Divergence of FSW

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NASA Techn'icalPaper 1685 c . 1 ',#1685

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Divergence-. f Forward-Swept ,Wings

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TECH LIBRARY KAFB, NM

N A S A Technical Paper 1685

Wind-Tunnel Experiments onDivergence of Forward-Swept Wings

Rodney H . Ricketts and Robert V. Doggett, Jr.Langley Research CenterHamptou , Virginia

National Aeronauticsand Space AdministrationScientific and TechnicalInformation Branch1980


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SUMMARYAn experimental study to investigate the aeroelastic behavior of forward-

tow speeds in air. Three models having the same planform but different airfoil2. Linear analyses were performed to provide predictions to

lated and evaluated t transonic speeds for accuracy in predicting staticTwo "divergence stoppers" were developed and evaluated for usen protecting the model from structural damage during tests.

INTRODUCTIONForward-swept wing designs appear to offer selected aerodynamic performanceimprovements over conventional aft-swept wings, such as higher lift-drag ratios,). In addition,hese designs may allow for improved fuselage-volume arrangements, by having themore rearward. Two powered, forward-swept wing aircraft, both

f German design, are known to have been builto take advantage of theseimprovements. These aircraft include the World War I1 vintage Junkersu 287(ref. 2) and a 1960's business jet (ref. 3 ) . Until recently, serious consider-to an unfavorable static aeroelastic characteristic, namely, static divergence(in this paper, referred o simply as divergence). Potential gains in aerody-

1970's, however, developments in composite structuresechnology appeared to offer a solution to the problem of structural massincreases required in the design of forward-swept wings. Analytical studies by4) showed that divergence speedsor forward-swept wings of compos-ite materials cane increased substantially by optimally tailoring (arranging)increases in structural mass above a so-called "strength design." As a conse-

.S. Air Force and the

(ref. 1).

'Freon: Registered trademark of E. I. du Pont de Nemours Co., Inc.


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The objectives of the present study are1 ) to provide some basic experi-mental data and analytical comparisons to aid in understanding divergencharacteristics of forward-swept wings; and (2) to develop wind-tunnel exmental procedures applicable to studying divergence.To accomplish the first objective, nine cantilevered wing models weretested in the Langley Transonic Dynamics Tunnel (TDT). Seven of these modelswere flat-plate wings tested to determine the effects of aspect ratio anleading-edge wing sweep on divergence speeds in the subsonic region,wo addi-tional models were constructed with different airfoil shapes to determineeffort of airfoil section on the divergence boundary in the transonic reIn this paper, the models are described, test results are presented, andculated results are presented for comparison with experimental results.The second objective was accomplished by developing and evaluating suical response techniques for predicting the divergence condition (dynamic psure) using response measurements made below divergence. In this paper, six

different methods are described, and an application of eachs presented. Twoof these methods were recently developed by Wilmer. Reed 111, and their deri-vations are presented in appendix. In addition, two divergence "stopper"devices were developed to prevent model damage if divergence occurs durintunnel tests. These two devices, a "flow-diver ter" and a "model-constraine'are also described.Use of trade namesr names of manufacturers in this report does notstitute an official endorsement of such productsr manufacturers, eitherexpressed or implied, by the National Aeronautics and Space Administration.

SYMBOLSAeakynamicmplitude, VIR aspectatio,(s/c)C strain-gageroportionalityactor,/degC chordength,C1 O lift coefficient at CI = 0cla lift-curve slopeCm, c moment coefficient about aerodynamic centere istance etween lastic xis nd erodynamic enter,frequency, Hz

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torsional spring constant, N-m/deglift per unit span, /mMach numbermoment about aerodynamic center, N-mmoment about elastic axis,-mcompression load, Ncritical buckling load, Ndynamic pressure, kPadivergence dynamic pressure, kPasemispan length, mangle of attack due to aerodynamic loads, degroot angle of attack, degangle of attack when me = 0 (E = 01, deg= aR - ao, degdeflection, nnninitial deflection, mmdivergence index parametermean strain-gage output, Vslope of E-versus-aR curve, V/degleading-edge sweep angle, deg (forward sweep is negative)air density, kg/m3

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TEST APPARATUS AND PROCEDURESModels

Geometry.- Seven semispan flat-plate wing models were tested duringstatic divergence investigation. All the wings were untapered and had a sespan length of . 508 m. In planform, the models differed only in aspect ratiand leading-edge wing sweep. The models had full-span aspect ratios of 4.08.0 and wing sweep angles of o, -7.5O (only = 8.01, -1S0, and -3OO. Theplanform geometries for these models are shown in figure.

Two additional models with 10-percent-thick airfoil sections were tesThese models had a planform identical to the flat-plate models with aspratios of 4.0 and wing sweep angles of1 5 O . One had a conventional airfoil(NACA 64A010); the other hadn uncambered (symmetric) supercritical airfoilsection.2 These two models, in conjunction with a flat-plate model with siplanform, were used to determine effects of airfoil sectionn the divergenceboundary in the transonic region.

Construction.- All the models were constructed of 2.29-mm-thick aluminualloy plate, For the flat-plate models, the leading and trailing edges wererounded to a semicircular shape. For the models with airfoil sections, a lweight plastic foam was attached to the aluminum plate and then shaped the desired airfoil section. Transition strips (No. 46 carborundum grit) withwidth of 0.025 chord were added along the 5-percent chord linen both the upperand lower surfaces of all the models to assure that the boundary layer wturbulentInstrumentation.- Each model was instrumented with resistance-wire strgage bridges located near the wing root. The bridges were oriented to betive to either bending or torsional strains.Vibration characteristics.- The first three natural frequenciesfirstbending, second bending, ndorsion - were measured for each wing model. Forcomparison, mode shapes and frequencies were calculated for the flat-platemodels using the PAR finite element structural analysis computer program(ref. 6). Both measured and calculated frequencies for the flat-plate modelsare presented in table I. The associated calculated node lines are shown infigure 2 and were substantiated by abbreviated measurements. In figure 2, thetorsion mode is the second mode for aspect-ratio-4.0 models, and the secon

bending mode is the third mode. This order is reversed for the aspect-ratio-8.0 models.

Model Mount and Divergence StoppersThe model wings were cantilever mounted outside the tunnel-wall boundlayer on an -beam support fixture attached to a remotely controlled turntab2This section was an early supercritical airfoil (designated NASASC(2)-0010) derived from the familyf cambered airfoils presented inreference 5 .

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A splitter plate was mounted to the support fixtureo provide a reflectionplane for the model. The turntable provided the capability of changing thewing angle of attack during the test. A photograph showing the model mountingarrangement is presented in figure .Because of the potentially destructive nature of aeroelastic instabilities,

precautions are commonly taken to minimize the risk of model damage duringtunnel tests. In the present study, two devices (each attached to the supportfixture) were developed for preventing excessive model deformations duringdivergence. These devices are described in detail in appendix A. One device,called a "flow-diverter" (shown inig, 4 ) , is simply a hinged plate thatdeflects the airstream when its deployed. Deflecting the airflow changes therelative angle between the flow and the wing leading edge and in effect rethe forward sweep, It is shown later that this situation yields higher diver-gence dynamic pressure. In addition, the dynamic pressures decreased by theshielding effect that the flow-diverter offers; that is, the wings exposed tolower velocities in the wake of the device. The other device, called"model-constrainer" (shown in ig, 5), consists of a pair of arms that are hingedothe support fixture at one end and have wheelsr rollers at the othernd,When this device is deployed, the arm swings out the span of the model, and twheels bear on the wing upper and lower surfaces to stiffen the model and reit to its undeformed hape, Both devices were demonstratedo prevent diver-gence from occurring at dynamic pressures at least3 percent greater than thewing-alone divergence dynamic pressure.

