Table Of ContentComputational
WinEdn ginee1r ing
Proceeodfti hneg s
1tsI tnernaStyimonpaolso inu m
ComputaWtiinoEdnn agli ne(eCrWi9En) 2g
Tokyo,Japan2,12A-3u1,g99 u2s t
Editbeyd
S.M urakami
InstoifIt nudtues Stcriieanlc es
UniveorfTs oiktyyo
TokyJoa,p an
1993
ELSEVIER
• • •
AMSTERDAML ONDON NEW YORK TOKYO
ELSEVIESRC IENCPEU BLISHERBS. V.
SarBau rgerhart2st5r aat
P.OB.o x2 111,0 0A0E AmsterdaTmh,eN etherlands
Reprinftredo mJ ournoaflW indE ngineerainndIg n dustAreiraold ynam4ic6&s 4, 7( 1993)
ISBN0:4 4841 678 8
1993E lsevSiceire nPceu blishBe.rVs.A lrli ghrtess erved.
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Preface
TheF irsItn ternatiSoynmaplo siuomn ComputatioWnianld E ngineering
(CWE92)w ash elda tt heU niversiotfTy o kyoi nA ugust1 992u,n dert he
auspicoefst heJ apanA ssociatfoiro Wni ndE ngineerainndgt heI nstitouft e
Industrial SUcniievnecres,oi ftT yo kyo.
Thea imo ft hiSsy mposiuwma st oe xplotrhee c hallenpgoesse bdy t her apid
developmeonftC omputatioFnlauli Ddy namic(sC FD)w ithitnh efi eldo f
engineerCiFnDg .i sa lready essteonr teisaela rch concweirtnhfle udi dfl owi n
civieln gineerainndgi ,t fsu rthpeort entfoira alp plicatiinwo inn de ngineering
ish ighlpyr omising.
CFD developmeadi nliynt hefi eldosfm echanicaanlda eronautiecnagli neer
ingG.r eastu ccehsass b eena chieviendp redictsiuncghr elativseilmyp lfleo ws
asc hannefllo w,a irfl owa rounad w inge,t cH.o weverp,r oblecmosn cernianigr
flowi nw inde ngineerairnefg a rm orec omplicaItnem da.n yc asetsh,e c urrent
CFD technolobgoyr rowefrdo m othefire ldiss t husi nadequaatned n ew re
searcahn dd evelopmeanrteu rgentrleyq uiriendt hifise ld.
State-of-tphaep-earfrrsot m alolv ert hew orlwde rep resentaettd h iSsy mpo
siuma,ff ordinrge searchienrw si nde ngineertihnego pportuntiotp yr esent
theimro str ecenfitn dingcso ntributtoit nhgeo veradlelv elopmeofnt th efi eld.
A hosto fr esearchaenrdse ngineerresp resentbiontghi ndustarnyd t hea ca
demiwco rladt tendtehdi Ssy mposiuwmh,i chw asd esignteodi llumintahtee
presepnatr ameteorfts h efi elda,s w elals t os uggefsrtu itafruela fso rf urther
research.
Twenty-thtreeceh nicsaels siownesr eo rganiziendc ludifnogu rs pecial
sessiofnesa turitnwge lvien vitsepde akeorust standiinnt gh efi eldosf c ompu
tationflauli dd ynamicasn d winde ngineerian wgo,r kshofpo cuseudp on
numericaanla lysoifts h ei nteractbieotnw eeflnu idfl owa nds tructuvriablr a
tiona,n da videsoe ssiwohni chd elveidn tcoo mputegrr aphifocrs t urbulent
flowfieldasr ounsdt ructures.
Selectpeadp erfrso m theS ymposiuamr ec ompiliendt hiPsr oceedivnogls
ume.T hes ummarioefst hew orkshoapn dt hev idesoe ssiaorne a lsion cluded.
Thee ditowri shetsh iPsr oceeditnogs se rvaes a vehictloep romotfeu rther
developmeinnct o mputatiownianlde ngineeriIn wgo.u ldl ikteo e xpremsys
sincegrrea titutdoae l lt hea uthorfosr theicro ntributions.
FinallIey ,x tenmdy sincetrhea nktso t hem anyi ndividuaanldts h eo rgani
zatiownhso a ssistientd h es tagionfgC WE92l istiendt hef ollowipnagg eI.n
particuIl waoru ldl ikteo e xpresmys special thtaonP krosf essMo.r M at
sumotoK,y otoU niversiatnydD, o ctor MAa.c hidIa.,L SU.n,i versoift yT okyo,
for theigrr eacto ntributaisot nhsec hairmaonft heP rogrammiCnogm mittee
andt hes ecretagreyn eraolft heS ymposiurme,s pectively.
