Time-Domain of

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Time-Domain Simulation of Vortex-Induced Vibration for Deepwater Marine Risers

by

©Peter fvla, B.Eng.

Athesissubmittedto the Schoolof Grad uat eStudies inpar tialfulfillment of the requirementsforthedegree of

Mast erof Engineering

FacultyofEnginceringand AppliedScience Memorial UniversityofNewfound land

Febru ary 2012

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Abstract

The engineeringchallenges of Vort ex-InducedVibration (VIV) formarinerisers areofgreat concern asoffshoreoperationsmoveintodeepwater. TheVIV phenomenoncrea tes fatigueissues andcouldcauseperm an entdamagesin risers.An accuratetoolfor analyzingriserVIVisimpor t antfor the safeopera tionofoffshore drilling andexplora tion.Riserstypicallyhave anext remelylargelength-to-diameter ratiowhich makesdirectscalingnearlyimpossiblein physicalmodel testing- this naturallyrequirestheuseofnumericalmethods.

In thiswork,atime-domain numericalmodelfor simulat ingVIVof deepwat er riserswasdeveloped. A novelforcingalgorithmthatutilizesthehydrodynamic coefficientsoffinite segments ofariserwasadopted topredicttheexternalforces onariserduetofluideffectsand risermoti on.Thepredicted externa l forces are then appliedontheriser.Aglobal-coord inate-based finiteelement modelwas employed to computetheresponses of theriser.

The computationconsistedofatwostep process: sta t icand dynamic analysis.

The stat icanalysis iter at estofind the equilibrium profileof theriscri s),then the dyn amic analysissolves the equat ionofmotionateach user-d efinedtime step. The program outputstheresponsesand thereactionforces (tension)of theriser (s)atany user-definednodes.

Thenumericalmodelwascoded ill Fort ran90and validatedby comparingprogram outputswith pub lished experimental dat a.Validation stud ies werefirst conducte don mooringlines, and the comparisonshowedthat the finiteelementmethodwas ableto

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capture thononlinearbehaviour oft.h(~seslenderstruc tures.Withconfidencein the finite elementmod el,theVIV forcingalgorith mwasimplementedin theprogram.

Valid ati onst udies werethen extendedtotheVIV predictionofa6 met errigidpipe withspring boundary cond itio nsanda13 meterlaboratory scaletop-t ensioned riser.

Thecomparisonsbet weenthepredictionsin this studywit h the experimentalresults arc genera llyingoodagreement.

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Acknowledgem ent s

Iwould liketoexpressmy sincere gra ti t ude tomy supervisor, Dr.Wei Qin,under whose guidanceand directi on thisresear chwas car riedout. Thank stoMr. Don Spencer ofOceani c ConsultingCorporat ion,for thetheoreticallessons givenat the beginningofthisresearch.

Thiswork was conducte dat Memori alUniversity of Newfound landthro ugh fundingsprovidedbyPetroleumResearchAtlant icCanad a (PRAC),IvIITACS,and theResearchandDevelopm ent Corporation (RDC). Iwould liketogratefully acknowledge theIundingsprovidedbyPHAC,I\IITACSAccelerat eIntern ship,the HDCOcean IndustriesStudent Research Award, andthefellowship fromtheSchool of Grad uat eStudies,Memorial UniversityofNewfoundland.

Iwouldalsoliketothank mycolleaguesintheAdvancedMarineHydrodynamics Laboratory,whom notonly providedtechnical guida nce011variousnumericalmethods but also madetheoffice afriendlyplacetowork in.Also, specia lthank sto allother fellow graduatestudentsforthehelpandsupport providedthro ughoutthe courseof this study.

Mydeep est appreciationgoes tomyparents,sist ers and Elim for their patience andsupport. Theywerealways availablewhencalled upon, and made sureIstayed sanethro ughoutthe courseoftheprogram.

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List of Figures

1-1 HiserTypes.

1-2 Typ icalDeepwa ter CurrentProfiles(from Li,2005)

1-3 StrouhalnumberversusReynoldsnu mberfor circularcylinders (from Blevins,1990).

2-1 NumericalVIVPredictionModels. 19

2-2 CFD l\lodels . 21

3-1 Ocean icConsulti ngCorporation'sVIVtest appara tus. 32

3-2 Lift Forcc Coefficients 34

3-3 Venugopal DampingModelforLow and HighReducedVelocities . 35

3-4 LiftForceCoefficients(Rotat edView) 36

3-5 Zcro CrossingAnalysisofaVibra ti on Cycle(fromSpencer etal., 2007) 37

3-6 Interpolationgrid. 41

3-7 Current profilesavailableinthepresentmodel. 42

4-1 Top TensionComparisonofaCatenaryMooringLine. 48 4-2 TopTens ionTimeSeriesfor0.15for cedmoti on amplit ude at0.48Hz 52

4-3 Sensitivityto No.of Elem ents . 55

4-4 Sensitivitytotimestep. 56

4-5 TopTension forSample2 57

4-6 TopTension forSample3 57

4-7 TopTensionfornon-dimensionalmoti onamplitudeof0.03. 59

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4-8 Top Tensionfornon-dimensionalmotionamplitudeof 0.05 . 60 4-9 Top Tensionfornon-dimensionalmotion amplit udeof 0.07. 60 4-10TopTensionfornon-dimensionalmoti on amplitudeof 0.09. 61 4-11Comparison ofnon-dimensional dynami ctension. 62

5-1 RigidriserVIVforuniformcur rentspeed of 1.1ui]« 65 5-2 RigidriserVIVforuniformcur rentspeed of 1.6ui]« 65 5-3 RigidriserVIVfor uniformcur rentspeed of 1.8ui]« 66 5-4 RigidriserVIVforuniformcur rent speedof2.4ui]» 66 5-5 RigidriserVIV foruniformcur rentspeedof2.6 ui]« 67

5-6 AmplitudeRatiovs Nomina l ReducedVelocity . 68

5-7 DelftVIVexperimentalset up 70

5-8 Computa tionalModelof theDelftExp erim ent. 71 5-9 Case1Crossflowvibration envelopeobta ined from cur rent modelwith

50,100, 200elements. 73

5-10Case1 TimeSeriesofCrossflowVibra ti onatthemiddle of theriser . 74 5-11Case1Crossllowvibrationenvelopecomparison betweenresultsfrom

experiments,Shear7 , Norsk Hydr o,andthecur rent model 74 5-12Case3 Crossllowvibrati onenvelopeobtained from current modelwith

50,100,200elements . 75

5-13Case3 TimeSeriesofCrossflowVibra ti onat themiddleoftheriser . 7G 5-14Case3 Crossflow vibrati on envelopecompa rison betweenresult sfrom

experiments,Shear7,Norsk Hydro,and thecurrentmodel 76 5-15Case6Crossflowvibration envelopeobt ained fromcur rentmodelwith

50,100, 200elements. 77

5-16Case6 TimeSeriesofCrossflow Vibrati onatthemiddleoftheriser. 78 [i-17CaseGCrossllowvibra ti onenvelopecomparison betweenresul tsfrom

experiments, Shear7,Norsk Hydro,and the current. model 78

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5-18 CnsoI)Crossflow vibration envelope oht nincdfromcur rent model with

50,lOO,200element s . 79

5-19Case9 TimeSeriesofCross flowVib ration atthe middle oftheriser. 80 5-20Case9Cross flow vibration envelopecompa rison betw eenresult s from

experime nts,Shear?',Norsk Hydro , and the cur rent model 80

5-21 Max cross flow vibrationacross all mod els . 81

5-22 Mincross flowvibrationacrossall models . 82

A-ICoordinate Syst em . A-2

B-1 Degreesof freedomfor two rodelements B-3

B-2FlowChartforStati cAnalysis . B-7

B-3 FlowChartforDyn amicAnalysis . B-ll

C-l Case1 TimeSeriesofCross flowVibra ti on at 0.25L C-2 C-2Cascl TimeSeries ofCross flow Vibrati on at 0.75L. C-2 C-3 Case3 TimeSeriesofCrossflow Vibrati on atO.25L C-3 C-4Case3 TimeSeriesofCross flow Vibration at O.75L C-3 C-5Case6 TimeSeriesof CrossflowVibrati on at O.25L C-4 C-6 Case6TimeSeries ofCrossflow Vibrati on at O.75L C-4 C-7 Cas e9 TimeSeries ofCrossflow Vibra ti on at 0.25L C-5 C-8Case9 TimeSeriesof CrossflowVibrati on at0.75L C-5

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List of Tables

4.1 Paramet ers ofa Catenary MooringLine 47

4.2 Resultsfor Cate na ry Linesubjected tohorizont alanchor force 50 4.3 Paramet ersusedin Faure'sForcedOscillati onExperim ent 51 4.4 Parametersof themooring syste m onboardSSVHcnri kIbsen 53 4.5 Environmental loadsfor FullScaleExperiment. 54

4.6 Measu redvs,l\IAPS-l'v1oorin gTension 58

4.7 FullScaleCharact eristicsof Kitney and Brown'sExperim ent. 59

5.1 Solid CylinderProperti es. 63

5.2 Properti esoftheriserusedintheDelftVIVexperiment 69 5.3 Cur rentspeedand toptension of theDelftVIVexperiments 70

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Nomenclature

CF D Computationa l fluiddy nami c CVAR Com pliantverticalaccessriser DNS Directnumerical simu lation EoM Equationsof motion 1"0 Fat iguedam age FE l\'1 Finitc cleme ntmod el FL Fat iguelife HCR Highl y complia nt riser JIP Jointindustryproject LES Large eddysimulation

~dODU Mobile offshore drillingunit.

