~ ~ ~ -ditrbne are repate astearolaan lmtd.eaainapast epeaetoe

ner th maiu anl-f-tak---..-.p- th i'oi hr truhotteosiltoncce

sure phtorah permi a ler isictontobmad btwenth seayropodcile sncroou Mutil-exo epoorps oeetnflw fecslikd oaifilocilain n te tob mseaig n eer-nfgwhtero ntwek

Fig.l 4.rbledng afdetralink edgt e cneoa vortical deo n ihistntnes are 7present. sInl eeostance

elemeg. o, 75 epacycle) a d th sptchl diecio chngsptal aotedexot appareit (dfi l 2, 0-7 i)stein-

sures bhetwreen tuernitc an clear diutinctiondSobe

Under oscillating conditions where a dynamic turbances. which ten,! to return flow to the atioil

4

surface. Unless strong forces are acting to reat- Table Itach flow at specific points in the oscillatory cy-cle or at specific points along the airfoil, the Independent Variables for Photographic Studyflow line disturbances may appear to have little di-rection. Reynolds Reduced' Mean Oscillation

Number Frequency Angle Angle

Helin 2 recently showed that small oscillationangles can effectively reattach separated flow if 60,000 0.25, 0.5, 0.75 12.9- 1, 30, 50they are used in conjunction with high oscillation 100,000 0.25, 0.5 12.90 IQ, 30, 50rates (Fig. 3). Quantification of approximately 300 140,000 0.25 12.90 10, 3%, 50

photographs revealed several conditions under which

flow attachment at or before the trailing edge couldbe attained. Leading edge vortical development also the airfoil for increasing times during a single as-was observed. Single, instantaneous (< I msec) vi- cillation cycle represents the apparent mean veloc-sualizaticns of the flow revealed specific struc- ity of the vortex center over the airfoil. On thetures charazteristic of flow perturbations caused by average, the velocity of vortex movement from thesmall oscillation angles and large oscillation rates leading to the trailing edge of the airfoil was 35-(Fig. 4). Since the shedding of the weak vorticity 45% V. Vhereas straight line segments on thesewas not tied precisely to the oscillatory frequency, plots indicate a uniform velocity of vortex movementthe flow field appeared characteristically "blurred," from leading to trailing edge, curvature and/or dis-suggesting turbulent separation (Fig. 2). More ac- continuity corresponds to a delay or hesitation incurately, large oscillation rates at reduced oscilla- the movement of the vortex center. The more clearlytion angles induced flow attachments that were poor- defined curvatures in these plots indicate maximumly synchronized both spatially and temporally with delays, and correspond to the presence of the larg-the oscillation parameters. Similar vortical devel- est vortical structures observed. The reduced fre-opment, induced by leading edge separation, was ob- quency parameter (K) was very useful in predictingserved at most static stall angles. During oscilla- the relative position of the vortical center overtion, however, a characteristic bending of the flow the airfoil surface during the oscillation cycle,toward the airfoil surface occurred before the flow for a variety of Reynolds numbers and oscillationreached the trailing edge of the airfoil. This flow angles. However, the delays in vortex movement overreattachment inevitably occurred during the down- the airfoil surface could not be predicted from thestroke portions of the oscillatory cycle. The high- values of K employed in these tests.er oscillation rates (higher values of K) were asso-ciated with flow reattachments appearing well before It should be noted that this parametric studythe trailing edge was reached. Thus, the flow dis- was performed without endplates on the oscillatingturbances sur=arized below seem to belong to a con- airfoil. As also found by Carr et al., II the tun-tinuum of dynamic effects that originate with small nel wall effects on vortical generation mechanismsangle rapid oscillations, which induce relatively were negligible at both the elevated values of K andmodest flow disturbances, and include larger angle the large fixed values of a examined in the presentrapid oscillations, which elicit relatively strong study. A series of photographs taken both with andflow disturbances. without endplates at a Reynolds number of 60,000,

K - 0.25, and a - 150 ±5' showed no discernibleIn order to determine the effects of the flow change in the overall flow disturbances visualized

variables on vortical development, a photographic at mid-span of the airfoil. The endplates were aban-parametric study was conducted across a range of in- doned for the remaining tests since they placed adependent variables (Table 1). As expected, the on- great deal of stress on the oscillation drive mecha-ly condition that did not generate clearly discern- nism, and .they severely limited the oscillationible vortical structures in multiple-exposure flow rates that could be employed in subsequent tests.visua-lization photographs was the oscillation angle±10 around modest fixed values of a. As indicated In order to characterize the magnitude of theabove, any elicited vortical structures were undoubt- velocity disturbances generated by the leading edgeedly poorly synchronized with the oscillatory cycle, vortex, linearized hotwire measurements were madeEven oscillation angles of ±30 generated only modest- over three chord locations at various positionsly synchronized vortex structures in multiple-expo- above the airfoil surface (Table 2). The probe loca-sure photographs obtained at Reynolds numbers of tion was held fixed relative to the wind tunnel whilelno,000 to 140,000. At a Reynolds number of 60,000, the airfoil was oscillated. For each test, dataany vortices generated by ±30 oscillations were em- were collected for oscillation-phase triggered, sin-bedded in other, more random, flow disturbances. In gle velocity profiles across two successive completethese flow visualization studies, the largest and oscillation cycles. Ten such individual runs were=cst .t1l-synchronized vortices occurred at increased trigger-synchronized in order to match correspondingvalue. of the reduced frequency parameter, at higher initial angles of attack, and to permit numerical-.nles of attack, and at higher oscillation angles.Chnes in Reynolds number did not have major effects,n vort city across the values tested in the present Table 2study. Independent Variables for Hotwire Study

