Vortex-induced vibrations of risers: theoretical, numerical and experimental investigation

Title

:

experimental investigation

Auteurs:

Authors

:

Cédric Le Cunff, Francis Biolley, Emmanuel Fontaine, Stéphane

Étienne et Matteo L. Facchinetti

Date: 2002

Type:

Référence:

Citation

:

Le Cunff, C., Biolley, F., Fontaine, E., Étienne, S. & Facchinetti, M. L. (2002). Vortex-induced vibrations of risers: theoretical, numerical and experimental investigation. Oil & gas science and technology, 57(1), p. 59-69.

doi:10.2516/ogst:2002004

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1Institutfrançais du pétrole, 1 et 4, avenue de Bois-Préau, 92852 Rueil-Malmaison Cedex- France

2 Département Génie mécanique, École polytechnique, 2500 Chemin de Polytechnique, H3T1J4 Montréal(QC)- Canada

3 École polytechnique, Laboratoire d’hydrodynamique, CNRS, 91128 Palaiseau Cedex- France

e-mail: [email protected]@ifp.fr- [email protected] [email protected] [email protected]

Résumé— Vibrations d’un risersoumis à un écoulement: étudethéorique, numérique et expérimentale — Les vibrations engendrées parle relâchertourbillonnaire dansle sillage d’un cylindre soumis à un courant peuvent créer une fatigue importante dans les tubes utilisés par l’industrie offshore pour amener le pétrole ou le gaz du fond de la mer jusqu’à la plate-forme ou le navire de stockage. Ce sujetfaitl’objet detrès nombreusesétudeset,àl’Institutfrançais du pétrole,plusieurs modèlessont développés pour prédirela durée de vie de cestubes. Les méthodes vont d’une simple analyse modale de laréponse delastructurejusqu’à uncalculcoupléfluide-structureavecrésolution deséquations de Navier-Stokes. Autravers du projet Hydlines, descampagnes d’essaissont menées pour validerles différentes approches.

Mots-clés: vibrationsinduites par vortex(VIV),riser,fatigue, offshore.

Abstract—Vortex-Induced Vibrations of Risers: Theoretical, Numerical and Experimental Investigation — Vibrations duetovortexsheddinginthe wake of acylinderexposedto acurrentcan createfatigue damagein risers used bythe offshoreindustryto bring oil and gasfromthe seafloortothe platform or off-loading vessel. Extensive researchis conductedinthis domain and atthe Institut français du pétrole, several models are proposedto predictthefatiguelife of such pipes. The methods rangefrom simple modal calculationstofully coupled analysis ofthefluid-structureinteraction and resolution ofthe Navier-Stokesequations. Throughthe Hydlines Project,experiments areconductedtovalidatethe various approaches.

INTRODUCTION

If a current impacts on a circular cylinder, fluctuating forces are created dueto vortex-sheddinginthe wake.Ifthe cylinder is mounted on springs, the forces induce a displacement ofthestructure, whichinturn, modifiesthe flow,leadingtoafullycoupledfluid-structureinteraction. The displacement ofthecylinder underacurrentisreferred toasa vortex-induced vibration(VIV). Muchresearchis available on the subject and more details can be obtained in various books orreviews: Marris(1964), Sarpkaya(1979), Bearman(1984), Griffin(1985), Chen(1987), Blevins (1990), Sheppard and Omar (1992), Naudascher and Rockwell(1994), and Williamson(1996).

Theindustrialinterest for VIVis based onthe fatiguethat a long cylindrical structure can experience. The main applicationsarechimneysandcablesfor bridgesinair,and pipes, towing cables, and mooring lines in water. The focus ofthe present paperisthe risers usedinthe offshoreindustry to carry oilfromthe bottom ofthe oceanto afloatingfacility. Reviews onthespecifics of VIVinrisers are givenin Pantazopoulos(1998).

Thefatigue dueto VIVcan bethe dominantfatiguein some risers configurations. An example of well-head failure is provided by Hopper (1983). A drilling riser was installed ina depth of 1450ft of water. Measurements ofcurrents were performed during the drilling operation. A fatigue life estimate dueto VIV was undertaken usingthesecurrents. Calculations predictedfailureafter 29 days,theactual in-service life being 27 days. The failure due to VIV was also confirmed byrealtime measurements ofriser balljoint angle. Withthe arrival of deep and ultra-deep offshore field, and new configurations of riser (steel-catenary risers (SCR), hybrid risers, etc.), any design must nowinclude an analysis ofthefatigue dueto VIV.Ifthe damageisexpectedto be too great, anti-VIV devices are proposed. The most commonly-used arestrakesinstalled alongthe pipe on the most exposed area. Otherstechniques can befound in Zdravkovich(1981), Every et al.(1982),and Bruschi et al.(1996).