Wind TunnelThe present investigation was conducted in the Langley Transonic DynamicsTunnel (TDT). The TDT is a continuous-flow, single-return tunnel with a 4.88-msquare test section (with cropped corners) having slots in all four walls(ref. 7 ) . The flow is generated by a motor-driven fan. The tunnel is equipped

to use either airor Freon 1 2 as the test medium at pressures which vary fromnear vacuum to slightly above atmospheric. The range of Mach numbers is fromnear zero to1 .2 . Both the density and the test-section Mach number are con-tinuously controllable. The tunnel is equipped with four hydraulically acti-vated, quick-opening bypass valves. When model instability is encountered,these valves are actuated to rapidly reduce the dynamic pressure and Mach numin the test section.

Test ProceduresLow-speed tests.- Divergence tests of the flat-plate wings, evaluation ofthe subcritical response divergence prediction techniques, and evaluation ofthe divergence stoppers were conducted simultaneously in air at atmosphericpressure. For these low speed tests, the determination of typical divergencepoint proceeded in the following manner. With the angle of attack set at somelow positive value to keep the model lightly loaded insingle direction,the fan speed was increasedo the desired test-section dynamic pressure. Thisinitial dynamic pressure was chosen to be relatively far below the divergencecondition. At this dynamic pressure, data were collected to evaluate the sub-

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critical response methods. This process involved stepping the model through range of angles of attack and acquiring data at each angle. The model wasreturned to its original position, tunnel speed was increased to a slightlhigher dynamic pressure, and model response measurements were repeated. Thisstepwise increase in dynamic pressure was continued until divergence wasreached. When divergence Occurred, damage to the model was prevented eitherdeploying a divergence stopper (if one had been installed),r by actuating thefour bypass valves in the tunnel.

Transonic tests.- Tests conducted in the transonic regime used Freon2 asthe test medium. The following procedure was used to vary Mach number anddynamic pressure (shown in fig.). With the tunnel evacuated to aow stagna-tion pressure, the fan speed was increased until the desired maximum testnumber was reached. The dynamic pressure at this tunnel condition was rela-tively far below the divergence dynamic pressure. Subcritical response datawere collected at this tunnel condition in the same manner as described flow-speed tests. Next, while the Mach number was held constant, the test-section dynamic pressure was increasedy bleeding additional Freon2 into thetunnel through an expansion valve. When the desired dynamic pressure wasobtained, tunnel-flow conditions were held constant, and subcritical responsedata were again acquired, This process was repeated until either divergencereached or sufficient subcritical data were obtained to predict the divergecondition at this Mach number. During this process, the flow-diverter divergestopper was used to protect the model from damage.To define the divergence condition at another Mach number, the fan spewas decreased until the desired Mach number was obtained. With the Mach numagain held constant, the procedure of acquiring data and stepping the dynapressure was repeated in the manner just described. In this way, the divergenboundary was defined throughout the region of interest.Data acquisition.- During the tests, the output signals from the modelstrain-gage bridges were recorded on oscillograph strip recorders. The SpectraDynamics Corporation 330A Spectrascope (spectrum analyzer) was used to detefrequencies and peak amplitudes. The tunnel data acquisition system was usedcalculate and display the parameters needed for the subcritical response predtion techniques.

TEST RESULTS ND DISCUSSIONExperimental results acquired during the testing of models can be diviinto two categories: ( 1 ) data from model tests at low speeds in air, and(2) data from model tests at transonic speeds in Freon2 .

Low-Speed ResultsAll flat-plate models were tested at low speeds in air at standard aspheric pressure. Results of these tests are presented in figuresand 8 forthe aspect-ratio-4.0 and aspect-ratio-8.0 wings, respectively, as plots ofdynamic pressure versus wing sweep, Calculated flutter and divergence bound-

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Aspect-ratio-4.0 wings.- The calculated results presented in figureforthe aspect-ratio-4.0 models are similar to the results presented by Diederichand Budiansky (ref. 0) and show that two distinct instabilities, divergence andflutter, exist with varying wing sweep. As shown in the figure, the calculateddivergence dynamic pressure increases as the wing sweep changes from30 to Oo.Conversely, the calculated flutter dynamic pressure decreases as the wing sweechanges from 30 to Oo. The flutter mode is primarily wing first bending butcontains a small amount of coupling with torsion and second bending. The calculated flutter frequency for the unswepth = Oo) model is 18.5 z.

The measured divergence and flutter points shown in figureare in goodagreement with the calculations. The 15O and0 forward-swept models experi-enced divergence instabilities. The unswept model experienced a flutter insta-bility and had a measured flutter frequency of 21.0z.Aspect-ratio-8.0 wings.- Calculated results presented in figurefor theaspect-ratio-8.0 models appear more complex than results for the aspect-ratio-4.0 models. Three separate calculated instability boundaries are shown forthese wings: a divergence boundary and two flutter boundaries. Two of theinstability boundaries are similar to those described for the aspect-ratio-4.0wings. One is a divergence boundary in which calculated divergence-dynamicpressure increases as the wing sweep changes from30 to Oo. The other is theupper calculated flutter boundary in which the flutter dynamic pressuredecreases as the wing sweep changes from30 to Oo. This flutter mode isprimarily wing first bending but contains a small amount of coupling with sbending and torsion. The calculated flutter frequency or the unswept modelis28.9 Hz.The other calculated flutter boundary shows up as a "hump mode" in theanalysis. Traditionally, the hump mode is characterized by the damping-versus-velocity curve shown in sketch (a). This curve moves upr down with variationsin air density p . (At some densities, for example, p l , the hump mode lies

Sketch (a)totally below the zero-damping line and therefores not unstable.) In fig-ure 8, however, the humpappears for sweep anglessecond bending but has aing. Calculated fluttermodels are 48.1 and 47.9

mode seems to be a function of wing sweep and dis-greater than Oo. The flutter mode s primarily wingsmall amount of coupling with torsion and first bend-frequencies for the 7.5O forward-swept and the unsweptHz, respectively.7


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men tMeasured divergence and flutter points shown in figureare in good agree-with calculated results. The 5O and 30 forward-swept models experienceddivergence instabilities. The 7 . 5 O forward-swept model experienced a flutterinstability at 6 . 4 Hz that had the appearancef a second wing bending mode.( A node line existed near the wing tip.) This instability agrees with the cculated hump mode. The unswept model experienced a flutter instability withflutter frequency of 0.0 Hz. A region of significant response was observed,however, fram q = 4 . 1 to 6.2 kPa in which the primary model response fre-quency was about 5 . 0 Hz. This is probably a region of low damping for thehump mode.