The creat ion and f.te of the highly synchro-nized, strcn; vor:ccit'-.,-rc carefully charictrrizzed Feynulds Reduced Mean Oscillation

Ir. oricr to dctcr-in,. .hich flow disturbances were Nu~ber Frequency Angle Angle

attrilut.tblL to such trong .,rticity. From the,:,tc. :*;!i (12/cycle), *the 7ov,'.ent of the vortex 60,C3 0.25, 0.5 0', 1S° 1° , 5

ctntcr w' plotted as it migrate* across the airfoil 100,C3 0.25, 0.5 15 °, 5o

•:acc !r= cc, rai2 in:' ed-c (F! i . 5). The l 0.25 00, 1S' l°, 50

' n.1 th' line rcprescntknj verex pezoion

1.0

0XX0 0

0- £0 0.7 0M Z 0

0 U K=0.25 K=0.5 K07

0J0 0.5A c-RE NO.= 60.0000

0.25. RE NO.= 100.000&-RE NO.= =140.000

L 0.0 1

2 T/~ 7rc 27T/cJ 37r/i27Q 3IVc~jTIME (SEC) TIME (SEC) TIME (SEC)

Fig. 5. Vortex center location on airfoil surface during the oscillatory cycle.

VTO0 POSVmpo P05 V.5 (CM)' MID (2 CYCLES)

(C) E(2 CYCLES) 1.31 61.28 41.. 61.41 2 1.13 4

0.68 3

0.2 10.54 20.2 10.53 1

0.16 0.5

0 27vc~j 4*w(j2~j4'aTIME (SEC) RE_____________ 8 I TE TIME (SEC)

RE N.=14.000 1.18 18LE K=0.251.0 6

I m=5*1.25 10T=O ID t,, 5'1.13 8

(0.50) a-auf +CCOWT 1.01 6

V. 1.07 -4

02 7r/( 41Vc I

TIME (SEC)

Fig. 6. Velocity measurenents at selected points during synchronous vortical development.

averaging. The synchronous triggering also allowed refers to the distance of the hotwire probe from thecorrL1.2tioV; of th4 hotwire m-easurenents with flow airfoil surface (in cm) when the angle of attack wasvi!outlization. Figurc 6 is a typical exar.;le of at the mean oscillation angle.tht: -,cr. oed ho)twire miuruTmi.nts obtained for a

t~~cctperiod. Tic v-Aoclty rca ,nftides corre- Figure 6 Is Illustrative of the results ob-;v',nd to the intantaneous velocity comiponents at tined for a set of experimncntal conditions thatT 9 .1aof attack). %VelocitieS at Sub- gonerats. stronc. synchronous vorticity in the flow.

r-.-'uat t1=v-:. in thu L)!cillatorv ptriud wvrc ob- AL the luading edpe (T . 0. 0.5 cmr) the probe wastamred iro:, thte hotwire signil traLCe.. Position closest to the airfoil for the bottom'f two tracts.

6

Throughout the oscillatory cycle, only minimal ye- Another temporal effect of the shedding vor-

locities were noted at these positions in the flow tex can be seen in Fig. 6. A maximum velocity dis-

field. As the airfoil moved through the oscilla- turbance occurred at the leading edge at approxi-

tion cycle, a vElocity maximum occurred (T- n/(,) mately the .aximum angle of attack (T - 0). This

as the airfoil attained the minimum angle of attack. maximum was seen both ht later time periods and

Since the probe was no longer shielded from the later portions of the oscillation cycle at the mid-

freestream by the leading edge of the airfoil, it chord and finally at the trailing edge. The delay

appeared to record the unobstructed velocity maxi- in the velocity perturbation appearance at these

mum. The hotwire velocity profiles indicated a sim- sites was presumably an indication of the time re-

ilar type of blockage. effect when the probe was 1o- quired for the vortex to pass from the leading to

cated at the airfoil trailing edge. At T - 0 (max- the trailing edge of the airfoil.

