Some Effects of Tip Fins on Wing Flutter Characteristics

8/12/2019 Some Effects of Tip Fins on Wing Flutter Characteristics

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N S T E C H N I C L N O T E NASA TN D 7702

-?

Hampton Va. 23665

SOME EFFECTS OF TIP FINS O NWIN FLUTTER CH R CTERISTICSby Robert C Goetz nd Robert V . Doggett Jr.Langley Research Cerrter

- +6.1e76N A T I O N A L A E R O N A U T I C S A N D S P AC E A D M I N I S T R A T I O N W A S H I N G T O N D . C. O C T O B E R 1974


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1. RapDrt No 2. Govmmrnt Accrrion No.NASA TN D-77024 Title n SubtitleSOME EFFECTS OF TI P FINS ON WING FLUTTERCHARACTERISTICS

7. AuthodsJRobert C. Goetz and Rober t V. Doggett, Jr

9. WormingOrgmintion Name nd AddrasNASA Langley Research CenterHampton, Va. 23665

National Aeronautics and Space AdministrationWashington, D.C. 20546

5 Supplementary Notes

~3 Raipimt s Catalog No

October 19746 M o rm ~n g rprnization Code

8 ?erforming Organization Repott No.L -9644

10. Work Unit No

11. Contract or G rant No.

13. Type of Repon and P a ~ doveredTechnical Note

14. Sponsoring Agency Code

6 AbstractA wind-tunnel investigation has been conducted over the Mach number range from about

0.6 t o 1.2 to determine the effects of l arg e tip fins on the flutter cha rac te ris tic s of a sweptwing. The basic wing configuration had an asp ect ra ti o of 0.95, leading-edge sweep of 400, andtrai ling-edge sweep of 21. Two of these configurations were modified with tip fins of 600dihedral and had effective aspect ra tio s of 1.5 and 2.2. In general, t he res ul ts indicate that theaddition of ti p fins reduces the f lut ter speed, with the la rg er fin having the grea te r effect.

Comparison of the experiment al flutt er s pee ds at Mach numbers between 0.60 and 0.90with calculated values obtained by using doublet-lattice unsteady aerodynamic theory was good.Analytical resu lt s where str uct ura l and aerodynamic effects of the tip fins were isolated i nl i-cated thxt the reduction in flutt er speed produced by the addition of the fins was caused by botheffects, with the structural effect being the more pronounced.

7. Key Words (Suggested by Authods)) 18. Distrlbutlon StatementFlutterTransonic speedsNonplanar surfaces

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STAR Category 329 . Security Classif. (of this report) 20. Securtty C l a d . (of this page) 21. No. of Pages 22. R I C ~

Unclassified Unclassified 31 3.25For a le by the National Tc hn ic d Information Service, Springfield, Virginia 22151


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SOM EFFECTS O T P FINS ON WIN FLUT TER CHARACTERISTICSBy Robert C. Goetz and Robert V. Doggett, Jr

Langley Research CenterSUMMARY

wind-tunnel investigation ha s been conducted ove r the Mach num ber ran ge fro mabout 0.6 t o 1.2 to determ ine the effect s of l ar ge tip fins on the flut ter ch ar ac te ris tic s ofa swept wing. The basic wing configuration had an asp ect ra tio of 0.95, leading-edgeswee p of 40, and trailin g-ed ge swee p of 21. Two of th es e con figu ratio ns we re modifiedwith tip fins of 60 dihe dral and had effec tive asp ec t rati os of 1.5 and 2.2. In ge ne ral,the res ul ts indicate that the addit ion of t ip f in s reduc es the f lut ter speed, with the la rg erfin having the greater effect.

Comp arison of the exp erimen tal f lut ter sp eeds at Mach num bers between 0.60 and0.90 with calculated values obtained by using doublet-lattice unsteady aerodynamic theorywas good. Analyt ical res ul t s where stru ctu ral and aerodyn amic effects of the tip f insw ere isolated indicated that the reduction in flu tter sp eed produced by the addition of thefins 'vas caused by both effects , with the stru ctu ral effect being the m ore pronounced.

INTRODUCTIONFo r the vehic le des igns emerging for spa ce t ranspor ta t ion sys tems, i t i s ev ident

that interact ive effects from both a s tead y and unsteady aerody nam ic viewpoint a r ebecoming mo re signif icant . These vehicle designs ar e combinations of m ult iple bodiesand l if ting sur faces ; the la t te r a r e d ic tated by requ i rem er+= or the maneuverabi li ty andthe stab ility and control during the asc en t, reen try , glidir. , and landing ph ase s of flight.Lif t ing-surface concepts that appear at t ract iv e for sat isfying these requ irem ents mayhave the fea tur e of nonplanar inters ectin g sur fac e sr.,aments. One such concept is aswept wing with la rge t ip f ins .

