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102 J.HYDRONAUTICS V O L . 10,NO.3

Rotating Cylinder for Circulation Control on anA irfoilJ.S. Tennant*FloridaAtlanticUniversity, BocaRaton,Fla.andW . S .Johnson and A .Krothapal l i JUniversity of Tennessee,Knoxville, Tenn.

T he lift a ug m enta t io n e f fec to f arota ting cylinder locatedat thetruncated trail ing edgeof abo dyi spresented.A sy m m etr ica lairfoil m o de l w i th a trai l ing-edge cy l inderw as tested in a lo w-speed wind tunne l , and the l iftproduced as a fun ction of cylind er speed was d etermined for cyl inder speeds up to three t imes the freestreamv e loc i t y .Since thel i f tw as atta ined at a 0 geom etric angle of a ttack, thel i f t - produc i ngp henom enon is called c ir-culat ion co ntro l , w h ich re sul t s f ro m th e a lteration of the wa ke reg io n by the s pinning cy linder .T h e lift co e f -f ic ient w as f o u n dto be a l inearf u n c t i o nof theratioo f cyl inder speed to freestreamvelocityan dreachedav a l u eof 1.20 at a speed ratioof 3 .0 . A com parison is made w i t ha lone spinning cyl inderin a crossflow magnuseffect )and the cy l inder- forebody co m bin a t io n repo r ted h ere in .T he cyl inder-forebody pair pro duces h ig h er va lueso fl i f t at ag i v e ncyl inderspeedand al inearresponsei nco ntra stto theno nl in ea r re spo nseof thelonecy l inderat lowcyl inderspeeds.

NomenclatureCL =l i f t coe f f i c ien tCp =su r face p r e s su r ecoe f f i c i en tU = local velo cityin thebounda ry laye rU cv l cylinder sur f ace speedU e velocity at the edgeof theb ou n d a rylayeri/oo = und is tu rbed f r e e s t r eam ve loc ityY =dis tance f r o m wa l l6 ' l o ca l bounda ry - laye r th icknes s = speed rat io Ucvl/Ux)

IntroductionCI R C U LA TI O N c o n t r o l by the use of a ro ta t ingcylinder as the t ra i l ing e lement in a cy l inde r - fo r ebodypair (Fig. 1) p roduces , in e f f e c t , an a u gm e n t a t i o n of thewel l -known m a gn u s e f f e c t f o r ro ta t ing cy l inde r s a lone . L i f t isachieved on the body combina t ion by an a d j u s t m e n t of thet ra i l ing wake which is in i t ia ted a t the loca t ion o f thesepara t ion points on the u p p e r and lower sur faces of thebody. By mea ns o f boun dary -lay er contro l , these separa t ionpoints are m o v e d , and the wake t ake s on a new t ra i l ing direc-t ion. Although th e boundary-layer contro l descr ibed here ini sby moving wall , i t could be ach ieved by o ther means , such ast angen t ia l s lo t b lowing or area s u c t i o n .T he u n iq ue a spec t o fth is cy l inde r - fo r ebody l i f t ing dev ice is tha t l i f t may beproduced by a symmet r ic a l body at zero angleo f a t t a c k , andth e a m o u n t o f l i f t can be contro l led by va r ia t ion in theamount o f boundary-layer contro l applied . In the case o fmov ing wa l l bounda ry - lay e r con t ro l , t h e amou n t o f l i f t isrelateddirectlyt ocylinder rota t ional speed.An a l t e r a t ion o f th e wak e f low grea t ly changes thee f f e c t ivebody shape as "seen" by thepo ten t ia l f low field s u r r o u n d in gth e body and i ts v iscous sur face boundary layer . In order tocause the po tent ia l f low b es t to descr ibe the external f low withthe a l te red wake, it isnecessary to add c ircula t ion to thenon-c ircula tory so lu t ion . O f cour s e , l i f t then can be ca lcula ted bythe Ku t t a - Jou kow sk i th eo r em, and thus w e have th e name c i r -