Transonic-Speed ResultsThree models were tested in the transonic-speed range in Freon2 up toM = 0.9. The purposes of these tests were1 ) to acquire transonic data and( 2 ) to determine the effect of airfoil shape on divergence.l l these models

had an aspect ratio of. 0 and a wing sweep of15O. The models had threedifferent airfoil shapes flat plate, conventional, and supercritical. Infigure 9, the measured divergence dynamic pressure for each model is presenteas a ratio to the dynamic pressure at M0.6 for different values of Machnumber. As shown in the figure, the region of minimum divergence dynamicpressure, or the so-called "transonic dip," occurs at an appreciably lowernumber for the conventional airfoil than for the supercritical airfoil. Also,the width of transonic dip appears to be narrower for the conventional aithan for the supercritical airfoil. The flat-plate results show a decrease indynamic pressure in the transonic range, but a minimum was not observed. Anysis using linear aerodynamic theory shows a transonic boundary in good ament with measured flat-plate results. Linear theorys therefore useful forthe analysis of thin wings. For accurate analysis of thick wings in the tran-sonic region, however, a more sophisticated theorys needed.

SUBCRITICAL RESPONSE TECHNIQUES DESCRIPTION AND EVALUATIONSubcritical response testing techniques are frequently used in fluttertesting to predict a flutter instability before it occurs (ref.1 ) . Becauseflutter is often a destructive phenomenon, such predictive methods allow anapproach to the instability with a minimumisk of damaging the model. In manycases, confidence in these methods is high enough to define a flutter in

ity boundary without actually experiencing flutter.A similar procedure was desired or use in divergence testing. Thereforeseveral methods were investigated to predict static divergence based on thresponse of the model at dynamic pressures below the stability boundary. Thesmethods can be classified as either static or dynamic in nature. The staticmethods include inverse mean strain, Southwell, divergence index, and constanload. The dynamic methods include inverse peak amplitude and frequency. Forall these methods, data were acquired and analyzed in the transonic regioconstant Mach number with varying dynamic pressure. Inhis manner, shifts incenter of pressure due to Mach number changes were eliminated from the dat

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The s i x methods were eva lua ted on several models a t various Mach numbersw i t h similar r e s u l t s . For i l l u s t r a t i v epu rp os es , however, o n ly h e Mach 0 .8r e s u l t s f o r t h e a s p e c t - r a t i o - 4 . 0 f l a t - p l a t e m od elwith a wingsweepof -15O a rep r e s e n t e d . A t t h i s Mach number, t h e model ex per ime nta l lyd ive rged a t a dynamicp r e s s u r e of 2.52kPa.Discussionandevaluat ionofeach subcr i t i ca l methodf o l l o w s . Two new methods,divergence ndexandconstant oad, a re d e r i v e d nappendix B.

S t a t i c M ethodsThe basic d a t a t h a t were u se d i n t h e s t a t i c pred ic t ion m ethods are pre-s e n t e d n i g u r e1 0 . Data f o r a rangeofmodelangles of a t t a c k were a c q u i r e din he manner p re v i ou s ly d e s c r i b e d n h es e c t i o n "Test Procedures." A f i r s t -

o r d e r least-squares f i t was used t o c a l c u l a t e t h e slope X a n d h ea n g l e a0of heequa t ion E = X (aR ao) f o r h ed a t a a t eachdynamicpressure.I n v e r s e mean s t r a i n method.- One of th es im ples t p red ic t ion m ethods i s t h e

inve r se mean s t r a in ech n iq ue , which eva lu a te s hec h a n g e n h e e c i p r o c a l oft h e mean st ra inw i t h h ech an ge n dynamic pre ssu re .This method t a k e s advan-tage of t h e a c t h a t h e wing t i p d e f l e c t i o n , h u s , h e roo t bending moment ands t r a i n , e n d o w a r d n f i n i t y as t h ed ive rgencecond i t ion i s approached. Con-v e r s e l y , h e n v e r s e so f h e parameters tend oward ero a t divergence.There-fo re , thedivergencedynamicpressure i s t h e p o i n t a t which he nvers e means t r a i n i s zeroand i s p r e d i c t e d by e x t r a p o l a t i n g a second-order least-squaresfit of thes u b c r i t i c a ld a t a .B e c a u s e t h e d a t a most o f t e nd i s p l a y e d a "concaveup" s ha pe po s i t iv es e c o n dd e r i v a t i v e ) , h e i t was r e q u i r e d t o be "concave up"or l i n e a r n h e i m i t i n g case.

I n f i g u r e 1 1 , h e r e s u l t s o fapp lyi ng h is method a t model anglesof a t t a c kof 0.09O nd 0.17O a re presented .For hesecases , hepredic teddynamicpres-sure i s w i t h i n 4 percen t o f t h e measuredvalue.

Southwellmethod.-Thismethod was developedby R . V. Southwel l n1932 t op r e d i c t t h e c r i t i c a l buckling oadof a column oadedaxia l ly ncompress ion( r e f .1 2 ) . n1 9 4 5 , it was sugges ted by AlexanderF lax r e f . 13) t h a t h i smethodcould be used ins t u d y i n g a e r o e l a s t i c problems l i k e divergence. TheSouthwel lequat ion is

where 6 is t h e n i t i a ld e f l e c t i o nm e a s u r e d a t e r a l l y a t t h em idd leof hecolumn, 6 i s t he e f l ec t ionm easured from 6 fo r e a c h x i a lo a d P, andPC, is t h e c r i t i c a l buck l ing oad .Equation (1) i s similar i n form t o t h ee q u a t i o n h a tc h a r a c t e r i z e s h ee l a s t i c def l ec t ionofan a e r o e l a s t i c system as divergence i s approached. See,


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for example, eq. (B1Oa) ina p p e n d ix B . ) For he aeroelast ic sys tem he corre-spondingequationbecomes

where < is t h e n i t i a l wing root a n g l eo f a t t a c k , a, i s t h ea n g l e of a t t a c kdue t o aerodynamic load, q i s the ynamic ressure , nd q D i s t h e i v e r g e n c edynamic p re s s u re . When a e i s p r o p o r t i o n a l t o t h e model s t r a i n measurement &th rough he qua t ion a, = CE, where C is t h ep r o p o r t i o n a l i t y f a c t o r , equa-t i o n ( 2 ) can be p u t n h e o r m

which i s l i n e a r n & and /q w i t h slope q D . I n i g u r e 1 2 , d a t a are pre-s e n t e d n h i s form f o r t w o ang lesof a t t a c k . A f i r s t - o r d e r least-squares f i tof t h e d a t a was used to p r e d i c t h ed iv e r g e n c ed y n a m icp r e s s u r e( s lo p eo f h el i n e ) n h e s e cases. The pred ic tedv a l u e s a re w i t h i n 4 percentof hemeasuredd ivergencedynamicpressure .

An ad va nt ag e nus i ng h i s method i s t h a t h eb a s i cd a t a f i g , 1 0 ) o n l yneed to be a c q u i r e d a t a s i n g l ea n g l e o f a t t a c k . However, care m u s t b e a k e n nc h o o s i n g h i sa n g l e so t h a t h e a l l a w a b l es t r e n g t h o a d s o f h e model are n o te x c e e d e db e f o r e h ed iv e r g e n c ec o n d i t i o n i s i d e n t i f i e d .

