Vortex Shedding From Oscillating Bluff Bodies

8/16/2019 Vortex Shedding From Oscillating Bluff Bodies

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nn. Re Fluid Mech 984 6 9222rht © b l eview c ll rih reerved

VRTE SHEDDING FRMSCILAI BU BDISP W epatent of Aeonautcs, Ipeal ollee, London W7 , Enland

NTRUTNhen paced a ud stea, soe bodes eneae sepaaed o ove asubsantal popoon of he suface and hence can be classed as blun shapeded bu bodes, sepaaon s ed he e ede, whee on blu bodes th contnuous suface cuvaue the locaton osepaaon depends boh on he shape o the body and he sae o he bounday laye At lo Reynolds nubes hen sepaaon s occus,

he o aound a blu body eans sable bu as he Reynolds nube s nceased a ccal alue s eached beyond hch nstabltes deelopThee e ed o ozed uned we oon doaned oon o a cobnaon of bo Reula voe sheddn hesubect of ths acle s a donant featue of odensonal blubody akes and s pesent espece of hethe he sepaatn bounday layesae lana o ubulent It has been the subect o eseach o oe than a centuy and any hundeds o papes hae been tten In ecent yeasvoe shedn has been the opc of Euoech eetns epoed on byM Maull 7 d Beaan Gh 80 and oehee eew h ee udee Bee We 7

Voe seddn and eneal ae tubulence ndue ucuatn pessues on the suface o he enean blu body and f he body s exble hs can cause oscllaons Oscllaons eced by ote sheddn ae usually n decon noal o ha of he fee sea and apludes as lae as .5 o 2 od dee ay e eoded ddon o heeneatn body any othe bodes n s ake ay be foced no oscllaon

Boadband foce ucuaons, nduced by tubuence poduced n he oaound a blu body, aely lead o oscllatons as seee as hose caused byoe hedd Soe o o eod n, uh h ove

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y R o y a l M e l b o u r n e I n s t i t u t e o f T

e c h n o l o g y ( R M I T ) o n 0 5 / 2 8 / 1 6 .

F o r p e r s o n a l u s e o n l y .


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96 BEARMAN

ents o blu boy eelop etn oes n phse ith the boy'sveloity y lso le to le oslltion pltues llopn s one ele o n instblity heeby soe blu boies n ett eney o u ste n sustin oslltons n ths eie only vbtons use

by vote shen e onsee o ulle susson o oinue btons the ok o lens (1977 s eoeneelent sueys o otenue oslltons o blu boies hve been

itten b kinson (1974 n Sky (1979 It is hoe tht the esent e ill oleent these evies n ve n ootunity toeonse soe o the es pesente n the n the ht o oe eent

eelopents The oty o peous epeent ok n ths e selte to ote shen o u ylnes Mthetl oels

eeope to peit voteinue oslltons e so nly onene

ith this boy she hs eoupton ith the ul ylne s uste on nube o uents the ost pesusive e tht it is n pont stuul o n s onnnly esone by Mokovn(19 tht t pesents henn unentl poble o u ehnsts In the pesent ee hoee ote shen o btn blu boes o ous os s onsee n oe to enty oon etues e bein th susson o ote shen o e blu boes

IXE BLU BIEAlthouh thee is no olete soluton to the ble o vot shen e hve esonbly le nsht nto the ehns n oels e ontinuousl bein eveloe to esibe it thetilly e 966hs en n eteely useul physl espton o the ehns o the ototon eon A key to n the oton o otesteet ke s the utul nteton beteen the to septn she yes It s postulte by e (196 tht vote ontnues to o e by iultion o its onnete she lye untl t s ston e�ouh to he oosn she lye oss the ne ke he ppoh o opositelysne otty n suent onentton uts o uthe supply oulton to the on ote hh s then she n oves o onste

es voteoton oel s illustte n ue 1 by sethshoin n instntneous lent lne tten ntinent plys n ipont ole n vote oton n iue 1 ntes sevel

entnent poesses ntne u () s enue nto the on ote he ( ns ts y nto the eelopn she lye The nekeeon beteen the bse o te boy n the on vote oslltes in

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OSCILLATING BUFF BODIS 9

fi dl hwig w Gd e and oe uthe ud c teoaly entaned nto t. Entanedo (, hch contan oe ud th ootely ned otcty to that n te on ote te laet o te tee o. e otoa nue 2 ho oke laent aound a lu ody and the nteacton eteen one hea aye and the ote on on the oote de o the ake clealy een.

Sne ote oaton nole the n o o o ootely ned otcty the tenth o nddual ake otce ll e le than the total culaton hed o one de o a lu ody dun a heddn cycle. ae

Johanen (927) and Rohko (95) etated the ate o heddn o culaton o a lu ody y conden the ean ae eue. heate o heddn o cculaton at a eaaton ont en aoately dr/dt u hee Ub the ean eloct at the ede o the ounda laye at eaaton. Aun that eue ean ontant thouh ahea laye hen � = U2(1- CpJ hee U eetea elocty and CP

the ean ae eue oeent ae (1976) ha ondeed theaddtonal ontuton to /t o unteady elote eneated at the

eaaton ont ut onluded that t an e neleted. ene the actono the onal cculaton that ue ote oaton gen y the eeon

(2 )

heerv the tenth o a ake ote and the ody Stouhal nue nD/U, hee n the oteheddn equeny and D a chaac tetc denon o the ody uually the ody dth)

In ode to alulate an etate ut e ade o the tenth o the ake otcevae Johanen (927) and Rohko (95) he ound rv y athng a eaued ote onecton eed to a edted alueotaned o a utale aay o dealzed ont ote ae ohanen

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A c c e s s p r o v i d e d b y R o y a l M e l b o u r n e I n s t i t u t e o f T




