Hayashi, Tsutomu

Waka, Ryoji

Yoshida, Toshihiro

Yoshino, Fumio

Tottori University Research Result Repository

A Theory of Circulation Control by′rangentialBlowing, Applied to a Circular Cylinderin Uhiform Shear FlowbyFumio Y∝HINO*,TSutomu HAYASHI*,Ryoji WAKA*,Toshihiro YOsHIDA料(Received June 17,1983)The aow around the two―dimensional circular cyl?der With talagential blowingirnlnened in the uniform shear flow was examined analytically by aid of theperturbation method and the inviscid potential theory 「Fhe effect f introducti n of飩ear in the upstream flow 、vas compared 都/ith the experilnental resuit  Thetheoreticai curves representative of the pretture distribution on the circular cylnderMIas enough to reproduce the experilnental result The correlation between upstreamshear, characterized by a nondirnensional shear parameter ′て, and the pr ssuredistribution lvas shoMァn satisfactory by even the sirnplified theory1.IntroductionThere has been cOnsiderable study on the effect of boundary control for lift generation onvarious configkAration of bodies such as an aerofo』r a cir ul r cylinder. Various studieshave considered boundary-layer contr01 by blowing air through narrow tangential siot on thecircular cyHnder.Two―dilnetti nal aerodynanlic characteristics on the circular cyli4der withtangential blowng have been inuminated by detail measklrements of authcrs,(1)～(3)but th∝estudies have been concerned with cylnders inllnersed in uniforna f19w in the wind tunnel.Thetheoretical expression for the flow neld has been prOposed by J.Dumhanl(4)that distributionof norlnal pressure on the surface of circular cyhnders with tangerltial blowing can bedi〔モribed by inviscid,incompressible,uコseparated,potential flow theory.In various practicalapplcations,ho、vever,the existence of the velocity gradient in the upstream ccJmplicates theaerodynamic characteristics on the circular cylinder with tangential blowing. Thereforekno、vledge of the effect of shear on the distribution of normal pressure on the cylinder isdesirable for the practical application.奉 Depaiment of Mechanical Engineσing*孝 PЮsent Addressi Solay CorporationFumio YOSHINO and Tsutomu HAYASHI andA Theory of Circulation Control by TangentialUniform Shear F10wRyoii WAKA and TOshihirO YOSHIDA:Blo、ving,applied to a Circular Cylinder inThe purpose of the present study is to further illuminate theoretically the effect ofintroduction of shear in the upstream flow on aerodyna■lic characteristics for circularcyhnder.Specifically,the prirnary goal is to calculate the pressttre distribution included theeffect of shear flow and to see ho、v well the theory reproduces the experunental resdt.CとC´C,ぅC ″´C9C「Cμκ買鳥」暁Ъ θα「先ιT島必2.Nomenclaturenft coeficieritpressure coefficielltbase pressure coefficientnlinゴum presstlre coefficientcoefficient of source(=?/R暁)coericient of circulation(=「/買しりmomelatum of the blowing air per u?t span/1pδ供 )shear parameter of the u?form shear flow(=2R/しをx∂y/Эz)radius of the model cylnderReynolds ntlmber(=2暁貿/ン)velocity of the uttiform ttar flowvelocity at the centre(see Fig。1)polar coordinates(see Fig.1)angular location at sotlrce measured unclockwise froni the rear stagnation pointwhich would be predicted with potential theory in u?form flow(see Fig。1)streng世l of circulationangular location of the for、vard stagnatiOn pointstrean■fLInCtion in the whole fieldstreana function in the u?form aow fieldstream fLlnCtion in the pertubed shear flow field3.The Flov ModelA cとcular cylnder with its axis normal to a unifor■l inciderlt flow has synlrnetricalseparation points and he pressure distribution on upper and lower surfaces, When thecircular cylinder is submerged in u?form shear flo、v, smal lift due to uttynllnetricalpressure distribution on the cyhnder is produced for a function of the upstrealn velocitygradient,While a rnethod for delaying separation by jets through the slots is used to increasethe momentum of the retarded fluid in the boundary layer on the surface.When the slot onthe upper surface only is in use,the flow follows that surface and increases the lift coefficientacting on the cyhnder.To reproduce the n。