Waka, Ryoji

Yoshino, Fumio

Tottori University Research Result Repository

Visuahzation of the Flow around a CircularCyhnder with Tangential lnieCtiOnbyFunaio YosHINO* and RyOji WAKA*(Received May 31,1977)In this paper, we repOrt the results that were those o£the tlow visualiza i naround a circular cylinder with tangential inieCtiOn of water submerged inuni£orm llow.  The visualization technique is the dyetilanent method.  It isthe main object to iltavestigate the behavior o£ the vortic s £ormed on the sur―face of the circular cylinder and the side―wall,and shed into the wake ott thecylinder. It was£ound that three kinds o£ vortices were formed near thetunCture Of the cylinder and the side―wall, which are quite consistent withthe interence frOm the experiment tin the low speed wind tunnel in our labo―ratry.l  lntroductio■lVe had already describedi)that there 、vas a seconda y flow caused by a strongvortex shed fro■l the surface of the cylinder into the 、vake.  Therefore, it 、vasthought that the flow around the cylinder was no longer two‐dimensional but three‐dimensional near the side―、vall.  It ?vas not found so far, however, ho、v this vortexwas formed and behaved in the wake of the cylinder, that is, the fine structure ofthe vortex system was not clear, Moreover, it is very difficult to quantitativelyanalyze such a complex flo、v obtained in the 、vind tunne12).Then, we designed and constructed a 、vater tunnel for visualization of the three‐dimensional flow of the kind mentioned above.In this paper, 、ve first describe the 、vater tunnel and second present some photo‐graphs of the flo、v around a cylinder with tangential injection of 、vat r. The flowwas visualized by means of the dyefilament tIBethod.2  NomenclaturesL r and z = cOOrdinate axes(see Fig. 5);力   = Width of the slot ;D  = Diameter of the cylinder ;*Department of ?Fechanical EngineeringRePorts of the Faculty of Engineering,Tottori University,Vol.8θ   = Angle measured clockwise frona the leading edge ;θデ  = Angular position of the slot ,5「∞ = Uniform velocity in the water tunnel ;″  = h/1omentu■ェof iet at the Outlet of the slot;寺:粗!与∬iと事il=弗>ρ and ν = Density and kinematic viscosity coefficient of 、vater, resp ct vely.3 Experirlllental apparatusThe water tunnel had been designed by us, constructed by the employeO of theuniversity.The water, stored in the tank on the r∞f of our laboratory, flows into the 、vatertunnel after passing through a main valve and two flow meters, After that, it inturn passes a submerged weir, t、vo nylon screens of 、Thich mesh is 100 or the per‐centage of voids is O, 7じ3, a nozzle and a test―section.Fig. l shows the 、vater tunnel,  The test―section of the square cross section hasthe dimensions 200脇η in width and depth and 600″″ in height, and the four side‐、valls are made of the transparent acylic―resin plates 、vhich are 10ηηη in thickness。It is a feature of this 、vater llnnel that the water flo、vs vertiCally from the bottomto the top of the test‐section。(D submerged wetr(2)TwO nylon screens(3)Noz zle(4)Test_secHonFig。 1。 water tunnel. Fig. 2.  CrOss section of the model cylnder.Fig.2 sho、vs the cross section of the cylinder used in this experiment. The modelcylinder is hollo、v one 、vhich has dimensions 30″,%昭in uter diameter,,ン助吻%in inner21le1 0|??科鶴S端辞穏ζ離鑑Xttittm?Z?