The p re d i c t io n methodca n be improved i f a l l t h e ba s i c da t a ( f i g , 1 0 ) a r eu s e d n h em e t h o d . n h i s case, the method i s modif ied so t h a t h e s l o p eX (where X = / 6 ) o f h e bas ic d a t a i s u s e d n s t e a d of a v a l u eo f t r a i n a t as i n g l e n g l eo f a t t a c k . Equation ( 3 ) then becomes

I n f i g u r e 13, a r e s u l to f a p p l y i n g h i s m ethod i s p r e s e n t e d a s a p l o t of Xversus X/q. Again, a l i n e a r e a s t - s q u a r e s i t was used t o p r e d i c t h ed i v e r -gencedynamic pressure ( s lo p e ) , which i s l e ss than 2 p e r c e n t lower t h a n h emeasuredvalue.

Divergence ndexmethod.- The diver gence ndexmethod i s d e r i v e d i nappendix B. This method i s basedon he same e q u a t i o n as theSouthwellmethod;however, th e es ti ng p r o c e d u r ea n dg r a p h i c a lp r e s e n t a t i o n of t h e t e s t da ta a red i f f e r e n t . T h e t e s t procedure c o n s i s t s ofmeasuringm o d e l s t r a i n as t h ea n g l e

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of a t tack i s v a r i e d f o r a series ofconstantdynamicpre ssu res (shown i nf i g . 1 0 ) . A t each ynamic pressure qn, the slope An i s measured ndhedivergence ndex parameter An is computedrom the qua t io n

w hereh eubsc r ip t r denotes a r e fe rence ond i t ion ,w hich i s u s u a l l y associ-a t e dw i t h h e lowest va lueofdynamicpr es su re . The number of An v a l u e s h a tcan be c a l c u l a t e d i s 1 less t h a n h e t o t a l number of d i f f e r e n t d y n a m i cpressuresf o r a n y g i v e n r e f e r e n c e c o n d i t i o n .

A s shown in pp en di x B, A i s r e l a t e d t o q by the o l low ing quat i on:

A = 1 -(i)T h i s is a s t r a i g h t i n e which passes t h roughun i ty a t q = 0 a n d n t e r s e c t s h eq-axis a t hep r e d i c t e dd i v e r g e n c ed y n a m i cp r e s s u r e q D .

R e s u l t s of ap p l y i ng h i s method are p r e s e n t e d n i g u r e 1 4 . From the basicd a t a f i g . 101, fourva lueso f A were c a l c u l a t e du s i n g i v ev a l u e so fd y n a m i cpre ssu re . The d ivergencedynamicpressure was determined romequation ( 6 ) byapplying a f i r s t - o r d e r least-squares f i t t o t h e A v e r s u s q da ta nd a l cu -l a t i n g h eq - i n t e r c e p t . The l e a s t - s q u a r e s i t was fo rced h roughun i tya long heA-axis.The predicteddivergencedynamicpressure i s w i t h i n 1 p e r c e n to f h emeasuredvalue.

Th is method a ppe ars to g i v e accura te r e su l t s even forva lues ofdynam icpr es su re ar removed rom thed ive rgencecond i t ion .Th i s i s a t t r i b u t e d t o t h ei n c l u s i o n o f h e L i n t e r c e p t n h e d a t a . Much accu racy is g a i n e d n h el e a s t - s q u a r e s f i t by h a vi n g h i su n i t y p o i n t so far removed from t h e r e s t of t h ed a t a .

Constant-loadmethod.- The f i n a l s t a t i c method t o be d e s c r i b e d i s t h econstant-loadmethod, a lso der ived nappend ix B. I n h i s m et ho d, h eaerody- -namic oadmeasured by th es t r a i ng a g e s o n h em o d e l is h e l d c o n s t a n t as t h edynamic pressure i s increased oward a d ive rgencecond i t ion .T om ain ta in h i scons tan t oad , heang leof a t t a c k i s v a r i e d .

This method is basedon he same e q u a t i o n as t h a t u s e d i n t h e d e r i v a t i o n o fthedivergence ndexmethod. The eq ua t i o n or h i s method i s ob ta ined by rear-r ang ing equa t ion ( 3 ) :

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By de fi ni ng E t o be c o n s t a n t ,h e q u a t i o n i s l i n e a r n @ an d q . Thedivergence. ynamic pressure qD occurs when q?i i s e q u a l to z e r o or, i no t h e rwords, when crosses t h e- a x i s .

Inapp ly ing hecons tan t - loadmethod to t h e basic d a t a i n f i g u r e 1 0 , t h evaluesof E are determinedb y f i r s t e x t r a p o l a t i n g h e d a t a a t eachdynamicpressure to theno- load (E = 0 ) c o n d i t i o na n d h e nu s i n g h e e l a t i o n s h i pa = C~R- Qo. The r e su l t s o fapp ly in g he method are p r e s e n t e d n f i g u r e 1 5 .A l i n e a r e a s t - s q u a r e s i t was used t o e x t r a p o l a t e t o @ = 0 t o p r e d i c t h ed ivergencedynamicpressu re . The predic tedd ivergencedynamicpressure i sw i t h i n 1 percen tof hemeasuredva lue .

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DynamicMethodsI n a d d i t i o n t o t h e s t a t i c methodsprev ious lyexp la ined , two methodsof

ana lyz ing hedynamics igna lf rom hes t ra in -gagemeasurements were i n v e s t i g a t e dt o d e t e r m i n e h e i ra c c u r a c y np r e d i c t i n gd i v e r g e n c e .B o t hm e t h o d su t i l i z e d h espectrum ana lyzer to o b t a i n h e d a t a . T h emodel was t e s t e d a t a no-loadcondi-t i o n a n d was randomlyexcit ed by t h e airstream.

I n v e r s e p e a k amplitudemethod.-Thismethod i s b a s e d o n h e a s s u m p t io n h a tthedynamicamplitude of thedivergencemodel ends toward i n f i n i t y as t h ed iv e r g e n c ec o n d i t i o n i s approached.The nverse of t h ea m p l i t u d e , h e r e f o r e ,w i l l approachzero , A similar approach was f i r s t us ed by S a nd fo rd e t a l .( r e f , 1 4 ) to pred ic t t h e f l u t t e r i n s t a b i l i t i e s ofan a e roe la s t i c model.

Th ismethodofd ivergencepred ic t ion was a p p l i e d n h e f o l l o w in g m a n n e r .The da ta fo r he dynamicmethods were o b t a i n e d a t t h e same time as t h o s e f o r h es t a t i c method. A t eachdynamicpressure , a spectrum of hedynamic esponseofth e model i n a no- loadcondi t ion was recorded. Thewing f i r s t bend ing mode wasi d e n t i f i e d f ro m h e spectrum, and i t s p e a k response was m e a s u r e d . n i g u r e 1 6 ,r e s u l t s of a p p l y i n g h i s method are p r e s e n t e d . The i n v e r s e so f h e p e a k mea-surementsa re p lo t t e d a g a i n s t d y n a m i cpressure . The da ta were e x t r a p o l a t e dus ing a second-order l ea s t - squa res f i t t o pred ic t hed ivergencedynamicpres -sure , which i s t h ev a lu eo f h ep o in tw h e r e h e n v e r s ee q u a l sze ro , The pre-d i c t e dd i v e r g e n c ep r e s s u r e i s w i t h i n 2 percen tof hemeasuredva lue .

Frequencymethod.-Anothermethodwhichuses he spectrum of t he dynamicresponse i s b a s e do n h ef a c t h a t h e f req uen cy of thedivergence mode i s zeroa t d i v e r g e n c e . F o r h i s e a s o n , h e n s t a b i l i t y i s c a l l e d s t a t i c d i v e r g e n c e , )Frequencies rom spectrum d a t a a re used t o " t r ack" th e wing f i r s t -b en d i ng modefrequ ency rom he no-wind val ue t o zero .