imum angle) the trailing edge was beneath the hot-

wire probe, effectively shielding the probe from Synchronous, spatially discrete disturbances

the freestream velocity. As the airfoil angle de- were not generated at stall mean angles for the Rey-

creased, the velocity neasurement grew to maximum nolds numbers and reduced frequencies tested (Fig.

coincident with the passing of the trailing edge to 7). Flow remained attached over the airfoil sur-

positions above the probe location, face throughout the entire oscillation cycle. Ve-locity measurements at the trailing edge (Fig. 8,

At probe positions in excess of 8 cm above the 0 cm, a - 00) show the response of the hotwire

trailing edge, 6 cm above mid-chord, and 2 cm above probe to the airfoil oscillation. Two separate

the leading edge, other periodic maxima occurred velocity minima occurred in each cycle as the hot-

during the cycle. These maxima appear to reflect wire probe was aligned with'the trailing edge. It

the velocity induced by the passage of the leading was necessary to increase the mean angle until the

edge vortex across the airfoil surface. The larger critical stall angle was exceeded during an oscilla-

the perturbation, the larger the magnitude of the tion in order to generate strong leading edge vor-

shedding vortex. As the vortex size increased, the tices. At a - 0* ±50, two standing vortices devel-

velocity fluctuations became more pronounced oped, one each on the upper and lower surfaces of

throughout the entire spatial grid of flow measure- the trailing edge of the airfoil. Though relative-

ments around the airfoil. ly small in size (: 0.1 c in diameter), these dis-turbances reained over the complete oscillatory

The phase relations between the hotwire dis- cycle of the airfoil with a circulation in the same

turbance caused by the passing vortex in the far direction as the leading edge vortex. Similar

field and the maximum hotwire disturbances in the trailing edge vortical development was seen by

near field close to the airfoil surface at the these authors in studying the trailing edge genera-

trailing edge do not necessarily correspond to each tion of discrete audible tones.13

other in a simple fashion. It will be shown subse-quently that a vortical disturbance induced at the Small oscillation angles (Fig. 8) produced ye-

trailing edge and the leading edge vortex in the locity fluctuations with little evidence for vor-

far field result in the strongest vortical develop- ticity. The apparent "smooth" response of the hot-

ment and interactions. Once vorticity is initiated, wire signal, even under known flow separation con-

oscillation phase angles appear clearly secondary ditions, was a result of averaging the hotwire sig-to these strong vortical interactions. nals over multiple oscillation cycles. In effect,

VORTEX DEVELOPMENT VORTEX DEVELOPMENTv_ DEPENDENCE ON MEAN ANGLE y. DEPENDENCE ON OSCILLATION ANGLE

s 1.1a V_ 2s _04- _o_

.,S3 2 1.10 1.44 4 ________ 1.17WJ.04 2~40, .6 3 0.76O S 1 1.16 O.3 1 1 0.16

O.MMID EO 140.0 MI

0.6 4 ' 4 1.0 V"l

e -+2.6 1.01 -_____,_____ 0.62

0.36 0 ,,. 00.36 0 --f 0 0.16T.E. TA.

'69 3 _________ 1.10 0.16 S1.2 4 1 .

OM ,.J . o.30 1 0.16MID MID0

05 1 a 10. is 1.16

11..6 1O 1011 10 1.21

1 1.01 a. 4 4______ 4 Ole

00

I TA. TIEU

F,,. ;. ff+t i nean angle on *t(rtlral I %p. h. .!fvct. of srn:ll] osfc l itrin mi ,1 (o1i

u,.v .lor-.,nt.r . ,

VORTEX DEVELOPMENTDEPENDENCE ON K & Re

IV. Oun5* : a 61L.E. v. MID v. T.E.

V. Pos V. Pa v. po

411 5 *tOsO.8AAI aIs 4

ago I0.40 R z 6.000

0.05 14 __ _ _ _ _ _ _ 6.00 00 .4 4 0 . 2 0 . 2 0

0.2? 08

112- RE- 140.0000.4 S00

t.24 0.13 I 00. 20tl

a"

1.0 is RE100.000otO 1 K;0.25

.1 20.L20 1 1.9 2~5*

033 .01 i

204 RE- 60.000

124 S 0.10 4

025 1 030 1

0 2Th E 4.00 21r*.Ja Ta,)4 rA0 27rfA 4 'rA..iTAN (SEC) TA (SEC) TME (SEC)

Fig. 9. Reynolds number and reduced frequency effects on vortical development.

