Waka, Ryoji

Yoshino, Fumio

Tottori University Research Result Repository

AA/1ethOd Of Data Reduction tO Obtain the TwO‐DirlensionalAerodynaHlic Characteristics of a Circular Cylnder、vithTangential BlowingbyRyoii WAKA・and Fumio YOSHINO*(Rece?ed June ll,1982)Thr∝different methOds Of data reduction、vere devised tO determine the inducedangle of attack Of a circular cylinder with tangential b10,ving as a function Of liftcoef■cient The experimental values Mrere corrected by making use Of the inducedangle of attack thus obtained,COnseqllently,the most iecOmmended methbd of themwas chosen t9 0btail the tWOidimelasiOnal aerOdynamic chaηcteristics Of theCIInder,and O?me eXamples of them were presented.l  lntroductionln general the experiments on two‐dilnensiOnal aerodynanlic characteristics of variOusbodies such as an airfoil,a circular cylinder and sO forth have been carried out at the mid‐span of a two‐dilnelasional ttOdel by taking the slnmetry into account.Then the so‐canedtwo‐dimensional modelis the One which has usually end―plates at both ends of the model orspans both side‐wans Of the test section sO as to keep twO_di:nensionality of the main flow.However, the author's found from the investigatiOn(1)on a circular cylinder with tangentialblowing that even if the mOdel was the twO‐dirnensiona1 0ne,the flow near the cyHnder―side‐walljuncture was a cOmplex three‐dimensiOnal flow cOmposed Of three kinds of vorticeswhich rolled up a strOng trailing vortex downstream of the cyHnder.Therefore the experimental values On aerodynamic characteristics Obtained at the mid‐span of a two‐dimensiOnal model are influenced by the induced angle of attack,ThOugh it isnecessary to ehn?nate this effect frOna the experimental values fOr determination of the twO―dimerlsiOnal characteristics Of the cylnder,the estirnatiOn Of this induced angle of attack isvery difficult under present condition, because of the lack of the known “truc" twO_dirne囃10nal characteristic values and also the breakdown Of the l(utta_JOukowsky cOnditionin this case.In this report three different simpler methOds Of data reductiOn are described to determinethe induced angle of attack at the n?d_sp n as a fu ction of lift cOefficient.Some examplesごorrected by the mOst recommended method Of them are presented for a circular cylinderwith tangential blo、ving.*Department Of ?lechanical ElagilaeeringRyoJI WAKA and Furnio YOSHINO:A Method of Data Reduction to Obtain theTwo―Dirnensional AerOdynanaic Characterittics of a Circular Cylinderwith Tangential BIowing2  NomenclatureCι,C(0)I SeCtiOnal lift coefficient at theコnid‐spanC,0(0)I SectbnЛ drag coefndent at the mid‐spanC●DR♂yノら銑砲ぅちαFλνpressure coefficient(momenttlln of the iet per unit span)/((1/2)ρ」″つ}diameter of the mOdel cylinderReynolds number(=1/D/ν)velocity of the unifornl flowcoordinate taken in the starboard direction from the■lid‐spanangular location of the blowing slot                langular location of the■linirnunl pressure pointangdar、vidth of the separation regionangdar location of the upper separation pointinduced angle of attackaspect ratio of the model cylinderkinematic viscosity coefficientsuffix∞indicates the t、vo‐dilnensional value.3  Experilnental apparatus and lmethodThe apparatus for this experiment was the same one aざdescribed in the references(2)and(3),and it iS not described here in detail.!呼村tiOn_ptαteFig.l  Cross section of the model cylnder.Fig,2 Test section of the wind tunnel.Figs. l and 2 show the cross section of the model cyhnder and the test section of the、vindturnel,respect?ly.The diameter of the cylinder,D,is 100%勿and the height of the blowingslot is cOnstant,0.59%ηタ2,across the whole span The static‐pressure holes of 335 in number inall are distributed circumferencially at ten span、vise locations on the cylinder. The model.   