I n i g u r e 17 , t h e r e s u l t of a p p l y i n g h i s m eth od i s p r e s e n t e d . A second-o r de r e a st - sq u a re s f i t was used t o p r e d i c t h e d iv e r g e n c e dynamic p r e s s u r ewhichoccurs when th e req ue nc y equals zer o. The predi cteddivergencedynamicp r e s s u r e i s w i t h i n 1 p e r c e n to f h e measured va lue .

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Remarks on Prediction MethodsIn general, the static methods seemed to consistently give better qualidata than the dynamic methods. The subcritical data from static methods weremore repeatable and showed less scatter throughout the dynamic pressure range

It was particularly difficult to acquire good quality frequencies and dynamamplitudes for data below. 0 Hz. The methods which use a linear fit of thesubcritical data for predictions werer e accurate than those which use asecond-order fit. The linear fit methods converged to accurate predictions morerapidly (farther from qD) than did the nonlinear methods. The Southwell,divergence index, and constant-load methods consistently yielded similar predictions. This situation appears to be true because the three methods werederived from the same basic equation (eq.2 ) ) , Of these three static methods,the Southwell data contained the least amountf scatter. Although the examplegiven previously in the paper shows that the inverse mean strain method isaccurate, other examples showed it to be conservative by underpredicting thedivergence dynamic pressure. This result may be due to the choice of thesecond-order curve fit for extrapolation. hyperbolic curve fit, for example,might be more appropriate.

CONCLUSIONSAn experimental study of the static aeroelastic divergence of forward-swewings has been described. Nine platedels, two of which had airfoil sectionsattached, were used in the study. The models were wind-tunnel tested at lowspeeds in air, and at transonic speeds in Freon2 to determine divergencecharacteristics. Subcritical response testing techniques for predicting diver-gence were formulated and evaluated.wo divergence stoppers were developed and

tested to determine their effectiveness in protecting a model at divergence.The important results follow:1. A divergence-stopper device, such as the flow-diverterr the model-constrainer, can be effectively used during divergence testing to help protecthe model from destruction.2. Linear theory accurately predicts the aeroelastic behavior, includingdivergence and flutter, of thin forward-swept wings. For accurate predictionsof divergence characteristics of thick wings in the transonic region, a morsophisticated theoryis needed.3. The aeroelastic divergence boundary can be accurately defined using scritical response testing techniques.

Langley Research CenterNational Aeronautics and Space AdministrationHampton, VA 23665June 16, 1980

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APPENDIX A

DIVERGENCE STOPPERSWind- tunnel tes t ing of aeroelast ic models o f t e n j e o p a r d i z e s t h e modelb e c a u s e n s t a b i l i t i e s s u c h as f l u t t e r a n d d i v e r g e n c e p r o d u c e a r g e , r a p i d l yi n c r e a s i n g model d e f o r m a t i o n s h a tc a n e a d t o s t r u c t u r a l f a i lu r e . I t is com-

mon practice, therefore, t o take p r e c a u t i o n s d u r i n g e s t i n g to minimize he r i s kof model damagewhen an aeroelastic i n s t a b i l i t y i s encountered. As mentioned i nthe bodyof the p a p e r , h e a p p l i c a t i o n of s u b c r i t i c a l r e s p o n s e t e s t techniquesi s one way t o minimize r i s k s . However, even ina p p l y i n gs u b c r i t i c a lm e t h o d s , itis usua l lynecessa ry to determine a t l e a s t o n e i n s t a b i l i t y p o i n t to v a l i d a t e t h emethod.

Another means of r educ ing he r i sk of model damage is to conduct aeroelas-t i c model s t u d i e s i n wind t u n n e l s h a t h a v e a means of r a p i d l y r e d u c i n g flowdynamic pressure.These methods i n c l u d e spoilers t h a t are dep loyed n t h e tun-n e l d i f f u s e r t o p r o v i d e a c h o k i n g ef fec t andvalve-pipingarrangements hat areused to s h o r t c i r c u i t t h e flow between he low-speed l e g of t h e t u n n e l a n d h ete st -s ec t i o n plenum hamber.T h e s p o i l e r is u s u a l l yv e r ye f f e c t i v e ,b u tb e c a u s el a r g e o a d s c a n develop o n h edevice when it is dep loyed , he spoiler isu s u a l l yu s e do n l y n small tun nel s . The valve-pip ingsystem is more applicableto l a r g e u n n e l s ( i .e . , theLangleyTransonicDynamicsTunnel )and does no thaveas much effect as t h e spoiler. However, inb o t h cases, t h e wind tunnelmust beequippedwith t h e d e v i c eb e f o r e it can be used .Both equi reextens ivemodif i -c a t i o n s to t h e u n n e l .

Othermethods of minimizing he r i s k of model damage in c l ud e ph ys ic a l l yr e s t r a i n i n g t h e model w i t h cables which are normally slack b u t become t a u t whenth e model de f l e c t i on each es a preset value .Al thoughsuch es t ra in tmethodsare u s u a l l y e f fec t i ve inminimizing model damage, t h e p r e s e n c e of cables d i s -to r t s t hef lowover t h e model and may change i t s aeroelas t ic character is t ics .

I n h e p r e s e n t s t u d y two d e v i c e s , or i n s t a b i l i t y stoppers, t h a t can be usedto prevent damage to aeroelast ic wind-tunnel models d u r i n g e s t i n g were devel-opedanddemonstrated uccessful ly.Bothdevices are mechanica l ly simple, capa-b le o f r a p i da c t u a t i o n a t any t e s t c o n d i t i o n ,a d a p t a b l ef o ru s e nany windt u n n e l , n o n i n t e r f e r i n g w i t h t h e f l a w f i e l d around t h e model ,a n d n o n i n t e r f e r i n gwi th t h e dynamic character is t ics of t h e model. Forpurposes of d i scuss ion ,on ed e v i c e i s referred to as t h e f low-diver ter ,and he other is r e f e r r e d to as t h emodel-constrainer . The purpose of t h i s appendix is to describe each of t h e s edevices .

Flow-Diver te r DeviceThe f l aw -d ive r t e r is i l l u s t r a t e ds c h e m a t i c a l l y i n f i g u r e s 1 8 and 19. This

d e v i c e was d e v e l o p e d o ru s e nd i v e r g e n c es t u d i e s of forward-sweptwings.Thesimplest form o f t h i s de v ic e is a h i n g e d p l a t e t h a t i s mountedupstream of t h e

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APPENDIX Amodel. I n thes toredposi t ion f ig . 1 8 ) , theplate is recessed i n the wind-tunnelwall , o r sp l i t t e r p la te , so tha t here is no aerodynamic interferenceproduced by theplate . For th in p la tes , a f l u s h mounting w i t h the wind-tunnelwall is sa tis fa ct or y. When t h e device is actuated f ig . 191, theplate isdeployed in to the air str ea m by a quick ac ti ng , remotely co ntr oll ed , pneumatic orhydraulicac tuato r. When theplate is deployed, the flow is dive rted over t h eoutboard portion of the model, which has he e f f e c t of reducing the sweep angleof the model. T h i s reduction i n sweep ang le ncreases hedivergence speed.Furthermore, the dynamic pres su re is decreased by the shie ldin g eff ec t tha t t h eflow -dive rter offers ; he wing is exposed t o lower v e lo c it ie s i n the wakeof thedevice.