Inthe present paper, a short review ofthe vortex shedding is presented. Then,several approaches are proposedto compute the fluid-structure interaction. The first approach is based onthe modal response ofthe structure; such a method is widely used in the industry since it is fast and provides a simplelifetime estimate. The second, more detailed approach requires solving the structural equation in time together with an equation which modelsthefluid. Thethird approach involvestheresolution ofthefull Navier-Stokesequations, instead of a simple fluid model equation. Finally, the results of a set of experiments on a cable with multiple diameters are described. They will provide benchmark casesto validatethe different methods.

1 VORTEX-INDUCED VIBRATIONS

The VIV phenomenon depends on various parameters. For the fluid, the two main parameters are the Reynolds number Reandthe Strouhal number Stdefined by:

(1) where Uisthe fluid velocity,D,the diameter ofthe cylinder, νthe kinematic viscosity andf_vthe shedding frequency. The fluid-structure couplingis characterized bythereduced velocity U_r:

(2) where f_mis an eigenfrequency ofthe structure.

Theshedding ofthe vorticesissketchedin Figure 1.It creates forces both in the cross-wise and stream-wise directions. Studies(Naudascher, 1987; Vandiver, 1987; Torum et al., 1996)showthatthein-line vibrationsarean order of magnitude smallerthanthetransverse vibrations. In -line vibrations can also occur bythemselves and constitute a fatigue problem for the free-span length of pipes on the sea -floor. Theyare usually notaconcernforriserssincethey appearatlowerreduced velocity. Axial vibrations(Huse et al., 1998)area by-product ofcross-flow vibrationsandare observed whentheaxial deformation duetothecross-flow vibrationstriggers aresonant axial mode.

The lock-in phenomenon occurs when f_vand f_mare close toeach other,correspondingto U_r≈ 1/St.Inthiscase,the shedding frequency becomes equal to the eigenfrequency of the structure. The vibration amplitudeisthen maximum, and thecorrelation betweentheexcitationforcesalongthespan increases dramatically. In any case, the amplitude of vibrationislimitedtothe order of one diameter.

Figure 1

Vibrations of a cylinder submittedto vortex shedding.

Flow In-line vibrations Crossflow vibrations Axial vibrations U U f D r m = Re UD St f D Uv = = ν and

2 MODAL APPROACH

The modal approachis described by various authorsto compute the vibration amplitude of a structure (Iwan, 1981; Lyons and Patel, 1986; Moe, 1991; Bokaian, 1993; Nedergaard et al.,1994). Thefirstapproximation usually assumesthatthe cross-flow displacements arethe most dangerous,andrestrictstheanalysistothecalculations of these displacements. Thesecondapproximationconsists of calculatingthefluidforce ona given modeindependently, neglectingthe cross-interactions betweentheforces.

2.1 DeepVIV

DeepVIV is a module of the finite element code DeepLines (2000) which performs VIVcalculations. Theamplitude of vibrationandtheresultingfatigueare obtained based ona modalcalculation oftheresponsetoasteadycurrent. The structureis defined by elements: cable, bar or beam. A static analysisisfirstcarried outtofindtheequilibrium position, followed by a modal analysis, andfinally by VIV ca lcu-lations. Thereis alsothe possibility of reading a pre-existing modal database, whichis useful when alarge number of modesis excited.

DeepVIV proceeds asfollows:

– Calculations ofthe modes ofthestructuretakinginto account the external fluid displaced which is accomplishedthrough an added mass coefficient.

– Selection ofthe potentially excited modes withtwo criteria:

•the modeis mainly perpendiculartotheflowandthe

structure(shape);

•thefrequency fsatisfiesthereduced velocitycriterion:

given St,thereduced velocitycorrespondingto Stis U_r=1/St,andthe modeisexcitedifitsfrequencyis located between U_r–∆U_minand U_r+∆U_max. Thelock -inarea onthe mode offrequency f_iiscomposed ofall the points whichsatisfythecriterion.If morethan one modeisselected,the mode withthefrequency nearest toU_ris chosen.