150n???????‐‐?‐‥Reports of the Faculty of Engineeirng, TottOri X」niversity,Vol 13cyHnder is mounted at the center of the test section and passes through two partition‐plates(hereinaner referred to as“side‐wall'り。The tructllre of the cylinder,side―walliu Cture is thesame one that is shown in Fig。4(a)of the reference(3)Or Fig。1(b)of the reference(4).The experunent was carried out by varing λ, 9,and C″nder the condition of constant'Pιof 2.lx105. whenえ=三4 and 6, らwas kept constant at 90°. On the other hand, 、vhen λ==8,three different locatiOns ofらwere uSed,that is,ら=50190°and 120°.C/1 was varied ttom 0to about O,3 for all the cases rnentioned above.The spanwise and circumferential static‐pressure distibutions were measured with amultitube manometer.4 Experimental resultFig. 3 shcjws the relation between θ″and Cι(θ2‐Cゼ relatiOn).θ″increases gradually withthe increase of Q. It iS found frotti this figure that the nlinirnum pressure point on thecyhnder, except the one due to jet,moves downstream and the influence ofえon θ″begins toappear,as Cι increases.――十。?，? ?? ?。?，? ?? ?? ?????え―・◇・-6-―ロー  ー4Re=21x105CIFig.3 Rclation between θtt and C.0,50 9012090901  1  1  1  1CtFig,4 Relation betveen θとand C.OOO◇ロ入68864CdC」。        ~Fig.5 Relation betveen c and c.9'50901209090?????????????????。???????????ィ?Re=2J X1054      Ryoii WAKA and Fulnio YOSHINO:A Method Of Data ReductiOn tO obtain theTwo―DimensiOnal Aerogynanic Characterittics Of a Circular Cylihderwith Tangential BIbwittgFig, 4 shows θ留_(勇 relation. θ″ increases monotonicaHy with the increase of c eXCeptWhen Ct is conSiderably sman.Theinfluence of λ on θ″ appears betw en え==4 andえ=三6,8,as Cι increases,Fig.5 shows(勇―Ctt relation,When(勇increases,C″decreases once and takes the ininilnumvalue,after that Cど increases again as Ct increases. CF iS Inainly given by the suol of theprofile drag coefficient, こ池。, and the induced drag coeffiCient, C。ど, in this experirnentalReynolds number. And Ctto decreases to nearly zero almost independently of λ and C″どincreases depending on え as Cι creases. Taking account of this, the behavior of CFagainst c mentiOned above can be explained by、considering the ratio of the increment ofC,to that Of(勇 when C iS large.ヽVhen cr iS large,′Cどど/」ctt and the value of CP for eachof え==4, 6 and 8 become smaner as ぇ incre s s. Then the influence of え on Cち app arsaS C inCreases.5  1)iSCussion5‐1′rhe method of determination of the induced anttle Of attackT、vo effects must be considered to obtain the two‐dirnensi nal charac eristics from theexperimental values of the cylinder with tangential blowing.One of them is the effect of theside‐wan and the other is that of the induced angle of attack,The range affected by the side‐waH has been already evidenced experirnentaHy for this mOdel cylinder,and it、vas l.8D,atthe maximunl,froni the side‐waH oward the n?‐span12).Then if九二≧4,the t、vo‐dilnensionalcharacteristic values are obtained fronl the experirnental ones at the mid‐span by cor ectingthe effect of the induced angle of attack.In this report three different silnpler lnethods are devised to determine 2,by cOnsideringthe following t、vo experimental facts.First, when Ct is large enough,the flow around thecyhnder is approximately a potential flow with circulation around it.Second,the spanwisedistrbutions of c″,lift oefficient nOrmalized by Q,are congruent and independent of〔ン,and they are alrllost exclusively dependent on λ only(not shown here)Now each method is described below.