ShuzoM urakami
SymposiuCmh airman
Symposiuomr ganization
S.A kabayas8h i Y.M atagi8
H.A kao7 M. Matsumo4t•o7 •8• 1 0
J.EC.e rmak6 T.M iyata7
H.D aiguuji6 T.M izutani7
A.G.D avenport6 A.M achid?a-l o
K.D eguchi8 Y.M orikawa8
M. Endo7 S.M urakam1-i3•9•1 0
J.HF.e rziger6 T.N omura-810
K.F uji8i 7• K.O gawa8
Y.F ujin7•o 8 A.O kajim7•a8 • 01
K.H ama7 M. Ohba8
K.H ibi98 • T.O hkuma57••8
M. Hino6 Y.O hsaki7
J.C.RH.u nt6 W. Rodi6
I.I mai6 T.S aito8
T.l namur-o108 H.S akata7
Y.I shida8 K.S ato7
H.I shiz6a ki M. Shimura98 •
M. lto6 N.S hirai6s hi
J.K anda?- lo H.S hirato8
S.K ato-710 T.S tathopou7l os
A.K awaguchi8 Y.S uyama8
H.K awai-710 T.T akeda7
H.K itamura 7 T.T amura-810
M. Kiya7 Y.T amur?a- lo
N.K obayashi8 T.T anaka8
T.K obayashi7 A.Y oshiza7w a
B.EL.a under6
1Ch airmaonfC WE92
ChairmaonfO rganiziCnogm mittee
2
ChairmaonfE xecutiCvoem mittee
3 ChairmaonfP rogrammiCnogm mittee
4
5 ChairmaonfW orkinGgr oup
Memberosf S cientAidfivci soBroya rd
6
Memberosf O rganiziCnogm mittee
7
Memberosf E xecutiCvoem mittee
8
Memberosf P rogrammiCnogm mittee
9
1Me0mb erosf W orkinGgr oup
JouronfaW li nEdn gineaenrIdin ndgu aslAt erriodyna4m6&i c4s,7 (31-91993 ) 3
Elsevier
On theS imulatioofnT urbuleFnlto wP astB luffB odies
W.RODI
InstiftouHrty ed romechaUnniicvse,r osifKt aryl sruhe,
D-750K0ar lsruGheer,m any
ABSTRACT
Thep aperr eviews calcpuelrfaotrmieotdno s- daotfve o rtex-shefldodwpi ansglt o ncgy lindaetr s
higRhe ynolndusm berwsh erteh ee ffeocfst t ochatsutribcu lfelnutc tuastuipoenrsi mpoons ed
th2eD p eriosdhiecd dimnogt ionne edtsobe simulaTtheede .x periegnactehse wriedtv ha rious
statistical mtoudreblrusal negnicfrneog m algebreadidcy -vismoocdietltys oR eynolds-stress
equatmioodne lasr seu mmariasneddd iscusasneddc ,a lculaotfiv oonrst ex-shefldodwpi ansgt
cylindoefvr asr iocurso ss-seacrtei opnrse sTehnetseceda .l culaatiroceno sn frontweidtl ha rge
eddys imulatwihoennse vpeors sibalneda, c omparative doinstc huevs asriiooncu asl culation
methoidssg iven.
1. INTRODUCTION
Thef lopwa sstl endbelru,ffb odieissfr equentalsys ociated witvho rpteesrxhi eodddiicn g
causidnygn amilco adionngt heb odieMse.t hodfso rc alculatthieun ngs teafdlyo awn dt he
dynamlioca dianrgoe f g reparta ctical imIpnot rhtipasan pceoern.,l vyo rtex-shefldodwpi ansgt
loncgy lindiescr osn sidewrheidci hst wo-dimensiinto hnema ela nA.t l owR eynolndusm bers
thefl oiws a l amin2aDrp ,e riomdoitci ownh iccha nb ec alculfaatierdwl eylw li tphr esent-day
numerimceatlh od(es. [g1.2 ,] A)t.h ighReery nolndusm berwsh,i cuhs ualolcyc uirnp ractice,
stochatshtriece -dimentsuirobnualflleu nctt uatairosenu sp erimpoonst ehde2 Dp eriodviocr tex
sJ:.ieddimnogti on. Tishi ilsl ustriantF eidg1 .,w h erfei st hei nstantaneouosfa q vuaalnutei ty,
f ist het ime-mevaanl ue,t hep eriodic
r
fluctuatiotnh,e s tochasttuircb ulent
t'
flucuatiaonnd< f> tehnes emb(loerp hase-) t I
averagveadl uTeh.et urbulfleunctt uathiaovnes
a considereaffbelceot n t hep eriomdoitci on
whicnhe edtso b es imulaitnea d c alculation
methodT.h eraer ev arious possfoirb ilities
be
doinsgo O.n ew ould tos imulattheee ntire
fluctuating bmyos toilovni ng numerically the
3D unsteaNdayv ier-Steoqkueast ioTnhsi.s
methocda lled direct sniummuelraitciaoln
(DNS)is p resently foenalasyti r bellea tively T
lowR eynolndusm ber(ss abye loRwe 104).
=
Att heh igheRre ynolndusm berosfp ractical
intertehsedt i ssipaptairvotef t het urbulent
motiohna s ssumcahls lc alceosm parweidt thh e
cylinddiearm ettehrai ttc annboetr esolivnea d
Fig1 :P eriodaincd s tochaflsuticct uations
numericcaall culatTihoenn u.m beorf g rid
inv ortsehxe ddiflnogw
poinrtesq uitroer de soltvheim so tioinn creases
approximaatsRe el3y.