For applications i n which the model is mounted off th e wind-tunnel wall ona sp l i t t e r p la te , two p la te s maye used (shown i n f i g . 20 ) . The inner platediver ts he flow behind the s pl i t te r pl at e so t ha t t he a i r i s channeled over theinboard port ion of the model through a hole i n th e sp li tt er pl at e. The purposeof t h i s inner plate i s to relieve he suction press ure behind the oute r plate,which functionsas hepreviouslydescribedsingle-platedevice, and to allow itto bemore effective i n turning he flow. I f a more gradua l urnin g of the flowi s required, a multisegment outerp la te can be used. A two-segment device isshown i n f igure 21 .

Both thesingle-plate ( f i g . 18) and the two-plate ( f i g . 20) flow di ve rte rswereused i n thepresent study. Both a pp lica tion s proved ef fe ct iv e i n rapidlyretu rnin g he model to an undiverged con ditio n. Although the s t a t i c deformationwas reduced, th e models d i d experience sane randandynamic response th a t wasapparently produced by turbulent f low off the edges of theoutboard plate. Therandm response was le ss fo r th e two-plate case, andwas notconsidered t o beexcessive i n eithercase.

Model-Constrainer DeviceThe model-constrainer, which is shown schematically i n f igure 2 2 , i s appli-cab le o both fl u t te r and divergence tes tin g. As i l l u s t r a t e d i n the igure, hedevice consists ofanarm that is hinged a t oneend to the spl i t te r p la te (ortunnelwall). A pai r of s o f t wheels, o rro l le rs , i s attached o heother endof the arm. When thedevice i s actua ted, he arm ro ta te s awayrom thewall,and the wheels r o l l along the upperand ower su rf ac es of the model, t h u sretu rning he model t o i t s undeformed shape and pr ev en ti ng ei th er st at ic ordynamicmodel defl ec ti on . The device is operated by a remotely controlled pneu-

matic,orhydraulic,actuator. To minimize erodynamic in te rf er en ce , thedevicecan be recessed i n the wind-tunnel wall, sp li t t er pl at e, orfuselage half-body,depending on theapp lication . Although the illu str at io nsa refo rappl ica t ion oa forward-swept wing, the device i s equ ally app licable to aft-swept wings foruse as a f l u t t e r stopper. For aft-swept wings, thedevice would bemounteddownstreamof t h e model.The model-constrainer was hown t o be very e f fe c t iv e i n res t raining themodelwhen divergenceoccurred. An advantage of t h i s device over the flow-di ve rt er was tha t th e models d id notexperience random exc it a ti on .

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APPENDIX B

DERIVATION OF Two METHODSFORPREDICTINGSTATIC DIVERGENCE OF

WINGS FROM SUBCRITICALTEST DATAWilmer H . Reed I11

Langley Research CenterI d e a l i z e d Aeroelas t ic System

I n h i sa p p e n d i x , a d e r i v a t i o n i s given fo r t h e e s t i n g e c h n i q u e s e f e r r e dt o i n t h e bodyof thepaper as the"divergence ndex"methodand he"constant -load" method.Thesemethods a re developedon he basis of a s i m p l i f i e d aero-e l a s t i c systemwhich i s assumed t o r e p r e s e n t a " t y p i c a l s e c t i o n " o f a f l e x i b l ewing. A s shown in i g u r e 23, t h e typical s e c t i o nc o n s i s t s o f a r i g i d a i r f o i lmountedon a t o r s i o n a l s p r i n g l o c a t e d a t t h e e f f e c t i v e e l a s t i c a x i s of t h es y s -tem, The base of he p r ing an be i n c l i n e d a t an ngle CIR r e l a t i v e t o t h eflow d i r e c t i o n as a meansf l i f t o n t r o l . The a n g l ee p r e s e n t sh e twistof t he p r ingdu e t o aerodynamic loads on thea i r fo i l . Thus, he e rodynamicang leof a t t a ck of t h e a i r f o i l i s t he ig id -bodyang lep lusan nc rem ent dueto a e roe la s t i c deformation

The l i f t f o r c e per u n i t p a n 2 a c t i n g a t t h ea i r f o i lc e n t e r of p r e s s u rean dt h e manent abou t the erodynamic enter mac are , r e s p e c t i v e l y ,

where by de f i n i t i on , is independent of a n g l e of a t t a c k .Thus, theaerodynamicmanent abou t t h e e l a s t i c a x i s i s

I+ = e2 + mac

where e i s thedis tancebetween heaerodynamiccenterand he e l a s t i c a x i s(e i s po si t i ve when theaerodynamiccenter i s forwardof he e l a s t i c a x i s ) .For a f l a t - p l a t e a i r f o i l i n tw o-d im ens iona l , ncanpressib le f l o w , c l l 0

and %,c are zero, nd quation (B4) becomes simply

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To retain the simplicity f this form of the moment equation for themore general case in whgch C Z , ~ nd Cm,aC are nonzero, it is convenientto introduce an angle shown in figure 23 and defined as-a = aR - a

where a is the rigid-body angleof attack for which the aerodynamic momentabout the elastic axis is zero. The value f a required to satisfy the con-dition me = 0 is, from equations (B2), (B3), and (B4), found to be

The general form of equationB5) now becomes

This is the aerodynamic moment about the elastic axis whichs balanced by thetorsion spring so that

Substituting equation (B8) into equation (B9) and solving for ae gives

where

(B1 a)

(B1 b)

Because the denominator of equation (BlOa) vanishes as+ qD, causing thetwist of the spring to become infinitely large, qD s the dynamic pressure atdivergence. Furthermore, because dynamic pressure s always a positive real

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APPENDIX Bquantity, equation (Blob) indicates that divergence can occur only when e0,i.e., when the elastic axis is behind the aerodynamic center.

From equation (BlOa) the divergence dynamic pressure maye expressed interms of the experimentally determined quantities q, or, and ae.

To relate divergence predictionsor an actual wing structure to thosederived for the idealized two-dimensional section treated here, the quantityae in equation (B11) is assumed to be proportional to the outputf a straingage on the wing structure which senses elastic deformation of the wing load as in the equation

A typical set f data taken during the testf a wing structures illustratedin sketch (b) The data are linear and have a slope1 such that

E

0

Px

0 aOSketch (b)

aR

Divergence Index MethodThe test procedure or the divergence index method consistsf measuring astrain-gage output as the anglef attack is varied at constant dynamic pres-

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APPENDIX Bsure. A series of such measurements are taken at successively higher dynamicpressures, Si, 92, . . ., qn, holding Mach number constant if mpress-ibility effects are significant. Letting be the slope measured at qnand using equations (B12) andB13), it is easily shown that

Letting x, and qr be values for a reference condition that s well belowthe xpected ivergence ondition, he atio s ormed o liminate Csuch that

where qr < qn < qD. Solving equation (B14) for qD yields

Thus, for each set of -versus-aR measurements taken at different values of,a new prediction of qD is obtained from equation (B16).To provide a convenient graphical display which further aids in the estmation of the divergence dynamic pressure from subcritical data, a so-called"divergence index" parameter is defined as follows:

Values of A are computed from the following equation:

An application of the equations to a set of subcritical datas illustrated insketch (c). When plotted against q, the parameter A decreases linearly withnegative slope (-9D-I and crosses the q-axis at divergence.