the averaged velocity data indicated a lack of spa- In general, velocities of the leading edge vor-tial and temporal synchrony between flow distur- tex increased with higher oscillatory frequenciesbances and airfoil motion. At certain positions (reduced frequencies). Increases in peak flow ye-above the trailing edge (Re - 140,000; a - l*; POS locity of 5 to 8% were obtained when the reduced= 6 cm), velocity perturbations that were synchro- frequency was doubled from 0.25 to 0.5. When thenized with the oscillating airfoil existed. Above reduced frequency was held constant, the velocityand below those measurement points, however, the peak, corresponding to vortical passage, was in-velocity disturbances were poorly correlated with versely related to Reynolds number; increases inairfoil oscillation cycle. Reynolds number reduced the apparent velocities of

the leading edge vortex. At reduced frequency ofThe effects of Reynolds number and the reduced 0.25, the normalized velocity increased 16.8% as

frequency parameter on the passage of vorticity Reynolds number was reduced from 140,000 to 60,000.over the airfoil are given in Fig. 9. The strong- At K = 0.5, the normalized velocity increased 6.9%est vortical disturbance (1.68 V/V,) occurred at a as Reynolds number was decreased from 100,000 toReynolds number of 60,000 with a reduced frequency 60,000. These velocity increases were calculatedparameter of 0.5. Velocity measurements were nor- from measurements over the trailing edge. Whenmalized to freestream velocity in order to judge peak velocities were examined at mid-chord, changesthe relative contribution of each of the experi- in normalized velocity again showed an inverse re-mental parameters on vortical development and move- lationship with Reynolds number. Increases in ve-ment. With expanded plots of the same traces, it locity magnitudes of only 2 to 3 were typical atcan be shown that the greatest time delays in the mid-chord hotwire positions. Thus, small velocitypassing of vortices over the airfoil surface corre- decreases mid-chord were amplified into more strik-late positively with increasing strength. This was Ing decreases at the trailing edge. It was notalso sho-n to be true in the vortex location plots clear if the vortical strength was actually reducedsu:-7arized in Fig. 5 for the quantified flow visu- with increasing Reynolds number, or if the net ve-alizations. It is important to note that each mea- locity change at the trailing edge was si.-ply a re-sure was ebtained indt.pendcntly. In additlcn, the flertion of some other flow perturbation. Flow in-flow visualiza:ion relied predo.inantly on the use teractions produced as the leading edge vortexof the 10-inch chord NACA 0012 airfoil, while most reached the trailing edge of the airfoil were theof the hotwire anemro etry (corroborated by visual- most likely causes of :he: e vortical velocity dif-ization) relied on tests of the 6-inch chord NAC\ ferences.0015 airfoil.

Such a pos5ibi!ity prompted a detailed study

8

_~ L~

r f -

---.------

Fig. 10. ; Th deeomn oftelaigeg otxadteidueeto h riigeg otx

(A)~ ~~~~~' Th ifi.atiigmxiu ic ngesosa otxiiiae tteledn de

(B)~~ ~ ~ ~ Th dontemeeet-ftegoiglain devre permdcodadbnstrealine towad th airoil tp suface

(C)~~~~~~~~~~~~~~~~~~~~~~~ Th rwn-otct hw ontemeeetslclzdjs ha ftetaln de

(D) s te vrtexpases he tailng dgecouterflowis ndued fom he otto.sufac

Re - 000r .;=a nl -15 ''5'.

Approxmatel 20 eposure at ech osillat rpae ng .

9

of how the leading edge vortex interacted with llthe elements of the surrounding flow. It was al- .ready amply clear that the leading edge vortex had ,

one of the most dramatic influences on the overall ,

duedtrilngede orexisgeerte wthcicu ."- ,_ " - ..,:..,i -,-, , ..... "....

flow field. Figure 10 depicts the sequence of flow-interactions charactrititc of a dynamic stall vor- . . . ,

tex when passing over the airfoil to the trailing I,.- .. . .. .. ..edge and shedding into the wake. The series begins(Fig. 1iA) as the vortex is generated near the lead-.. 0- ., - -

ing edge and begins to move toward the trailing -ege. .At mid-chord (Fig. 1lB), the rapidly increasing sizeof the vortex is evident, Corresponding temporally , -

with the rapid growth, the vortex center slows its . J.

movement toward the trailing edge. The larger vor- -tax covers much of the airfoil surface (Fig. 10C). ".- .'As the vortex reaches the trailing edge, a flow re-.- ,

versal from flow around the trailing edge to the top .. .-...

surface of the airfoil occurs (Fig. 10D). The in- ~ '

duced trailing edge vortex is generated with circu-. "lation opposite in direction to that of the leading .

edge vortex. Complete separation of the leading '

edge vortical flow from the airfoil surface occursas the trailing edge vortex grows rapidly (Fig. 10t). ~~=-The leading and trailing edge vortices combine into 'a tandem structure which sheds into the wake in uni-son. Within two chord lengths downstream of the 4 4 Aairfoil, the size of the combined leading edge- " .

trailing edge vortical structure exceeds the airfoil ' .

chord diameter by at least a factor of two; the flow :'-* '--* : - ."lines exhibit dramatic vertical displacements sug- • -" -

gesrive of rapidly decelerating vorticity.