01675-/96310/06$.©00 1 99-E3l seSvciieerPn ucbel iBs.hVeA.rl rsli grhetsse rved.
4
A methotdh acta n abpep liteos di tuatiaothn isgR he ynonludmsb eirsts h lea rge-eddy
simulatiownh i(crLheE sSo)lo vneltsyh lea rgerm-ostciaTolhene .e ffecotft hsem all-scale
motitohnac ta nnboert e solovne gdai vegnri nde edtsobe modelleTdh.ie sffe citsm ainly
dissipativei,s w ii.tehd.r fraeownmnte hrpega yro tft hsep ecttrhuacmta ben resolTvheed .
effeccta nb ea chieivnet dw ow aysT:h e usounaeil st hrouags hu bgridm-odseclaf loer
detenrimnitgu rbusltreenstis netrsod ucbeytd h seu bgridl-efs lctuaucatitohonets h;pe ors sibility
ist ol eatvheee n erwgiyt hdrtaonw uamle rical dbaym npaui mnegri cal tshciahtne trmodeu cae s
certaamiounn otfn umerdiicasls ipThaet LEiSo nm.e thiodps o tentivaelrlyy powberufLtuE lS,
calculaartveie orcnyos stalnyhd e ncthee irsie n teirnem osrtee c onocmailcc ulmaettihoodns .
Attemwpetrste h eremfoardee simultautreb ulienvn ocerext -shefdldoiwwnigst sht atistical
modelwsh icdhon orte soalntovo yef t hset ochatsutirclb eumnott ibounat v eriaogtue a tl together.
Fort hfleo wsc osnideirnet dh ipsa peorn,l2 yD e quatnieoentdsobe solved, which are the
ensem-balveeraNagverid-e Stoekqeusa tsci oonntaiRneiynngo sltrdess <sUeisU dju et ot he
avearginpgr ocedTuhrees.se t ressesa,l suwonh diecrhpg eor iovdairtcii ao'nn>s e,et do b e
determbiyn esadt atitsutribcuallme ondceSelo . ftaurr,b ulmeondceedl esv elopetde satnedd
extensifovres lteya fdlwyos w ertea keonv earn da daptfoerdu sei nv ortex-shedding
calculaTthieao dnasp.t aitnivoonlr veelsag tt ihRnee ynolds tsotre enssseemsbv leer-aaged
velocititehsae d daintdoi fto inm e-depteenrdmiesnntr t a nspeoqruta tifootrnu sr bulence
p eters.
aram
Whent hpee rioflduicct uaatriaeol nsasov eraogueted,q uatdieosncsri btihtneig m e-mean flow
are obtIanti hneeisdne.a , d dittioto hnRe e yonldsstr essceoser,lra tiinovnosl tvhipene gr iodic
fluctuaaptpieowanhrsi cthh eanl so tnobee emdod elleAdsi. it s d ififcutloat rr ivaeta g eneral
modeflo r tchoersarete iloannsds inncoei nformaotinto hnde y namlioca driensgu frlotms
steacdayl culatthiaiopsnp sr,oi asoc fhl imiitnetde arneds tni odsti scufsustrehdeh re rTeh.e
paperrei vewtsh eex perigeanicnese odf awri tthu rbulmeondceefl osrv ortex-shedding
calculoaftfl ioownassr oucnydl inodfev rasr icoruoss s-saencdct oinofrnostn htesws iet thh e
fewL ESc alculaavtiaoinlsa ble.
2. STATISATLIT CURBULNECEM ODELSE MPLOYED
Sattisttiucrablu lmeondceehl asv teh tea sokfd etenrimnitgh Ree ynolsdtrse ss<eus( uj'>
appeariintn hgee n sembvleer-aagNeadv iSetro-keeqsu iaotnIsnt. h isse cttihotenu ,r bulence
models are introducehda vbebe reiunes feildny t hwveho ircthe x-shceadldciunlga tions
reoprtientd h e nseecxtti on.
Eddy-vismcoodsesil.It nsy i mpmloedres lt,h e Reysntroelsdassrer ese lattote hdgre a dients of
theen sem-balveervaegleodc <iutiit ehsr ough thee dfodlyl-ovwiisrncegol saittiyo n:
(> )
, I lit a< Uj > +a < u;.> 3 ()1
-< u;u>;= < > -2< k> a< ; ;
Thev ariaotfit ohnee d dvyi sco<Vsatix t;oy v esrap xa;ca en dt immeu sbet determintehde by
turbulmeondceFelo .rt hiDse,n egt a l[>.3 u]s etdh ael geberdadiyc- vismcoodsedilut ety o
BaldwainndL oma[x4 T]h.i esm plotyhsve a nD riemsitx ing-lengitnth h neme oadre-lw all
regiionnc,l utdhiveni gs cous sIunbr leagyieofrnu.sr tahwearyfr omt hwea ltlh,ee d dy
viscoissri etlyad tieercdt tloay s ingvelleoc iatnydl engthc-hsacraalcet oeftr hirisestg iico n.