Wings wi th la rge t ip f ins a r e a concern to the aeroe las t ic ian s ince the i r s t ruc tura ldesign might be signif icantly influenced by f lut ter c learan ce requirem ents . For exam ple,if the m as s of the tip fin is not negligib le in rel atio n to that of th e wing alon e, the flut te rspeed i s modified by i ts pres ence . W hereas a change in mas s distr ibution is known tohave a lar ge effect on the f lut ter speed, the assoc iated change in aerodyna mic forc es m ayals o be a s ignif icant factor .


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Concern over designs where aerodynamic in terfere nce may be important to f lu t teris not new. when T-t a i l design s began to eme rge in the ear l y 1950ts , i t was quickly rec -ognized that a better und erstanding of ae rodyn am ic inte rfer enc e was needed to determ inethe f lu t ter chara cter is t ic s of these aerodynamical ly complex designs. Th is need resul tedin the development of unsteady aerodynamic theories applicable to T-ta i l6 such a s thosepresen ted in referenc es and 2. In addition to analyt icai s tudies som e experim entalT- ta i l f lu t te r re su l t s a r e ava ilab le . For example, se e re f s . 3 and 4 .) Another ar ea thathas receiv ed attention i s tandem-mounted wing- horizo ntal-tail configurations. Sev era lwind-tunnel-model flu tte r studie s have been conducted on wing-tail configurations, a nds o m e r e s u l t s a r e p r e s e n te d i n r e f e r e n c e s 5 and 6. Unsteady aerod ynam ic theo ries havebeen developed fo r application to wing-tail configurations. A kernel-function pro ced ureis presen ted in re fe rence 7, and the doublet-lattice method is described in reference 8 .Some exper iments1 f lu t te r re s u l t s a r e compared in re fe rence 6 with ana ly tica l re su i t sobtained by using both kernel-function an d doublet-lattice unsteady ae rodyn am ic methods.Addit ional com parisons between experimental and analyt ical resu l ts a r e presented inreferen ce 9 . However , a sea rch of the available l i ter a tur e indicated that the re ar e nopublished f lu t ter resu l ts in the range f ro m high subsonic to low supers onic speeds forwings with large tip fins.

Accordingly , the pres ent invest igat ion was undertaken to determ ine the importanceof the aerodynamic inte rfer enc e effects on the flutte r cha rac ter ist ics of a swept wing hav-ing a t ip f in and to compare experimental and analyt ical resul ts fo r subsonic flow obtainedfr om application of th e doublet -lat tice method.

The experimental program was conducted by using s im ple sem ispan models in theLangley 26-inch tran sonic tunnel over the M ach number range from about 0.6 to 1.2.Th re e model configurations w er e tested . The basic wing-alone configuration had anas pe ct rati o of 0.95, leading-edge sw eep of 40, and trai ling -ed ge sw eep of 21. Theother two model configurations had the same leading- and trailing-edge sweep angles, buttip fins with 60 of dihed ral with no toe-in) w ere added so that the resultin g m odels hadeffective aspect r a t io s o 1.5 and 2.2. All mod el confi gurati ons had 10-p ercen t-thickNACA 64-s er ie s a irfo i l sect ion s and wer e tes ted a t zero angle of a t tack. A coupled-modeflut ter analysis based on doublet- la t t ice unsteady aerodynam ics was perform ed fo r Machnum ber s of 0.60, 0.80, and 0.90 by using calc ulated mode shap es and m ea su red freq uen -cies ; the resu l ts of th is an alysis ar e compared with measured res ul ts .

SYMBOLSbr re fe rence semichord , mf frequency, Hz


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flutt er rrequency, Hz

frequen cy of sec ond natur al mode, Hzstr uct ura l damping coefficientMach numbermass , kdynamic pressure , ~ 2 ~ / m 2 kPa2velocity, meters/secondflutter-speed index para met er, vbrw2 lreference volume, m3ma ss - ra t io pa ram ete r , PVdensity, kg m3reference c ircula r frequency, 2nf2, rad /sec

Subscripts :c calculatede experimental

MODELSDescription

he basic model configuration (wing alone) used in thi s investigation was a s em i-span, aspect-ratio -0.95 wing with no dihedral and having lead ing -edg e sweep of 40 andtrailing-e dge sweep of 21. Two oth er models, con sistin g of thr bas ic configuration withtwo different lengths of wing-tip extensions added at a dihedral angle of 600, were testedin an effort to deter mine the effects of a tip fin on the flutter c har act eri sti cs of the basicwing. The fins had the sam e leading- and trailing-edg e sweep as the ba sic wing and were