The induced trailing edge vortex possessed in- in,teresting small-scale characteristics. Rather than " -consisting of one s tall vortical structure which '..rapidly grew at the trailing edge, the vortex wascomposed of streamlines containing multiple smaller .. ,,"..

vortices. These small vortices ultimately coalesced 5, ,into one large vortex. A similar flow phenomenon.. ,

was recently observed by Frevmuthl4 in his investi-gations of airfoils in linearly accelerating flows. 7'

i hereas the leading edge vortex induced flow vrW a i

reattachment to the airfoil surface, the trailingedge vortex resulted in complete flow separation, [tnwhich extended upstream to the leading edge. Thistotal separation occurred as the trailing edge vr-. Ntex reached maximum amplitude immediately prior toor coincident with shedding into the wake.

The striking interaction led to another photo- - .

grap'.ic study. The initiation and interaction of .

the trailing edge vortex with the leading edge vor-.tex were examined with variations in Reynolds number, .; .

reduced frequency, =ean angle, and acmplitude of os-cilla-,ion. The parameters that affected the devel--epmnent of the trailing edge vortex paralleled re-.suits obtained for the leading edge vortex. Test.conditions that generated the most temporally andspati Ally synchronous trailing edge vortices siri-larly produced the most temporally and spatiallysyncrcrnous leading edge vortices.

The dependence of the trailing edge developmenten the mean angle of attack is illustrated in Fig. Fig. 11. Effects on the leading and trailing edge11. The largest interactions between the leading vortical interaction from variationi in.and trailing e-dge vortices occur at greater (Z 15') the mnean angle of attack at Re -6,)'sean ang les of attack. At smaller angles (-. 5'), K -0.5; a - ±5*. %adest mean angle sthe dcvelopment of vertical instabilities is evident (20' and l)") induce strong v.orticalon both airfoil surfaces at the trailing edre. As mnteraction in the wake. eao an;,Ieb ' 10natvtd earlier, si::ilar vertical structures hIave :aen elicit little temporally :,:..clrunuus flu-.noted under nonoscillating crenditions at small an- structure. At 0' and 3-, cmall. tc.mporallygles oft attack and m.ay be linked to bcuidsry laycr GV~nChrcn.-ou5 vu'rt"'CC! shed 0iazaetransition. from t~iu airfoil traiiling edi;,_.

10

IrI

Fig ". 12 * . Effet. on the • l edn an triln eg

Re n l' .,-. e at ... - ' ..,.., a , - J Fig 13 Ef e t -o.n. .- the le d n a d t a li g e gK .0 -5 _t:n i nt rac i o i s ev d n vu t a i n e a t o f ro va i ti n "" "i n" " : '

at R e. .- '0C O th b ot t o

"ht ~ r p w a th- -cl l t n f r q en y at P --' , 6 0 , , 1

t ake .t , a-.. - ,5 . -. . t 0 H

•IO , 0 a n 1 3 ,0 0 r e u c t h n e -t c s': A t 3 - ,i'

..0 . ... -a r e ut . ,i n

..!;;: f . .. ..

si t of t h .;ca

t o .l h c - : a c v n e c i f i

-. o

.. . . .. - . , a ,- : .. .. -

• -"---s , . . ....

- - " - *. . .

Ui t " " ' . , . .- " - " -.: ' '

t • r .-- -.- " ,

t *

-. ' _o. . -

v-I,.-_"- " -

* . -. .,- ."

votcd p.r.i-.lo vralo3i .. .

Fie.n1. ldfnt~ bra m 1" u _5, Fg 3 fet on the leading and trailing edge '

K =0.5. Strcng interaction ja evidcnt vortical int.eraction from variations inat Re = 60,CCO; the bottom photograph was thu as i1Latjcn frequency at I = uO,c.C0;taken at a later point in tho oscillatory - = 15; a * 50

. Free 1.1 to 5.0 Hz,cycle. Increase in Reyuolds number te-pura~ly syzchronous vortical interac-(O,000 and 130,00) reduce the £nten- tion is evid.e.-.. At 3.0 11:, a reductionsity of tile interaction. lIn th tcr~rarl dependence en airfoil

osciliction occure.

11

--J

+5"a Rynolds number of 60,000, as in previous results.Less definitive interactions occurred at higher

- . R-e. . . . -. ynolds numbers. The inverse relationship between" " -- Reynolds number and leading edge vortical develop-

ment also held for the trailing edge vortex; in-

- - creased values of Reynolds number resulted in di-minished interaction between the leading edge andtrailing edge vortices.

The reduced frequency parameter of 0.5 wasW "associated with the largest, most easily resolved

vortices (Fig. 13). Lower K values were associatedwith reduced spatial-temporal dependence of flowfield on the oscillation frequency. This reduceddependence resulted in small spatial or temporalinstabilities recognized as "blurred" resolution[ ' -"' "" ::' ; '" ' '" in the visualizations of leading and trailing edge

- :;. -" % vortical interactions (Fig. 13).