boundarsy<V, lta iysce arlculbaastiecdfra olmtl hyve e locgirtayd iaetanp to sitiwohenr tIneh is
grdaienwte,i ghwt>i etdth h wea ldli starnecaec,h measx iam uImnw. a kree gio<Vnts ,i s
determbiytn hemdea xmiumd eficvietl oacintdy m tahxei mvueml ocigrtayd ieinntt hw ea k>ae ta
particcruolsasr- sCeocntcieopnt.tu hasilisl myp,el ded- yviscmoosdietdlyo enso ste etmo b e
versyu itfoerf dl wosw itlha rsgeerp arartegiioson.n
5
A concepmtouragele lnye mrodaelli st hke- mEod el whrieclhat theeeds d vyi sco<sVitt>ty h e
turbuklienneettin ce r<glyoa nidt dsi ssipraati<toEen>a ndde termtihdneie sstri buotitofto hne se
twot urbulence frpoammr oadmeelt ertrsae nqsupaotrTitho enm so.d el emipnlv ooyretde x
sheddcianlgc uliasats itroanisg htfoerxwtaredno sfti howeni detleys kt-emEdod elfo rs teady
flows.
Franektae l[ .5e ]v aluCaatnetdwa enlCdlo le[s6d']a tfoarv ortex-sflhoewpd adsaict ni grc ular
cylianndfodeu rn tdh sautb stantieaxliw srhtee greti heoedn dsvy i scoisnsie tgya tainhvdee n ce
theed dy-vicsocnocsieisipt ntyv aThleisdree.g iocnosrr esptoofln odware as whheirseta onrdy
transpeoffretco tfts u rbulqeunacneta irtideeo sm inTahnets.pe r ocesasrepeso or(liayfta ll)
descrbiybe eddd y-vimsocdoeslisthayen ndtc hee msodee lmsu sbet expecttose hdo pwo or
perforfomrav nocret ex-sflhoewdsd.i ng
Reynolds-stresmso-deeaQlnusdda etriivoant. i Rveeysnolds-stre(sRsS-Eem)qod uealtsi on
accofournh ti staonrtrdya nspeoffretcb tyss o lvmiodnegltr ansport foerqt uhaietn idoinvsi dual
Reynosltrdess <sue(su jA'g>a.is ntr aightforwardo fse txetamedonyds eialorsnee sm ployed.
FranakneRd o d[i7 a]d optthesedt andRaSrEmd o deolfL aundReere,ca en Rdod i[ 8w]i,t h
walclo rrecttoti hopenr se ssurtee-rmsdstru ateioG n i bsaonnLd a und[e9Jr]a .n s[s1o0un]s ed
ana lgebsrtraeimscos d e(lA SMi)nw hicthhd ei fferesntrteiesaqslu atwieorens si mpltiofi ed
algeberqauiact biyom nosd eals sumptaiboontushtc e o nvecatniddo inff ustieornm s. The
assumpotfRi oond i i[sa1 d1o]p tienwd h ich hainsdtrt aonrsyp toerrtim nst h<eU ijU>
equatiaornrese lattoted h eeq uivtaelrmeisnn t <tlhoe- equattihoenei.vr a luoaftiC oann twell
anCdo les'Fdraatneakt,ae l [.5 fo]u ntdh tahti aspp roxiInim sac toinosni demroarrbeel ayl istic
thanne gletchtheii nsgta onrtrandys portte ramlst ogfoertt hhneeor r mal sbtruteths iasittens so t
sos uitfoarbt lhese h esatrre ssAests h.ke - E eddy-mvodieslbc aossiicitamylp lltyih enese glect
ofh istaonrtrdya nsptoerrtmt shu,es oef a na lgebsrtraeimscods e lc aben expecttobe rdi an g
modesitm provement.
Near-wtraelalt meWnittt.hh vea ritouursb ulmeondcedeli sff,e raepnptr oawcehrteees s fotre d
handltihnneeg a r-rweagliOlon nea. p proaacdho pwtaedst h ues oefw alflu nctiionwn hsi cthh e
viscsouubsl aiysne orrte solbvutethd fie r sgtr ipdo iinslt o cated outsBiadsei ctahlilsy ,l ayer.