Tra i l ing-edge blowing for c ircula t ion contro l with bluf fbodies has been repor ted by severa l inves t iga tors , inc ludingN e u m a n n 1 a n d K i n d .2 More r ecen t ly , Ambros ian i3 presen-ted an analy s is o f an e l l ip t ica l a ir f o i l with c ircula t io n contro lby blowing based on modern com puta t ional techniques .Wal te rs 4 reported a series of wind- tunne l tests of camberedelliptical a ir fo i ls with c ircula t ion contro l by blowing andrepor ted re la t ive ly h igh l i f t c oef f ic ie nts a t low blowing ra tes .L o t h 5 repor ted th e succe s s fu l app l ic a t ion of the concept o fcircula t ion contro l to a small STOL a i r c r a f t . A s tudy byW a g n e r ' combined bo th area suct ion a n d t angen t ia l b lowingon as ingle model and f o u n d th ee f f e c t s ofbothto be addi t ive.His measu r emen t s ind ica ted tha t s ignif icant increases in l i ftcould beobta ined.Only l imited work on circula t ion contro l by moving wa l lhasbeen repor ted in thel i t e r a tu r e .F or examp le , B r o o k s6 per-f o r m e d an exper imenta l s tudy o f c ircula t ion contro l due to aro ta t ing cylinder at thet ra i l ing edge o f ahydro fo i l in a wa te rtunne l . H e emp loyed a 1 .9-cm-diam cylinder with a sym-me t r ic a l hydro fo i l h av inga chord of 14 cm and aspano f 6 .35cm and measur ed l i f t coe f f i c ien t sa t speed ratios up to 1 .64,whe reh eobta ined a va lueo f 0.22 a t zero angle o f a t t a ck . T hemode l had a largegap (abou t0 .15 cm) between th e f ixed andmoving su r face s and was opera ted at a Reyno lds number ofa b ou t 1.3x 106 based on model chord.L ee 7 pe r f o rmed w ind- tunne l s tud ies of a submar ine s a i lp lane model with a ro ta t ing cy l inde r at the t ra i l ing edge f o rcircula t ion contro l . This model had a cylinder diameter of16.2 cm, an overa l l chord of 165 cm, and a span of 117 cm .Resu l t s inc luded ove r a l l measu r emen t s of l i f t , p i t ch ingm o m e n t , and y a w in g m o m e n t as a f u n c t i o no f cylinder speedand geometr ic angle o f a t t a ck . The gap be tween f ixed andmoving su r face s w as around 0 .17 cm, and tes ts were un -de r t akena t a Reyno lds numberof 3 x 106 .The spec i f i c ob jec t iveo f th is s tudywas to de te rminet he l i f tproduced by moving wall c ircula t ion contro l on a two -d imens iona l mode l as a f unc t i o n of the wall ve loci ty and to

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J U L Y 1 9 7 6 C I R C U L A T I ON C O N T R O L O N A N A I R F O I L 10 3F i g . 1 Mod el crosssection. F L O W

a trailing-edge cyl inder, as shown approximately to scale inF i g . 1. The model had a 47-cm chord, a ma x imum thicknessof 11.4cm, anoseradius of 3.2 cm, and w as mo unted at zeroangle of a t tack between the top and bot tomwal ls of the testsection to s imulate two-dimensional condit ions . Thin steelstrips wereused at therearof the model so that the resultinggap at the point of tangency between the fixed and movingwall would be small and could be adjusted over a narrowrange . T he 7.6-cm-diam hollow a luminum cylinder w asmounted on a center steel sha f t and was rotated by a 1-hpvariable-speed electricmo to r ,which wascapableo fspeedsu pto 25,000 r p m . A total of 40 static pressure taps were spaceda r o und th e midspan of the body except, of course, on themovingsu r face .Lift DeterminationT he li f t force producedby cylinder rotat ionw asdeterminedby th e integration of measured s tat icpressuresover th e f ixedwall por t ionof themodel.A suitableextrapolat ionw asmadef or the moving wal l por t ion , which const i tu ted only a smallfraction of the mode l chord . All data were t aken at a -f rees tream velocity of 20m/sec, which produced a Reynoldsnumber o f 6.4xl05 based on the model chord . T he wal lvelocity was varied up to around three times the f rees treamvalue, and the gap between f ixed and moving surfaces wasvaried f rom 0 . 0 4 to0.12cm .Flowfie ld ExaminationIn order to obtain a better unde rs t and ing of the f lowphenomena involved, the f lowfie ld a r o und th e body w asexamined by three d i f f e r en t procedures . These were : 1)visual iza t ion of the wake region using a smoke probe , 2)measurement of boundary- layer velocity profiles on themoving surface, and 3)determination of the shift in forwards tagnat ion point caused by thecylinderro ta t ion .The smoke probe was used in order to correlate wa k ebehavior wi th cylinder speed. Extensive pho tographs of thisregion were taken, and the st reamline pat tern was evident invirtually every case. The smoke probe also was used toexaminetheregionof in tersec t ionbetweent hemode la nd t u n -nel wall f or secondary f lows, which could destroy the t w o -dimensional nature of the resul ts . Thesestudies led to the in-clusion of a fillet a round the model-wall intersection whichvirtually eliminatedsecondary f low inthis region.A 0.04-cm-diam bounda ry - l aye r total pressure tube w asused to determine velocity profiles on the moving surface ap -proximate ly 2 cm downs t r eam of the f ixed forebody . Thesemeasurements wereunde r t aken todemons t r a tehow thebo un -dary layer is energized by m om e n t u m t r a n spo r t f r om th emov ing wal l .The displacement of thef o rwa rdstagnation pointa s afunc -t ion of cylinder speed illustrated the relationship between therotat ingcylinderand the circulat ionab ou t th e entirebody . Aunique procedure involving a moving tu f t was employed todetermine the s tagnat ion-point locat ion. This procedure in -volves the a t tachment o f a single t u f t of very f ine thread to af la t r i bbo n , w h i c h was guided chordwise a rou n d th e body toeyeletsnear the trailing edge, an d then bo th endswere routedoutside th et unne l to an opera to r . The opera to r could t rans-