RANS Reynolds average dNavierStokes Re Reyn olds Numbe r SCR Steelcatenary riser

St Strouhal numbcr

TLP Tensioned-logplatform TTH Top-tensionedriser VIM Vortex-inducedmoti on VIV Vortex-inducedvibrati on

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A amplitudeofvibra ti on A' crossflowamplituderati o ilk interpolationfunction B buoyancyforceperunitlength CD Drag coefficient CDO Stead ydrag component Cf-\, Lift coefficient CM Addedmass coefficient D Diam et eroftheriser D(t ) Time-dep end entdragforce E elasticmodulus oftheriser

Jo

frequencyofoscillation

In

^Nat^{ura l}^frequency

resultan tforce

Fd hyd rodyn amicforceperunitlength FS hyd rostat ic forceper unitlength

H torque

momentofinertia of the crosssection lengthofthe element L(t) Time-dep endentliftforce

M resultantmoment

Nk sha pe functi onsofaquadr ilat eral

P'" interpolationfunction 1'., hyd rostaticpressure R radiusof theriser

T tension

T

effectivetension To Periodof oscillation

Flow speed

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U· Redu cedvelocityfromfreevibrat ion Ui k coefficientsin int erpo lati onfunctions V tot al wa terparticleveloci ty Vi tangentialvelocity

V:~l rela tive fluidvelocity normaltoriser

\T tot alwaterparticle acceleration .

\T" wat erpar ti cleaccelerat ion normaltoriser VII Reduced velocit yfromforcedvibra t ion

app liedmomentperunitlength appliedforceperuni tlength positionvect orof riser r, com po nentofr ini^thdirection

velocityof riser ion normalvelocity ofriser

accelera tionof riser r" norm alaccelera t ionofriser

unit tangent vector 1''' principal normalvect or

arclengthalongtheriser time

weight perunitlength

w

c1fectiveweight

Lagrangian mult iplier .Am coefficientininterp olation function

Kinematicviscosityofwa ter massper unit lcngth 0i j Kronecker Deltafunction

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Chapter 1 Introduction

Theana lysesof thebehaviour of risersoperati ngin highcur rentenvironment is a crit icalpartof theriserdesignprocess.Engineersmustanalyzethepot enti alrisks thattheseriser systemsmightbesubjected to, and designtomitigat e such risksfor operation.Oneof themaindesignissuesformarin erisers, suchas steelcate nary risers,isthe accura teevaluat ionof fati guelifedueto vortex-ind ucedvibrations.This dep end son theaccuracy of VIVresponsepredicti onmodels.

Variouspredictiontoolsforanalyzingvortex-inducedvibrationshave emerged from decad esof researchand development ,but offshore opera tionsstill identifygaps betweenthepredict edresp onses and thoseobserved inthefield. Vortex-indu ced vibrations on risersiswell-known,butitis adifficultproblem forana lysisand predicti on.Thephysicsbehindthisphenomenonisnotfullyunderstood;hencethe predicti onmodelsfor VIVareinadequatefornewdesignsand risers opera ti ng in deepwater.

1.1 Background and Motivation

Marinerisersoperat ingin theverti calwat er columnareexposed to currentHow.The combinationofcur rentspeed,risergeometry andsur face roughness causes vort icesto

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be shedinthevicinity oftheriser.Whenthevor tex shedd ingfrequency approaches oneormoreofthenat uralfrequenciesoftheriser ,resonan cevibrat iontakesplace.

Thisphenomenon isknownaslo ck-in.Whenlock-inoccurs,thevort ex shedding frequencyis cont rolled by thevibrationfrequency. This createsaforcefeedb ack phenomenonon vortexmotion andstructuremotion.Under certainconditions, risers vibrate atlarge amplitudes once they reach the lock-inzone. Whenmultiplerisers arelocatedincloseproximityin deepwater,VIVcanpotentially lead to theclashing ofadjace ntrisers. Thiswouldlead to suspensionofoffshoreoperation,orresultin serious financial loss andenvironmental dam ageiftheriser(s)hreakoff due tofatigue issues.

TheVIVou risers arefurt hercomplicatedhyuncert aint iesillcurrent flow.

Currentvelocities arebothspa tiallyand temporallyvariable,and theirmagni tu de anddirectionsmayherandom,makingVIV predict ions even moredifficult.Most of theresearch onVIVassumesa consta nt orshearedcur rentprofile,tored ucetechnical challenges inexperimentaland numericalprediction.This,however,isnever the case encountered inoffshore.

VIVanalysis hasbeenconductedusingbothphysicaltestin g andnumerical models.Physicaltesting,thoughbelieved tobemoreaccur at e,is generally notcost effectiv e and requires special testingfacilities. Computational fluid dynamic (CF D) mod els arenotpracticalduetolimitingcomputerresources andat presentcanonly capture VIVatrelativelylowReynolds(Rc)numberflows.High Renumberflowsin CFDarethe goalof futuredevelopment (Lie etal.,2011).

Thecommonindustr y practiceforanalyzing riserVIV istheuse ofsemi-empirical linear mod alfrequencymodels.Thesemodels,developeddecad esago,weretailored topredict VIVon verti caltop-tensionedriserssubjected touniformorshearedcur rent flows.Asoperationsmoveintodeeperwater,vert ical top-t ensionedrisersmightno longerbefeasibledueto complexenvironmentalconstraintsandthetypeoffloaters theserisers areconnecte dto.Therefore,the modal frequencyapproachisinsufficient

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to simulateVIVfordeepwaterrisers.Toeliminate thelimitati onsoflinear approaches and overcome some of thechallenges menti oned,anefficient time-domainmodelis developedinthiswork . This approachtakesinto considerationthenonlinearit ies from riser geomet ry,sea bott omconditions, andenvironmental loads.Thedeveloped model canbe easily incorporated intodesignofriserswith strakes and fairin gs.

1.2 Marine Risers

Risersareusedtotransport fluids (hydrocarbon, drillingfluids,etc. ) from subsea facilit iesto asurfacevesselorviceversaduringoffshoreoperations. Riser concept selectionsaremainl ybased011thetypeoffloater(vessel)employed,theirresp ective motion characteristics,and thewaterdepthof thefield.

As showninFigurc 1-1,therearefourmaintypes ofrisers commonlyemployedin offshoreoperations.Mobileoffshoredrillingunit (I\IODU) risersaretherisersused attheearlyageof offshore explorat ion. Thisisa typeoftop-tensionedriser(TTR) but itsdesignhasbeenrefinedsince the early 1960s(Bost eret al.,2004).

Figure1-1:Riser Types

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Thesecond typeisTTR.They can bedrillingorproductionrisers ora combination of both.TTRsaremost commonlyusedonspars ortension-leg-platforms(T LP)due to thesevessels'low heavecharacteristics.Theserisersrequirethe sur facevessel to possess good moti oncharacte rist ics. Whilebeingent irelyvert ical,theserisersarealso suscept ibletolateral movementwhen subjectedto windandwaveloads.As aresult, theycanexpe rience significant loads at thetopandalsoat thetouch-down point.A commonpracticetoredu cethesehighloadsistofitbuoyancy cansatcert ain points ontheriserstoincreasethebuoyancyforce andoffset theweight . Inaddition,motion compensatorscanalsobe employed tokeep constanttensionloadsinthe risersby movingthefacilitiesverti cally asneeded.

Thecompliant risers consistof steelcat enaryrisers(SCR)and flexiblerisers.In deep er wat ers,SCRsare commonlyused on TLPs,FPSOs, spars,and fixed struct ures.

Dueto thecurved natureof theserisers,theserisers can handl e some lateralmovement butarevulnera bletolargemovements.Flexiblerisers areusedinshallower water or inopera tions wheretheflexibl e characteristicsarerequi red.Theirabilitytotolerat e lat eralandvert ical movementsmakethemsuitableforfloatingvesselsthatare pro ne tomoremoti on.Therearedifferentconfigurations forflexiblerisers , suchas steep S,lazy S (bot h useanchored buoyancymodules), steep waveand lazywave(bot h wit h buoyancymodules).These configurations helptoredu cetheimpact son flexible risers whentheyare exposed toexterna lloads.Hybridrisershavebeen employed fordeepwat eroperati ons. The arrays ofsteel pipes,connected totheseabed, are verticallysupported by externa l buoyan cymodulesandconnected tothe surface vesselbyflexiblejumpers.Thebuoyan cymodules arcinstalledat adepthwellbelow thefreesur face,preventin gthe steelrisersfromexperiencing waveloads.Thistypeof configura tion minimizestheimpact fromvessel motion-inducedvibra tionsin risers.

Anotheradvant age of thistype of risersistheredu ctionin bendin g st resses at the top and touch-downpoint s.These systemsrequire,however ,amore complicated inst allati onprocess and higherinstallati oncost.