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T he t o t a l m easu red m ass , na t u ra l fr equenc i e s f , and st r uc tu ra l damping g ofthe model s a r e g iven in t ab le I The na tura l f requencies , node l i nes , and s t i l l -a i r damp-i ng coe f f ic i ent s of t he f i r s t f ou r na t u ra l s t ruc t u ra l m odes w e re de t e rm i ned fo r a l l t h r e emodel s . The n a tura l frequi tncy for t he fu l l- f in -model f i f t h mode was a l s o de t ermined .T he ca l cul a ted and m ea su red f r equenc i e s and noda l pa t t e rn s a r e shown i n f i gu re 3 .T hese expe r i m en t a l da t a w e re ob ta i ned by exci ti ng t he m ode l s a t r e sonance w i th a n i n t e r -rup t e r a i r - j e t s hake r u s ing t he l g s and t echni que . F o r t he se t e s t s t he m ode l s w e rea t tached t o a m a ss i ve backs top . T he m oun ti ng a r r ange m en t w as e s sen t i a l l y t he s am e asthat used for mount ing the mode ls in the wind tunnel. Th e damping data w e re ob ta inedfro m the decaying osc i l l a ti on tha t resu l t ed when the pul sa t ing air j e t f r o m t h e s h a k e r w a sabrup t ly cut off . The ca lculated modal data we re obtained :,y using the NASA Struc tura lAnaly sis NASTRAN) Com puter Pr og ram . NASTRAN s desc r i bed i n de t a il i n r e f e r -ences 10 and 11 Quad r i l a t e ra l s t ru c tu ra l f in i t e e l emen t s NASTRAN QUAD2) we re usedto model t he s t ruc tur e for t he ca l cu la t ions . Thi r ty-s ix e l em ent s we re used for t he wingportion of all t h r ee model s ; 24 e l emen t s wer e used for t he ha l f -t ip - f in por t ion ; and60 e l emen t s wer e used fo r t he fu l l- t ip - f in por t ion . The ar rang eme nt of t he qua dr i l a t e ra le l em en t s is shown in f igure 4. A comp ar i son of t he ca l cu la t ed and measu red node l i nes

se e f ig . 3) i nd ica t es fa i r ly good agreement . Al though a l l t he f requencies ag ree r easo n-ably wel l, o rd inar i ly the bes t agre emen t would have been expected fo r t he ba s i c wing

or i en ted a t ze ro angle of a t t ack wi th re spec t t o t he f re e- s t r ea m f low. Th e two fin mod-e l s , r e f e r r ed t o he rea f t e r a s t he ful l- f in and half - f in m ode l s, had e f f ec t ive a spec t r a t i o sof 2.2 and 1.5, respec t ively. The effect ive asp ec t ra t io is de f ined a s t he sq ua re of t hesemisp an norm al i zed by the to t a l wing ar ea a f t e r t he f in has been ro t a t ed in to the p l aneof the wing. Both the wing and the f ins had 10-p ercent -thick NACA 64 -s er ie s ai r foi lsec t ions para l l e l t o t he flow. The f ins were re l a t ive ly l a r ge co mpa red with the wing;for t he fu l l- f in model t he f in p l anform a re a was about ha lf t ha t of t he bas i c wing, an d forthe ha l f- f in model t he f in p l anform a re a was s l i gh t ly l e s s than one- th i rd tha t of t he bas i cwing.

F i g u r e 1 i s a photograph i l l us t ra t ing the three model configurat ions . A ske tchgiving the geo met r i c pro per t i e s of t he model s i s p resen ted in f igure 2 .

Th e mod els we re of sim ple sandwich const ruc t ion, co nsist ing of a 0.2235- cm-thicka luminum-al loy core to which ba l sa wood was bonded with the gra in or i en ted perpe ndic-u l ar t o the core . The ba l sa wood was machined to g ive the des i r ed NACA 64A010 a i r fo i lshape . The a luminum-al loy core of t he model was a l s o used to suppor t t he model in acant i l ever fash ion a long the forward two- th i rds of t he model roo t. Res i s t anc e- types t r a i n gages w e re m ount ed on the m ode l c o re t o m e asu re m ode l dynam i c r e sponse .

P hys i ca l P rop e r t i e s and V i bra ti on C ha rac t e r i s t i c s


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model s ince th i s s t he s imp les t s t ru c tu ra l configura tion . However, be t t e r agre eme ntwas obta ined for t he two model s with ti p f ins which a r e s t ru c tura l ly m or e complex thanthe wing model . The bes t frequen cy ag ree me nt wa s obtained for the ful l-f in model .Al though no speci fic explanat ion i s avai lable, i t should be pointed out that so me un cer -t a in ty was in t roduced in to the ana ly t ica l model s ince i t w as ne cess ary to es t ima te thest i ffn ess pro pe rt ie s of the ba lsa wood and of th e adhesiv e used to at ta ch the balsa-woodcover ing to the a luminum-al loy core . The s t i f fness pro per t i es of t he a luminum wereknown, but it was n eces sary t o es t im ate the prope r t i e s of t he ba l sa wood and the adhe-siv e by use of typical values of s im i la r ma ter ial . The est im ated values of Young s mod-ulus used for t he ba l sa wood and for t he adhes ive we re 2 .83 GPa and 3 .45 GPa, res pe c-t ive ly. The adhes ive was assumed to be 0.056 cm thick.