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OCILLATING BLU BO 99

found a . fo a at plate, and Rohko etated a .43 a the aveaevalu fo a ula ylnd, 9 de, and at plate Mo dtaldanalye have ben aed out by Bloo Gad (19 and ave(97, ho ued dun vou vote to epeent the ake. Aan by

athn eaued and alulaed ake velote an tate of rv ould be found. The eultn value of a ae loe fo a ula ylnde Bloo Gead found to be beteen . and ., dependn on the Renold

nube, and fo a Dhaped ylnd ave etated a 2.The poe of healay ntaton and ulaton eduton

tel ll llutatd n th nual alulaton of Abnathy Konaue (19 The epeentd to paallel hea lae of opponn b o of pont vote. The o ee dtubed and alulaton poeded untl loud of vote eebln a vot tt fod

ont vot of oppot n thn the loud, and th valu of alulated fo the nueal epeent about . Althouh thee alulaton ay not have bn ad out th th utot athatalo they epeent a ve potant tep foad n the undetandn of the ehan of vote heddn. The ho that t the peene of toha lay ath than th blu body tlf, that paly eponbl

fo vot hddn The peene of the body eely ode the po by allon feedbak btn the ake and the heddn of ulaton at th epaaton pont.

Abnathy Konau ponn ok ld to the dvlopnt of th detevote ethod fo alulatn vote heddn fo blu bode.Gead (1967 dvlopd a la ethod but nludd a ula ylnd n the o ld. uth povent follod apdl. A bluntbad body a tuded by leent (973 and an nlned at plate by apkaya(197 ulaylnde o ha been alulated b eenbauh Mahall (9, apkaa hoa (199a, b, tanb (98, andtanby on (1982 u ntnt h not to eve the ahvntand hoton of th dtvot thnqu, but eely to note that t ha bo an potant thod fo odln todnonal blu bod o

Muh of the epeental eeah nto vote heddn onen the nuene of dtubane. In addton to Reynold nube blubody ohave bn found to depend on fato uh a bodyufa nh, aptato, ndpat dn, o tubuln, bloka ao, and aout no level. Anothe potant ndn ha been that todenonal bode n unfo o ae unlkel to hed todenonal vote The lak of to

dnonaty an b aed by nvtatn the pan vaaton ofo untady quantty elated to vote heddn, uh a utuatnufae peu, etonal l foe, o a utuatn vloty ut outde the

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200 BAMAN

sh l son Th colon bn to ons dstn t s vn b

Rez) = ele2/e2 (2.)

e s t qunt und consdon nd 1 nd 2 o sons dstn t. Sn th n o s to dnsonl tn J = J. Th olon lnh L s dnd b h nl

Re ) . (2.)In th n o Rnolds numbs btn 1 nd 105 o ul lnd vs btn bout 3 nd 6 lnd dts s S

1979 Sdd bods nt vocs colon lnhs o sl od o squ ston D V 1966 Poh 1971L 1975 mn bsu 198. o l noml o omn Tumn hv ound L D. om hs su nts t n b ddud tht lthouh th utul ntton btn tos ls tt lds to t nton o vot sddn b vson t sns couln s ovl k

As t st to o onstnt ossston blu bod s dudvo shddn bcos k lou t nv sms to coll

ds l t l 99 dtd vot shddn bnd lts ovn st to don to n st to o unt. Vot sddn bnd ss s bn obsvd b Acnbc 1974 nd bnd cul dss nd ons b lvt 1967 On lostto blu bods th ocs ntd b vot shddn too k to cus n snntoscllons. Wooon 199 hs obsvd dun ndtunnl ss on

odl hn sts o cul oss ston tht snnt vot nducd oslltons unll to ou o chmn hh to dmtts lss tn o 6

otvl sll dtus om sttl todmnsonl on dons cn v l nunc on vo sddn. T ct o mld on vo sddn o bod o ccul coss ston hs bnstudd b st 1969 nd th t o n sh on blu bod thd ston s bn nvsttd b Mull Youn 1973 n bot ss t Stoul nub bsd on lol dt o lol vlot sot tnds to th vlu o lndl bod n uno oMull Youn ound n s o shddn ocud d

qun n clls ndn bod dts In both css tvotsddn olton lnt s tl dud od th tsvlu n th quvlnt todnsonl obl bus o t snsvton n t shddn qun.

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T BUFF BI 2

Ru vx hddin n b iuy diud if h in in i n ih Tnn (172 h invid h f viu iind mi n h d f uniind in fund h v hddin ud ud nd d dud if h

iin d d bk h ih in inumnn (1 xd in n iu yind by i fd nd vd n u vx hddin Anh mf h uin f hddin y nnih in in i h f u ind in h u niin im 5 x < R < 5x 1 bn uii nd ii [h nmnu u d

h i idni h ud by Rhk (11 h ii i ud in f nii] In uii h niin fm min uun u ihin in ub nd h

in f h uin uun undy y k und h ynd hn h u nn m h u k dn ndm in h n nd ih in in i A hih Rynd nub niin u ihin h hd undy y, ih in in ihd nd uv hddin un

LLATNG BLU BEhn bu bdy i iin in uid m hn i i d m ih n imd iin vx hddin n b dmiyd Th iin vid mn f uin h n hn f h dy nd hi uuy u in in in h

in nh inin f h v h h bdy min n k n f h inbiiy mhnim h d vxhddin n h nd by vx hddin und vibin u dy n hv vy inin din fm h und d

n Cnin iin my nd y h dy h b u uuy iin dv fm n inin n vx hddinnd xiby mund bu bdy In by imn iinf u di my vindud fd y mhin fnin nd viy min Simi inin my dud y viin h , nd in i f imn n quin yind Ph (11 ud u unn du nvyiin Au ni n dv d iy ivii in h und u dy hih my d mdiin

f h vhddin h imi h dud by bdy min Th inin bn vx hddin nd und h n invid y k (1 17 (11 Ahid (17 ndh n (17