、v field theoreticaly,including such separated flo、v or wake around thecyhnder,is generaly difficult.Dumham however has proposed that the distribution Of normalpressure on the surface of the circular cylinder with tangential blo、ving coul  be discribed byinviscid,incompressible,unseparated, potelltial■ow theory. Sinc  th s theory ho、vever asbeen developed for the cylinder submerged in u?form flo、v、vithout veloc ty gradient, theReports of the Faculty of Engineeirng,Tottori University,Vol 14―→ XlFig。l The flow model and coordinate systempresent study will be enlarged to include the flow around circular cyHnder submerged inunifornl shear flow.Figure l shows the model cottidered and the coordinate system. The now around thecircular cyhllder is generated by adding a circulation at the centre of the circle,a doublet,asink,and a sotlrce to the upstreanl ?ear flow.The circulation r at the ceritre of the circlerepresents the circulating flow which in actuality in generated by blo、v g air through anarrow tangential slot on the surface of the circular cyhnder. It will be seen that theseparated flow or wake region is so wide that the theory gives a very poor approxirnation tothe pressure distribution. The sotlrce 2? is therefore added to represent the displacementeffect of the、vake. And also the sink c of half the strength of the source is placed at thecentre of the circle to ensure that no streamline crosses the surface4.TheoryThe perturbation method is used to represent the field of the uniform shear flow farupstream.Velocity distribution of the u?forni shear flow is represented in accordi4g with theprinciple of superposition of a constant velocity しL and a slght pertubed flow with linearyvaried smal velocity(し4。/2R)K t as in the foHowing equation:y=醗|十寿z)=晩(1+券/SIn′)……………………………01t is conve?e t to、v rk with the strearn function to solve the problem.Therttore its streamfunction isぬ=幌(Z+希Z2)=J熔?′+器Q∞S効}…… ……………………・121FumiO YOSHINO and TsutOmu HAYASHI andA Theory Of Circulation Control by TangentialUniform Shear FlowRyoji WAKA and TOshihirO YOSHIDA:BIowing,applied to  Circular Cylinder inwith slllan constalat vorticity ω∞=F 発/2R.In the whOle flow field the streanl function should be satisfies the differential equation≠弓手十1解=等……………………………・・l働which exprettes thЮ phy ical fact that vorticity is constant along streanllines in absence ofviscosity. The boundary conditions areupstttam:″=中 dn θ十等 Q一∽s24碇挺 科… … … …… 0surface:  ″=01f the dirnensiOnless shear parameter Иf is small,it se ms likely that the flow will departonly slightly froHl the solution for irrotational motion On that assumption the streamfunctiOn T is tentatively statedЩЪ′:Ю=時(″,θ)十琴Tl(7,θ)…………………………………….… ……〈働where yo is the basic solution which indcate the streanl function around the circular cylinderwith tangential blowing inllnersed in the u?fornl flow wi out vorticity.For an applicationwith the in?霊id and lrOtational motion,far upstream the vorticiFy Valtishes,lea?ngLaplace's equation▽2翌馬三三O so that its solution is(4)FO=Jc(′ピ井)sh′+券bg考+身(2 cos lvq″2+R2_2だcoミアー T一θ)″―R cos(π―F一θ)―α―θ)―・(6)Substituting into the full equation 13)the relation(5)and(6)and equalhng terms include theshear parameter κ yields for the first―order perturbation ム, i  should be satisfied that堺■チ俳十井緋=辛…………………………………⑦The bOundary conditions are蝉Кam:吼=竿Q―脱のお/→∞surface:  Fi=O        as 7=R・…………………………………………… (8)This is as readily solved by separation of variables,so that its streana functiOn is鴫=竿 Q―戯 の十霧 ∞ジ θ 學 … … … … … … …・ 動Consequently,collectillg result of equations(5),(6)and(9)gives the complete solution.Reports Of the Faculty of Engineeirng,Tottori University,Vol 14              33Because the circllmferential velocity on the surface of the circular cylnder is(yp' 庁R=(13チ生)卜R,the Coef■cient of nOrmal pressure at any angular location θ is given byC =´1-((791″=P/yc′=1-(2 Snθ+手(1 2cos2′)十多一与cot(こ者折生))2…10where Cr=「/Rtt and C?=α/R5宅.The results calculated numerically for the pressurecoefficient Cちis p10tted against θ in Fig。