FLUTTER EXPERIMENTSWind Tunnel

Th e investigat ion was conducted in the Langley 26 -inch t r ans on ic tunnel over theMach number range from about 0.6 to 1.2. Th is t rans on ic blowdown tunnel has a n octag-o na l t e s t s e c ti o n w hi ch m e a s u r e s 6 6 c z ac ro s s t he f l a t s and has s l o t i n each co rne r .The tunnel i s capable of opera t ion a t s t agnat ion pr es su re s up to about 517 kPa. Dur ingope rat ion of th e tunnel, the re of the or i f i ce (second minimum) i s p re se t a t a g ivenvalue; s t he s t agnation press ure , and thus the dens ity, s i ncreased , t he t es t -sec t ionMach number incre ase s un t i l t he or i f i ce becom es choked. The reaf t e r , a s t he s tagnat ionp r e s s u r e is fur th er i ncreased , t he Mach number rema ins approximate ly cons t an t . How-ever , t he a re a of t he or i f i ce may a l so be va r i ed du r i ng a t e s t run a s t he s t agna ti on p r e s -su re i s i ncreased , o r he ld cons t an t, s o tha t var ious opera t ing pa ths of Mach number anddensi ty may be followed. Both method s of ope rat ion we re used in the pr es en tinvestigation.

T e s t P r o c e d u r eThe model s t es t ed wer e mounted a t midheight on 7 .6-cm-diameter fuse l age

st ing (se e f ig. 5) which extended for wa rd into the low-speed region of the tunnel. Th isa r r angem en t p reven t ed t he fo rm a t i on o shock waves fr om the st ing nose which mightref l ec t f ro m the tunnel wal l s on to the model s. The s t i ng provided a r ig id mount for t h emodel s s ince the m as s of t he suppor t sys t em w as ve ry l a rg e comp ared with the m as s of

model. The fundamental freq uen cy of the suppo rt sy stem wa s about 6 Hz, well belowthe first na tur al freque ncy of an y of the mod els.

An opt i ca l sys t e m d i sp layed an image of t he m odel on a ground-g lass sc re en du r-ing the wind-tunnel tests . When flut ter w as obse rved visual ly, the ai rf low was quickly


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stopped in an effort to sa ve the model from being damaged s o that it could be utilized insubsequent test s. Before each te st run, with the model mounted in the tunnel, fre quen-cie s and damping coefficients for the fir st two natural modes wer e m easure d to be c e r -tain that the model had experienced no str uc tu ral damage, The tunnel stagnation pr es -sure , s tagnation temperature , tes t -section s ta t ic pressu re , and model s tra in-gagesignal s were continuously recorded on a direct readout reco rde r. Visual rec ord s of themodel motion were obtained through the use of two high-speed m otion-picture cam era s.

FLUTTER ANALYSISSubsonic flutte r calculations wer e made fo r al l three models over the M ach number

range from 0 60 t o 0 90 The flutter equations in matrix notation were expressed inte rm s of g enera lized moda; c oordinates, and the tradi tio nal V-g m ethod of solution wasused. The calculated natur al mode sha pes we re used in conjunction with the correspo nd-ing measured natural frequencies.

Flutter charac teris t ics for a l l th ree m odels w ere determined by using doublet-lattice unsteady aerodynam ic theory. The doublet-lattice unsteady aerodynamic force swere determined by using the method describ ed in refere nce s 12 and 13. The doublet-lattice method re qui res that the lifting su rface be subdivided into trapezoidal boxesarrang ed in stream wise columns. The arran gem ent of boxes used is shown in figure 6The same arrang eme nt was used for the wing portion of a ll three models. Th ere were50 boxes on the wing, 35 boxes on the half fin, and 50 boxes on the full fin. The two fin sshown in the figure have been ro tated down into the plane of the pape r s o that the viewis normal to these surface s. Fo r the doublet-lattice method, a line of acce ler atio npotential doublets is placed a t the one- quar ter-ch ord statio n of eac h box. An aerod y-namic influence coefficient matrix s generated which r elat es the f orc e on the boxes tothe downwash on the boxes. The for ce ac ts at the ane-q uar ter -ch ord point, and thedownwash point where the geo met rical boundary condition of tangential flow i s satisfi edis at the three- quart er-ch ord station. Both the force and downwash points ar e locatedat the box midspan station. The aerody nam ic influence coefficient i s used in conjunctionwith the mode shapes to determine a generalized aer odynamic force matrix.