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22 BEARMA

Practica xamp of ortxinducd ociation uch a tho di cud by audachr ocw (8) inariaby ino mor copicatd tructur and ow nironmnt than tho tratd in undamnta intiation Windxcitd ociation o towr and chim

ny tac or xamp ( cruton 963), ar actd by th har and turbunc n th approachin ow a tructur ha a numbr o poib od o ibration and thi i an iportant actor to b conidrd whn dtrinin th ortxinducd rpon o on ndr bu bodiuch a cab (Rabr Grin 96 Ptr 982) A iportantappication ara or bubody rarch i in th d of marin tchnooy

whr bodi ar xpod to wa currnt or a combination o both(Grifn 98, Grin ambr 82) En in th abnc of a man ocity, whn th ow i pury ociatory ortx hddin can ti b th

doinant chani (Baran t a 98). Pror on th practica ninrin probm ha bn mad poib throuh th undrtandin aind rom undamnta tudi

Oscillations of a Flexibly Mounted Blu Bodyortx hddin ot commony induc ociation in a dirction tranr to tat o t tram at ow pd wr t rquncy ohddin concid with th rquncy o ociation o th body. axiumociation ampitud occur or a ran o th rducd ocity UjND

whr N i th body ociation rquncy If th ortxhddin frquncy rom on id of a bu body i , thn th rducd ocity for maximumapitud i co to j whr i in by DjU It i inicant that it inot prciy qua to th inr o th trouha nubr

ach tm a ortx i hd a wa uctuatin dra i nratd andociation can b inducd inin with a uid ow Thi occur at a rducd

ocity qua to approximaty j2. Anothr orm o wa intabiity ha bn obrd for circuar cyindr in a ran o rducd ociti than j2. Vortic ar hd in ytric pair and ony o into th amiiar tard arranmnt om ditanc downtram o th cyindrThi ymmric hddin i inducd by th motion of th body and i ri to a orc in pha with th body ocity. Inin ociation caud by ti ct ha not bn obrd or bodi in air but in dnr uid uch a watr, whr th ratio o th ma o uid dipacd to th ma o th body i ubtantiay ratr riou ociation can occur nin ociation o thi yp on uca arin pi ha bn rportd by Wootton t a(92) Comparion btwn mod xprimnt and fu ca ha bn

carrid out by Hardwic Wootton (93) and Kin (94)A comparion carrid out by Kin (194) of th inin ociation of a od cantird circuar cyindr at a ynod numbr of 6 x and a

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w�L«

0' 15-

OILLTING BL BOI 2

.o- 1 r , 0

j ' � 0·0' / ; ' ) I , X \

1

J � X

l(� ': r : X

f

X

-X

3 Votex-excied nline oscillaons of a exble canilevere cicua cyliner inwae. 0, Re 6 1'; Re 6 14: in each cae 2MJpD .8 (Kng 97)

fullcale pile a a Reynold nuber of x i hown n igure hewo region of inabily caued by he wo deren hedd ng paern areerl iibe The iu pliude of ocllion were le hn Dd hece uch ller hn hoe eperieced i oreecied croow ibrio. uce udenl reerch h bee crred ou o fully explain he orgn of he excng foce n he yeric hedding rege Hardwic Wooon (9 obered ocillaon Reynoldnuber of 6 , bu Grin Rberg (98 repor h here a lower lii of abou below whch inlne ocillaion are no eced wer ere epere he bee crred ou Td e

l (9 wo orced clder o oclle le wh ow reduced elociie i the range under conideraio They ocillaed a circular cylinder a a xed apliude of .4D a a Reynold nuber of 4. o poe excng force w found lhough he ud dapng force eered b he oion of he clinder wa conderably le han h clculed u qued ow nd u he eured dr coecie. i inriguing o wheher or no n eciing force wouldhe been eaured if he ocillaion apliude hd been reduced

Equtio of Motio for Flexibly Mouted Blu Bodyonider igid wodieniol blu bod plced ol o a ow of eloci U d oued o pri The equio of oio or he bod

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204 M c b w

M++Ky F(t), (3.)

wh

y h c h b M h f

vc g c oc wh h g h gK h o h g Ft h oc. co c f b 4OMN wh O h c cc g (K jM12 j2 No h qc o h bo Th cg oc h bo c b x cc Cy wh Cy F)/!pU2D Th cc cc h

coo hy co o h o o c cg c c h oclg bo b l h c b

co g oc o u h og c b h colx ch vx hg cv v v h g o c h gh-h q (3.). c q (3) c b w

(32)

qo 3 g o h c b o cb h o h v - co o ochg bc gllog o vox hg. ch o h ch o b

b w h b g b h oog coc Cy h co o b h c h v co h v oc cc bl b hg c. lgl v-c clo h oc h bo lco c h qc n whch l co o NoWh b bo pg vx hg h c h xc b o h gl


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OSCLLAT BL BOS 2 0

y coig h o of giu of h viou i quo(3.4) ( io 74) i c b how h fo lgluoclio of boy wh DjM gh b yiclly of o0 h fqucy of boy ocillio houl b clo o i ul fqucy Thi i co by xi ui uch w wh DjM y b of o uy h fqucy of ocillio of h boy c b cby fo u fqucy. Th y o li of blu boy o vo hg giv byquio (35). f pDj2M i ll uch h n � No, h quio (3.)

c b lc by

• ( D ) ( U ) = 8n s < Mb ND

(3.6)

c fo quio (3.4) (3.) (36) h h h gl < y xly io ol. Th o lu o o o o bu o h of i h wih h boy vlocy. c u of h col ucuig v foc coc(h f o h lif cofci) o g of oy blu boy h will gv lil ico of h ly liu of oio ofiil bo xbly ou.