thqeu antaittt higierssi p do ianrtre e lattote hdfe r icvtieolno bcaistoeynd t haes sumpotfai on
logarivtehlmoiccdi itsyt riabnudto iflo onc eaqlu iliobfrt iuurmb ul(epnrcoed uction
dissipDaetniegota n l)[..3e ]m plotyheledo w-Reynoldvse-rnsuoimftobe hnkre - mEo dedl=u e
toN aganaon dT agaw[a1 2v]e ry tnheweaa rl lIsnt. h is mfoudneclt,ii novnosl ving the
viscoasnitdth wyea ldli staapnpceewa hri cahra eb seinntt h set andka-mrEod d eFlr.a nakned
Rod[i7 a]n Jda ns[s1o0tn]e satt ewdo -laapyperroi anwc hhi cboht,hi nc onnecwtiittohhnk e - E
modealn dt hReS Eo rA SMm odetlh,ve i scsouubsl awyaesrr e solwvietadhs impler one
equatmioodned lu teo N orriasn dR eynoldsI nt [h1it3sh],ve. e locityo fts hcteau lreb ulent
motiiosan l dsoe termfrionmte hd<e l o-equbautttih loeen n,gs tchai lsne o dte termfrionmae nd
<£>-equRaattihotenhr.le, e ngth-scalei spd riesstrcirbaiunbtdiei npdo ar,nt icaul lianre ar
distribiusuti soewndh icidsh a mpneedart hwea lalsi nt hvea Dnr imeisxti ng-mloedneglt.h
3. LES MODEL1ESS 1ED
Inl arge-seidmduyl atthiteoh nrse,e -dimensional time-edqeupaetnaidroeenn st Navier-Stokes
solvneudm ericatlhleyra;el bmlyo tihoanvsi sncga lleasrt gheartn hm ee sshi zaerr ee solved,
inclutdhi2enD pg e risohdeidcd fliuncgt uaTtihoinsssi .m uladtoienoson dt i stinbgeutiwsehe n
thefsleu ctuaanttdih olena sr gert-usrcbausllteeoc nhta flsutcitcu aOtfic oonusrt.sh efie,n etrh e
numerigcraiulds etdh,fie n eirst hsec aolfet hmeo tiotnhsac ta nb er esolAvsew da.s
mentioanlerde aatld oyRw,e ynonludmsb earlfsll uctumaotitnigco anbnse r esolbvuentdo a,tt
higRhe ynonludmsb eTrhsee. ff eocftt h uen resoslmvaeldl -msoctiaoolnnet hree sollvaerdg er
scamloeti onne etdobs em odelTlaemdu.er taa l [.1 4l]e atvhesi ism ptloty h dea mpienffge ocft
6
thtehiirr du-powrsidcnehdrue smfoeerd d iscrectoinzvientcget rmTitshoh.edne yo n octa ll
thmeeitrah l oadr ges-iemdudtlyea ctihobnnui adtq i urefie nciittff ee-rdmeentchyeoe idtit,a s
quastie-LcEhbSne icqauautetsh heei, g Rheeyrn noulmdbcseo srnisd beyrt ehdet mhs,em all
scamloet cioouncl edrn tlnayoi tr ebseo bluvoten dtl hyle a rsgceamrlo-et iWointt.hh is
appcrhto,ha einrsoed irceocntotr nto hlde a mpeiffneagcn ttdh miusbs ete xpetcdote epde nd
ont hger eimdp loTyhaeep dp.r porauoccdhse usrp rigsoiodrn egsluyln tessx et(c stbeiueot n )
itismp licnaotictol naesnas drh obueel xda mined.
are
Thmeo rues uaanlad,l csooin dsemroerpder owpaetyroa ccofourtn htee ff eocftt h e
unressomlavleld- sictsaso li em utmlhowaitiitsotten hha e io dafs ubgrid-Tshc3eaD le model.
timee-nddNeeapnvtSi teorek-qeusa stioolnrvseee pdsr eenqtu aatvieornoasvgt eehrcde o ntrol
voluomfte hnseu megrrioicrdwa, hl a ietsq uiveaqlueanfrtitoo,mwn hsi tchshem all-scale
mothiaobsne efinlt oeurTteh.dae v eirnoagrfg iltienrtirnodcguoe crlreastbe itownetseh ne
unresfloulcvteuda tiwnhgi acvcahetss l tr oecosinstt ehriseee sso lveadnn dme otebtode i ons
simuwliaatt hem doM doedlse.il msti tolh saetr a ttiusrtibcualle ncieun s tmehom,eda eilns are
diffnecrbeee itnhtgah ltee nsgctadhlo ee sn enteobodt e d eterbmucitanb neet d a kaestnh e
messhiM zoesc.to mmiotsnh s ei mepdldey -vmiosddceuoltesS o im tayig nosr[1k5yI] tn.h is,
thseu bgriedd-vdsiycs aclioerss e ilttatoyth seetrd a riaonttf eh r ee somlovtieaodnnt d hm ee sh
siMzuer.a keatam l[1i. 6 1,7 e] mpltohyseetd a QSdmaargdo rmiondisentkl hy eL iErS
calculations.