Subsonic lifting-surface theory kerne l function) was a ls o used to calculate theflu tte r ch ar ac ter ist ics of th e basi c wing model at a Mach number of 0 80 The techniqueused to generate the kernel-function unsteady aerodynamic fo rces w as based on thatdescribed in reference 14. Fo r the kernel-function method, a linear integr al equationwhich rel ates the pres su re dis trib dio n to the downwash at selected control points on thelifting surfac e i s solved numerical:^ for the unsteady pr es su re distribution. The down-wash at the control points s a function of th e stru ctu ra l mode shape s used in the analy -sis The kernel-function method generat es di rectly a gen eralized unsteady aerodynamic

5

6


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forc e ma trix. Th irty- six control points were used in the kernel-function analy sis. Thelocations of the se points ar e indicated by the c irc ula r symbo ls in figure 6.

Since the aerodynamic models for the doublet-lattice and kernel-function methodswere different from the structu ral model compare figs. 4 and 6), it was nece ssary tointerpolate the modal deformations determined at the structural grid points to the modaldisplacements and stream wise slopes required at the aerodynamic points. This tr an s-form ation was accomplished by using the sur face spline function describ ed in re fe r-ence 15. Since the su rf ac e spline function i s based on the sm all deflection equation ofan infinite plate, it is very good for interpolating str uc tur al mode shape s. In interpo-lating the modes for the two mod els with tip fins, two spline functions were used. Onespline function was generated by using the modal displacements on the wing portion, andthe second was generated by using the modal displacements on the fin portion. Themodal deformations along the juncture between the wing and f i n portions were includedin the generation of both spli ne s to as su re continuity in the interpolation .

The V-g method of flut ter solution re qu ir es many solution s of complex eigenvalueproblem with the reduced frequency a s a para m eter and i s relatively expensive in te rm sof computer costs. Since one of the most costly pro cess es i s the determination of thegeneralized unsteady aerodynamic forces, it has become more o r l es s standard practiceto calculate the generalized aerodynamic fo rces for a relatively sm all number of valuesof the reduced frequency pa ram ete r and to interpola te these fo rce s for their v alues at ala rg er number of reduced frequ encies. Interpolated aerodynam ic fo rce s were used toobtain the calculated flutter resu lts presented in this paper. A natural cubic spline wasused to perform the interpolation. A disc uss ion of the use of cubic spli ne func tions foraerodynamic force interpolation is presented in reference 16. Fo r the doublet-latticecalculations, the aerodyn amic for ces w ere calculated at 6 values of reduced f;.equencyand interpolated to 50 value s of reduced frequency. Fo r the kerne l function, the re were20 calculated values and 400 interpolated values.

RESULTS AND DISCUSSIONThe basic experimental flutter resu lts a r e presented in table I1 and figure 7. The

d t presen ted in the figure include the variations with Mach number of the m as s- ra tioparameter p, of the flutt er -frequency ra tio f f f 2 and of the flutter -sp eed index pa ramet er VI. The flutter-speed-index-parameter curves represe nt stability boundaries,with the stable region no flut ter) below the curve. Th is pa ram ete r depends on the phys-ica l pro per ties of the model, in pa rtic ula r the stiffness, and the atmo sphere in which itopera tes. When plotted a s the ordinate against Mach number, c urv es of constant dynamicpre ssu re are l ines parallel to the Mach number abscissa. The ma ss-ra tio parameterp is defined a s the ra tio of the m ass of the model to the ma ss of a rep rese ntat ive


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surrounding volume of tes t medium. The volume used in thi s s tudy s that contained inthe conical f rus tum having base d iam eter s equal to the res pec t ive m odel root and t ipcho rds and a height equal to the s um of the individual spa ns of t he wing and tip fin po r-tions where the Bpan of the fin is mea sure d in the plane of the f in. The se volumes forthe wing, half-fin, and full-fin mo del s we re 2061.9 cm3, 2504.5 cm3, an d 2740.6 cm3,respectively. The second natural frequency f2 was used s the reference frequency.The sam e reference length br was used for a l l thr ee models . Thi s length o 6.26 cmwas the sem ichord at the three-q uart er-s pan stat ion of the wing port ion of the models.

No unusual t re nd s a r e shown by the data presen ted in f igure 7 fo r the half -fin andfull-fin models. Th e flut ter boundary is s im i la r to tha t usual ly observed, namely ,mo re o r le ss cons tant va lue a t subsonic spee ds fo llowed by a decr ease in f lu t te r -speedindex at t ranson ic Mach numb ers with a sh arp i ncr ea se in f lut ter-spe ed index s t heflow becomes supersonic. No experim ental f lut ter re su l ts wer e obtained for the basicwing model. T hi s m.odel did not flutte;: w ithin the avail abl e oper atin g ran ge of the windtunnel . At t ranson ic speeds this model was tested at dynamic pr es su re levels of about140 kP a which s considerably above the f lut t er boundary determ ined fo r the other twomodels.