The oscillation angle had a major effect onthe repeatability of the flow perturbations. Athigher oscillation angles (±5') the vortical inter-action was well defined both spatially and tempo-rally, and was synchronous with airfoil oscillation.

.... At ±3 this dependence was not as evident. Finally,.at oscillation angles of ±10, little temporal or

spatial dependence on airfoil oscillation was noted", "'.' 4 ...... ''', ,":" .:'(.''' ' , for trailing edge vortex development. Without the

.existence of single instantaneous flow visualiza--tions (Fig. 14), these multiple-exposure photo-

graphs would easily be mistaken as evidence forfully turbulent flow separation; the presence ofvortical structures, though somewhat variable spa-tially and temporally, would not be recognized.~Discussion

With flow visualization and hotwire anemometry,we have documented that an airfoil oscillating si-

. "- ' N" . - ' nusoidally around or above its established staticstall angle elicits a leading edge vortex whichthen induces a trailing edge vortex. Whereas theleading edge vortex maintains flow attachment as it

+1* .' moves over the airfoil surface toward the trailing.' ,-edge, the induced trailing edge vortex generates

cataclysmic, instantaneous, complete flow separa-tion. Visualization and anemometry findings indi-

cated a flow perturbation continuum that extends,from static stall and minimal oscillation condi-

tions through moderate and strong oscillation con-ditions. Virtually the same patterns of vorticity

-and separation were observed across all conditions,I"" but these patterns were temporally and spatially

fixed with an oscillating airfoil, and more capri-cious with static stall conditions. In the latterinstance, the flow perturbations gave the appear-ance of turbulent flow separation. The establishedsignificance of the leading and trailing edge vor-tices, and the e~pirically demonstrated control

Fig. 14. Effects on the leading and trailing edge that can be exerted over the interaction of thesevortical interaction from variations in vortices, suggest that select parameters as well asthe oscillation angle at Re - 60,000; select pitching motions r.ay yield valuable, exploit-am - 15'; K = 0.5. At -5*, the induced able flow attachment in the absence of cataclysmicvortical interaction displays well- flow separation.defined :vnchrony with airfoil oscilla-tion. At reduced oscillation angles The generation of the leading edge vortex and(:20 to -11), the elicited flow !:tructure the subsequent induction of a vortex at the trail-bcu7.-s less dcpndurnt un airfoil oscil- ing edge were most clearly demonstrated with alatiun, large (15") anple of attack and a large (±5o)

pitching notion of the airfoil around that angle.The leading edge vertex a~pvars as a small separa-

As exectrd, P,,ynolds nu..ber effucts (F!.-. 12) tion bubble as the airfoal pitches upward, acculmr-were Lnversely relatcd to ,.-par~t v,,rtic.. r- ating the f!,:w. The vortex becom.es rore discern-actisa str~ng;.: . A -tron; . i1tura~tijn uccsrrvu aL ible as the lcaglin! edge -cculerates towa.ro maximum

12

oscillation angles. When the airfoil begins to de- dence on airfoil oscillation phase. Here, the pat-celerate at maximum angles of attack, the vortex tern of vortical development was truly unsteady whengrows both away from the top airfoil surface and to- referenced to the airfoil oscillation. The quasi-ward the trailing edge of the airfoil. Flow attach- steady vortical characteristica were absent. Thisment is readily discernible at this time. If suffi- does not, however, rule out some other as yet undis-ciently energetic, the growing vortex may slow sig- closed periodicity underlying such flow structures.nificantly in movement tcward the trailing edge. Atthe exact moment that the first vortical streamlines From the observations of the current study, itof the leading edge vortex are positioned above the is clear that elaborate flow structures can be con-trailing edge, a vortex is in!tiated from the stream- trolled in the vicinity of an oscillating airfoil.lines of the bottom surface flow. This trailing Careful selection of the dynamic oscillation param-edge vortex, driven by the leading edge vortex, eters in conjunction with select pitching motionscauses rapid, complete flow separation over the air- may yield valuable, exploitable flow attachmentfoil surface. The trailing edge vortex grows rapid- while minimizing the effects of flow separation.ly, with flow of opposite circulation to that of the Generation of highly repeatable flow structure withleading edge vortex. %,hen leading and trailing edge even minimal airfoil oscillation was readily docu-vortices appear to be of equal size, they shed into mented. The leading edge vortex induced completethe airfoil wake. Interactions of these vortices in flow attachment. Maximal flow attachment wasthe wake lead to an apparent vertical flow, passing achieved by increasing vortex residence time on theat freestream velocity, bounded downstream by resid- airfoil surface. Both larger reduced frequency val-ual leading edge vorticity and upstream by residual ues and oscillation angles yielded increased resi-trailing edge vorticity. This interactive wake dence time.structure remains sufficiently cohesive to be ob-served many chord diameters downstream. Elicitation of the trailing edge vortex led rap-

idly to the adverse effects of complete flow separa-The major initiating determinant for the devel- tion. Airfoil pitching phase brought the airfoil