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1.3 Ocean Currents

Oceancurrentsplay an integralroleinoffshoresystemsdesign; theyare oneofthe mainsources ofenvironmental loads.Thedesignofany offshore struct ure orsubsea syste mmust take cur rentinto account,thro ughoutthe entire designprocess,toensure the integrityof suchsyste msisnotinfluencedbyextremecur rentcondit ions.Insome cases,dueto operatio nal demands,somesyst emsmustalsowithst andhigh current with ou tjeop ardizingoperat ions.

Ocean cur rentsarethemovement of waterwhen acted uponby external forces.

These exte rnalforcesincludeCoriolis,pressure gradient,friction,andcent rifugal forces.The Cor iolisforces areduetotherotati on of the eart haround its axis.Asa result,theoceanwatersmoveto therightin thenorthernhemisph ere, and tothelcft in thesouthe rn hemisphere.Theamoun tof movementdepend son flow speedand thelocation alongthelati tudes(Randall, 1( 97).

Thepressur egradient forcesarisedueto thehorizont al cha ngein pressurebetween highand lowpressur eflows.Thedifferencein pressur ecausesthewatertoflowfrom highpressur eareastolowerpressur eparts.Themagnitudeofflowdep endsonthe magnitudeof thepressur e gradientinallthreedirections.

Frict ion forcesaretheconsequencesoftur bulentedd ies interactingwit hthemean flowand init iatingfrictiona leffectsintheflow. Eart h'srotati onalongits tiltedaxis generatesacentr ifugal forcethatalsoinfluences curre nt flow. The centrifugal force genera tedhasa stro ngverti calcomponent (gra vity)whilethehorizontalcomponent isnegligible.

Theexistenceof theseforces causeoceancur rent to exhibit irregularpattern s alongthewater column.A typicalchart todescrib ecur rent ofaregionin theocean isacur rentprofile.An ocean cur rent profileprovidesengineerswithaveragecur rent velocities alongthowat er column.Thisinformationisused toevaluate thebehaviour of risers subjected to theseloadingcond itions.

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1 1.5 currentspeed(m/s) 0' - -...1..---:.- - ----'--- - ----'-- - --'----1

o

Figure1-2:TypicalDeepwater CurrentProfiles(fromLi,2005)

Duetothefactthatrisershavelar geaspect ratio (length/d iameter),theytend tobevulnerableto cur rent loads.Oceancur rentsarethemaindriverforinducing vibrati onsin risers.Inaddition, currentprofilesvaryfrom region toregion.Figur e 1-2showstypical cur rent profilesfor theGulfofl\Iexico,\VestAfricaand FarcesGap.

Thesharpcha ngesincurrentspeedalong thewatercolumn,intheGulfof Mexico forinstan ce,can inducelocalvibrati onsatsome lengths alongtheriser. Oncelocal VIVdevelops,and undercerta inconditions,it tendsto propagatethro ughthe entire riser andproducevibrationof the entire riser.Inaddition,a criticalcurrentprofile toconsiderinthedesignprocessfortheGulfofMexicoistheloopcurrent,asshown

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inFigure1-2.Thisisaspatiallyvarying cur rent,havin g edd iesattached toit,and hashighsur facevelocities ,The combinationof loop current and bigwaves canpose poten ti alriskstooffshorestructu res andth isisusu ally thelimiting; environme ntal load casein riserdesigns. Thenumericalmodeldevelop edin thisworkwill take ar bit rarycu rrent profilesinto considera t ion,thereforeitisnotlimited touniformor shea red currentprofiles.

1.4 Vort ex-Induced V ib ration

VIVoccursin manyfieldsofengineeringfrompowercables tohea t excha nge rarra ys tomarinerisers. Unlikeman yvibrat ionproblemsinwhichtheexciti ngforceis independentof thestructuremoti onitself, theexciting forcein VIVisafu nctionof motionparamet ers ,Inotherwords,VIVisself-excitedsincethemoti onitselfgives riseto the exciting force.

1.4.1 St a ti on a r y Cylin derVIV

For afree st ream with speed, ,movingpas ta stationary cy linde r withdiam eter D,pressureinthefluid par t icles cha ngesandapproachesthe stagnat ion pressur e at thelead ing edgeofthe cylinder.Thisincreasein pres sureslows theincom ingflow forward and formsboundar ylayers on bothsidesofthe cylinde r. In highReynold s numberflows ,theboundarylayers separa tenear thewidest area(sid e)ofthe cylinder whichresul tsin theform ati on of twoshear layers aftoftheflow.Theinner shear layer movesat amuchsmaller ratethantheouterlayer;hen ce,theselayersthen slip intothewakeregionand forms vor tices(Blevins,1990).

Forastat ionarycy linde rsubjected toaunifor mflow,vorticesare shedata frequency thatisproporti on alto theratioofcur rentspee d tocylinderdiameter.

fs =St~

^(1.1)

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whereStistheStrouha l muubcrwhichdependsontheReynoldsnumbor ofthe flow and the surface roughness ofthe cylinder,as shown inFigur e1-3.Inthefigur e,the lowerboundary showsthe St.plot.foraroughcylinder andtheupperbound aryisthe St.dep end enceonRefor a smoothcylinder.

~ /'

/

i

U

/

--~

~

^{~ "'~I}^•^~.- ^{. . .}

^.L ^....

Ii

r

^r _ . F - - -

Figure1-3:St.rouhal numberversusReynoldsnumberforcircularcylinde rs(from I31evins,1990)

TheReynoldsnumber ofaflowis adimensionlessquantity that isdefinedasthe ratio ofinertialforcestoviscousforces,as shown inEquation 1.2.

Re ='lJZ

1/ (1.2)

whereI' isthekinematicviscosity.

For stea dycurrent. flows,therearegenerallyfour flow regimesidentifiedbytheir corres ponding He range. Inthe sub-critica l ran ge,300<He<150,000,boundary layerislamin aruntilsepara tionoccur s at.approximate ly80°aft. of the cylinde r stagnation point. Vortex shedding in this range isperiodicandst rong(I31evins, 1990).Thedrag coefficient.inthe sub-critical rangeis almostconstant.ata valueof 1.2.

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TheHerangebetween150,000and 3,500,000is called thetran sitionalregime.

Thcboundarylayeraround the cylinderisunst abl e, separates,andthen becomes turbulent.Separationoccursat140°aft ofthestagnationpoint.Thedrag coefficient dropstoabo ut0.3. Thethree-dimensionaleffcctof vort ex sheddingarises,and event ua llyupset stheregularshedding process andgives awider arrayofshedding frequencies.

All flows above an Heof:1,500,000arccalledsuporcritical in VIVstu dies, Inthis ran ge,thevortexsheddingisre-establishedwit ha tur bulent bound arylayer.Thc vortex sheddingfrequencyishighlyvariabl e andthewakebehindthe cylinder isno longerorganized.

1.4.2 Flex ibleCylinderVIV

Flexibl e or flexiblymoun tedcylindersaddanotherlevelofcomplexity.Flexibility meansthevort exshedd ing will producemore cylinder moti on,whichwill inturn disrupt thevor tex shedd ingpat terndescribedin theprevious sect ion.Thevortices shed behindflexible cylindersinteractwith, andexcite, the cylinderin boththedrag (inliuc) and lift (crossflow)directions-and themoti onoftho cylinde r in tum disrupts thevortices -formingacoupled forcefeedbackphenomenonknownasvort ex-indu ced vibra tio n.

Whenvortices areshedat frequenciesclosetothenaturalfrequenciesofthe cylinder, lock-inoccurs. Thevortex shedding frequencyisthcn synchronized with the st ruct uralvibration frequ ency,producinglarge-amplitudevibrati ons.However , thisincreaseinamplit ude ofvibra t ion islimitedbytheincreasein hydr od ynami c damping associated with thelargerstruct ura loscillatio naswellasthe self-limiting natureof vort exst rengt h.Thisself-limit ingnatu reof VIV usuallylimitsthevibrati on amplit udes to belessthan1.1timesthediameter. Inaddit ion,lock-in is also associated withan increasein the corre lationlength,vortex st rength,aswell as the amplificationofdragloads.

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Experimentshave shown thatliftforcesoncylinde rssubjected toVlVoccurat thevortex shedding frequency.Thedragforces;however,werewitnessedto oscillat e at twicethevortex sheddingfrequency.Thisimpliesthatvortices,travelingin the inlinedirection , areshed from thecylinde r with halfthevortexsheddingperiod(T/2).

Thisisbecauseof thealte rna tesheddingof vor ticesin theinlinedirecti on.Dueto theasymmet ricnatureof vort exsheddingin the crossflowdirection,thelift forceis shedat aperiodofT.Hencethedirection ofthelift forcedepen dsonwhichsideof thecylinder fromwhichthevort icesarcshed(Falt isen,1990).Thiswill be reflect ed in thehydrod yn ami cforcesformulationin thelatersections.