°n Л he Fbw around a αtuЙrdiameter and 200解孵 in spanwise length. The water iet iS injected along the surfaceof the cylinder frola the slot. This siot has a constant width of O.42%η, oVer thewhole span (See Fig. 3).The circular cylinder can be rotated circumferentially, so that the slot can befixed at any angular position. The water used for the jet is supplied into the in_side of the cylinder from one end of it,so that it may be possible for the jet to havea span、vise velocity cOmponent. To elilninate this, many fan‐shaped plates are in‐serted inside of the cylinder and these plates are set perpendicular to the cylinderaxis at about equal spanwise space.  Their size becomes gradually larger accordingas the water flows downstrearn inside the cylinder(see Fig, 3).we used three kinds of dyes as tracer, that is, they are methylen blue(blue),rhodamine B (red)and fluorescein (green). TheSe dyes are forced out into the uni‐form flow through the comb―shaped eighteen‐nozzle rake that is made of stainlesssteel pipes of l.0解留宅in diameter at 10解%珍 in ervals(See Fig。 4).Fig. 8. Model cyユinder a4d fan‐shapedPlatest章峯華Fig。 4.  Comb‥shaped eighteen―nOzzle rake.Reports ott the Faculty oE Engineering,Tottori University,Vol.84 ExperiJmental methodWVe carried out the calibration of thewater tunnel in the first place. It wasfound by means of the dyefilamentmethod that the flow in the test―sectionwas laH?nar in the velocity  rangebetween O 躙 IS and 90盟駒/s.Thevelocity distribution of the flow inthe test‐section was examined in theabove―mentioned velocity range bymeans of the hydrogen―bubble method.It was then confirmed tbat the flow inthe test―section was uniforn■in thesame range of velocity except for thevicinity of the side―、vall.After the calibration,the water tun‐nel、vas slightly changed, that is, two    ′′′nylon screens were changed to be re‐movable,but it was experimentally con―firmed that this change did not affectthe flow quality in the test―section.Fig. 5 shows the coordinate systemof this experiment and Table l the ex―Fig. 5, Coordinate system.XC―)????peril■ental conditions of each visualization of the flow.Table l Experilnental conditions.o二 visualization砕紹牌 講監i°WI鵜i乳争ギ翠皐&i∞ |In the experiment,R¢,CP and tt are independent variables and he observationwas made at various combinations of them. The experiinents were carried out inthe sy■llnetrical plane (ズ= 0夕″″)and in the starboard sections of the cylinder(ズ< O η″η)。こ器ぽ端解墨 監蹴絲監ざhua.Znon Лぬe mow around a Orcdar5 Results and5,l Uniform flo、v in the test―sectionThe flow direction of the unifor■l flow infor convenience,?‐‐‐‐，Discusslonall plates is fro■l the left to the rightO.X専-65ぎ8:旱06ぐ&:30″060504+IOOy(mm,(a) In■etttp■ane (b) Out■et―p aneFig, 6. velocity distributions in the iniet…and outlet‐p anes of the test‐sectio4 :7.=11・物物/S,Figs. 6 (a) and (b) ShOW the typical velocity distributions measured、vith thehydrogen―bubble method at the three spanwise positions in the inlet―and outlet―planes of the test―section, respectively, where う「ひ ndicates the velocity at the centerof the test―s c ion. The increase of the velocity near the side―walls knay have b encaused by the curvature of the nozzle and the disks magnetically attached to theside―walls in order to tighten a platinuni wire for the hydrogen―bubble method.The boundary layer thicknesses of this case are about 15吻η,and about 40,夕″% at thinlet―and the outlet―planes of the test―section, respectively. It is found that theVeやCity di,tributions at yじ= 99ηη/S have the same tendency as at yc = 11。