Free and Fored VibrationF-vbo x o ccu cy w hv b co by Gi Rbg (8). Plo of oclio liuvu uc vlocy ouc Fgu 4 wh i c b h fo l vlu of h ig 2MsjpD h x u oclo liu ly h . Two fuh o hou b o i Figu 4. Fi h u o i h wo c occu iil vlu of uc vlociy. h w i h ucvlocy h b fo ug h ocilio fqucy u w. Sco wy fo h xu o h lu co qu i h wo c Th o ghly cy u h x o ov ow b of uc vlocy wh h o highly cyl w o ov uch bo g

Alhough i h c o by G Rbg i vlu of h g l o l xu o hi o ocly lwy occu Sy (78) h o h fo owvu of h -ig h ool

ig c h o ly Th c b xc foquio 3.4) (3.) wh low vlu of 2MjD iuc ho fqucy hc h ocilio liu. Gf

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BEARMAN

Y

0 · 3

4

Fe 4 Cross-ow amplitude versus reduced elociy fo ccua cylnde. ae, 2/D 7.6, b 5.1 10 2bJD 039; ..., a, 2/D 68,b 43 10 2b/D 0.29 (G n Rameg 1982)

pmann (77) and arpaya (78) ha suggstd th us arespse parameter Sg 8n2MS22. Sarpkaa 1978 ha nudd rm a paramtr study th sparat and mnd ts thstrutura dampng th nndmnsna mass and th rspns paramtr that th maxmum rspns a yndr s grnd y th rspns

paamt an ny alus gat than aut unty.I th au D/ s suntly smal s that th rspns an

prdtd usng Equatn (3.) and t s assumd that th rdud ty mamum spns s qua t th nrs th Struhal num thn/D sn 4• sng suh a atnshp th ampltuds sl atn ry ratng u ds an usd t stmat th xtatn sn , th r nt ut phas wth h dspamnt. Gn pmann (77) ha gathrd tgthr stmats sn r a ruar yndr rm arus xprmnts and ths ha n pttd nFgur aganst a sad amptud rat 2/D. Th paramtr s th

mda rspns at and has n usd n an attmpt t rlat data rm antrd and ptd yndrs and ylndrs mng n paral mtn F ynds n paal mtn 1 Th ndatns mFgur 5 ar that th xtatn nrass n th ang amptuds up taut .D and thn drass suh that thr s n xtatn ynd anamptud rughy D

On th mst ntstng as w as dtald nstgatns nt th

rspns y ratng yndrs has n ad ut y Fng (18).Hs st nwn rsuts, ths n a ghty dampd ruar yndr arshwn n Fgur . dsrd that hghr amptuds w ahd

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13/28

'7

zV

OSCILLATNG BUFF BDES

,0" \ \

�

.j : � \ ,• / I / \

�

\

A + \ I 6,/? \ 0-

'

7

A plot of sin < versus double amtude. Circular-cylinder data gatheredtogether by Grn Koomann (1977) and Grin (1980) The legend for the dt oints isgiven in Grin (1980

when redued eloiy was inreased oer a eran range han when was decreased bac oer he same range Ths hyseresis eec has sce been hesube of muh disussion, bu i has sll o be fully explained. eng also

measured he phase angle , and i an be seen from igure ha his aries wh redued eloiy.xperimens suh as hose of Feng (98) demonsrae ha he ow

around a freely ibraing blu body can change ery rapidly wh hanges in reduced eloy Se aryg he reduced elocy also hages heaplde ao an be ey dl o deene he elae poaneo ese wo ees o he resulng ow eld. Hene a number o

esgaors hae hosen o arry ou ored osillaon experimens in which he amplude ad frequeny of he moio an be aried a will ach

mehod has is adanages and disadanages bu he foredibraionechique has he mporan bee ha ondiions can be closely onolled oweer, due o he neaon wh he sruural paraees,

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14/28

208 BARMAN

nN

�

100

J / f

/ e

D� 0 °

0·6,\ f; YOt'

/

)

UNFir 6 Oiion reii o reely ibing iru yiner i MJpDz 04. oreeing requeny; + yiner requeny; e ngle; oiionmliue Feng 6

a md ag h dud ad ampud audd a da xpm kl mpa a a F a updd lu d ag a a adamplud a aumd ha h am d d a a ama ampud a dud ad Rd um h hw pa wll da h d am pum ha h p pu h h upa Th aaa pa d ugg ha ad da w a h am.

34 The Iuece f By ti Vrte SheigRah ag lud w ha dd a u ga hag ha u h hddg ha Phap h

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OSCLLATNG BL BOES 20

wo bsow cs h c o voxshig qc b bo qc ov g o c voci h lg ics i coio gh h occs wh voxshig qc coicis wih h bo qc. h ov o h bo ovis s o choiig h o o hig og i gh. h hsho oscilio i qi o cs g icss i h colio gh s o h sh o h b bo cosiio Fo cicl cli h ciic v o D is bo 0.05 b o bois wi shg sio i b sigic ow Fig 7shows x o h ics o s wis coio o h ow og sq-scio ci wh i is oc io oscilio li oYD . c vloci wh h vox bo qcis coici ( Obs 82). h colio coci i fo b sig cig sss wo ois o i c o h ci ic . h cig ss sig h b o o o h h vohg c h h colio wol hv b v cos o i coss h s Ahigh Ros bs sl-sc cios cs b bc

lil o b ch c b bo ovh "g o c ov wic voxshig qc is

oc o h bo qc is o oscillio lih g h li h lg h g o c. I ss o Fg

0

0

0( z)

0

0

00

6 8 0 1 1 z

Fr 7 Correlation of surface pressures measured on a sde face o a square-secton

cylnder versus spanwise separaton body statonary Body oscang wth D 01 U/ND wtn lock-in n 7.35; U/ND 62; 70 1.0 (Bearman Obasju 92)