– Calculation ofthe modal amplitude: a balance betweenthe lift force and damping gives the amplitude of each mode. The lift can be reduced by taking into account an experimental correlation length. The hydrodynamic dampingis based on Morison’s formulation (1950) ofthe dragforce, hencethe use ofa VIV dragcoefficient. A “self-damping”is alsoimplemented whenthe modal amplitude becomes higherthan one diameter, which representsinthe modelthefactthat VIV havealimited amplitude. The lift force is a function of both the amplitudeandthe Reynolds number. Theliftcoefficient has been validatedthrough experimental results. Anti-VIV devices are modelled by areducedlift coefficient.

Thelift forceisthen applied onthe structure and solvedin the frequency domain on the modal basis of the structure. A classical fatigue analysisis performed based on Miner’s rule (DNV, 1996), withthe contribution of eachload itothe bendingstress(∆S_i)andits period(T_i)tothe damage given by:

(3) The constant Cand bare given by afatigue curve:

(4) where Nisthe number ofcyclestorupture underthestress range (∆S). Rayleigh’scorrection, whichisconservative,is also available, as well as Goodman’s method(Lalanne, 1999) whichtakesintoaccounttheratio ofthestaticstress with respecttothe yield stress.

2.2 Examples

2.2.1 Drilling Riser

A 790 mlong riseris pinned atthe seafloor andtensioned at thetop. Sevenareas of different hydrodynamic diameters, representingthe buoyancy modules,are definedalongthe cable(from bottomtotop) asindicatedin Table 1.

TABLE 1

Variation ofthe diameter alongthe riserlength fromtopto bottom.

Thelength ofthe section andits diameter are provided

Length (m) Diameter (m)

180.0 0.533 240. 1.12 15.0 1.12 70.0 1.17 135.0 0.533 125.0 1.00 25.0 0.533 TABLE 2

Variation of current velocity with depth

Depth (m) Velocity (m/s) 0 0.4 100 0.5 200 0.5 300 0.2 400 0.3 500 0.4 900 0.4 N S C_{( )∆} b₌ D n N S CT i i ib i =

∑

∑

The pipe itself has a constant diameter of 0.533 m with a thickness of 0.016 m. Thetoptensionis equalto 3.25·106_N. The current perpendiculartothe riseris defined as a function of depth (Table 2).

For St= 0.2,theexcitedfrequenciesaresummarizedin Table 3(obtained with an added mass coefficient of 1).

TABLE 3

Excited eigenfrequencies ofthe riser

Mode Frequency (Hz) 2 0.439E – 01 3 0.675E – 01 4 0.921E – 01 5 0.116E + 00 6 0.141E + 00 7 0.164E + 00

In orderto performthefatigueanalysis,thecurrentis assumedto be constant all year round. The significant results of the VIV analysis are the root mean square (RMS) vibration amplitude and the fatigue life due to bending stresses.Inthis particular case, we obtained:

– maximum RMS amplitude: 0.59 m at 697 mfromtop; – minimumfatiguelife: 145 years at 704 mfromtop. As can be seen from Figure 2the amplitudeis dominated by mode 3, which is the most energetic mode. Nonetheless, the most dangerous modeforfatigue calculationisthe seventh.Itsfrequencyis morethantwicethefrequency of mode 3, which doublesthe number offatigue cycles per year. Alsothecurvature ofthe modalshapeassociated withthe higher modeislarger, creating greater stress.

The maximum fatigueislocatedinthe bottom part ofthe riser, due to the varying tension along the riser. For a given

mode,the nodes arelessspaced out neartheseafloor, leadingto higher stress andfatigue.

2.2.2 Steel Catenary Riser

A steel catenary riseris pinned atthe seafloor andtensionned atthetop (Figure 3). Itslengthis 1200 m,the water depthis 1000 m. The diameterisconstantat 0.533 m,thecurrentis perpendicular to the riser and its characteristics are given in Table 4.

Figure 3

Steel catenary riser with current perpendiculartothe structure.