2 which also give the variatioh Of curves against theparameters tt Cr and C270 0° 3600°270      3600-20-2-4-6-9(Cl)Fを,2 Theoretical curves representative ofagainst the parameters Xi Cr,and C?:va?able,(b)X=0.03,Cr=5.0,C iS a(b)the variation of pressure distribution(a)Cr=4.0,CT=1.0, and【 is avariableHowever,algebraical expressioIIs for the characteristic values such as an angle of for、vardstagnation point,sιor an angle at the minimum pressure coefficient θ″can not obtain easilyfrom the above fonnula for cρ.Then in the special case for no source at rear portion of thecircle,友ι.C=0,it iS p∝s ble to make fomulations for θtt and θ″usi g a condition of ЭCP/Эθ=0,舞三務lH7生~に′″ぉF■(1/4)κ21)/Fll…………………………10Substituting the values of θ″E=π/2 and C9=o intO equation (10), the coefficient of themlnlmum pressure ls-0.60-040-02000200.400.60Cq2.502.側1501000.50000Cヵ″=1-(2+(3/4)/十Cr/2π}つ・………………………………………………………………・・1)Fumio YOSHINO and Tsutomu HAYASHI and Ryoji WAKA and TOshihiro YOSHIDA:34   A TheOry of Circulation Control by Tangential BIowing,applied to a Circular Cylinder inUniform Shear FIowThe lift coefficierlt due to normal presstlre is obtained by integration which is taken rightround the counter of the cyhnder.cι=_ち12πc,sill θ dθ=Cr+江………………………………………………10For purposes of conve?ence,i  the comparison between the theoretical evaluations and themeasured results, the lift coefficient c is used instead of the circulation coefacient cr.Substituting the relation (13)into equation (11), the angular location of the forwardstagnation point is偽=前コ     … … … … … … … … ⅧIt have been point out in the u?fOrm flow(κ=0)that as the lift increases the wakecorltracts and the need for a source dilninishes,above a lift coefficient Q Of abOut five,asirnple potential flow as such a special case C?=O is good enough.“)5。Comparison with Experi】■entsAlthough ntxnlerous studies have been made of pressure distributiOns around circularcyhnders,most studies have been not cOncerned with cyhnders immersed in the uniforrn shearfio、v There is not rnuch available information on the effect of shear on distribution of nor?alpressure on the cylinder,especially in the study of the cylinder with talagelatial blowingTherefore the theOry is compared with mettured results for twO diStinct cases,(1)a simplecircular cylinder without slot immersed in the u?form sh ar f10w,(2)a circular cylinder withthe tangential blowlng irnmersed in the u?for  sh ar f10w, to see ho、v well the theoryreproduces the experimental results.A theoretical curve which gives the variation Of the pressure coefficient for no source andno circulation((島=0, Cr=0)is showll against l θ l in Fig。3 which also contains plots ofthe measured pressure distribution according to Adachi and Kato(5)for a sirnple circularcylinder at 8)(103。f the Reynold`ntllnber.It will be seen that there is fair agreement withthe experilnental result in the neighbourhood of the forward stagnation point,but the resultsdiffer enOmouly around the rear Of the cyhnderiln the catt of the tangential blowillg, a typical example for the comparison betweentheoretical curves and experrnental results is shown in Fig, 4. In these experilnents, ameastlred condition fOr two given shear parameters K二十0.045 and-0.045,is働=0.30 andら=100°at the Reテnolds nmber R?=6.0×104.AIthough the Reynol偽nulnb r a so has anirnportant inauence on the flow, at the near region of this Reynolds number the lanlinarseparation is colafirmed at about θ=±80°on bOth surfaces of an unblown cylinder.Operatingthe tangential b10wing on the upper surface only,the laHlinar separation is foHOwed quicklyby re―attachment as a turbulent boundary layer、vhich o ly sep rates much later, i.e.it isshown in Fig.4 that the retarted separation reach at about 175°ne  he rear st gn tionReports Of the Faculty of Engineeirng,TOttOri University,K=0,040 Re岳800X103Expettment TheoryHigh  o  ―――Low60Vol 141.00.50-0.5-1.0-15-2.0-2.5=3.0,θつつつ00-2-4-6…8-10-12鞭器P浮静E辮民K=_lilt:TheOryCr=6.1腿 識 。一 K=0,045-―― -0045Fig.4 A typical example for the COmparisonbetveen thcory and exper4nentFig。