2.0 -

1.0

0.0

-1 .0

- 2 . 0

O 0 0 G

0.0 0.2 0.4 0.6 0.8 1.0

F i g . 2 A typical surface pressure distribution 03 3 . 1 1 , gap = 0 . 0 4c m ) .1.41.2i . o0 .80 .60 .40 .20 .0

G A P = 0 4 c MA G A P = 0 8 c wH G A P = 12cM

0.0 0,5 1 ,0 1 ,5 2 ,0 2 .5 3,0 3,5

F i g . 3 Li ft coeff ic ient vs the ratio of cyl inder speed to freestreamvelocity .0.60.50.40, 30,20,1

0,0 0 1 2 3 4 5 6

F i g . 4 Co m pa r iso nw i t hdatafrom Re f.7 .byi n teg ra t i on . The l i ft coef f ic ien t producedby the mo del as afunction of cylinder speed is given in F i g . 3 for each of thethree gaps tested. It generally isas sumed tha t an increase inthe gap between f ixed and moving walls should decrease theeffectiveness of moving wal l boundary-layer control byremoving the high-speed f lu id a t the movingwal l far ther f romthe low-velocity region in the boundarylayer wherecontrol isdesired. In f ac t , for the caseo f acyl inderat the leading edge,Johnson andT e n n a n t8m easured as igni f icant ga pe f f e c t .It should be noted tha t th e model produced relatively highwind- tunne l blockage (16 ) a n d , consequent ly , the ex-9

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4 T E N N A N T ,JOHNSON,ANDK R O T H A P A L L I J.H Y D R O N A U T IC S

0, 0 0 ,2 0 .4 0 . 6 0 ,8 1 .0

PLEMENT

STGNTI

1 00

0 . 7 5

0 . 5 0

0 2 5

n .n

f

\ . ...0.0 1.0 2 0 3,0UCVLnr

F i g . 8 Measureddisplacemen t in forward stagnationpo in t .

F i g . 5 Movingw all boundary-layer velocity profiles .

F i g . Smokephotographyo f w a k eregion j8 = 2.14).

6=0 0

F i g . 7 S c h e m a t i crepresentation o f w a k eregion for v ar ious cy l in-de r speeds.

A compar i son also can be madewi th th edata o f B r o o k s ,6w ho reported a l i f t coe f f i c i en t of 0 . 2 2 at a speed rat io of 1.64.T hecor responding va lueat the samespeedra t i of r o m thedatain F i g . 3 appropr i a te ly adjus ted to the s a m e aspect ra t i o is0 . 1 6 , w h i c h is r ea sonab ly c lo s e , con s ider ing t h a t th e mode lswere no t very similar indes ign .

2 5

2 0

1,51.00, 5

M E A S U R E D P R E D I C T E D

1.0 3,0

F i g . 9 Forw ard s ta g na t i o n- po i nt d i s p l a cement v s l i f t co e f f i c i ent byD o u g l a s - N e u m a n n m e t h o d ) .g r a d i e n t . It h a s been shown by s eve ra l i n v e s t i ga to r s1 0 1 2 t h a tsucha f l ow reversa ln e a r a mo v i n gwa l lis , ine f f e c t , b o u n d a r yl ayers e p a r a t i o n .W a k e O bs erva t i o ns