1.5 Ri ser Fatigue

Thedesignofrisersisan iterativeprocess.With thehelp of APIorDNV sta ndar ds (API RP2RDor DNVOSF201),initialsizing of riser(s)is obta ined basedon specificatio nsand theenviro nment in whichtheriser(s)willoperate.Oncethe sizing isknown,ana lysesareexten ded to staticana lysis (configurati on ),stormana lysis, VIVanalysis,vesselmoti onind uced fa tigue, and VllVIana lysis.Thefati guedam age inducedfromVlV,VIIvI,and first andsecond order wavesmust satisfy designstandard recomm end ati onsbeforethedesigniterationiscompleted.Typically,thesestandar ds require adesignlifeofgrea ter than 200years fora20yearserv ice.Thefatiguelife at anygiven pointis given by

FL= 1

FD(VIV+VIM+WaveIndllced) (1.3) whereFL isthetotalfati guelife,and FD isthefati guedam agefromVlV,VIM,or waveind ucedloads.Fati guedamageisaresultof stressfluctu a tionsthat causesma ll defectsin therisermat er ialtogrow. This canleadtoriserfailureover time.The fati guelifeof risersystemsareoftendomin at edbyVIVo

Tomakeaccurat efati guelifepredicti ons,theVIV responsesmustbeaccurately

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as sessed to avoidover or underdesign s.IftheVIV resp on seunderpredi cts,thefatigu e lifewill increas e andresu lt in possibl efailureduringits service life.For conserva tive predictions,thefatigu elifewilldecrease andresultinanoverdesign .Thepredicti on ofVIV playsa majorroleindet erminingthefati guelife of risersduring thedesign pro cess,and helps enginee rs to arriveat cost effect iveandsafe design s.

1.6 Vortex-Induced Vibration Suppression

Riserdesignsusu allyfailtomeetfa tigu e crite riasetbyAPIor DNVstanda rds aftercompletingthefirstfat igu e ana lysis. Design ersmaychooseanumberof ways toim provethefati guelifeof theriser bein gdesign ed. Theoret ically,VIVcan be supp ressed byincreasingtheamo u ntof damping(structuralandhydrodynamic), increasin gthe st iffness,and decreasin gflowsepara tion(Blevins,1990).

Thedesignermaychoosetomodifyingthemassand ten sion of theriser. The former can bedoneby cha ng ingthe sizeoftheriserorby subt rac ting buoyancy.

Thelattercanbe achievedbymodifyingthe st iffnessthrough pre-tension ing of the riser. Based onaSt rouhalnumber(~0.2),thepre-t ension ingwillchange the naturalfrequencies of theriser awayfrom theStrouhal frequency. Thiswillavoid vortex ind ucedreson a nt oscillat ionsinboth the inline andcross-flowdirecti onswhen subjected to currentloadin g.

Inadd it ionto adjustingthenat uralfrequencies of theriser, amore common ap proach isthroughthe use ofvortex sup pression(ad d-on)devices suchas stra kes, fairings , orcombinationof the two.Thesedevices are fitted aro und theriser. Their existe nce preventstheformation ofanorganizedvort ex st ree tandredu cesvortices formedinthevicini ty oftheriser.

Strakes

Str akesacttodisrupttheflowpat ternaro u ndtheriser andpro duceweakervor tices.

Thiscansuccessfullyredu cethevortexshedd ingforces.However,onedrawback of

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strakes isthattheytendtoincreasethedragload ontheriser. Thisincreasein drag load can potentiallylead to clashin gofadjacent risers(Baiand Bai,2005).This increasein dragloadisstilllowerthanthatexperienced by abarepipeundergoing VIV.

Fairings

Fairin gsarefittedaround risers andacttostreamlinethcflowaroundrisers and consequentlyreducesvortexshedd ing.Thesedevicesarefreetorot at e aroundthe riser;therefore,theyadjustdirectionsdep endin g011thedirection oftheincoming curre nt.They arcmosteffectiveat suppressingvortex shedding whenthorisers arc verticaloralmost verti cal.Asaresul t ,they are more commonly seenon TTHsand verticalpar tsofSCHs.

There arealsodisadvant agesof usingfairin gs.Themostimportantoneisthe induction ofa complexphenomenonknown as galloping.Thisis generallycaused by inst ability of the st ructure whensubjected tocur rent flow.Gallopingvibrat ionis differentfromvrvin thatit doesnotrequirethevibrat ionfrequencytoreachthe natur alfrequencyof thest ruct ures.It.is alsoself-excited, andgenerallypossesses an ovalvibrat ionshape.Fairingsarealsolessreliableduetoitsfreedomtomove aro und theriser 'scentralaxis;therefore,VIVmayormaynotbe suppressed.

For cedvibrationexperiments havealsobeenperform edonstrakesand fairings, andthe corresponding hydrodyn ami cforce coefficients havebeen collecte das a functionof reducedvelocitiesandamplit uderatios.Thesecoefficients canalsobe used asinput intheprogrambeingdevelopedin thiswork, and predictresponsesfor riserswit hst.rakesor fairin gs.

1.7 Deepwater Challenges

Insha llower wat er applications, vibrati onson riserswithshorterlengt hs can be capt uredusingalinear modalfrequency approach -suchastheprogr amShear7 .

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Indeepwat er opera tio ns, muchlongerrisers areadopte dforvarious applications.

Thepredicti on of riserVIV fordeepwat errisersismore complicated. Due toload andgeomet ric nonlin eariti es,thelinearfrequency approach isnolongervalid.

Deepwat errisers aresubjecte dtoflow (cur rent andwave)variationalong their length , aswellaspossiblevessel-induced motionfromthetop. \Ve canconsidertwo resp onseregimes:lock-inisnotinitiated , andlock-intakesplace alongaparti cular spa nof theriser.

AccordingtotheworkofVandiv er(1993),lock-inmaynot occurgivenoneormore of three condit ions:(1),theclampingis sufficiently largetosuppressflow-induced motion,(2),thevorticesdonot shedat thenatur alfrequ ency of themode(s),and

lor

(3), wide excitat ionband widt hcoveringthenaturalfrequencies of multiplemodes- giving risetorandom vibrations alongthelength oftheriser.Thefirsttworeasons are easilyunderstood and implementedin numericalmodels.Thethirdreason is highlynonlinear and difficnlttopredict, anditdepends onthe flow cha racte ristics andthe number of resonantnatur almodes,thisrequires adetailedaccountforthe materialproperties of theriseraswellas accura terepresentat ionofcur rentflow.

Lock-in,however ,ismorelikelytooccurindeepwat erfor severa l reasons. Curre nt speedsarehigherin deepwat erthanmany sha llowwat erlocati ons(Allen,1995).

Theincreaseinslendernessratio(LID)redu cesthenaturalfrequ encies of risersthus allowingeven lower currentspeeds toinduceVIV.Thevari ati onincur rentalong thelongerwaterdepth,islikelytoexcitemulti-modalrespon sesalongtheriser.

Additionalcomplexity ariseswhen multiplerisers,opera t ingalong thewater column, interact wit heachot her(inter ference) .Forinst ance,wakeind uced vibrations ona riser ,in tand emwithanot herriser,can increasethemagnitudeof riservibra t ions.

Wakeinducedvibra tions canalsoamplify dragforces andcause riserclashing.

Thehighestlevelofuncertaintyand high st ressoccursatthetouchdown point or thefairl ead connection point ofSCR in deepwater. TheSCR responsesinthese regions arecha rac te rized byintermit tentlylaying and liftingmoti ons(Grantetal.,

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2000).Thisis anotherreasonthatfrequencydomainsolutio n isnotadequate,asit requiresthetouchdownpoint tobefixed.

FordeepwaterriserVIVanalysis,itisdesiredtohave anumericalmodelthatis notrestrict edinloadandgeometricnonlinearity,is abletomodeldynami cboundary conditions (i.e. cha ngingtouchdownpoints) , andtheVIV forcingalgorithmshould coverarangeoflock-inand non-lock-inbehaviours.

1.8 Outline of Thesis

The scopeofthisworkincludes thedevelopment ofatime-domaincode forthe ana lysis of riservortex-inducedvibra tions.Withthe aid ofadvancednumericalmethodsand highqualitytestdata,anefficientandaccura tesemi-empirical time-domainprogram isdeveloped.Thisprogrameliminatesmanyof thelimit at ionsofthetraditional linear mod al frequencyapproach.Thisthesisis subdivided into6chapte rstologically present the rationalebehindtheresear ch,mathematicalIornmlat.iou,andtheresults obtained from thisresearch.

Chapter2givesaliterat ure survey ofthemethod ologiesadopted inriserVIV researchand the currentindustrypracti ce. Thiswillincludediscussion on three classes(CFD, semi-empirical,andexperimental)ofprediction models.

I3ased011thelitera turereviews anda collectionofexperimentaldata , Cha p ter 3presentsthenewapproachado pted in thisresearch. Therationalebehind the selectedapproach,theacquisitionofexperiment aldat a , aswellasthenumerical meth odadopted willbediscussedin det ail.

TheVIVcodeisimp lementedusingFor t ran 90. Validationstudiesarcgiven in Chapte r 4andChapter5. Chapter4presentsthevalidationof theprogramfor mooringlines(excludingtheVIVpart ),andChapte r5present svalidationstudyfor riserVIV.