In te rm s of the f lut ter-sp eed index par am ete r , com parison of the f lut ter bound-a r y f o r the half-fin model fig. 7 a)) with that of the full-fin m odel fig. 7 b)) would leadthe r ead er to bel ieve that the ful l-f in configurat ion s l e s s suscep t ib l e t o f l u tt e r . Th i sis not the true si tuat ion, however, s inc e the ful l-fin m odel f lut tered at lower dynamicpr es su re s than did the half-fin m odel over the Mach number range of the study. Nor-mal ly the f lu tte r -speed index param eter VI is success fu l in c or re la t ing f lu t te r da tabetween sim ila r configurat ions; however, thi s was not t rue fo r the wing-t ip configura-t ions fo r this s tudy. The variat ion o f lu t te r dynamic pre ssu re wi th Mach number fo rboth of th ese m odels is presente d in f igure 8. Both s et s of data show the s am e trend,namely, a mo re or le ss cons tant va lue at subsonic speeds , dram at ic dec reas e in thet ransonic range , and an increas e in va lue a t superson ic speeds . Fo r both models , thet ransonic minimum dynamic pre ssu re was about 4 5 pe rce nt of th e value at Mach 0.6.Although no f lut te r data w ere obtained for the b asi c wing model , it s known that i t s f lut-te r boundary is considerably above those of the mod els with f ins. As mentioned prev i-ously, th e wing model wa s teste d t t ranson ic Mach numbers to a dynamic pr es su re of140 kPa. There fore, i t can be concluded that the addit ion of the f in s to the basic winghas a s ignif icant adverse e f fect on the f lu t te r charac ter i s t ics . Fur ther , the la r ge r thef in, the gre a te r is the dec reas e in f lu t te r speed .

Exper imenta l and analy t ica l f lu t te r boundar ies for the two models wi th t ip f ins a r ecompared in f igure 9. The da t a a r e p r e sen t ed a s t he va r i at i on wi th M ad , number of t hef lu tte r -f requency ra t io and the f lu tte r -speed index parameter . The exper im,?nta l curv es


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shown a r e the fa i red curves f ro m f igure 7 Additional analytical flutter results, includ-ing basic wing model data , a r e pzesented in table 1II The calculated resul ts in the f ig-ur e wer e obtained by using a four-mode analysis with doublet - la t t ice unsteady aer ody-namic forces and the dens i t i es cor responding to the ex pe m t ~lica ~ l u e s . One ca lcu lat ionw a s m a de a t M 0 80 (se e table III(c)) for th e full-fin . . ,ode1 by ~i .?g five natural m odesin the ana lys i s . S ince th i s resu l t was a lmos t the sam e a s the four -mode resu l t , i t wasass um ed that the use of fou r modes was sufficient to ins ure convergence of the flut tersolut ion. Also, som e calculatcd f lut ter res ul ts ere obtained y using den si t ies differ-ent f rom the experimental values to as se ss the sensi t ivi ty of the calculated f lut ter s peed st o mass- rat io effects . Although the calculated f lut ter spe eds did indicate a sensitivity off lut ter sp eed to changes in density , no large effect was observ ed over the range of thestudy. In general , the calculated f lut te r resu l ts predict higher f lut ter l requencies andspe eds than we re found experime ntally. However, the agree me nt between the two se ts ofdata is considered to be good and shows that the doublet- la t t ice unsteady aerodynam ictheory can be used with som e confidence in predicting the fl utte r spe eds of wings withlar ge t ip f ins .

As has been observed, ther e was a marked reduct ion in the f lut ter speed when at ip fin was added to the bas ic wing model. Th is effect could be caused by both st ru ct ur aland aerodynamic effects. An analyt ical s tudy was made to sep ara te the aerodynamic andstru ctu ral effects , and the res ul ts of th is s tudy ar e shown in f igure 10 T h e d at a a r epre sen ted in the for m of the variation of f lutter dynamic pre ss ur e with Mach number forthe wing model, the full-fin model with no aerod ynam ic forc es actin g on the fin portion,and the full-fin model with aero dyna mic fo rc es acting on the fin. Additional calculatedf lu t te r resu l t s fo r all t h r e e c a s e s a r e p r e s e n t e d in t a bl e III All res u l t s p resen ted in thef igure wc re obtained by using the doublet- la t t ice unsteady aerodynam ic theory with theexception of a M 0 80 resul t obtained b:; using kernel-funct ion aerodynam ics for thewing model. It is interest ing to note that the kernel-funct ion and doublet- la t tice res ul tsa r e a lmos t the same. The ca lcula ted fu ll -f in model resu l t s a r e the same a s those pr e -sented in f igure 9(b). Flut te r ch ara cte r is t ics for the ful l -f in model without aerodynamicforc es on the f in (hereaf te r r e fe r red to a s fu l l f in wi thout ae rodynamics ) were ca lcu la tedby using a f ive-mode analysis and the densi t ies corresponding to the ful l- f in model expe r-iment, A check calculation at M 0 80 using only four m odes fo r th is configurationgave the sam e resul t a s wa s obtained by using five modes. (See table III(d).) Con se-quently, it can be ass um ed that th e flu tter solutions using five n10dc:j fo r the fu ll fin with-out aerodynam ics case have converged. The basic-wing-model resu l ts presented in thefigur e were obtained by using four modes and an a i r density of 2 701 kg/m3 Fo r boththe bas ic wing model and the full fin without ae rody nam ics c ase , additional calculationswe re made with densi ty a s a var iable to determine whether any s ignificant m ass -rat ioef fec t s were presen t . (See tables m (a ) and III(d). ) No signif icant ma ss-r at io effects