N u m e r o u s obse rva t ions and pho tographs o f th e wakeregion were m a d e w i t h a s mo k e p r o b e loca t ed j u s t ups t reamof the mov ing wal l adjacent to the f ixed s u r f a c e . A t yp ica lp h o t o g r a p hi s shown in F i g . 6 for a speed ra t ioo f 2 .14 . F igu re7 rep resen t s an a t t e m p t to charac t e r i ze th e w a k e reg ion fo rv a r i o u s va lue s of the ra t io o f cy l i nde r su r f a ce speed tof rees t ream veloci ty . I t i s observed t h a t f low s epa r a t ion occur snear the in t e r sec t ion o f t he f ixed and mov ing wa l l s w h e n thecyl inder is not r o t a t i n g . Th i s po in t o f s epa r a t ion sh i f t s as thecyl inder speed isin c reasedu n t i l it reaches th emode l c e n te r l i n eat aspeed rat ioo fa r o u n d 4 . 0 .S t a g n a t i o n - P o i n t Lo ca t i o n

The lateral displacement of the f o r w a r d s tagna t ion po in t a smeasuredby th e mov ing t u f t technique is shown in F i g . 8 as af unc t ion of the ratio o f moving wall ve loci ty to frees treamveloci ty . The relat ionship i s l inearover the range of thedata,with some sca t te r at low speed ra t i os , w h e r e th e s h i f t w as d i f -f i cu l t to read prec ise ly .F igure 9 p resen ts a predic t ion of thes t agna t ion point location as obtained f r o m a po ten t i a l f lowanalys is . T he body con f igu r a t ion w as i n p u t to the Doug las -N e u m a n n potent ia l f low p r o g r a m ,1 3 and the e f f e c t of thecylinder was s imula ted by the impos i t ion o f var ious a m o u n t so f c i rcu la t ion on the so lu t ion . T he var i ed c i rcu la t ionproduced a correlat ion between l i ft coef f ic ient ands tagna t ion-po in t d i sp lacemen t , as s h o w n . The co r respondingexpe r imen ta l lyde te rmined co r r e la t ion also is shown in F i g . 9 ,and the close agreement be tween predic ted and measured

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JULY 1976 C I R C U L A T I O N CONTROLO N A NAIRFOIL 1058 0

6 0

4 0

2 0

0 0 0 ,0 0 .5 1 ,0 1 ,5 2 ,0 2. 5 3, 0 3 ,5

Fig. 10 Comparison of cylinder forebody configuration wi th lonecyl inder. Curve A: cylinder-forebody based on cyl inder diameter;curveB :lonecyl inder; curveC :cy l inder- f orebody basedo nchord) .

velocity to f reest ream velocity and the Reynolds numberbased oncylinderdiam eter . Curve A in Fig. 10representsthelift coefficient obtained in this study based on cylinderdiameter . Curve B showsSwanson ' sresults for alonecylinderat the same Reynolds number based on cylinder diameter(1x 105) .T he lift for the cylinder-forebodypairis seen to be alinear funct ion of speed ratio, whereas th e lift produced bythe lone cylinder ischaracter ized by a sharp dip at low speedratios. This dip, according to Swanson, results f rom asym-metr ical boundary-layer transit ion and , consequent ly, var iessignif icantly with Reynoldsn u mb er . In addit ion to somewhathigher values o f lif t coef f ic ient , th e linear response of thecyl inder- forebody pair represents a considerable advan tageover th e nonlinear response of a lone cylinder in mos t ap-plicat ions .The curve labeled C inFig. 10 is the lif t coef f ic ient for thecyl inder- forebody pairbasedon the model chord. I t shouldbenoted that th e li f t f or this mode l can be augmented signifi-cantlyby operat ion at an angle of a t tack .Conclusions

A rotat ing cylinder at the t ra i l ing edge of a t runcatedstreamined body is an e f fec t ive me a ns of developing l i f t bycirculation control, and the li f t produced is greater than thatfor a cylinder a lone . The re la t ionship between l i f t an d cyl in-de r speedi slinearfor the cyl inder- forebody pairwhich isnor -mallya considerable advantage in a control func t ion over thenonl inear response of a lone cy l i nder . T he exper imenta levaluation of l i f t coef f ic ient by m e a n s of measur ing th edisplacement of the f o r w a r d s t agna t ion po in t re la t ive to i tsposi t ion when there is no l i f t ( i .e . , zero c i r cu la t ion ) is anadequa t ea l te rna t i ve to integra t iono f thep res sure d i s t r i bu t i onoverthe enti rel i f t ingbo dy .