3 Comparison betveen simplぜied lれOryand experil■entpoint.The shear parameter bring to effect on the region of H?nilnum presstlre and backpressureo Selecting the theoretical parameter Cr, C?and α so as to obtain good agreementbetween the theoretical curve and the experrnental curve under arbitrary blo、ving condition(C″, ら),the eXperiinental result can be reproduced by the theory.Any unseparated―flow theory predicts a rear stagnation point whiCh is a silagtdarity in thistheory9 whereas in practice the boundary layers separate from both upper and lower surfaces,leaving a region of constant prttsuer around the back.Therefore the calculated distributionshould be truncated at the observed base presstlre,ignoring the theoretical singularity and itsiHllnediate neighbourhood. The calculated distributions for given parameters κ=±0.045,Cr=6.1,C9=0.25 and α=- 8.5°are also shown in Fig。4,and it agrees fairly well withexperrnental plots except for the region of the back pressure,and also reprOduces the effectFumiO YOSHINO and Tsutomu HAYASHI andA Theory of CirculatiOn Control by TangentialUniform Shear FlowRyoji WAKA and TOshihirO YOSHIDA:Blowing,applied to  Circular Cylinder inof the direrence Of the shear parameter.Because an angular distance of the stagnation point from the horizontal axis is acharacteristics value which indicate an effect of the difference of the shear parameter κonly,the relation of the forward stagnation point,sι s a functiOn of the lift coefficient C isinustrated in Fig.5, and it shows the goOd agreement between theory and experilnent,especially in the range of small lift coefficierlt. 1■owever, in the theory the graphs of θsιagainst c are calculated from equation(14),whereas in the experimelttal results the resultanthft coefficient due to measured normal presstlre distribution is Obtained by graphicalevaluation of the integral.Because the minimum prttsure coefficient Cち″iS alsO a characteristic value、vh ch is underthe influence of the shear parameter,he relation Of c,agaillst the hft cOefficient is shownin Fig.6.Solid curves are calculated ttom the equation(12)in which the relations of Cr=働=30°60°100°K= 0045 gl  △  。0     □ △  o-0045 1B  A  ●Re=60x104。??…6-8丘-10K=-0045K=0045Fig.5  The relatio■of the forward stagnationpoint against the lift coefficientFig.6 The relatio■of the minimum pressurecoefficient against the lift coefficttntQ―江 and κ=±0.045 are substituted.The colnparison with exper?ent show the excellentagreement in the range of larger lift coefficient than about five.This excenent agreementmeans that as the lift increases the wake contracts and the need for a source dime?shes,sirnplified potential theory(Cc=0)is good enough to indicate the effect of the shear.6。ConclusionsThe flow around the t、vo―dimeコsional circtdar cyhnder with tangential blowing immersedin the unifOrHl shear flow was exanlined analyticany by aid of the perturbation method andthe inviscid, incompressible, unseparated, potential theory. The theoretical curvesrepresentative of the distribution of the pressure coefficient on the surface of the circularcyhnder Or the aerodynamic characteristics such as the angldar distance of the forwardReportS Of the Faculty of Engineeirng,TottoFi UniVersity,Vol.14              37stagnation point oF the minimum pressllre coefficient were compared with the experimentalresults, to sCe ho、v w u the theory reproduces the expeFimental resultsj especiany in theintroduction of the shear in the upstream flo、v.And we obtained the following conclusions.(1)The theoretical ctlrves representat?e 9f the distribu iOn of the pr∝sばe c efficient areenough to reoroduCe the experimelltal results on the cylinder immersed in the uniformmear aow wlth the shear parameter κ .(2)Even the simplified theory(C=0)iS alSO enough to show he effect of the shearparameter on the angular distance of the forward stagnation poillt and the灯?nilntlmpressure coefficient.References(1)YoShino,F,et altt Transactions of」SMIら4併410(198010),1890(2)Waka,R.,et al,,Proc,ht Symp.FIow Visualization,Bochurn,(1980),528.(3)Yoshino,F,,et al.,Bull.」SME,24192(198卜6),926.(4)Dumham,J.,J.Fluid Mech.33(1968),495,(5)Adachi,T.,&Kato,E,J.Japan sOciety for Aeronatttical&Space Sctences(Japanese)23256(1975),45

A Theory of Circulation Control by Tangential Blowing,Applied to a Circular Cylinder in Uniform Shear Flow

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A Theory of Circulation Control by Tangential Blowing,Applied to a Circular Cylinder in Uniform Shear Flow

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