Therobust ness of theprogramwasfirstshown byits applicat iontovarious static

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anddyna mic problems,andits extensiontoanalyzeVIVof risers.Conclusionsami rccommonda tionsforfurtherdevelopm entaredrawninCha pterG.

AppendixA present sthederivati on of the equations of moti onof a rod.Finite Elementdiscretizati on of the equat ionsofmotionandprogramflow cha rtsare shown inAppend ix B.

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Chapter 2 Literature Review

Research anddevelopment work on VIV begannearlya centuryago. Thereis a largebody of pub lish edlitera ture available onthetopic. Theliteraturereview inthiswork,therefore,mustbeselective. Inst ead of focusingon thephysicsof VIV,thisreviewis conducte donVIVpredicti on methodologiesandapproachesthat areapplicabletothefieldofoffshoreand oceanengineering. Thereviewexamines both numerical andexperimentalVIVpredictionapproachesadopte d byresear chers, and theirrespective st rengths and weaknesses.Thereviewis alsoextended toVIV suppressionmeth odologies.

2.1 Vortex-Induced V ibrat io ns Prediction

The accurateassessment of VIVfatiguerequiresaccurate computat ionofriserVIV responses.Thereareanumberof factorsthatinfluencethe accuracy ofVIVpredict ion models.Asnotedintheworkof Allen(1998),theaccurateaccount oftheparamet ers listedbelowhaveadirectimpact onthe accuracyof riser VIV prediction:

1. cur rentprofile

2.excitatio nandcorrelationlengthof liftforcesand vortex shedding

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3.frequency and magni tud e of thelift force exertedonthe riser as aresult of vortex shedd ing

4.hydrodynamicdampin g

5.riserstruct uralproperties andgeometry

Curre nt profileisthemostinfluenti alfact or in VIVpredicti on. For constant diameterandsur face roughness, cur rentspeed will determinewhetherriserVIV will takeplace or not. Forlongflexibleriserswith lownatur alfrequ encymodes,low cur rentcan theoreti cally excite VIV.

In semi-empiricalmodels, excita tionlift forcesare obta ined throughforced vibrat ionexperiments.Theseforcesarefunctionsofnon-dimensionalizedamplitude ratioandreduced velocity.Traditio nally,the excita tion length of theselift forcesin the spanwisedirectionmust alsohe accounted for in thesemodels. Correlat ionarises from thethree-dimensionalnatureof wake st ruc t ures behindcylinders. Acorrelation of 1.0 impliestwo-dimensionalflow. Undergiven flow condit ions,correla tio nin thespa nwisedirecti onisusu allydescrib edby empiricalcorrelat ion functi ons that dep endonamplit udeof vibra tion andspa nwisespacing.Thecorrela tio nlength is thendefined astheareaunderboth sidesof thc correlat ion functi on (Blevins,HJ90).

Thecorre lat ion length of vor tex shedding isnotnecessarilythesameas theexcitation length that is subjec ted toliftforces.Therefore,accurateestimat ionof VIVresp onses require anappro priateaccount for correlat ionlengths.

Hydrodynamicdamping,dep end ingoncurrent profiles ,isusuallymuchhigher thanst ruct uraldampin g. Likelift anddragforces,hyd rodyn ami cdamping also dep endsontheamplit uderatio andreduced velocity.Inotherwords,the amount of dampi ngdepends on the amplitudeand frequencyof vibrationof theriser.The computa tionof dampingisfurthercomplicatedbythelocation(spanwise) alongthe riser at whichdampin g applies.One of the significant weakn essesof most conunercial VIVsoftwaresliesin their implementat ion of thedampingmodel.

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Riser geometry and materialpropertiesmustalso becorre ctlymod elled. The mass, stiffnessand bendi ng charac terist icsmustbe cor rectlyaccountedfor.These propertieswill det erminethenaturalfrequencies andthe corres ponding mode sha pes of theriser. Thenaturalfrequencies areinverselyproportionaltoIcngth andmass and propor tional totensionand bonding st iffness.Thisis gcnora llycapturedusing thefinite element method.

2.2 VIV Prediction Methodologies

Thetwomain approaches tostudytheriserVIV phenomenonarc theuscofnumeri cal mod els and physical expe riments. Physicaltestin gisutilizedtostudy VIVto understandthe globa lresp onsesofariser design and insomecases supportnumeri cal modeling,Inadditio n,physical dataareusefulfor validatingnumericalprograms.

However,these experimenta l da ta setsare verylimited duetoproprietaryreasons, technical cha llengesin labtesting,andexpensesassociate d wit h large-scalefield testing. Conseq uently,research hasbeenfocused on developin gnumericalmodels forVIVana lysis ina cost-e ffectiveandefficient manner .

Numerical models arc usefulforunderstandin gVIV inthe absenceof physical testing. Mostoftheresearch cond ucte d onVIV hasbeenfocusedon t.henumeri cal mod eling ofthiscomplex phenomenon. The available numeri calmodelsarc summa rized in Figur e2-1.

CFD hasbeen gaining popul arit y as atoolforVIV resear chdueto advances in computa tion power.As shown inthefigure,CF Dresearchhasbeenfocusedon 2Dand 3Dsimulations.On theothersideofthe char tarethe semi-em pirical models.These modelsincludebothlinearfrequency simula tionaswellastime-do mainsimulations.

Thesemodelsarcdiscussedin thefollowing sections.

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Figure2-1:NumericalVIV PredictionModels

2.2.1 Computational Fluid Dynamics

Simulatin gphenomenonsuchasvortex sheddingaroundcylindersrequiresthe capturingof thebehaviorof turb ulent eddiesastheflowintera ct swit hthestru ctur e.

IIICFDsimulations,thisisconduct edusing advancedcomputa tiona ltechniquesto modeltur bulent flow.There areanumber of thesemodelsavailable andeachhave theirlimitat ions andstrengt hs.Figur e2-2 showsaflowchart of theseCF D models availableinthelitera ture.There are threemaintyp esofCF DmodelsusedinVIV research,namelyReyn oldsAveragedNavier Stokes(RANS),Large Eddy Simulati on (LES),andDirect NumericalSimulatio n(DNS).Since CFD isnot the coreof the current research,thesemodels and their applicat ions toVIVareonlybrieflydescrib ed.

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RAi\S com putes t.ho 'avoruges' of all theunste adin essinaturbulent flow.

In RANSformulation ,thevari abl e ofinterestmaybe writte nasthe sumofa time-va ryin gpart plusafluctu atin g compo nent(Forzlgorand Pcric,2002).Incsscnco, it computestheaveraged Reyn olds stressof a tur bulentflow.Unde r nANS,therearc three main subcategoriesof mod els:LinearEddyViscosity, NonlinearEddy Viscosit y, and Reyn olds Stress.

To obta in moredet ailsthantheleveltha tRANS computes,aLESmod elmay be em ployed . LES isbased011the noti on tha t themoti ons oflarge eddies play a muchlarger roleincarryingtho conserved properti es of tho entire flow and tha t smallereddiesarcless energet ic andcont ribute lessto the prop erti es ofthe flow.In anLES mod el,filteri ngisusedto sepa ra tethelarge andSillalleddiesin a turbulen t flow.This allowsLES toexplicitlysolvefor thelarge eddies andcompute the sma ller eddiesimplicitlyusin ga subgrid-scalemodel.Someof the subgrid-scale mod elsare showninFigur e2-2under LES.These subgrid-scalemod els arcem pirical. Therefore, LESsimulates thelar ge edd iesmorepreciselythanthe smaller ones (Ferzigerand Peric, 2002). This approac h is 3-dimensiona l,timedep end en t andcom putationa lly intensive.However,LES isvery attrac t ivewhensimulating highReyn oldsnumber flowswithcom plexgeomet ry.

Thehighestlevelof det ailaturbulencemodelcan provid eis thro ugh theuse of aDNS model.DNS doesnot approxima te nor averagethe motions ofeddies,beit largeor smallscales.Allthedet ails of the tur bulencearccapt ured; therefore,the computat iona ldom ainmustbe aslarge asthephysicaldomain .Thisrequir em en t putsaconstraint on the simulationasthenumber ofgrids(computa t iona l dom ain ) isdirectl ydep endent011compute rcapac ity.

Mostof thesemodelsare stillat theresear chst ageand havenot beenadopt edfor designduetoseveralreasons.Thesemodelsarecomp utationa llyintensive,ittakes along timetoarriveatasolutionandtheresultsareverysensitivetouserinpu ts.

Someofthemodels, suchasLES and DNS arc stillonly applica blefor relativ ely

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[owReynold snumberflows. Crit ica l Reyn oldsnumhorflowhasnotbeen availa ble ill DN"Smodelsduetolackofcomputercapacity.Researchcontinues inCF D for VIVcomputation with thehopethat com puter hard wareswill beabletohandl e DN"S simu lati onsathighReynoldsnumberflowill thencarfutur e.CF Dstudieson cylinder VIVforvarious configurnt ions (stationarycylinder,oscillat ingcylinder,and multiple cylinde rsimulatio ns) are summa rizedinthefollowing sections.

Figur e2-2: CF D Models

Simulati on ofaflowpast a stationa rycylinde r usin gLESor DN"Sgives resear chers someinterestin ginsightson thebehaviour ofeddiesin thevicinity of the cylinde r and how theyinteract.wit hthe cylinderitself.Whileit isnot feasibletouseONS forcrit icaland highReynoldsnumberflows,most oftheresearchtodatehasbeen focused onsimulation usin gLES.