(1)The method of theoretical calculation(method(1))This method has been already described in detail in our reports(2),(3).Now we give only anoutline of this method.In this method some asstlmptions were made to calculate αJ.Takingthe interference of the side‐walls into account,the lifting line theory Ⅵras apphed to estirnate2r due to the trailing‐shed vortex only, neglecting that due to the trailing‐filament vort xThen the spanwise distribution Of αJ along he cylinder axis is given as follows,α,=一士 整 1″'2COStty tanh晉打 ,where B is the semi‐sわan Of the cylinder,一B≦ノ≦B,and〃is half the height of the testsection.Now a″'s indicate the Fotxrier coefficients when the spanwise distribution of circulation isRepOrts Of the Faculty Of Engineeirng,Tottori University,Vol 13expressed in the Fourier series asДy)=B」(参十墓Iα″cOS子り. ・…………………………………………・。(2)On the Other hand,the relation between the swanwise distribution Of circulation and liftcoefficient is given by the foHO、ing equatiOn,駅ク)≒;1/DCtけ ・…………………………………………………・・(3)Then the induced angle of attack, 2ぅdu to the traililtg‐shed vOrtex can be calculated bymaking use of the spanwise distributiOn of the measured lift cOefficient,the truncated formsof Eqs.(1)and(2),and Eq。(3).(2)The method using θ″‐c relation(method(2))It is thOllght in general that θ″may be deteralined by the width Of a wake and the inducedvelocity.And the width of the wake is thOught北O vary accOrding to the value of θsぅwhichis the angular width Of the separation region on the cylnder.θ″decreases as θsb increases andθ″ increases as αどincreases.Therefore if the flo、v arOund the cylinder is asstlllled tO be two‐dirnensiOnal potential flow(αJ=0), θ2ollght tO approach asymptotically the constant value of 90°as先ぅdecrea es.In thecase of three‐dilnellsional fiO、v(αど≠0),if CL is large enough, θ″is scarcely affected by thewake、vidth but by the induced velocity only,because θsb decreases as (,t increases. Thismeans that θ t approaches asylnptoticaHy the value of 90°+αどas Cι increases, Moreover asmelltioned abOve,since the spanwise distributions of Q are similar and indepelldent Ofてンin the case of constant λ, it can be shOwn that 2,is proportional to Cと。Hence if an asymptote is drawn in Fig.3 so as to patt the point of θ″=9o°when cι=O andapproach the experimental values of θ″as cL increa es,the relation betweeli αザand Cとoughtto be deternined froni the gradient Of this asymptote.(3)The method using Q_〔務 relation(method(3》Since the spalawise distribution Of Ct(ノ)is sirn lar,it can be expressed in the Fourier seriesaS   Cι(2=な十整.14cOR争♂,14/here望4″is a function Ofえ.4ヵin Eq.(4)and α″in Eq。(1)are related to each other as fonows,40=と,O♀nd 4″〒Δα″・ Ⅲ…………………………………………………・・(5)Substituting these relations andノ=EO intO Eq.(1)yields αどat the nlid‐span,that is,αJ=―修墓lη4れa?争→♀=浄И(λ),    ……………………………………………⑥…………………………………………・・(4)6    Ryoil WAKA智混翌鶏遥霊r理亀ポ沼洛とhtta露温苦&iき許ピ4鵠嵩ギを離with Tangential BIowingwhere И(え)iS a function of λ.On the other hand,thO following relation between the sectional induced drag coefficient,Cどぅand C ιhOldSiめど=鮮材(か. ・……………………………………………………………・・(7)Therefore if the relation between(勇and c,どat the mid―span is known,Z(え)iS determinedfrom eq.(7),then αどfrom Eq.(6)。However, it is ittpossible to know θど,‐(勇 re ation empirically, since the profile dragcoeffiιient,Cど。,is varried according to C.Then in this report,two extreme values of c,fare assumed for convenience so as to deterl■in the value of Cni they are Cげ。=O and cど。=0,35.Re=2J X105え  8)8  508  908  1206  904  90??????????◇◇0     1(α)0123450 10Cd∞(b)                       (C)????2    3CdΦFig,6 Relation between Cぃand cぉ.(a)metOd(1),(b)methOd(21,(C)Case Of Cヵ= O in method(3),(d)Case Of Cど。