Netahrwe a elslp,e ictnih aveli lssycu oybuelstra hs,e c aoltfeh mseo ticoonnstr imboutstiotn g
thteu rbmuolmeetrnnattn issfe ra snmcdaa lnln ot bael arrgees-soeildmvdueyaldh ta i tiginho n
ReynnoulmdbsIe nmr ossL.tE cSa lcualhtai tRgiehoy nnsno mulbdeslr istk,heo e n oefs
Murakeaatml [i.1 61 ,7 ]t,h riesg iinsoo rnte soalatv lbeludb t r idbgyue sdia rn egl ation
betwtehweean sl hles atrrea snsdv etlhoaetct hi fietrg ysr tai wdafr yo mt hwea Mlulr.a ekta mi
a[l1 6 u] saer de lbaatisooenntd ha es sumopaflt oigoarni vtehlmodicicis ttryio btfuh ttieio mne
meafnl oMwu.r aekaat[lm 1 i7a ]d opWteerndae nrW de ng[l1e8a']p sp roiawnch hia cl hi near
(y+1 1.8o1r1)n p owlear(w y +1 1.8d1i)s troiftb huietsn itoannu tsva enleoiocsi ty
as�s uImsteh dob.uem le dn titohT�na aetmd ue rta[ 1 a4dl]in. do t iantrnsoypd euncceiewaa arll- l
treatmietnnh tqe uiars cia-lLcEsuS.l ation
Tamueratal [ 1.4a ]n Mdu rakeaatml [i1.6 r ]e paolrostn2o D L EcSa lcuolfva otritoenxs
shedfdliponwagc s ytl iInnd etrthsh2e.eDs t ei,m ee-nddNeepanvti ere-qSutaoatkrieeos n s
solavnetddh d ea mpeifnfogeft c htue n ressomlavlelmd-o stciiaasolg nea l ieenfi ttt hoe r
numeripcia[nl1g4o ]ird s sai mmuwliattthhSee md a gomroidn[es1lk6S] yu. na ngYd u a[1n9 ]
alrseop o2rDtL EcSoan l cuolvfao tristohenexsd-f dliponawgas c ti rccuyllaiurns dienrg the
Smaignosrskuybd g-rsimcoadl.Aee stl htebu urlmeonttai notdnhe ess envtoixra-tlees ttrching
mechaansissomwc iittahhtii aessld w sta hy-rdeiemenasnii mopnoiarnltg,ar netd ient is missing
i2nD c alcualntadht eaisroteenh se rneolfotar reg es-iemdusdli yatn tih troeuns ee nSspea.n wise
tburulsetrnutc tubreeoesbn s heiarenvvx eep de trasin m3dDeL nEcSa lcualnatdtih oecnsasen,
ofc ounrosbtees imuiln2aD tc eadl cuTlhaetasirreoea n tslh.iet krhe2 eD t ime-dependent
calcuulsaitsnitgoa nttsiu srtbiumcloaedlne bclutesth ,d e a mpiinntgr obdyeu icttehhdee r
numesrcihceatmlhe Se m oarg orinsky subgrciodn-ssicsdamelarela lbmeloryd el is probably
thani nttrhoadbtuyt c hseetd a ttiusrtbiumcloaedlane ncldes shmeanslccleeam rlo-et i(onnost
necespsearriwioildalyipl cp w)eh aetrnh g er iissdu fficifiennTeth.cle ay ll actueixoanm ples
presietnnh tneee sdxe tc sthiotowhn3 a DLt E cSa lcualraet icolnesat r2olD " yL EsSu"p erior
calcuIlstah toibuoealn ddsd h.ee dtr heia tnth 2 eDc alcuolfSa utnaignoY dnu sa[ n14 t]h,e
bounldaaywreaynrs o rte soalatvl aeltsd h g er uisdwe adcs o atrhstaehnrbe o undary-layer
thicAkm niexstosufs.rl peia pr,t iaannldo- -scslolinipdp iw taiisno trnosdt uoac cecdo unt for
thainsd, stehpea rpaotiwinaotsn p nroetdb iyct theefldio rwc alcubluatt iwoanss put in
threomupgihrr aeilticsoa.nl
7
4. CALCULATIEOXNA MPLES
Int hisse cticoanl,c ulaotfvi oorntse x-shfeldodwpisan scgty linodfev rasr igoeuosm etries
obtaiwnietsdht atitsutribcuallme ondceaeln sdL ESt echniaqrupeer se seanntdde ids cussed.
Somer emaroknts h aec curoafct yh per ocedaurrieen sp lahceer Feo.rv ortex-shedding
calculattihnoeun mse,r aicccaulr oaftc hyse c heemmep loiysoe fdp articiumlpaorr taasin ctca en
introdduacmep ionftg h fel uctumaottiinognT .a mureat 's[ 14q]u asi-cLaElSc ulaa tions
certaamionu onfts ucdha mpiinswg a ntaenddn ecesssianrncyoe m odeilsi ntrodufcoterdh e
In al.
dampienffge cotft huen resoslmvaeldl -msoctailHoeon w.e veirno, t hcearl culawthiiocnhs
simultahtee dampionfgt hteeuf rfbeucmltoe tnittoh nr oaus gphe cmiodaell( bei fotr t heen tire
stochamsottiiocon ro nlfoyrt hsem all-psacroatfil tet) h,ie n troduocftin ounm erdiacmapli insg
undesirIansb olmece.a siefsw asf ound utphwaitdn idf ferefonrtc hiceno gn vectteirmosn
introduscome usc nhu merdiacmapli tnhgva otr tsehxe ddcionugnl odbet obtaianneadds teady
solutrieosnu lHteendc.de i,s cretsiczhaetmioeofasn tl eassetc ond-aocrcduerra cy have been
useidnm osotft hcea lculraetipoonrsIt tse hdo.ube l ndo tehdo,w evtehrao,tt h deert aoiftl hse
numerciodceaeslm ploaylesdio n flutehnaecb ei ltiopt ryo duacnsedu staap ienr iosdhiecd ding
motion.