Atlur ietal. (2009)ut ilized a20 LESSmagorinskymodelto stu dy thewake

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structureofacylinder forcedto oscillat e and the samecylinde r thatwas self-excited.

TheReyn oldsnumberrange of500-8000was cond ucte d,andthe influence ofRe on thewake struct ure wasinvesti gat ed .Theinfluence ofoscillat ion frequency ami Reynoldsnumber onthewakebehaviour was shownwit h20simulations,butaprecise comparison withexperimenta lresultsisnotpossible as the3Deffectsonthewake struct urewasnotaccountedfor.

He etal.(2010)simulatedVIVofafioxihloriser, wit hanaspect ratioof250, inuniform curre ntflowataReynoldsnumberran ge of 100-12500.In their work, theriserstruct ure wasmodeledusin g afiniteclementmeth od (FEM)andthefinite volumemethodwas ado pted todiscretizethefluid domain .Themod elisbasedon the assumptionthattheflowislocally 20andstriptheory isadoptedalong the spanwisedirection of theriser .AtaStrouhalnumberofabout 0.17,theyfoundthat the envelopeofvibra tioninthe cross-flowdirection isapprox imately 4-6timesthe envelopeofinlinevibra tion .Themaximum cross-flowlimpIitudewas about1.20 and 0.250for theinlinedirection .

Multiple cylindersimulationsare also perform edwit h2ormore cylinde rs arranged inadesir ed configurat ion.Themain configurat ionsarecylinde rsarrangedintande m.

side- by-side,andstagge red.Carmoetal,(2011)carriedout2Dand 3D Ol'{S oftwo cylinde rsintandem.Intheirsimulat ion,the upst reamcylinde r is fixedwhilethe cylinde r inthedownstr eamwakeisfreeto oscillate inthetransversedirection .The 20simulationwasdone at a fixed Re of 150 and the 3Dsimulation was conducted atan Reof300 whilethered ucedvelocit ieswereva ried by cha ngingthe struct ural stiffness. Theresponsesofthe downstr eamcylinde rwere comparedwith the respo nses of asingleelasticallymoun ted cylinder.Itwas showntha tthe cylinde rinthetandem configuratio nexpe riencedhigheramplit udesof vibrat ionandawiderlock-inenvelope.

The aut horsbelievedthisdifferencewasduetothe oscilla to ry flowinthe gapofthe tand emconfiguratio n.This gap forcedthe st agnat ion pointtoalte rnate alongthe fron twallof thedownstr eamcylinder.

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Recent CF O research on VIVhas shown thatthc current state-of-the-artislimited bycomp ute rcapac ity. Thehigh estReynold snumberflow computed forVIVstud ies islimitedtoaround 15000forLESmodelsand lessthan 1000for0'Smodels .Thisis far belowthe Ilerangeobservedintheoffshor e,whichisusuallybeyondone million.

Consequently,CF Oapproacheshavenotbeenado pted forriscrVIVanalys is in design (Licctal.,2011).

2.2.2 Semi-empiricalModel s

Resear ch on VIVinthclastfewdecad eshasled tothe commercializa tionofa number of VIVpredicti onprogramsthathavebeen adop ted bytheoffshoreindustr y.

Thecom mo nthemebehind thesesoftware packagesisthatthey all makeuscof ex perime ntalhydrody namiccocfficicntsalongwith nu meri caltechniquesto evaluate VIVresponses ,Hencetheyarc"sem i-em pirical"models.Duetodillorcnccsin t.he assu mp t ions, analytical framework , andem pirical infor mationused in thesemodels , therehasbeenlargescatter inpredi cti onsfrom thesemod els(Larsenand Halse, }997).

Themostcom mon lyusedVIV programinthcindustr yisSHE A R 7. This program,developedat theMas sachu settsInstitute ofTech nology [Ml'T'),solvesthe crossflowvibrationof acylinderexperiencing VIVoThenumeri cal model in SlIE AR 7usesamode supe rposition method andpre-determinesthcnumber of modesthat arc likelytobesubject edtoVIVandcomputesthe cross-flowvibra tionbas ed on empirical hyd rody nam ic coefficients. Based on userinput dat a ,SHEAR7com p utes thepoten ti ally excited mod es.Amode cutoff treatmen tisutili zedbasedon input.

powerfor theidentifiedmodes ,If morcthan onemod eisexcit ed,the overla ps between themodesarc elimina te d. Theprogram thcncompu testhemod alinput power (cxcita t ion ),and themod al outp utpower(damping ).Modalpowerbalanceisthen donebyiterationuntil thcVIVam plituderatio (A/D)converges.Ateach iteration, thcprogramadj us ts theliftcoefficientand iter atestillconvergence(Vand iverand

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Li,2005) .SHEA R3D isanother modeldevelopedatlVIIT (Venugopal,199G)asan extensionof SHEA R 7.Asnotedabove,SHEAR7isonlya cross-flow predi ction program.Realizingtheinad equacyofthe2Dmodel,Venugopalextended themodel toa3Dmod el byincludingtheresponsesinthe inlinedirection.A differentdamping modelwasalso presentedin hiswork.

Asecondsemi-empirica l modelisVIVAorVIVAR RAY,wh ichwas alsodeveloped atIvIIT .VIVAevaluatestheriserresponseusing complex harm onicmodes . The amplitudeandphaseofeach modevar yalongthelength of theriser , sothey can either besta nd ingwaves,travellingwaves,oracombinationofthetwo.

VIVANA,developed by1'v1A RINT EK, isan FEl'vIbasedprogra mforanalyzingriser VIVoThisprogram isnota stand-aloneprogram inthesensetha tthe analysismust bedonewiththeaidofRIFLEX.RIF LEXis anFEN!packagedeveloped for thestatic and dynam icanalysisofslendermarinestruct ures.VIVANA alsoutilizes amodalor eige nvalueapproachforVIVana lys is. Staticanalysisandeigenvalueana lysis are first cond uctedusingRIFLEX.VIVANAthenidentifi esthepossibleexcita t ionfrequ encies aswellasthedominat ingonesandcomp utestheVIVresponsesfor each identifi ed frequency.Basedontheseresponses,fatigueana lysis iscarriedout.Thisprogramis alsobasedonalinearfrequencydomainapp roach,and neglectsthenonl inearit.icsor theproblem.

Anotherclassof modelsistheWakeOscillat orModel.Th iswasfirstproposed byBishopandHassan(19G4)andlateradop ted byIwanand Blevins(1974).The lwan -Bl evinsmod el,asutilizedinthecommercialsoft wareOrcaFlex ,utilized for ced experime ntaldata cond ucte dintheReyn oldsnumberrangeof10³to10⁵.Intheir work,the govern ingequationofa self-excite d fluidoscillat or wasderived. This govern ing equation,alongwit htheequationofcylindermotionformed thebasis of thenumericalmodel.

Recently,researchershave extended thesesemi-empir icalmodelstotime-domain simulations. Grant etal. (2000) developedatime-domainVIVsolver,ABAVIV.

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Thisprogra musesthefiniteclementpackageAI3AQUSalong withavrvalgor ith m tosimula te riserVIVrespo nsesinthetime-do main.TheVI Valgorith m used in AI3AVIV isbasedOIla correlat ionmodel proposedby Blevins(El90).The cross-flow vibrati on is excitedandmonitored todeterm ineifit iswit hi napre-d efinedlock-in criter ion.Whenlock-in criterion ismet,thealgorit hmsmoo thlytunestheliftforceto bein phasewit h theriservibrat ionvelocity.If not,the algorith m usestheStrou hal frequency astheliftforcefrequ encyandassigns itarandomphase ang le foreach correlation len gth alongtheriser(Grantetal.,2000). Thedeterminationof the lock-inregion,therefore,requirestheVIVfrequen cy,amplitudeandphase.AI3AVIV uses exponential modelin gtechniquestodeterminetheseparameter s ,based on the time-hi stor y ofvibrat ions.Thismodelwas showntocapt ure VIV reasonabl ywellfor afewriserconfigurations.Theprogram,however,isbasedonthe assumpt ion that vort icesareshedatafrequency correspond ingtoaStrouhal munber of 0.17.Thismay not bevalidwhentherisermotionsigni ficantly influen cesthevort ex sheddingpattern.

AI3AVIValsoassumed the ad ded masstobeindependen t of reduced velocities,and assignsavalueof1.0.

Arecentcontribution to time-domain VIV predi cti onis aprogramcalled SimVIV (Sidarta etal., 2010).Sim ilar to AI3AVIV,SimVIVado p ts AI3AQUSasthefinite elementeng ineand uses auser-subroutin eto comp utetheVIV forcin g.Sim VIVwas shown tocomp utebothinline andcrossflowVIVoThe crossflowvibrat ionisbas ed on the same theoryusedin ABAVIV.Theinlineresponsewassimu lated,butmore calibrat ion da taisrequiredtoimprovethe accuracyof thepredi ct edresponsesinthe inlinedirection.