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were noted over the density range covered. An examination of the data in figure 10compare upper and lower curve s) indicates that the re is a very large decrease i n the

flut ter dynamic pr es su re with the addltion of the full fin to the bas ic wing model. Fo rexample, at M 0.60 this reduction is 77 percent and includes both aerodynamic andstru ctu ral effects, By removing the aerodynamic for ce s fro m the full fin, it is possibleto determine what proportion o the reduction in flutter dynamic press ure s due to thestructural changes which occur when the f i n i s added to the wing. The flutte r boundarywithout f i n aerodynamic fo rce s is shown a s the middle curve in the figure. This flutterboundary is sub stantia lly lower than the basi c wing boundary. At M 0.60 the flu tterdynamic pr es su re i s reduced by 63 percent. The results i n figure 10 ini tira te hat forthe configuration studied i n this investigation, the greatest proportion of the reduction influtter dynamic pr ess ur e was due to the stru ctu ral and in ertial changes pr.oduced by theaddition o the tip fin. However, although the aerodynamic e ff ec ts we re t:maller than thestructural effects, they were not insignificant. The aerodynamic effect was responsiblefor about 20 percent of the total decrease in flu tte r dynamic pre ssu re. It should benoted that the relativ e proportion of st ru ctu ral and aerodyn amic effects of tip fins onwing flutier c har acte ristic s would differ for other configurations.

CONCLUDING REM RKSTh e effects of th e addition of two different tip fins lasic wing have been deter-

mined experim entally over the Mach number rang e fro1 ~t 0.6 to 1.2. The bas icwing had an as pe ct ra ti o of 0.95, a leading -edge swee p ot -00, and a trailin g-e dg e sw eepof 21. Both the sma ll and larg e tip fins had a dihedral of 60 and, in te rm s of surfac earea , were one-third and one-half a s larg e as the basic wing, respectively. The rindicate that the addition of t he tip fins r edu ces the f lu tte r speed, with the la rg er Ziilhaving the gr ea ter effect. No unusual behavior was noted in the variation of the flu tterspeed with Mach number fo r the modela with tip fins.

Comparison of the e xperimen tal flutte r boundaries at subsonic speeds with calcu-lated r es ul ts ob tained by using doublet -lattice unsteady aerody nam ic theory was good.The res ult s of an analytical study where st ruc tura l and aerodynamic effects of the tipfins were isolated indicated that the reduction in flutter speed produced by the addition ofthe fins was caused by a combination of struc tura l and aerodynamic effec ts, with thestru ctu ral effect being the mo re pronoumed.Langley Research Center,National Aeronautics and Space Administration,

Hampton, Va., August 12, ^ 974


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REFERENCES1 Stark, Valter J. E.: Aerodyn amic F or ce s on a Com bination of a Wing and a Fin

Os cilla ting in Sub sonic Flow. SAAB TEJ 54, Sa ab A irc ra ft Co. (Link iping, Sweden ),Feb. 1364.

2. Davies, D. E.: General ized Aerodynamic Fo rce s on a T -Ta i l Osci l lat ing Harmoni-ca lly in Subr., ,ic Flow. R. M. No. 3422, B rit . A.R.C., 1966.

3. Stahle, C. V.: Tra nso nic Effects on T- Ta il Flutte r. RM-24, T re Mar tin Cb., Feb.1959.

4. Ruhlin, Cha rle s L.; Sandford, May nard C.; and Ya tes, E. Car son , Jr.: Wind-TunnelFlu tter Studies of the Sweptback T- Ta il of a La rg e Multi jet Ca rgo Airplane atMach Num bers t o 0.90. NASA TN D-2179, 1964.

5. Topp, L. J.; Rowe, W. S.; and Shattuck, A. W.: Ae ro ela stic Co nsid era tion s in theDesign of Variable Sweep Ae ro ~l an es . Aerospace Proce edings 1966, Vol. 2, JoanBradbrooke, Joan Bruce, and Robert R. Dexter, eds. , Macmillan and Co., Ltd. ,C. 1967, pp. 851-870.

6. Mykytow, W. J.; Noll, T. E.; Huttsell, L. J.; an d Sh irk , M, H.: Inv estig atio ns C:?cernin g the Coupled Wing-Fuse lage-Tail Flu tter Phenomenon. J. Aircraft , vol . 9,no. 1 Jan. 1972, pp. 48-54.