1螂Is,but that at the higher velocity the boundary layer thickness at the outlet―pl ne isabout 15材″″,and thinner, and that the unifor■?ty of the flow is better.Figs, 7(a),(b),(c)and (d)are the streamlines of the flow iコ the typical sec―tions(atズ=0"″and…100協″)and at various y∞'s, They show that the flow islaminar and almost perfectly parallel both at the center of the section and in the?????．???Reports of the Faculty oE Engineering,Tottori University,Vol.8            25(C) y∞ =10″物/s, χ= -100″″(a)1/‐∞ =15胸協ノ/d,ズ= 0″物(b) y∞=90脇解/s,χ= 0物″             (d) y∞=90胞″/S,ズ= -100翔婢Fig. 7. Flows in the test_section.boundary layer,  Thus, 、ve conclude that this water tunnel is satisfactory to theflow visualization between the inlet― and the outlet―pla s in the velocity rang e upto 90脇物/s,5.2 Flow around the cylinder in the synametrical planeFigs,8(a),(b),(C)and(d)ShOヽV the flo、vs around the cylinder in the synlinet‐rical plane(ズ=0“め under the conditions that Rυ and θ′are maintained constant=0 (C)弟=(a) Cμ(b)第掌Fig.8.1        (d)第=3Flows around the cylinder :買夕=926, θデ=0°.(d) y∞ s26  鞘lれ箋端i∵棚亀鍬朗Xtti志渾ねuanzadon Л the Fbw around a GrcuЙrto 926 and O°, respectively,  and that Cμis varied from O to 3. It is seen from thefigures that,as鳥iS increased,he upper and lower separation points,he stagnationpoint and the streamlines around the cylinder move so as to increase the circula―tion around the cylinder, This、vas already described in detail in reference 2). Khr‐man's vortex street is seen to be formed■lp i  the wake though it is incomplete,and it is interestil■g that the street seems to be formed even ■vhen Cμ is 3.(a)買, =189                        (b)買ヮFig,9. Fttows around the cylinder i C,=6, θデ=0°.The flows are shown in Figs. 9(a)and (b)at tWO R♂'s(Rι = 189 and = 1690),when ttι and θデ are maintained constant to 6 and O°,respectively.It is found inthis case that the circulation around the cylinder is generatecl and is greater at thelarger R夕, so that the lift acts on the cylinder.(a)θチ=-10°,ち,=3.7 (b)θy=0°,島 =2.1(C)θデ=10°,第=1.1Fig, lo. Flows around the cylinder having the same stagnation point :R。掌 926.Figs,10(a),(b)and(C)ShOW the flows at tt。 =926 in which  and θデ readiuSted sO as to have the same stagnation point. The position of the stagnation= 1690Reports of the Faculty of Engineering,Tottori University,Vol.8            27point on the cylinder is deterHlined by observation. The strearllines except thewake are alinost alike althOugh θ′ and C′ι re different, SO, it is possible to ob‐tain the flow、Thich has nearly equal circulation.5。3 Flow around the cylinder near the side―wallWe described hitherto the flo、v in the synllnetttcal plane only and the floⅥ/th rewas nearly two―dirnensionalo Next, we present the photographs of the flo、v at a fewspanwise positions of the cylinder.(a)Cμ=11,ズ=-70,脇        (b)Cμ=5,χ=-90″"Fig. 11. Fiows near the side…wall :買σ = 189, θデ= 0°。Figs,11(a)and(b)ShOW the flows at X = -70″躍 and -90陶脇, respectively.The streaHllines of these figures are rolled up into the trailing vortex ; the strea■1‐lines of the lower side of the cylinder cross those of the upper side in such a waythat this trailing vortex is rotating in the same sense as a right―handed screヽv ad‐vances downstream. Fig. 12 is a platethat the trailing vortex is shed do、vn―stream from the surface of the cylin‐der. Therefore, the downwash acts onthe central part of the cylinder andthe upwash on the cylnder in theregion between the center of trailingvortex and the side―wa111).Fig. 13 is a photograph of a horse‐shoe vortex caused by the total pres‐sure gradient in the span、vise directionnear the stagnation point because ofthe boundary layer on the side―、val13).The dyefilament is flowing a、vay t  both sides of the cylinder. Fig.  14 is thehorseshoe vortex in the dowllstream.The vortex passing the upper side of the cylinder(the lift Side)departs fro■l the side―、vall and is rolled up into the trailing vortex.The vortex to have passed the lo、ver ide cr eps up、vard i st On the side―wall andseparates in tヽvo directions.  