Detaielxepde rimdeantatara celr ucfoirat lht ee stoifsn igm ulaptrioocne dIunrt ehcsea. s oef
unstevaodryt ex-shfeldodwipsnr,go pteers tiisnp go ssiobnllewy h ent ime-resolved
measureamreaenvt asi lwahbilcgehi vien formaotnit ohtnee mpovraarli aotifto hnee n semble
averaqgueadn tiatnidse esp artahtfeel t uucatiionntpsoe rioadnidtc u rbuolneenTsto. t he
authokrn'osw leodnglety,w oe xperimoeftn htikssi nhda vbee ecna rroiuetnd,a meLlyyn 's
[20L]D Am easuremoeftn htfesl opwa sast quacryel inadtRe er=2 2,000 (unfonrottu nately
yeptu blisahneCdda )n twaenlCdlo le[s6'f] l yihnogt -wmieraes uremoeftn htfesl opwa sat
circcuyllairna dtRe e=r 1 .x41 0sT.h es quare-cfylloihwna tdshe aerd vantthagasete paration
isf ixaetd ctohmee wrhse rael sloa minar-ttruarnbsuiltteainkotpen ls a cweh,i floetr h fel ow
arouanc di rccuyllairn tdhseeer p araptoiihonantts o b ed etermaispn aerodtf t hcea lculation,
antrda nsiotfti holena mibnoaurn dlaaryybe erf osreep ara(tsuipoenr cfrliotmwia)cy ha alv teo
bea ccounftoerHd.e ncteh,me o sdte taimloeddet le stwianscg a rroiuefotdr t hseq uare
cylinder.
Flopwa sstq uacryel indFerrasna.kn eRd o d[i7 c]a lcultahftele odpw a sats quacryel inadte r
Re=2 2,0s0t0u deixepde rimebnyLt yanl[ l2y0w ]i tthh ke- meo dealn dt hReS Em odeiln,
both cwaistwehas l flu nctainodtn hste w o-laapyperro ianwc hhi cthh nee ar-rweaglilo n is
resolwvietadho ne-equmaotdieoAlnt.t hseu ggesotfti hoaenu thMourr,a kaemtai l[ .1 7]
perforcmaeldc ulaftotirho sena sm tee scta swei tthh e3iDrL ESm ethouds,i tnhgse a me
calculdaotmiaoiinntn h pel apneer pendtiotc hucely alri nadsFe rra nakneRd o dTih.i esx tends
to4 .5uDp stroefat mh cey lin1d4e.rD5, d ownstreaanmdt o6 .D5 o ne ithero fts hied e
cylinIdnte hrse.p awni sdei rectthiweoi nd,ot fht hcea lculdaotmiaowinan s2 D.1 04x6 9x 1 0
gripdo inwtesrp el acientd h setr eamwliastee,ar nadslp anwdiisree ctrieosnpse,c tGirviedl y.
linweesr ceo necntratneedat rhc ey linwdaelrla sn,td h dei staonftc hefe i rgsrtip do ifnrto tmh e
walwla s. 02D2 w hicihst hsea maesi nF ranakneRd o dic'asl culwahteitnoh nesey m ployed
walflu nctiAottn hsie.n flow botuhnsedt arreya,m vweilsoec wiatssy e att t huen iform
approfalcovhwe locaintndyo v elocfiltuyc tuwaetiropenr se scrAittb heoedu .t fbloouwn dary,
zergor adiceonntd itwieorniesm posoendt ,h uep pearn dl owesri dbeo undasryimemse try
conditwieorenems p loyaendd, forb otuhnedp alraynp eesr pendtiotc hucely alri npdeerri odicity
conditTihoecn asl.c ulraetqiuoin1rs5e 0d, 0t0i0ms et etpors e apcehr iocdoincd itainowdne sr e
thecno ntifnouaren do t1h0e0r, 0t0i0ms et ecposv er1i3ns gh eddpienrgi Tohdese .n semble
averavgaeldu weesr dee termbiyne ends emble-aovveertrah gei1sn3epg e riaosdw se lals
averaogvinetgrh sep awni sdei recTthieco anl. cultaotoaiklo tno ge1t0hC0eP rUh ouornsa
FujiVtPs2 u6 0(0p epaekr form2aGnFcLeO PmSa)c hiFnoecr.o mparitsh2eo0 nc ,a lculations
witahs tatisticalm otdueorlfbF urlaenanknceRde o d[i7 t]oo k1 /h2o ur tfohRreS Em odelw ith
8
walfuln ctiaonn5ds hofourrt sht ew o-lRaSyEme odre lo na nIB M 3090( scamlaacrh ipneea,k
perfoce7 MF LOPS).