7. Laachka, Boris; and Schmid, Heinrich: Unsteady Aerodynamic F or ce s on CoplanarLift ing Su rfac es in Subsonic Flow (Wing Horizontal Ta il Inte rfer enc e). Jah rb.i967 WGLR, Hrirmann Blenk and Wer ne r Schulz, eds., c.1968, pp. 21 1-222.

8. Albano, Edward; and Rodden, William P.: A Doublet-Latt ice M ethod for C alculatingLift Distributions on Oscil lat ing Surfa ces in Subsonic Flows. AIAA J. vol. 7,no. 2, Feb . 1969, pp. 279-285.

9. Mykytow, W. J.; Olsen, J. J.; and Pollock, S. J.: App lication of AFF DL UnsteadyLoad Pred ict ion Methods to Interfer ing Surfaces. Symposium on UnsteadyAerodynamics for A eroelast ic Analyses on Interfering Surface s, Pt . IIAGARD-CP -80-7 1 Apr. 1971,

10. MacNeal, Richard H., ed.: Th e NASTRAN Th eo re tica l Manual. NASA SP-221, 1970.11. McCormick, Caleb W., ed.: The NASTRAN User s Manual. NASA SP-2 22, 19 70.12. Giesing, J. P.; Kalman, T P. and Rodden, W. P.: Subsonic Unsteady Aerodyn amicsfor Gen eral Configwat ions. Pa rt I , Val I - Dir ect Application of the Nonplanar

Doublet-Lattice Method. AFFDL-TR-71-5, Pt I Vol I, U.S. Air Force, Nov. 1971.


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13. Giesing J. P.; Kalm an T. P.; and Rodden W. P.: Subsonic Unsteady Aerodyn amicsfo r Gener al Configurations. P ar t I Vol II Com puter Pr og ram H7WC.AFFDL-TR-71-5 Pt. I Vol 11 U.S. A ir F or ce Nov. 1971.

14. Watkins C ha ri es E.; Woolston Donald S.; and Cunningham He rb ert J.: A Sys tem-atic Kernel Function P rocedur e fo r Determining Aerodynamic F or ce s on Oscilla t ingor Steady Fin ite Wings at Subsonic Speeds. NASA TR R-48 1959.

15. Hard er Robert L.; and Desm arais Robert N.: Interpolation Using Su rface Splines.J Aircraft vol. 9 no. 2 Feb. 1972 pp. 189-191.

16. De sm arai s Robert N.; and Bennett Robert M.: An Automated Proced ure for Com-puting Flutter Eigenvalues. J Aircraft vol. 11 no. 2 Feb. 1974 pp. 75-80.


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a)Half -f in modelf f z


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T BLE 11 EXPERIMENT L FLUTTE R RESULTS Concluded


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T

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F

RU

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Meh

umberm

Deac

Knuco

bHnm

Deac

Deac

Deac


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T

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RUCud

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Mehr

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tip

I--19.13-Figure 2 Model geometric properties All dimensions are in centimeters


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CalculatedExperiment

Mode 1: fe = 76 . 2 Hz f c 85.7 Hz Mode 2: f = 270 Hz f c = 251.2 Hz

Mode 3: f e = 490 Hz f c = 451.0 Hz Mode 4: f e m 766 Hz f c = 746.0 Hza) Basic wing model .

Figure 3 . - Measured and calculated node lines and natural frequencies.


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alculatedExperiment

Mode 1: f e = 40 .6 Hz f = 45.7 Hz Mode 2: f = 169.2 Hz, f = 170.9 Hz

Mode 3: f rn 217 Hz, f = 219.6 Hz Mode : fe 533 Hz, f = 514.0 Hzb) Half -fin model.

Figure 3. Continued.


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alculatedExperimentMode 1: f e = 29.2 Hz f = 31.4 Hz Mode 2: f e = 96.6 Hz f = 94.0 Hz

Mode 3: f e = 121.4 Hz 127.0 Hz Mode : f e = 350 Hzc) Full-fin model.igure 3. Concluded,


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Half fin

Full fin

Structural grid points

elements

WingFigure 4 NASTRAN structural model


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Half fin

Full in

WingFigure 6 Aerodynamic model


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2 14 6 8 1 0 1 2 1 4M

a) Half -fin model.Figure 7 . Experimental f lutter results.


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4 I I I4 6 8 1O 1 2 1 4Mb) Full f in model.

Figure 7 . Concluded.


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Theoryxperiment0 1 I I.4 .6 .8 1.0 1.2 1.4

Ma) Half-fin model.Figure 9. Comparison of calculated and experimen tal ilutter recu lts.


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heoryxperiment

b) Full-fin model.Figure 9. Concluded.


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Some Effects of Tip Fins on Wing Flutter Characteristics

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