opment of leading edge vortices appears to be the trailing edge up to meet the shedding leading edgenet acceleration about the airfoil surface. This vortex; this was seen to be an important factor innet acceleration is composed of both a "static" ac- the trailing edge vortex development. By employingceleration component, derived from the mean angle of nonsinusoidal pitching motions or by oscillating theattack, as well as a "dynamic" component induced by airfoil about different chord locations, it may berapid, large positive-angle pitching of the airfoil. possible to minimize the trailing edge vorticalLeading edge vortical development required sufficient growth, thereby reducing the adverse separation ef-rean angles (12.90 to 15') under both static and os- fects. Such studies must be pursued over a widecillatory conditions. Though the magnitude of the range of experimental conditions if exploitation ofnet acceleration appears to be the most important pa- the phenomenon is to be realized.rareter for vortical development, data were insuffi-cient to define the exact contribution of the static Conclusionsand dynamic acceleration components. Qualitativeconsequences of each for overall vortical develop- Many investigators are currently involved inment were evident in both the flow visualization and attempts to formalize the treatment of unsteady ef-hotwire data. fects generated by an oscillating airfoil or by a

pulsating flow around a static airfoil.5, 6 , ,9 ,ll,15The vortical initiation, development, and inter- However, the complexity of unsteady effects hinders

actions dependent on net acceleration displayed the comprehensive characterizations needed for pre-quasi-steady, temporally synchronous flow character- cise formalization; in many instances, broad assump-istics when referenced to oscillation cycle. Air- tions must be substituted for missing experimentalfoil oscillation phase clearly provided the crucial data. The present studies represent an attempt todynamic acceleration component underlying this syn- more fully describe the unsteady effects generatedchrony. Without a strong dynamic acceleration com- by an airfoil oscillating in varying amounts andponent, nonsynchronous unsteady vortical development speeds about fixed angles of attack. The resultingdorinated the flow. At minimal oscillation angles flow disturbances were complex, and required the use(i1' to !3'), both vortical development and travel of rapid (Z 7 usec), repeated (Z20) photographic ex-were temporally and spatially determined by airfoil posures synchronized with the unsteadiness genera-oscillation phase. Pus both the oscillation angle tors (NACA 0012 or 0015 airfoils) to reveal bothand reduced frequency parameter were increased, the quasi-static and turbulent elements of the flow.ensuing vortical dynamics became even more predict- Across a variety of combined experimental parameters,able. The dominant factor again was the dynamic ac- most of the resulting flow disturbances were foundceleration component induced by the pitching of the to be predictably synchronized, both temporally andairfoil. The quasi-steady vortical generation must spatially, with airfoil oscillation phase. Thesebe referenced to the airfoil oscillation; without flow disturbances were carefully documented by visu-this synchronous reference to the airfoil oscilla- alization and hotwire anemometry.tion, the same vortical generation would appear ca-

pricious, and could be mistaken for unsteady turbu- The flow disturbances of the present study,lnt fl:. ! eparation when averaged over several os- though complex, fit along a single continuum. Stat-C lldtis, ic stall or dynamic stall achleved with very small

dynamic parameters was typically associated withWith; the airfo l at both small mean angles and flow disturbances qualitatively quite similar to

s-jll ill sition .rclle, roelhI ess synchr(;nc.us v'r- those o bserved with dvnamIc still achieved witht.:al ; '';.t,,t l:-.inat,! the fl(.w structure. In largte dynamic paranetero. The major difference was

-, :ane , the ';tsit c arcclratic:n cr- pun: nt, that with b: ..Ill p.irameLt 'rs, f!uw stru turv vxiiblt--.t: t o :..;n I ern: j-st ites, a;;, 'ared to ed wide var lit on, in li.at ion ind time whln etri-

;pt .'a1. 711- luuin; e'; and en.uinr. tra. lii edge pared to iny rel rcncc ,':i the acillaIlng alr:ai 1.r .. rt ai s:ruturL r .:r r:. .t d 'u. L -I at. - ita lare dIrv ) iniL teard:i't. bath ti. 10L .l oll

13

and the time of flow disturbances were quite predict- Referencesable and reproducible when referenced to airfoil no-tion. In a sense, the static and small dynamic sit- iMeCroskey, W.J., "Unsteady Airfoils," Annualuations elicit the most unsteady (or the least pre- Review of Fluid Mechanics, 1982, pp. 285-311.dictable) flows. In contrast, strong dynamic condi- :1 artin, J.H.,.Empey, R.W., McCroskey, W.J.,tions elicit flow-airfoil interactions that are pre- and Caradonna, F.X., "Experimental Analysis of Dy-dictable enough to invite further manipulation for namic Stall on an Oscillating Airfoil," Journal ofpurposes of practical exploitation, the American Helicopter Society, Vol. 19, No. I,