2.2.3 Experimental Methods

Experimental meth odsprovidephysicalmean sofcollect ing meaningfulinsight on the beh aviour ofrisers subjectedto VIV.There arefourmaintypesofex perime ntsinVIV stud ies.Theforced vibra tio nexpe rime ntsareconducted toacq uire hydro dyn am ic

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coefficients011tlu:cylinder subjccrcd to forcedvibration.Thoseco(~(ficientsarc used insemi-empiricalnumericalmodelsto predictriserVIVresp onse.Thesecondtyp e of experiment isthefreevibrati on experiments.In thefreevibration experiments,the cylinde r isnot forcedtovibrat eand therefore capt uresthe"real"VIVresponses of the cylinde r. Bothforced and freevibration experiments uscrigidpipesto gainoverall behaviour ofa segmentofalongriser.Laboratory scalerisertestin g arccond ucted ona shorte r riserthatarcscaledto accommoda te thetestin gfacilit ies.Fullscaleriser testin garenormallydoneintheoceanduetolimit ing sizeofcont rolledlabora tory facilit ies.Bothof thesetypesof testingare cha llenging,butext remely usefulfor benchm ark validationofnumericalmodels.

ForcedVibrationExperiments

Forcedvibrat ionexp eriments arc cond uct edon finitelengt hsofacylinderin whichthe cylinde r isforcedto oscillateat aprescrib edamplit udeand frequency whilebeingtowedthro ughwat er(Sarpk aya,1978;Staubli,1983;Gopalkrishn an, 1993;Spencer et al.,2007).Thistypeof VIVexperimentallows the amplit udeand frequencyofcylinder vibrationto bealteredto obtaincorres ponding hyd rodynamic forces experienced bythe cylinder. Sarpkaya (1978)was one of the earliest tocond uct suchexperiments. Throughforcedvibrat ion experimentsatRerange of 6000to 35000,Sarpkayarep ort ed that themaximum amplit udeofcross flowvibrationswas 0.9diam et er.Bothin-ph aseandout-of-phasecomponentsof forceswerereport ed as functi ons ofamplit ude rati o(A/D ).

Staubli(1983)conducted forced experiments onelast ically mount ed cylindersat aReynoldsnumberrangeof 20,000-300,000andshowed the ad vantagesofthese experimentsinwhichtheamp lit udeandfrequencyvalues canbevari edtoobtainthe corres ponding lift anddragforces.Staubliobserved thathyst eresiseffect s arc dueto thenonlinearrelation betweenthefluidforceandoscillat ionamplit ude.

Fromforced experiments, experimenterscanobtainsurfaceplotsoflift(CIN ) , drag(CD)and added mass(CM )coefficientsasfunctions ofam plit ude rati o(A*)and

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reducedvelocities(Vu).

A' =~

^(2.1)

\fu =~o

^(2.2)

whereA istheamplit udeof forced oscillation, D isthe cylinde r diameter, isfree stream velocity, and

io

isthefrequency ofoscillation. Althoughforced experiments provideuseful dat aforrelatin ghydrod yn amicforcesto amplitudeand frequency of vibrati ons,theyare atime consuming wayofobtaining such data.Foreachcylinder, strakc,or fairin gconfigura t ion,alarge testmatrixofexperimenta lrunsneedtohe carriedout inorder toobtaintheseVIVforcecoefficient plots.

FreeVibrations

Unlikeforcedvibrationexperiments,freevibra tio nexperiments are conducted onafinitelength ofa cylinder in whichthe cylinderisfreetovibratedueto vor texshedding. Thisis amorerealisticrepresentati on ofVIVinanexperiment sett ing. Fromfreevibration experiments, one cantypicallyobta inA*versusU*plot , correlation dat a,andcylindermotion.

U'= ~

Din (2.3)

whereU'and[«isreducedvelocityforfreevibra tionexperimentsandnatural frequency of the cylindersegment,resp ectively,Theredu cedvelocityin freevibrat ions isa functionofnatur alfrequencyof the st ruc ture,whichisdifferentfromthe redu cedvelocityin forced experiments(Spencer, 2009).Thereducedvelocity versus amplituderatioplotsareuseful for validatin gVIV numericalalgorit hmstha t use forcedexperimentaldat a.

LaboratoryScale

RiserVIVexperimentsare alsoconductedon reduced scalerisers(Li,2005;

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Cha plinet al.,2005a)inalaboratoryset.t.ing and usethemeasuredresponsesto make apredictionof thefullscaleresponses.However ,riserresp onsesare extremely sensiti ve toReynoldsnumberand thenumber of modesalongtheriser.Thered uction inscalewillauto mat icallycha nge theReyn oldsnumber, andalsothenumber of modes to bepresent.alongthelengt h . Oneapproach isto increasethescale,but. thismean s a considerablelargefacilit.y(t.a nk) willbeneeded.Therefore,t.his approach isnot.

practi calfor deepwat errisers.Thesetypesofexperiments areuseful forvalidating numeri calmodels,especially in thecapturingof multi-m od alvibrati ons along the spa nwisedirect.ion.

La r ge scaletests

Themost expe nsive VIVexperimentsare those cond uctedinlakesoroceans wit hlargescalerisers. Thishasbeentraditionallyconductedaspart. ofajoin t.

industr yproject (,TIP)whichinvolvesanumberoforga n izat ionsorcompa nies with acommongoaltoadd ress current. industryissu es,suchasVlVpredi ction.This typeof testrepr esentsthemostrealist.ictest cond itio ns. However ,realistictest.

conditionscomewithincreasedtechnicalchallenges. For inst ance,themeasur em ent ofcur rent velocit.iesrequirethe calibrat ionand installationof alargenumberof instrumentati onsalongtheriser. Inaddition,the cur rent. velocities cannot be cont rolled in theocean .Therefore,thetest.sareusually conducted incalm wat er condit ions,and the cylinde rsor pipesarefirst assembled tothedesir edconfigu ration andtowed throughwater at adesiredspeed tosimulat.ecur rent. flow.

Vandiver(1983) conducted oneof thefirstlargescalecylinder testsin thelakeof Cast ine,Main ein 1975 and 1976.These cylinde rswere75-ft syntheticfiber orwire cableswit.h diam etersran gingfrom 0.64to1.59em.Thecurre nt. velocitiesinthetest s werespa t ially uniform andvari edwithtime,from 0.152to 0.162ui]«.Thevibra t ion respon ses,asobserv edinthesetests,weremostly single-modelock-invibrat ionwith amplitudesof onediam et er.Low-amplituderando m vibrationresponseswerealso observed.Oneof themostimportantobservati onswasmadewhen a900 feetwirerope

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of 0.71 cmin diam et erwas sub jecte d to amildly shearedcur rent.Lock-invibra tion wit hamplitudes of 0.5-1 diamet ertookplace at the50th mode.This confirmed that lock-inbeh avi ourispossibleforfloxihl opip esathighmodes.

Jongand Vandiver(HJ83)andVandiver(1983)cond uct edaG-weokexperiment atthe samesiteinCastine,Maine. Bothcable(3.18 cm in diam et er) andsteel pipes(4.18cm in diameter ) oflengt hs22.8Gmet erswereusedin this experiment.

Thetension,acceleration,meandrag coefficient,andcurre nt woremoasu rcd.The primarygoalsofthetestswereto det erm inethedifferen ceinthebehaviourofcables an dsteelpipes (of differ en t massratioand bendin gstiffness)andtomeasureand compar emeandragcoefficientswit hthose collecte dfromlaboratoryexpe riments.

Thedrag coefficientswer eshowntobehighandoscillatewithlargeramplit udesover 2.5hoursof dat afor the steel pipe andoscillat elessovertimeforthe cable.This finding conclude d that themassratio isimport an t forunderst andingVIV.Themass ratioisdefined as 7r/4 timestheratioof the cylindermassperunitlength overthe massper unitlength of thefluid itdisplaces.Thelowermass ratiocylindershave a broaderrangeoflock-in behv aiour than thehighermass ratio(Vand iver,1993).

Largescale expe rimentsarcalsousedtovalida tenumeri calpredi cti onmodels.

Forinst an ce, Grantetal. (2000)conductedafield testinthePhas e1 Highly Compliant Riser (HC R).JIP.Thetestprogr amme consiste dofthreediffer ent riser configurations:com pliantvert icalaccessriser(CVAR),SCR, andlazywaveSCR.

Amechani calactuator isinstalled to simulate dynamicvesselheavemoti on,and sign ificantintermittentVIV was obse rved. Thedatacollecte dfrom thesetests wereused asben chmark validationstudy for a time- do ma in VIV predi cti onmodel developedbyGrant etal.(2000).

Anotherrecentlarge scale VIVexpe rime nt tookplaceoffshoreMiamiin2005.

ThisGu lfStream testaimedto collecthighmodeVIVresponsedataonaden sely instrumented cylinde r,conductpa rtialand fullcovera geofst.rakes and fairin gson cylinde rs, andesti mat edragforcesoncylinderswit handwithoutst ra kesand fai rings.