A n n u . R e

v . F l u i d M e c h . 1 9 8 4 . 1 6 : 1 9 5 - 2 2 2






16/28

BARMAN

98) pot in Fiur th ran of captur is sn to xtn fomUjND 5 to 7.4 but in his xprimnt th circuar cyinr is ibrating

fry an hn th ampitu ao ari or thi rang of ru oity. n forc-ibration xprimnt whr th ampitu is h

onstant it is obr that th xtnt of th rang of captur pns on th apitu Th rang of captur aways ncompass th ruc oity whih i qua to th inr of th Strouha numbr maur for th boy whn stationary. Thi ruc ocity i rfrr to as th rsonant pont Th ocation of th ran of captur rati to th rsonant point pns ry muh on th shap of th bu boy Fng 198) ha masur t ortx-shin frquncy bhin a fry ibrain circuar cyinr an a shap cyinr. In th cas of th circuar cyinr th rang of captur bgin at th ronant point an xtn to high au

of ru ocity Th -tion show a irnt bhaior with thhih-ocity n of th ran of captur ut about coinciin with th rsonant point

Th ran of captur ha aso bn masur in foribration xprimnts for a arity of buboy shaps but no car pattrn mrsan it must b concu that th bhaior of ortx shing in this rang

pn ry muh on th boy hap. For a iruar yinr th ran of captur bgin at th ronant point Barman Curri 979); for a squarsction Barman

Obasau 98) -sction an at pat h ran of

captur stras th rsonant point an for a trianguar sction with on rtx pointng ownta th ang of aptu n at th ronant pointBarman ai 9. Th rasons for hs aritions r not unrstoo

Th rang of captur or o-in i a a inta of uc oityor whih ow conition about a bu boy chan rapiy with ru ocity. Th tim prio btwn th shin of ortics rmains onstant an hnc th Strouha numbr which is qua to th inrs of th ru oity hang Rarraning Equation 2) th nonimniona trngth of a ortx in th wa is gin by

3f it w uppos that th bapur ofint an th iruation fration r rmain unhang through ocin thn Equation 3 inicat that th strngth of th wa ortis shou incra with incrasing ru ocity Thi imp anayi ao shows that ampication of th ortx strngth compar with its stationary-boy au wi our if th

oin xtns to ru oitis abo th rsonant point. Support for th assumption that r is itt at by boy motion coms from ais196 who hows fo a -stion yin that = .26 whn it i

A n n u . R








17/28

ILLATNG L D 21

siony nd = 0.24 o-in wih D 0.2. nno e ssumed wh ny eny howee h ohe u-ody shpes w ehe n s wy.

n he oex-omon egon hee s eed etween he ong up

o he she yes no oies nd he ow ound he ody suh h sm nese in oex sengh n ed o n nese n se suon nd dg nd hene n nese in shed oiiy he seption pints. Suh suon s ey unse euse he ex oty n ed o eensonge otes howee s pesumed th ennen s o ono he ne-we ow. ene neeng wh he oex-sheddng nsy mehnsm my podue ge hnges in oex sengh se pessue dg nd seon uung oeen. The esus o es (197 o -seon ynde show whn he ok-n nge o D = 0 n nese n rvD o 36% nd deese n CP o 71% oped wh thexedody ues

Mesuemens sowng n nese n D on n osng u yinde hough ok-n he een epoed y on ned (19Sed (9 Tnid e . (93 nd Spy (9. se-pessue esuees on u ynde de y Snsy (976 e shown ngue 8 whee p/p (he o o he nmu ue o he se

6

o

/ Fe Raio o mimum aspssu ot o a ula ld a lok to valufo a staoa d vsus osllato amptud Stas 76

A n n u . R e

v . F l u i d M e c h . 1 9 8 4 . 1 6 : 1 9 5 - 2 2 2






18/28

22 BARAN

ssu cocnt t oc-n to th stton-cnd u) s otdgns D.· Bn s (77) h od s-ssu sunts on t -sh nd ngu scton h t onn donsm Th scon nd h l sho dcss n

s ssu oc-n. Rsus o h ngu scon nd squscton nstgd Bn Osu (82) ottd n gu nd sn o sho sl ho h no lcon n ssucton A ducd octs o ocn h th sctons ng

od o oscll quncs h hn h nu shddnuncs th s-sucon cocnts nd hnc h dg cocns dcll ducd. hs sus sho ht th sh o thtod th gon o u od dons o s son ons s n t on o n dtnng th sons o h o o

od ons.

2

·2

·

_ - t - - JV - x X x ,1 X

D

�

\ I f

\

�

t-_

.

D

V

-

7 U

F Bsrssr ccn rss c. qr scn n oslln 01 (Bn & sj 8) Tnl son : son \osclln, (Brn & Ds )

A n n u .

R e v . F l u i d M e c h . 1 9 8 4 . 1 6 : 1 9 5 - 2 2 2 . D o w n l o a d e d f r o m w w w . a n n u

a l r e v i e w s . o r g

A c c e s s p r o v i d e d

b y R o y a l M e l b o u r n e I n s t i t u t e o f

T e c h n o l o g y ( R M I T ) o n 0 5 / 2 8 / 1 6

. F o r p e r s o n a l u s e o n l y .


19/28

OSCLLTING BL BODIES 23

Wthn the loc-in ne, ll the lble eslts sho n increse in the ll ttn lt nt. Th d t dnnlt th t l -n n b extd t n th tnth hd te their xed-bd ls th incrss in rtx stnth ledin t

hhe les o re csed b the direct nence othe bod moementon the o eld t section. A common etre s redction n the lenth the otex-mton ein, th tne tice oin neer thee

Meement n lltn l lnde h ben de bso ssn (4) Jnes () () nd tbli (1).In these inestitions n hch the bod s oced to oscllte the hsenle beteen lit cttions nd bod dislcement s lso mesredTh nl th bl-bod he he l et o le elble s the tn hih h ben netted b Wlnn(14) Oti et l (4) m Mizt (15) nd Ben 98

A tcl set o r's crcrclinder dt s shon n Fe or orced ltde o ibrtion o yjD . Fe lOa hos the in he nent o ¢ nd Fe lOb the t-h mnent xttn n ¢ Thee elt indt tht the h nl hnedl thh l-n nd tht the btntl tx-ndd to excte osclltons onl t redced eloctes rond lso

oints ot tht the inhse or nert comonent o t the ont o xim excttion, hen exressed s n net coecient, hs le e l t tht or clinde ern smll-ltde ollton n till d Thi lt shs tht i th ntl een o slltin � lnd ld n te md n tll t thn t tx nnc similr reenc o oscillton ill be recorded The mximm les o the ot-o-hse comonents mesred b (8) he been inclded n th dt lotted in Fe . In s exeient the x exttn t UjND = hee th ntthe ted hihe l dd lit.