One 、vhich flo、7S dOヽVnstream (rightWard) continuesFig. 12. Trailing vortex Shed froni the SurfaceOf the cylinder.28 of the Flow around a Circular科鴛&訂畔漱°帆 乱1朗」性転〆おu7aliZa?onFig. 14.(a) Cμ =3=4.2                       (c)Cμ=5.4A paとof vortices on the side_wall :Rヮ= 375, θァ= 0°.HorseShoe vortex■n thedownstream.(b)Fig.?????．creeping and diverging on the surface. Irhe Other flows backed tlp into a pair of vortices described below.Figs. 15(a),(b)and (C)11lustrate the two vortices formedpstream and is roll‐on the side―wall iuStFig。 13. HorseshOe vortex,|Reporis of the Faculty of Engineering,Tottori University,V。1.8           29behind the cylinder. The arrows in each plate indicat, thO cOres of the vortices.Twoヤortices are formed as a pair,one in the upper and ittc other in the lowersides in the downstream of the cylinder,帝hen C2 華 0(not ShOwn here).The mechanism of the vortex forma‐tion may be thought qualitatively asfollows (see Fig。16),  the VOrticityvector of the side‐wall boundary layer,4, is transported froni far upstreamaid it is perpendicular to the mainflow velocity vector. The flow, how‐ever, is accelerated near the upper一and lower―su faces of the cylinder.Consequently,the vector 4 is inclinedagainst the main stream mear the cylin―der,that is,the vector B has two conl‐pollents Bi and島.And,the stream‐wise vorticity component B2 iS Stretch‐ed due tO the acceleration and thusthe vorticity is concentrated, so that a vortex is formed iuSt behind the cylinder.As pre?ously mentioned,the larger the tt iS,the larger the upwash near theside―wall caused by trailing Vortex is,「rherefOre, the two vortices on the side―wallmove upward obliquely behind the cylinder (see Fig.15).  TheSe vortices haveaxes of the spanwise direction and depart from the side―wa11. They are finallyrolled up into the trailing vortex.So far, 、ve described three kinds ofvortices,the first is a trailing vortexshed fronl the surface of the cylinderdownstrea■1, the second a horseshoevortex and the third a pair of vorticeson the side―、vall.  These vortices areall roned up int。。ne vortex, that is,a tralling vortex in the wake of thecylinder.The schematic vie、v of the vortexsystenl ls illustrated in Fig. 17.A pctr of vorlices On the si壺‐wo‖Fig. 17. Structure of the vortex system.6 Concluding remarksWe lllustrated the flow pattern and the vortex systeni near the side―wall. Th???????????????Fig. 16.  Mechanism of the formation of apair of vortices On the side・・wa11,30  柵 辞甥協髯瑠謀湘餓―綿執評SuliZatioa。こthe Fbv 4■Cund B CとcIIar   __three rnds of―vOrticeo roll up into ode voFteX・ttte soicalled trail?憲 ▼OFteX, andhis flow pattern quite veli.explains the stFeamlines on ttle side wan inustFated inF造・3.Of the Fefer弾●ol). MOreOveF,tとe r sult obtained tt thさfとow ?sualizaionis consistent wi色―he cOndusionsコュFefOrence l),nerere.nceつ Yoshino aれd Waka,Reporいof the FiCuI呼01 Engin∝rhg,Totto五univeFSitヵl■ (1976‐ヨ),1.め Yoshino 4nd Waka,RepOFtS OE―the Faculty oE E4-gineerttg.ToととOFi UniVerdty, 3-2 o973-3JI,25,|働 ThWii与OS,■・・InCompFeSSiblo Ae〕oこynamis,゛98の,551すOxford.

Visualization of the Flow around a Circular Cylinder with Trangential Injection

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Visualization of the Flow around a Circular Cylinder with Trangential Injection

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