Jan. 1973, pp. 26-32.Two strong flow disturbances documented in the 3 Rossow, V.J., "Lift Enhancement by an Extern-

present study have received very little attention in ally Trapped Vortex," AIAA Paper 77-672, June 1977.the work of previous investigators.4 ,5 It is clear 4Ohashi, H. and Ishikawa, N., "Visualizationthat a major unsteady flow influence derives from Study of Flow Near the Trailing Edge of an Oscillat-the trailing edge vortex. We have shown that this ing Airfoil," Bulletin of the JSME, Vol. 15, No. 85,vortex is directly proportional in size and strength 1972, pp. 840-847.to the leading edge vortex that induces it. The 5Williams, J.C., "Flow Development in the Vi-co=only reported cataclysmic flow separation associ- cinity of the Sharp Trailing Edge on Bodies Impul-ated with oscillating airfoils1 1 most certainly is sively Set into Notion," Journal of Fluid Mechanics,dependent upon the genesis and subsequent strength Vol. 115, Feb. 1982, pp. 27-37.of the trailing edge vortex. The other frequently 6McCroskey, W.J., "Some Current Research in Un-unheeded flow disturbance is the massive leading and steady Fluid Dynamics, Freeman Scholar Lecture,trailing edge vortical interaction in the wake. 197.," Transactions of ASME Journal of Fluids Engi-This dramatic interaction perseveres for appreciable n 1977, pp. 8-39.time and distance in the wake. Although the 7 HcCroskey, W.J. et al., "Dynamic Stall Experi-strength of this interaction has not been character- ments on Oscillating Airfoils," AIAA Paper 75-125,ized, it may have serious implications for rotating Jan. 1975.blades and turbomachinery. 8McAlister, K.W. and Carr, L.W., "Water Tunnel

Visualizations of Dynamic Stall," Journal of FluidsAs noted above, these dynamically generated Engineering, Vol. 101, Sept. 1978, pp. 376-380.

flow structures should be exploitable through varia- 9Johnson, W. and Ham, N.D., "On the Mechanismtions in airfoil shape, airfoil motion, and, perhaps, of Dynamic Stall," Journal of the American Helicop-altered boundary layers. Such dynamically generated ter Society, Vol. 17, No. 10, Oct. 1972, pp. 36-45.flow structures should be analyzed through experi- 10Francis, M.S., Kennedy, D.A., and Butler, G.A.,ments on simple models. For example, current experi- "Technique for the Measurement of Spatial Vorticityments4 focus upon flow structure elicited by linear Distributions," Review of Scientific Instruments,flow acceleration past a fixed airfoil. A wide Vol. 49, No. 5, May 1978, pp. 617-623.range of vortical structures has been observed, and 'lCarr, L.W., McAlister, K.W., and McCroskey,in .7any instances these vortices interact from lead- W.J., "Analysis of the Development of Dynamic Stalling to trailing edge of the airfoil in a manner rem- Based on Oscillating Airfoil Experiments," NASA TNiniscent of the interactions observed in the present D-8382, Jan. 1977.study. Similarly, the initiation and development of 12 Helin, H.E., "Flow Visualization of Energizedvortices is being studied in our laboratories using Separated Flow Induced by an Oscillating Airfoil,"oscillating plates in a zero-flow environment. paper presented at the AIAA Region V Student Confer-These zero-flow studies show vortical interactions ence, St. Louis, Missouri, April 26, 1982.similar to those observed by both FreymuthJ4 and our- 13Robinson, M.C., Luttges, M.W., and Kennedy,selves. Thus, the vorticity that we observed to be D.A., "Discrete Audible Tone Generation from an NACAinitiated by flow acceleration may exhibit some sub- 0012 Airfoil," in preparation.sequent autonomy from that flow. The vortices, once 14 Freymuth, P., personal communication, 1982.formed, may be embedded in ongoing flow, but remain 15McCroskey, W.J. and Philippe, J.J., "Unsteadyrelatively independent of that flow. Finally, Viscous Flow on Oscillating Airfoils," AIAA Journal,through boundary layer control experiments in our Vol. 13, No. 1, Jan. 1975. pp. 71-79.laboratories, we have discovered that most of thestrong dynamically elicited flow structures are in-sensitive to either large pressure increments or de-crements introduced at the airfoil surface near thetrailing edge. Although these experiments are con-tinuing, it is quite clear that new experimentaldata on unsteady phenomena can be obtained. Thesedata should preclude much of the current need forspeculation and assumptions in formal treatments ofunsteady phenomena.

Acknowledgments

This work has been sponsored, in part, by theU.S. Air Force Office of Scientific Research, Crant 4F5IA 1k 6oJOI-'',, Dr. Xichacl S. Francis, Project Manager.The technical assistance of I. 11ulin, D. Sutcliffe,K. A.-rosich. L. Stodicck, C. Somps, C. Boyajian,an, J. Bvul is appreciated. The manuscript was pre-pared Ly L. Sweney.