Vtns in the in-hse nd ot-hs comnents thh loc-inre csed rmril b lre hsenle chnes The hsenle

chnes mesred on cclr clnder oD . b Fen (168) nden Crri () r re nd oced brtons esectel, ehn n ie 1. he h n thee exent nd b mn th he den beten th tn 0° the nt the clinde nd the dislceent en (1) esed the hse

nle or nmber o cses ith derent strctrl dmns nd hence th derent ritons o D ith jND. sn hs dt it hs been osibl to nd nmb o mrment t jD = . o dierent

A n n u . R








20/28

5

'

(b) �Fgu 0 ft cocin vrsus rducd voc for forcd oscation of a circuar cindra 0 (a In-has cocn; () otofhas cocn (Sarkaa 1978

A n n u . R e v . F l u i d M e c h . 1 9 8 4 . 1 6 : 1 9 5 - 2 2 2 . D o w n l o a d e d f r o m w w w . a n n u a l r e v

i e w s . o r g

A c c e s s p r o v i d e d b y R o y a

l M e l b o u r n e I n s t i t u t e o f T e c h n

o l o g y ( R M I T ) o n 0 5 / 2 8 / 1 6 .



21/28

SI l U IS

///

Fgu 1 1 Pse-ngle esueens on oce n ee vbng cc clne 011 oce vbon Ben e 1979) ee vbon Feng 1968)

edued eoes Tese anges n pase ange ndae a e pon nan oslaon ye a w a fomng oex geneaes s maxmum f foe as dasay w ayng edud eoy Zdao (1) by examnng e owsuaaon sudes of en Haog (1934), eeWndos (1939) Ang e a (1974) and Gfn Rambeg (194), asnoed ow e mng of oex seddng anges oug e on ange

Hs onusons w ae osy dawn fom expemens on feeybang ua yndes sugges a ee s a sudden ange n paseHe noes a n e owe eduedeoy egon of e on ange eoex fomed on one sde of a ynde was sed wen e ynde was eae axu apude on e oppose sde W nease n edued eoy e ng anges suddeny su a e oex w e sae uaon as befoe s sed wen e ynde eaes e axmumampude on e sae sde Conoed foedbaon expemens aed ou by Beaan ue (979) a xed ampudes sow aaoug e pase ange ous oe a sa ange of edued eoy

s pogesse and no a dsonnuy.easueens of Cyrms (ooeansquae aues of y and pase ange

A n n u . R e

v . F l u i d M e c h . 1 9 8 4 . 1 6 : 1 9 5 - 2 2 2






22/28

6 BR

r sqr-sc cylr r rc br r rs 3 rscly r (75 sr l rcly l cylr b 45D l rs r Obs (8 s r c ssr srs crss s. A rs r sl srs s crs l rc ly c s

bcs s crss s br srly ls l rc sclls sqrsc cylrs sc crsl rc lcy s l crs cs c cs crclr cylr. s rsl ss

rc clrr yscl rs r r c bs bcs bs ls sr bl bs b crrcly ss sqr sc l b

r sscbl r-c sclls crclr cylrA rr rs r sqr sc s s byW Pris (7 s r rsc ll c cb crcl s r ll s scly l. yscs s rc rcss s lly rs

·1 AID

Fgu 2 Sr sctonxu vu of th rs cocn of uctutng ft Cym"surd i th ockn rng vrsus oston itud sttd fro rssursurnts Br & Obsu 1982) forc surnts Nkur & Mot197

A n n u . R








23/28

Fir 3 Sqr iour o b uio ur r of i f yr i ru ru oiy 0 D 5x, /D 1 /D = 5 Br Oju 1

4 RETN VRTEX-NUEATN

lhh h w am pmal a p a appaal f expemetal eult t wul t be pble lue wthut m bef u f t mth O aa t th ula l ha ha th m a. Sapaa (8) a Stabl (8)ha h mamt f -pha a -f-pha uua l f t allae h p f fel ba l qa3.2-3.5 The eul ae eua a mtat ha aa ba fm fba xpm a eleat xbl mte bl

b. mlat fat thee tat hw that fe-bat aa fm xpemal ep ha b u

A n n u . R e

v . F l u i d M e c h . 1 9 8 4 . 1 6 : 1 9 5 - 2 2 2






24/28

AAN

pedict oction meued n tot dieent epement whee omeo the mn pmete tht cn ect ccucnde ow e dieentSarpkaya (97) h pedcted the mmum mpitude meued bin & Koopmnn (977) t enod numbe between 00 nd 000 ug ocedibton dt meued oe the nge om 5000 to 25000.The good geement cheed uggest tht the Renod numbe m not e n mpotnt pmete o ocitng ccu cnde A mre eese mpua prgra has ee arred u y Sau (9) ada eampe hs preds the mptude meued y eng (97) o ow mdmpng pmete e hown n gue 4. Thee ome

ndcton o deent beho o nceing nd deceing educedey whh s a eaure o eng' measuremes. Sarpkaya (979) h decibed the conctn ew uounding the dt o eng nd dicue

the ases r nd agas the hyseress ee eg due to era sruuranonnete tubi eut ugget tht t cued im bnonneitie in the oce coecent the thn nonnet in the echnc etup.

en uie (970), inped by ihop & Hassas (964) obe ha a sa yderwae ma pssesses he hara tetc o nonine octo he epoed the ue o n de Poocitotpe eqution to epeent the phenomenon Thei mode whch ncopote nonine dmpng tem in n equton o

Cy,howed

condebe pome but pointed out b Pnon (94) i unbe to

o�o

o. oQ

5I

6

o 0

I

�

a

7

BU Figure Repne a reely ibatig cylinder wth 2MJ

=0 , experime Feg

1968);

- uma alulat Saub 981).