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Thetestwasconducted with a compositepipewithanouter diam et er of 1.43 inchesandalengthof50004feet. Thesedimensionswere chosen inorder to obtain moretha n 10 modesof vibra tions.Thepipewas connected toa resear ch vessel at thetop anda railroadwheel(weighing805poundsinair)atthebott om to providetension.This setupsimulatesatensionedbeamwit h pinned-pinned end boun daryconditions.Fiberopticstraingaugeswereinst alledtomeasur ethevibration responses.Oneinteresti ngfindingwastheoccurrences ofhigherharmonicsthat.are not ort hogonal to the crossflowand inlinedirection.Inaddition, struct uralresponses were observed to conta in theform of waveprop agati on(Marcelloet al.,2007).

Murrinetal.(2007)cond uct edahighmodeVIVexperimentonalarge-scaleriser thatwastowedoff thecast coastofNewfoundland,in TheCordelia Deeps.Theriser was130metersin length,withanouterdiameterof53mmand an innerdiamoter of -lflnnu.Thelargescaleriserwastowed atspeedsrangingfrom0.15to 1.25ui]«.For eachrim,thedat awasrecordedbytheaccelerom et ersfor 3minutes after thevessel speed hasreachedsteadystate.Thedat awas analyzedand to obta inaccelerat ion, displacement and thefrequencies of motion.Theresult sof multi-modalvibrations from this experimenthavenot yetbeenpublishedinthepublicdomain.

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Chapter 3 Time-Domain Model

3.1 General

Themodelbeing ado pteduses empiricalhyd rod ynamicVIVcoefficients from forced experimentsandformulatestheprobleminthetime-domain. Aspartof the JIP-Deepstarproject,alar gedat abase ofhydrod ynamicVIVcoefficients was collected onfinitesegmentsof risers and riserswithsuppression devices.Thesedata sets come from forced experimentsin whichthe cylinder(or riser segment) istowedthrough wat er at a consta ntspeed whilebeing subjecte d to oscillat ionata specifiedamplit ude and frequency (Spenceret al.,2007).

MostforcedVIVexperimentsconductedin thepast areforrelativelylow Reyn olds numberflows.Thislimit ation canbe oneof the fact orsinfluencing theaccuracyof VIVpredictions.TheforcedVIVexperimentalsetupshown in Figur e 3-1, however, is equipped to conduct forced experiments forhighReynoldsnumberflows (up to 1.8X10⁶).TheincreaseinHemakesthe collectedhydrodyn amic coefficientsmore valid for realistic applica tions.Inorderto utilizethese coefficients for longerrisers, anumericalmodel istobedevelopedin thiswork.This cha pte r willgive adetailed descriptionof thenumericalmodelbeingdeveloped andtherationalefor suchamodel.

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3.2 acc's Forced Experiments

Spencer etal. (2007)havecollected forcedVIVcoefficientsoncylinde rs usingthe highReynoldsnumberVIV test appa ratusatOceanic Consult ingCorporation(OCe).

The setupof these exper imentsis shown inFigure 3-1. In theseforced experiments, cylindersareforced to oscillateat aprescribedfrequency andamplit ude whilebeing towedthroughwat er.

Figur e3-1:Oceani c Consult ingCor pora ti on's VIVtest apparatus

Themeasur edhydrod ynami cforces acti ngonthe cylinde raredecomposedinto two components,liftand drag, acti ng at 90 degreestoeachother.Theoscillatio n occursintheliftdirection(cross-flow);theliftforceisthereforefurt herdecomposed

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intotwo components,one in phasewit hvelocity and theotherin phasewith accelera tion(addedmass).Theliftcomponent thatisinphasewithvelocitytend s to excite or dampen thevibrationinthecross-flowdirection. Thelift component that isinphasewithaccelerationalterstheapparentmass ofthe cylinde r. Further proces sing of the collected datawill giveforce coefficient(lift, drag andadded mass) cur ves that aredependent on non-di mensionalized velocity (reduced velocity) and amplitudeofoscillation(amplit uderatio).Forcedoscillat ionexperimentdatafrom the Deepst arfundedproj ect (Spenceretal.,2007)havebeenutilizedin thisresearch.

Thedat.ahaso ofcoefficientsusedinthepresentmodelinclud os added mass,drag, and liftcoefficientsthatdepend onthe amplituderatio(A*)andredu cedvelocities (Vn )fromtheforced experiments.Thisdatabaseofcoefficientswas collectedona bar e cylinder wit houtVIVsuppression devices.

Thedrag coefficient isregard ed asthehydrodynamicforceintheinlinedirection.

Thisforcehasaste adyandoscillating compo nentasdefinedinthefollowingSection.

The addedmassisapplied tothe crossflow directi on as this wasderivedfrom thelift forcesthatwerein phasewithaccelerati on. The added mass changesthe apparentmass oftheriserandsubsequentlyalte rsnaturalfrequency ofthesystem.

In thispresentdatabse,the addedmass(CM )coefficientscan beboth positi veor negati ve.Positi veCMmeans an increaseinappa rent mass andadecreaseinnatural period (Spenceretal.,2007).

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o C"_I

Figure3-2:Lift ForceCoefficients 0.5o -0.5 -I -1.5 -2 -2.5 -3 -3.5 -4

Theliftcoefficients(GIN ),in phasewit hvelocity,areplotted againstA'and VRandshownin Figu res3-2and3-4.In thesefigures,GU1showsbothnegati ve andpositi vevalues.PostiveG/.vmeansenergyisbeingput inthe syste m to excite vibrat ion,andnegative Civ repr esent s energy removedfrom the syste mand the vibra tionisdamped .Inother words,both hydrodynamic excita tionand damping areincludedintheGI,vdat ab ase.Thisisdifferentfromprograms suchasShcar?,in whichsepa ra te mod els areimplemented for excitationand damping.

Figur e3-3 shows theVenugopaldampingmod elthatisusedin Shear? In the Venugopal model,dampingisdefinedforred uced velociti eslessthan5 andgreater than8.Excit ation is assumedto occuratreduced velocitiesintherangeof5 and8, anda separa temodelisimplementedfor this.

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Corresponding tift coefficient,Venugopal (1996) dampingmodel

10 15

ReducedvelocilyUR=U /('o.P )

Figure3-3:VenugopalDampingModelforLowandHighReducedVelocities

Asnotedinthework of Spencer etal.(2007),Figures3-2ami3-4inthepresent databaseshowsimilarity in liftcooffirlents betweenVeuugopal'sdampingmodelat lowandhigh reducedvelocitywheremost ofthedamping occurred.Atlowredu ced velocities andhighamplit uderatio,theplotshows asteep decreaseinCLI,values . Athigherreducedvelocities,itisshownonthe surfaceplotthattheCLI,values arenearl yconst ant.However,thereisa"well"in Figur e3-4,showingnegativ eCIN valuesbetweenreducedvelocitiesof4.5 to 5.5with amplitudera tioslessthan0.6.

Thisisnotcaptured intheVenugopal dampingmodel.

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c"

Figur e 3-4: LiftForce Coefficients(Rot at ed View) 0.5o -0.5 -I -1.5 -2 -2.5 -3 -3.5 -4

A new approac h wasdevelop edin theworkof Spenceret al.(2007)tomakefull use ofthe availa ble highReyn oldsnumberVIVcoefficients.Intheirwork ,hydrodynamic dampingwasincludedas anextension of the liftcoefficientcur ves.TheVIVforcing algorithmado pte dinthiswork isbasedontheirwork.The algorithmwasthen implemented witha globa l-coor dinate d-base dfinite elementprogram to analyzeVIV onlongerrisers.

3.3 Time-Domain Forcing Algorithm

IntheDeepstart.est.programme,forced experiments wit h bothsinglefrequency and t.wo frequency component.scombined were conducted.Thelatter typ eincludesthe combinationoftwofrequencies such t.hat. the signa ls beat. toget.her and t.he amplitude va ries continuously.It.was shownthat.thelift force andaddedmassmeasuredfrom oneunsteady cyclewit.hamplitude,Aami frequency,fwas similar t.othosefound wit h multiple cyclesofconst.ant. period andamplitude.Thisimplies thatt.hefluid

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particl eshaveno memoryoftheir pat h,and that.onlythe currentsta te variables(A*,

\tJl)o[ the cylinder play arolein theloads experienced bythe cylinder(Spenceret al.,2007).With thisinmind,it.ispossibletousethe state variablesof theprevious cycle toestima te theforcesona cylinderinthenext cycle,assuming thatthe cylinder motiondoesnotcha ngedrastically[rom one cycletot.henext. Thisformsthebasis of thetime-doma in forcing algorithm in thiswork.The cur rentsta te variablesofthe cylinderaredetermined [rom theresponsesof theprevious cycle,and the algorit hm uses thesecur rentsta te variablestointerp olat e along thehydrodynam ic coefficient cur ves to det ermin eforce coefficients to beusedin thenext cycle.

Zero crossinganalysisof the cross flowvelocity isused to det ermin etheperiod (To)andsubsequently the amplitude of themotion[rom theprevious cycle.The determin ed amplitudeand frequency,along withflow speed,are ente red in Equati on 3.1and 3.2tofind the sta te variables(A*, Vll).

,-\

I \

I

\ I

I

\",

Figur e3-5:Zero CrossingAnalysis ofaVibration Cycle(from Spencer etal.,20( 7)

A*=Ymax -Ymin 2D

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