rman
FranaknedR odic'asl culwaittithoh nkes- m£o deuls iwnagl flu nctyiioenlsad s etde ady
soluatnindoo nv ortsehxe ddTihnegcs.ae l culwaetriceoa nrrsio eudwt i tahne xtenvdeerds ion
oft hper ogrTEaAmC H [21e]m ployasi tnagg ggreirdBe.od s c[h2 2h]ar se cernetpleya ttheed
calculwaittainh oe nwsl y decvodeel( o2pvDee dr soifto hnce od ed escriin[be 2d3 w]h)i cuhs es
an on-staggrgiedr geedm eHnetd .i odb taasi uns tained vortex-shedding solution. Periodic
vortex swhaearsadran ldsoiobn tga ibnyFe rda nakneRd od iw itthho et htehrr meodee lv ariaanndt s
inM urakeatma il[ '1s7 L]E Sc alculVaatilouonef.vs a riionutse pgarraalm eptreerdsiw cittehd
thev aricoaulsc ulation cmoemtphareoiddn Ts a b1l wei th expevrailmueTenhste.a l
parametceornss idearreareed t he
dimensiosnhleedsdsifr negq uency
(Strounhuamlb Setr fD /!Ia), thtei me
meand racgo ef= fiCcDi eanntdt he Tab1lI:en tePgralaram eters
amplitoufdt ehoses cilliantd iroangs
Turbceum lodeenlsL ESE xperi-
coefficCiDea nntdl icfote fficCLi,e nt [71]m etns
indicbayta e dt iTlhdeek .- £m odel two R:>E two-
yieltdoeod slhoewd dfrienqgu eanncdy layewra lll ayer
dracgo efficwiheintlthe,Re S Em odel k-£ fuctn. R SE
witwha lflu nctipornesd icttheeds e
parameitnge orosad g reemweinttthh e St .142 .163 .195 .312 Lyn. 315
measuremTehneLt EsS.c alculations Durao .193
produscleidg lhotwlveyar l uwehsi cahr e,
howevsetrii,ln fl a igroloyad g reemen-cto 17.9 2.152 .432 1.0 2.05-2.23
witthh mee asuremOennt thsoe.t her
hantdh,te w o-lRaSyEe rm odperle dicted
too hSitgrho unhuamlb earn dd rag ,,c, o 0.0. 383. 079. 12 -
coefficCioennsti.sw tiettnhht ie n crease
inC Di sar educotfti hobena sper essur,,,e ,. 3232 1.1 1.48 15.8 -
asc abne s eefrno mF ig2..T hifisg ure
CL
compartehsep ressduirset ributions
predicwtietdht hev arioumse thods
around the cylinmdeears usruerm[fe2an42ct,5es ]a tsw oimthe whhaitg hReery nolds
numbeArtts h.be a s(eC Di nF ig2.)t hLeE Sc alculraetpiroontdshu mece ea sucrpe-dv aolfu e
abo-u1t.fa 4ir wleyl wlh,i tlheke - m£o dealnt dh tew o-lRaSyEme odre lu ndearn-odv erpredict
cpr.e spectIintv heaelp yp.r oacshtianggn aftlio(owAn B ) tihsfe arier lya ggroeoedm ent
betweaelcnla lculaantdmi eoanssu remAelnotntsgh. se i dwea lolfst hcey lin(dBeCtr)h e
difference tbhmeeet awseuerne amnedtnh tvesa rious cailscc ounlsaitdiehorinagsbh leyr .
Therbeo,tv he rsiooftn hsRe S Em odealsw elalst hLeE Sc alculuantdieornp rtehdei ct
pressaufa rctet,h at fnueretdehxsea rm ination.
Fig3.d ispltahdyeis s tribouftt hiteoi nm e-mveealno ciatlyo tnhgce e ntraenldgi invee s
u
informaotnti holene ngotfth h tei me-avesreapgaerdaz toinobene hitnhdce y linder.
Experimdeantdtauat eloL yn[ 20a]nD du raeota l[ 26]i ncluTdheedd a.ta ag rfeaei wrellyl
int hnee ar-cyrleignibdouenttr,h aep protaotc hhfre eare e -strveealmo icsiq tuyid tieff erfoern t
reastohnaasrt ne o ctl eIanfrr o.n otft hcey lintdhreeer s,u alrategs a nionmt u cihn fluebnyc ed
thcea lculmaettihuoosnde bdu,tt h earrefe a ilralrydg ieff ereinntc hewesa kree giTohnek. - £
modeolv erpretdhilece tnsgo tfth hs ee parzaotniceoo nn siderafibnldyi.on fFgT r haineskta e l
[7i]ss u ppobrytD eedne gta l['3sc] a lculwaitttihhol eno sw -vReer soifto hnke - m£o dedlut eo
Naganaon dT agaw[a1 2I]ta. p petahrastt hk e- £m odel prtoodolui ctemtsol mee ntum
exchawnhgiec,ih nv ortex-sflhoewdi dsmi anignd luyte o t hpee riofdliucc tuaHteinocnes,.
theasreue n derpredOinct theoedt .h hearn bdo,t RhS E-movdaerli apnrtesdt iocsoth ort
separabtuibobnla ensdt, h eirsle i tdtilffee rbeetncwee etnhr ee sults woibttthha teiw noe d