= 0.35 inmethod(3)5‐2 The corrected experimental values by three different methodsFigs.6(a),(b),(c)and(d)shoヽv the typical examples of the experirnental values correctedReports of the Faculty of Elagineeirng,TottOri University,Vol 13by making use of three different methods described in previous section lt seems from thesefigures  that  an  the  corrected  experimental  values  indicate  the two‐dirn sionalcharacteristics of the cylinder fairly wel in comparison with the uncorrected values in Fig.5. And it was concluded by judging from various viewpoints that the most reco■llnendedmethod of theni tO obtain the two‐dimensional characteristics was the case of Cめ=O in themethod(3).In the case of the method(1),the spanwise distribution of C力is eed d to deternine α,andh S?te Of ЙbOrblls cЛc』atbn,協rger scattering tt hchded ? the corrected res』o Next,although the method(2)iS Simpler and easier than the others,the degrec of crror included inαFiS Strongly depended on the way ho、v to draw the asymptote in Fig.3.This means thatthere is the possibihty to include a large errOr in tYJ.Finally,in the case of Cど。=0.35 themethod(3),Ctt has a tendency to increase again after it reaches the rninimum value as Cぃincreases,which should not occur This method seems to estirnate the value of C″J too small.Conseqtlently,it is also concluded that the most recommended method to obtain the two‐dimensional characteristic values is the case oiCヵ=O in the n ethod(3).5‐3 Two‐dimensional characteristicsln this section 、ve present some exaコnpl s of rhe tw。_dimensional characteristic valuesobtained by making use of the method(3).Fig.6(c)shoヽv  the(9陣‐Cかrelation This relation is independent ofえand is approxiFnatedby a single ctxrve within experirnental scatter. εぃ dec eases rnono onicany as c∞ increases,and when cゎ>5,Cぃbecomes nearly equal t6 zerO.This result suggests that the flowaround the cylnder can be asstlmed to be approximately two‐dimensional otential flo  withcirculation around it without a、vake of the cylinder, 、vhen Cι∞>5.Fitts.7 and 8 show the relation of θ″∞and θゅ to c♪。, respectively.Though the uncorrectedvalues of θ″approach asymptoticaHy the valuc of θ″of 90°十αぅ as Ctt increases in Fig.3,thecorrected valutt approach asymptotically the value of 90°as cゎnCreases. When cヵ∞'>5, θ_has approxirnately the value of 90°.This restut is corresponding to that obtained from Fig.6(c).???1501005002000ζ1501000????Cle。Fig。7  RelatiOn between θИ∞and Cι∞.Ct∞Fig.8  Relation between θv∞and(勇∞.Re=2J x1 05O O ◇8  8  690120908      RyoJi WAKA and Fumio YOSHINO:A Method Of Data Reduction to Obtain theTwo―Dittens!Onal AeЮdynamic Characteristics of a Circulir C,lihderwith Tangential BIowing6  COnclusttonThree different methods of data reduction were devised to obtain the twO‐d r ensionalcharacteristic values of the circular cyhnder with tangential blowing. The experimentalvalues were corrected by making use of these methods.The conclusions are as foHows,(1) An the results corrected by three different methods give good two‐dirnensionalapproxirnationsof the aerOdynamic chracteristics of the cylnder、vith tangential blowing.(2)The most recommended method of them is the case of cど。=O in the method(3).(3) It is possible to asstxme that the flow around the cylinder is two‐dirnensi nal potentialflow with circulation around it,when cι∞>5.References(1)Waka,R.,et al.,Proc.Int.Symp.FIow Visualization,Bochum,(1980),528.(2) Yoshino,F.,et al.,Bun.JSME,24‐192(1981‐6),926.(3) Yoshino,F.,et al。Transactions of JSME,46-410(1980‐10),1890.(4)Waka,R.,et al。,Preprint of JS?[E,No.825■,76.

A Method of Data Reduction to Obtain the Two-Dimensional Aerodynamic Characteristics of a Circular Cylinder with Tangential Blowing

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A Method of Data Reduction to Obtain the Two-Dimensional Aerodynamic Characteristics of a Circular Cylinder with Tangential Blowing

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