Appendix:FiniteW ing CalculationsT he me thod o f De You n g a nd H a r p e r1 5 w as employed tomodi fy the two-dimensional resul ts for f in i te aspect rat ios .This is a mod i f i ed l i f t ing sur f ace theory in which the w ing is

replacedby aplateo f zerothicknessand the condition of zerovelocity no r ma l to theplateis applied at f o u r locat ionsacrossthe semispan a t the three-quarter chord l ine. Thi s procedurehas been f ou n d to be quite accura te , both f or highly sweptwingsand lowaspect rat ios .The absolute angle of at tack w as def ined as the rat io ofmeasured two-dimensional li f t coef f ic ient to the theoret icall i ft curve slope, 2ir. T he angle then was mul t ipl ied by the f ini tewi ng l i f t curveslopeobtained f rom R e f . 15 to get thelift coef f ic ient correspondingto a par t icularaspectra t io .N o r -mally, finite wing calculat ions a re applied only to bodieshaving a sharp trail ing edge whe re th e theoret ical lif t curveslope is know n to be 2?r. In thepresent case, th e b lu f f trailingedge mad e th e applicat ion of this procedure ques t ionable .However , compar ison of the results f rom this predic t ionprocedure with lif t coef f ic ient as af unc t i on of angleo f at tackobtainedon a blunt trailingedgemodelb yL ee7 indicatestha tth eprocedureisaccura tefor thecasesrepor tedhere in .

References^achman, G . W . , Boundary Layer an d Flow Control, Vol. 1,Pergamon Press ,New York , 1961 .2 K i n d , R . J . , A Ca lcu la t ion M e t h o d f o r Ci rcula t ion Cont ro l byTangent i a l B lowing a rou n d a B l u f f Trai l ing Edge," AeronauticalQuarterly, Vol .X I X , Aug . 1968,p p. 205-223.3Ambro s i an i ,J.P. and Ness, N. , Analys is of a Circulat ion Co n-trolled El l iptical Ai r fo i l , TR-30, Apri l 1971, D ep a r t m en t o fAerospace Eng ineer ing , WestVi rg in i a Un iv .4Wa l t e r s , R . E . , M eye r , D.P., and Hol t , D .J . , Circula t ion Con-t rol by Steady and P ulsed Blowingfor aCamberedEll ipt icalA i r f o i l ,TR-32, Ju ly 1972, D e pa r t m e n t of Aerospace Engineer ing , WestVirginiaU n i v .5 L o t h , J.L. an d Fanucc i , J .B . , "Flight Pe r f o r m ance o f a Cir-cula t ion Cont ro l l ed STOL," AIAA Paper 74-994, A ug . 1974, L osAngeles, Calif .6 B r o o k s ,J.D., "The E f f e c t o f a Ro ta t ingCy l inder at theLeading

and Tra i l ingEdgeso f a H y dro fo i l , Apri l 1963,U . S .N ava lO r d n a n c eTest Stat ion,N A V W E P SKept .8042,Ch i na Lake ,Ca l i f .7Lee, D.G., "Subsonic Force Charac t er i s t i cs o f a Low AspectRat io Wing Incorpora t ing a Spinn ing C y l i n de r , Rep t . ASED-329 ,June 1974 , Naval Sh ip Research and Dev elopmentCen te r .8Jo h nso n ,W.S. , Tennan t , J .S . ,and Stamps, R.E . , LeadingEdgeRota t ing Cyl inder fo r Boundary-LayerC on t ro l on Li f t ing Sur faces ,Journal of Hydronautics, Vol. 9, April 1975, pp. 76-78.9Pope, A., and Harper , J . , Lo w Speed Wind Tunnel Testing,Wiley,N ew Y o r k , 1966,pp. 315 and 316.10 Golds te in , S ., "LowDrag andSuc t ion Air fo i l s , Journal of the

AeronauticalS ciences,Vol . 15 ,April 1948,p p. 189-220.11Sears , W .R . and Te l ion i s , D.P., U n s t e a dy Boundary LayerSeparation,"Proceedings of the Symposium on Unsteady BoundaryLayers, International Union of Theoretical and Applied Mechanics,Vol .1, edited by E. Brenn er , 1971,Q uebec ,p p.404-407.12 T e n n a n t , J . S . , A Subsonic Di f fu se r With M ov i n g Wall f o rBoundary Layer Control,"AIAA Journal, Vol . 11 , Feb . 1973, pp.

240-242.13 Sm i t h , A.M.O., "Exact Solut ion o f t he N e u m a n n P r o b l e m ,Rept . ES26988,Apri l2 5 , 1958,Doug lasA irc ra f t C o m p a n y .14 S w a n s o n , W . M . , "The M a g n u s E f f e c t : A S u m m a r y o f I n-vestigations to Date,"ASME Journal of Ba sic Enginee ring, Vol . 83,N o. 3, Sept . 1961,pp. 461-470.1 5 D e Y o u n g , J . and Harper , C .W ., Theore t ica l S y mme t r i c SpanLoading a t Subsonic Speeds f o r Wings Ha v i n gArb i t r a ry P l a n f o r m ,Rep t. 921, 1948,NACA.

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