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APPENDIX B

1.0

A

"U

= 41

4Sketch (c)

When the measured data contain scatter, the accuracy of divergence prtion may be enhanced by applying the method of least squares. In this case, tunknown qD would be determined from a set of n equations (n > 2 ) whichrelate 91, 92, . . ., qn to the observed slopes x,, X2, . . ,, x,.Constant-Load Method

This method involvesvarying the dynamic pressure while controlling therigid-body angle CL so as to maintain constant strain measurement . A prac-tical advantage of this method over some otherss that it minimizes theisk ofoverloading the model as the divergence conditions approached during tests,Because the aerodynamic load is held constantae= Constant), from equa-tion (BlO) the derivative of c$i with respect to q, becomes

An illustration of this methods shown in sketch (a), which illustrates that@ versus q plots as a straight line with a negative slope ofae.iver-gence is indicated when @ = 0 , that is, when = 0 or, in other words, whenthe loadis developed entirely by the angle of attack associated with the aelastic deformation ae.

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APPENDIX B

0

E = C ons t an t

ae= 9 [

\'\

+

4Sketch (d )

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REFERENCES1. Forward-Swept Wing Potential Studied. Aviat. Week b Space Technol.,vol. 110, no. 5, Jan. 29, 1979, pp. 126-127.2. Holzbaur, Siegfried: Swept-Forward Wings. Interavia, vol. V, no. 7, 1950,pp. 380-382.3. Taylor, John W. R., ed.: Jane's All the World's Aircraft, 1970-71. McGraw-Hill Book Co. , c.1970.4. Krone, Norris J., Jr.: Divergence Elimination With Advanced Composites.AIAA Paper No. 75-1 009, Aug. 1975.5. Whitcomb, Richard T.: Review of NASA Supercritical Airfoils. ICAS PaperNO. 74-10, Aug. 1974.6. Whetstone, W. D.: SPAR Structural Analysis System Referenceanual - SystemLevel 1 1 . Volume 1 : Program Execution. NASA CR-145098-1 , 1977.7. Yates, E. Carson, Jr.; Land, Norman S.; and Foughner, Jerome T.: Measuredand Calculated Subsonic nd Transonic Flutter haracteristics of a 45OSweptback Wing Planform in Air and in reon-12 in the Langley TransonicDynamics Tunnel. NASA TN D-1616 , 1963.8. Watkins, Charles E.; Woolston, Donald S.; and Cunningham, Herbert J.: A Sys-tematic Kernel Function Procedureor Determining Aerodynamic Forces onOscillating or Steady Finite Wings at Subsonicpeeds. NASA TR R-48, 1959.9. Desmarais, Robert N.; and Bennett, Robert M.: User's Guide for a ModularFlutter Analysis Software System (FAST Version .0). NASA !I'M-78720, 1978.

10. Diederich, Franklin W.; and Budiansky, Bernard: Divergence of Swept Wings.NACA TN 1680, 1948.1 1 . Flutter Testing Techniques. NASA SP-415, 1976.12. Southwell, R. V.: On the Analysis of Experimental Observations in Problemsof Elastic Stability. Proc. Roy. S o c . (London), ser. A, vol. 135, Apr. 1,1932, pp. 601-616.13. Flax, Alexander H.: The Influence of Structural Deformation on irplaneCharacteristics. J. Aeronaut. Sci., vol . 12, no. 1, Jan. 1945, pp. 94-102.1 4 . Sandford, Maynard C.; Abel, Irving; and Gray, David L.: Development andDemonstration of a Flutter-Suppression System Using Active Controls. NASATR R-450, 1975.

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I I Measu red I C a l c u l a t e d 1A ' rndeg f 3 '2'l '3'2 'l 'Hz HzzzzZAspect r a t io 4.0

045.31.3 7.13.61.2.81546.52.2 7.54.21 -6.1

-

a7.2 42.80.56 .748.05.5

-3 0Aspect r a t i o 8.0

41.4 28.7 6.09.87.8.7 I-

0

60.43.2 7.06.41.2 6.61 560.05.5.37.2 42.8.97.559.86.3 7.49.8 43.8.0

-30 60.75.3.87.4 33.4.5aModel with 64A010 a i r f o i l contour .bModel w i t h s u p e r c r i t i c a l a i r f o i l contour .

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A = O o

Flow-. A = O 0

c = 0 . 2 5 4 m1

0A = -15 A = -3 0 0( a ) A s p e c t r a t i o 4 . 0 .

c = 0.127 ml - 4

A = -7.5 A = -15 0 0A = -30(b) Aspectratio 8 . 0 .

Figure 1.- Planformgeometry of theexperimental models.

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IIIt""IIIIIIIII'////////////////A

""0A = o

II"t-"I.iIi

A = Oo

Second mode

Third mode

0A = -15 A = -30 0'

(a) Aspect-ratio-4.0 models.

A = -7.5 0 A = - 1 5 0

(b) Aspect-ratio-8.0 models.A = -30'

Figure 2.- Calculated node lines for aspect-ratio-4.0 and aspect-ratio-8.0models. (Node lines for first mode are along the cantilever root.)

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L-78-1969F i g u r e 3 . - Typical modelm ou nte d o n s u p p o r t w i t h s p l i t t e r p l a t e n s t a l l e d .


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Figure 4.- Flow-diverterdevice nextendedposition orstoppingdivergence.


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6 7 8 - 4 2 9 1Figure 5 . - Model-constrainer device in extended position for stopping divergence.


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20 .o

10 o8.0

6 .O

4 .O4 3

kPa

2 .o

1 o.8

.6

Dive r ge nc e bounda r yq=?@v 4f/

//

0 .2 . 4 .6 .8 1 .o 1 .2M

Figure 6 . - Test procedure oroperation nFreon 12 i nLangley Transonic Dynamics Tunnel.

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g9kPa

lor EXPERIMENT0 l u t t e ra D i v e r g e n c e8 .

6 -

4 -

2 -

C a l c u l a t e d

-

-

- C a l c u l a t e dd i v e r g e n c e

S t a b l e

0 I I I I I-40 -30 -20 - 10 0 10

Figure 7.- Experimental instabilities (M < 0.3) for aspect-ratio-4.0wings compared with calculated boundaries.

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4,kPa

10

8

6

4

2

0

EXPERIMENT0 F l u t t e rA D i v e r g e n c e

C a l c u l a t e d

b o u n d a r i e s

S t a b l e

A

-40 -30 - 2 0 -10 0 10

Figure 8.- Experimental instabilities (M < 0.3) for aspect-ratio-8.0wings caupared with calculated boundaries.

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1.2

1 o48'M=O. 6

.6

. 4

EXPERIMENT0 F l a t - p l a t ei r f o i l"- C o n v e n t i o n a l a i r f o i l- - A - - S u p e r c r i t i c a l a i r f o i l

S t a b l e

.5 .6 .7 .8 .9 1 oM

Figure 9.- Canparison of divergence boundaries for flat-plate, conventional,and supercritical airfoil models. R = 4.0; A = -1 5 O.

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g = 2.39 kPa3 .2

2.8

2 . 4

2.0

1.6

1.2

. a

. 4

0

degR ,

.93 kPa

.125

Figure 10.- Basic data or subcritical response divergenceprediction techniques. R? = 4.0; h = -1 So; M = 0.8.