A n n u . R








25/28

LLATN B BDE 9

pr h ar-ampu har sr n ns xprmns.Varous oatos to th as artn urr ormuatn ha n proposed y op rn (93 an (9 and E. Brr [rportey Barman & raham (980 u h suns ar una rprua he sre ees espte an aemp y Iwan Bns (974 show hat a an dr o osaor-typ quaton an drd ro asu-mhas prnps appars ha h meh s n aequaey sr th ntraon twn ortx shn an oy ton.

rdton thods that auraty od th ow d around a uoy are he ones os ey to e sussu. Prsuay a t w oe whn w praa s h aros quans r h warun a u y at hh yns numr us a puer I s dut o prophesy when ths w happen ut n h an sm

rsarhrs ar xprmnn wh h us h dsr-orx mhod o o u-ody ows as ntond n an arr ston arpaya hoa (99a deeoped th od or a staonary ruaryndr owan hn app h sam hnqu a ry ran ndr seearpaya ha (979 an arpaya (979]. Th appan hs thnqu to osatn u oes s at an ary sta ut the rsuts arsuenty enoura to suest that t oud pro to a useu ethod

or arous u-y shaps

5. UG RERKurn th past tn yars r so hr ha n snant aans n th undrstandn o ort shdn ro osatn u ods.rhss h prm s y no mans soed and a nuer o asps requr urhr suy A mar unranty s n h hansm ha dtrns th phas o th ortxnu or rat th y n. A ratd unstd quston s th ro o h arody shap nrx-ndud osaons o u ods. haps thr than th r

nd to stud n ta ods wth x sparaon an a snantarody suh as a shap or a tranuar ston oud prod usuaddona es daa o proe preon mehos The onneon eween

re an or saons ns pursu urhr an an apshou ad t prt rsan rspons usn ata ro orosatons arred out unr dynaay sar ontons Th athe aa odn o rtxndud satns usn nonnar osar thory ad ow-d oputaon thqus s ontnun to deoped Th proe s a du one ut h ap ewn hory an

xprmn s n s

A n n u . R








26/28

220 Nia Ci

Aberath, H, Kroauer, R E 9. Thefomatio of voex steets. J. Flud Mech 0

Achebach, E 97 orex sheddig fromspheres J. Flud Mcho 09-

Agrii, Di Silvio, G., Zaardo, A 97Hdroelasticit stud of a circular cideri a water sream I Flw InducdStructural Vbratns ed. E. Naudascher,pp. 0 Berli Spriger 77 pp

Achibald, 9 Selfexcitatio of aacoustic resoace b vortex sheddig. J.Sund Vib 0

Bearma, P. ., Cuie . G 979 Pessueucuao measms o a oscllaig cicul clide. J Flud Mch9 -77

Bearma, P , Davies, M E 977 The ow

about oscillaig blu suctures. Prc. tC! Wnd Ej Buld Structurs 4th ed.K J Eao, pp -9. Cambridge Uiv.Press pp.

Bearma, P. , Graham, M R 90orex sheddig fom blu bodies i oscillator ow A repor o Euromech 9J Flud Mh 99

Bearma, P . Obasau E. D. 9 Aexperimeta stud of pressure ucuatios o xed ad osciaig suaesectio clies. J Flud Mch 9 97

Beama, P. ., Tuema, D. . 97 Aivestigatio of he ow aoud ectagular cliders. Aeraut Q 9-7

Bearma, P. ., Graham, M R., Nalor,P, Obasaju E. D 9 The rle ofvoices i oscilator ow about buclides. Int Symp. Hydrdy OcaEg Trdhm Nry -

Berger, E., Wille, R. 1972. Periodic fow phenomena. Ann. Rev Fluid M echo 4 : 313-40

Bishop R E D assa Y 9 he liftad drag forces o a circular clider

oscillatig i a owig uid Pr. R SLdn Sr A 77 7Blevs R D 977 Fldud brts

New York a Nosrad Reihold 3pp

Boor, M. S. Gerrard, J H. 9Measuremes of turbue votices i aclider wake. Pr R S ndn S. A9 9-

Calvert, R 97 Experiments on the ow-speed o pas coes. Flud Mh.7 79

Cemes R. R 97 A iviscid model of

twodimesioal vorte sheddig. FiMeh 7 -Davies, M E. 97 A compariso f thewake structue of a satioar ad oscia

ig blu bod, usig a coditioal averagig ehiue. J. Flud Mh 7 09-

Deebaugh, D., Marshl, J 97ime developme of he ow abou aimpusivel started cider. AAA J 90-

De artog P. 9 The vibraio probems i egieerig. Prc It Cnr ApplMch, 4th, Cambrd, pp

Fage, A, Johase, C 97 The ow of airbehid a iclied at pate of iitespa. Brtsh ARC R M 102

Fai, R Lawford, J A, Ere, R C. 99o speed experimes o the akecaacescs of a plaes omal o aair seam. Brtsh ARC R M 30

Feg, C C. 9 Th masurmnt Jvrtxndud fts n w past statnary and

sclltg crculr d D-sct cyldrsMASc thesis. Uiv. B Columbia,acouver

Gaser, M 99 orex sheddig from sleder coes a o Reolds umbers. Flud Mch -7

Gaster, M. 9 Some observatios ovortex sheddig ad acoustic resoas.Brtsh ARC CP 4

Gerrard, J. H. 9 The mechaics of theomaio egio of votices behid blubodies. J. Flud Mch 0-

Gerrard, . 97 Numerica computaioof he mgiude ad feec of he lifo a ccula clider. Phls Trans RS Ld Sr A

Gri, O. M. 90 OTEC cold water pipedesig for problems caused b vortexexcied oscillatios Nl Rs Lab.Mm. Rp. 457

G, O. ., Koopma, G. H. 977 Thevorteecited lift ad reactio forces oresol vibatig cliers J SudV 4 : 44

Gi O M Rambeg . E. 9 Thevore-street akes of vibraig cliders

J Flud Mh 3-7G O. M Rambeg S 9 Someece studies of vote sheddig ithapplicatio o maie tubulars ad risers e Reo Tho 0

Hardwick, J D., ootto L R. 97 Theuse of model ad full-scale ivestigaioso maie strucures Int Symp obInd Keik U.K Pap. 7

Harte R T Currie G 970. iftoscillator mode of vortex-iduced vibratios. J Eng Mch Dv ASCE 977-9

Hoji . Taeda, S. 9 Vrex wakes foscillatig circular ciders. Rs InstAppl Mh Rep.