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2 . 4

2 . 0

1 .6

.8

.4

0

- -ct = 0 . 0 9 0qD = Intercept = 2 . 5 8 kPaI

-ct = 0.17'

= Intercept = 2 . 6 1 kPa - 4 \.5 2 kPa

.4 .8 1 .2.6 2 .o 2 .4. 8

4 9W aFigure 1 1 . - S t a t i c in ve rs e mean s t r a i n method for predict ing divergence.

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5

4

3

E , V

2

1

0

qD, exp = 2.52 kPa

-a = 0.09q D = S l o p e = 2 . 6 1 kPa

0

. 2 .4 . 6 .8 1.0E/q, V k P a

Figure 1 2 . - Sta tic Sou thw ell method for predictingdivergence.

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1.0

.8

. 6

.4

.2

0

D, exp = 2 . 5 2 kPa

qD = S l o p e = 2.49 kPa

.1 .2 .3 - 4 .5

x / q , (V/deg) /kPaFigure 13.- Improved s ta t i c Southwell method forpredict ingdivergence .

36


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1 . 2

1 o

.8

A .6

. 4

.2

0

q,, = Intercept = 2 . 5 1 kPa

5 2 kPa

(4,W aFigure 14 . - Staticdive rgenc e ndex method for predict ingdivergence.

37


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.7

.5

. 3

.2

qD = Intercept = 2.50 kPa

Figure 15.- Sta t ic con sta nt- l oad method for predic t ion of divergence.

38


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0 . 4 .8 1.2 1.6 2.0 2 . 4 2.84, kPa

Figure 16 . - Dynamic inverse peak amplitude method for predict ingdivergence .


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7

6

5

4

3

2

1

0 .4 .8.2.6 2 . 0. 4 2.84, kPa

Figure 17.- Dynamic frequency method fo r pr ed ic ti ng di ve rg en ce .

kPa

40


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Rem0t e l ycon t ro l l ed

Pneumat icactuator(hydrau l i c o re lec t ro -mechanicalactuatorsca n be used also)

Wind-tunnel wall

D i v e r t e r p l a t e

Figure 1 8 . - Flow-diverter device with diverter plate n retracted position.


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Air

Remotelycontrolledivot / / / /valve

Pneumatic actuator

Wind-tunnel wall ShaftI \ \ \ \ \

Wind-tunnel wall

Diverterplate

G?\ DivertedairflowFigure 19. - Flow-diverter devicewithdiverterplate nextended

p os i t ion to stop divergence.


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Pinnedshaf t o rpushro dwithr e t u r n s p r i n g )

Wind- t unne1

I n n e r d i v e r t e r

S p l i t t e r p l a t e

Model'Ui gu re 20.- Flow-diverterdevice w i t h a d d i t i o n a l p l a t e to d i v e r t

boundary-layer air .

I n n e r d i v e r t e r

S p l i t t e r p l a t e

O u t e r d i v e r t e rp l a te

Diver teda i r f lowUFigure 20.- Flow-diverterdevice w i t h a d d i t i o n a l p l a t e to d i v e r t

boundary-layer air .IpW


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Pinned shaft (orpush rod with spring)

Wind-tunnel wall Gear or linkage

diverter plate

Figure 21 .-Flow-diverterdevicewithsegmenteddiverter plate.


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Wind-tunnel wal l

"Sliding sleeve

Soft wheel(multiple wheels orro l ler sr eferab lein some appli catio ns)

\ UI \Tension springFigure 22.- Model-constrainer device for stopping divergence nretracted and extended positions.


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f 1

Wind

IFigure 23.- Idea l i zedaeroe la s t i c system.

I


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I NASA W-16851. Report No. I 2. GovernmentAccession No. I4. Title and Subtitle

WIND-TUNNEL EXPERIMENTS ON DIVERGENCE OFORWARD-SWEPT WINGS

-7. Author(s1Rodney H. R i c k e t t s and Robert V. Doggett , Jr. -9. Performing Organization Name and Address -NASA La ng le y Re se ar ch Ce nt er

Hampton, VA 23665

12. SponsoringAgencyNameandAddressNat ional Aeronaut ics and Space Adminis t ra t ionWashington, M: 20546

-

3. Recipient's Catalog No.5. Report Date . ~

Ausust 19806. Performing OrganizationCode

8. Performing Organization Report No.L-1354910. Work UnitNo.505-33-53-011 1 , Contract or Grant No.

13.Type of Report andPeriodCoveredTechnicalPaper14. SponsoringAgencyCode

15. Supplementary NotesAppendix B by Wilmer H. Reed 111, LangleyResearchCenter .

16. Abstract ~~~ iAn ex per im ent als t udy to i n v e s t i g a t e h ea e r o e l a s t i cb e h a v i o ro ff o r w a r d - s w e p tmodelswithvarying aspect rat ios andwing sweep a n g l e s were t e s t e d a t low speedsina i r .T h r e em o d e l sh a v i n g h e same p l a n f o r m b u td i f f e r e n t a i r f o i l s e c t i o n s( i . e . , f l a t - p l a t e ,c o n v e n t i o n a la n ds u p e r c r i t i c a l ) were t e s t e d a t t r a n s o n i cs p e e d sinF reon@l2 .L inea rana lyses were performed to p r o v i d ep r e d i c t i o n s to compare withthemeasured aeroelast ic i n s t a b i l i t i e s which i n c l ud eb o t hs t a t i c d ~ i v e r g e n c ea n df l u t t e r .S i xs u b c r i t i c a l e s p o n s e e s t i n g e c h n i q u e s were formulatedandevaluateda t r a n s o n i cs p e e d s fo r a c c u r a c y np r e d i c t i n g s t a t i c divergence . Two "d ivergencestoppers" were developedandevaluated or u s e i n p r o t ec t i ng he model rom s t ru c -t u r a l damage dur in g tests.

1 wings was co nd uc ted n heLang l eyTransonic DynamicsTunnel. even f l a t -p la te

17. Key Words SuggestedbyAuthor(s1 1 ~ ~~ ~A e r o e l a s t i c i t yDivergenceDivergence stoppersForward-sweptwingsS u b c r i t i c a lr e s p o n s e e c h n i q u e s -

19. Security Classif. (of this report) 20 . Security Classif. (of this page)U n c l a s s i f i e d U n c l a s s i f i e d

18. Distribution StatementU n c l a s s i f i e d - UnlimitedSubject Category 051 21 . Ni60f Pages 22 . PriceI A03

For sa le by t he Nat iona l Techn ica l n forma t ion Serv ice , Spr ingf ie ld , V l rg ln la 22161 NASA-Langley, 1980


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. .National Aeronautics and ' ' , ~ T H I R D - C L A S S BULK R A T ESpace Administration , I '_ .

, , ~ 'Washington; D.C. > .20546Offic ial Business

.Penalty' for Private Use, $300 - . .. .

i

1 1 IU,A, 0 7 0 8 8 0 S00903DS1 ' ,- DEPT OF THE AIR FORCEAF WEAPONS LABORhTORYBTTH: TECHNICAL L I B B A B Y (SUL)K I B T L A N D BFB NH 87117,

I , . \"

,Postage and Fees PaidNat ional Aeronaut ics andSpace Administrat ionN A S A 4 5 1

( ' I _ '

Divergence of FSW

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