Iwa, . D., Bevis, R. D. 9 A model for

A n n u . R








27/28

vorte indued osillation of strutures Appl Meh. 4 : 58 -86

ne C W 1968 ny i e gen y x ing gestatioary ad ocillatig cylider at highReynolds nmber ASM Pap 8-F-

Ki 1974 e-ecie ciin i yin in ey nOhore Teh Con Pap OTC 9

Land R 97. A mathematial model ovorteeited vibratios o blu bodies Sound Vib 42 29-34

Lee B E 97 The eet o turbulence onthe surae pessure eld o a squae prismJ Fluid Meh 69 263-82

Mi W A M 97 B in x eing repot onuromeh Fluid Meh 4 094

Mau

Youn R A 973 Vore

sheddi from blu bodies i a shea ow Fluid Meh 60 409Meie-Win A 1939 Fe

shwinue n yinn i gihmssige Flssikeitsstom Mncheneh Hohsh Hydraul Inst Mitt 9 -22

Min M V 964 low aound iularylinders A kaleidosope of hallenni penen AM p Full epFlows pp 10218

M T 97 Uny)jts ad wakes of oscillatig retangularpisms ng Meh Div ASC 0 8-7

well D 1980 ratialExperienes with FlowIndued VibrationsBelin : Spriner 849 pp

Naumann A Mrsbah M ramer 966 he onditios of separation· andvorte ormation past ylinders AGARDCon Pro ep Flow 4() 3974

Otsuki Y Wsiu K omizawa Oy A 197 A n n e eeiciniiy pii wi qsetio Sound Vib 34 23348

Parker, R 966 Resonance eets in wakesheddin rom parallel plates some epeien bin J ound Vib 62-72

Parker R 967 Rnn in weingom p paes : alulatioso resonant reuencies Sound Vib 3343

Pinn G V 974 Mathematical modelsof ow-indued vibrations In FlowIndued Strutural Vibration ed E pp 81-127 Bin ping4 pp

Peter R 98 Vorte shedding rom avibrating able with attahed spherialbodies in a in e w Naal eLa Memo e 44

B B 221

oha 97 On untead ow patlnders of square ross setion i Qn My Cl, ni Lnn

Reg S E Gifn O M 976 Veiycorrelation and vorte spacn in the wakef a vibratin able Fluid ng 98 08

R A 94 h drg n eingeqeny winin iNACA Teh Note No 69

Roshko A 96 xperimets o the owpast a irular cylinde at very hihReynolds numbe Fluid Meh 0 346

apkaya, T 97 An ivisid model o twoienin e ing ninn ypiy y ep w an nlined plt Fuid Meh68 09-28

arpkaya, 978 u< ore on oanylinders Waterw, Port Coatal OeanDi AC 1 27-90

py 1979 V-ince iin J Appl Meh 46 41-8

arpkaya, choa R 979 nviscidmodel of twodimensional vorte sheddinby ic yine AIAA 7 93-00

Sapkaya, hoa R L 979 A disretee nyi w inyn ney iing i yin eh ep PS69S9 NavalPostgrad Sch Monterey Cali

cruton 963 On the windexited osilin staks towers and masts nWnd ets n Buldins nd trutures 798832 Lnn Mey'iny O 8 pp

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kop R A. Gri, O M 973 A model for exexie enn pn yin J ound Vi 27 22-33

Stasby P 976 Base pressure o osillat

ing cirular cylinders ng Meh DiASC 0 9-600ny K 1981 A nri y

ex eing n n w iyin Aeronaut Q 3248-7

tasby K io A G 98 hemportae o secondary sheddin i twoinin w rin at very igReynolds number Aeronaut 33 023

i T 981 Calulation o the vibration n eiy ne yin ingeperimetal data rom forced osllation

ASM Sp Fud/Strut nteratonTurboahiner pp 9-24ni Oi A Wnb Y 1973

iiy ci cyine iing in

A n n u . R e

v . F l u i d M e c h . 1 9 8 4 . 1 6 : 1 9 5 - 2 2 2






28/28

222 ARMAN

nio o o n a ak J Fd Meh61 : 768

anne 9 eo o en ebae a o n bln aiinee Au Q 23 523

Vick B 966 Flctatn lit an aon a on cine o qae coectonn a oo an n a ben ea Fuid Mh 494

Wazonk M A Pakinon V 979obn ct o allon inabilitan vox eonance In P t C!Wid E uid Ses th, FtCis C a V2 2

Wl M Gibon . 1979 nactono inc on i o at a qa

lan a n a c J Sd Vb67 011

Wknon, R H 9 h txiduddi b yids en Bo K

Wooon R 969 T ocaion ola

cicla ack in n P st C E43 39Wooon R Wane H, anby R oo H 972 ciaion il n an c o tll-cal xint a na.CIRA h Re

Zavkovc M . 98 Moicaon vo in n t nconzatonan ASME P WAFE 8 .

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v . F l u i d M e c h . 1 9 8 4 . 1 6 : 1 9 5 - 2 2 2





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Vortex Shedding From Oscillating Bluff Bodies