Thelineslinkingthestructuretothe node onthesea-floor

representsthe nodes which are checked againstthe bottom of

the ocean. Z Y X 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 100 200 300 400 500 600 700 800

Distance alongtheline (m)

R MS a mp lit ud e ( m) incr 0 0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 0 100 200 300 400 500 600 700 800

Distance alongtheline (m)

In ve rs e of fa ti gu e l if e ( 1/ ye ar) incr 0 Figure 2

Amplitude andinverse of fatiguelife of a drilling riser. The amplitude of vibrationis dominated by mode 3 whilethe most dangerous mode

TABLE 4

Variation of current velocity with depth

Depth (m) Velocity (m/s) 0 0.5 100 0.5 250 0.4 300 0.4 500 0.1 1000 0.1

The bending modeinthe cross-flow direction are automa -ticallyselected bythecode. Theexcitedeigenfrequencies with St = 0.2 areshownin Table 5.

TABLE 5

Excited eigenfrequencies ofthe steel catenary riser

Mode Frequency (Hz) 3 0.494E – 01 4 0.713E – 01 5 0.927E – 01 6 0.114E + 00 7 0.136E + 00 8 0.159E + 00 9 0.182E + 00

Theresultsfromthe VIV analysis are:

– maximum RMS amplitude: 71E-01 m at 983 m from the top;

– minimumfatiguelife: 66 years at 1100 mfromthetop.

In order to increase the life expectancy, VIV suppression devices modeled with an efficiency of 80% areintroduced on the first 420 m from the riser top. It implies that the existing force applied onthe structure atthetop ofthe riseris reduced by afactor 5.

With VIV suppression devices, we obtain:

– maximum RMS amplitude: m 0.93E – 02 m at 803 m; – minimumfatiguelife: 0.23E + 06 years at 1100 m.

Theamplitudeandfatiguealongtheriserare givenin Figure 4 for the case with anti-VIV devices. The graphs indicatethat, evenifthe amplitude of vibrationislarge onthe whole length of the riser, the fatigue is located near the touch-down point. The modal curvature in this area is much higherthanintherest ofthe pipe,the nodes ofthe mode being more concentrated. The main effect of anti-VIV devicesinthe area of maximum current velocityisto reduce the vibration ofthe high modes(bending mode 8 and 9in our case), which arethe most dangerousforthefatiguelife.

2.2.3 Remarks

The modalapproach givesa goodestimate ofthefatiguelife andallowstostudya widerange ofcases quickly. None-theless,the shortcomings ofthe methods arethefollowing: – Itislimitedtocross-flow vibrations(butin-lineforcing

could also beintroduced).

– Itrequires bending modes perpendiculartothecurrent. Thisis alwaysthe casefor a drillingrisersince each bending modeis definedin any direction perpendicularto the normal ofthe riser section, duetothe symmetry ofthe configuration. The modal basisisinfactcomposed of pairs ofeigenvectors withthesamefrequency. For more complex geometries(steel catenaryriser, exportlines, etc.) computations haveto be performed with a currentin or out ofthe plane ofthe structure.

0 200 400 600 800 1000 1000 0.01 0 0.002 0.004 0.006 0.008 R MS a mp lit ud e ( m)

Distance alongtheline (m)

incr 0 5e-06 4.5e-06 4e-06 3.5e-06 3e-06 2.5e-06 2e-06 1.5e-06 1e-06 5e-07 0 0 200 400 600 800 1000 1200 In ve rs e of fa ti gu e l if e ( 1/ ye ar)

Distance alongtheline (m)

incr 0

Figure 4

Amplitude andinverse of fatiguelifein a steel-catenary riser with anti-VIV devices onthe first 420 m. The maximum damageislocatedin

– Thecurrent must besteady,therefore wave-effect ortop motion cannot be taken into account. An extension of the methodto unsteadycurrentis possible(Le Cunff et al., 1999), providedthatthe modesare notaffected bythe motion.

– Even for a steady current, the frequencies and phases can evolveintime. To describesucha phenomenon,a more refinedfluid modelisrequired.

– The variouscodes based ona modalapproach depend on empiricalcoefficientsandcan predict differentamplitude on a similar case(seeforinstance Larsen and Halse, 1995). 3 REFINEMENT OF THE FLUID CALCULATIONS 3.1 Fluid Modeling

3.1.1 Review ofthe Models

The objective ofafluid modelconsists ofreproducingthe forceexerted bythefluid onthestructureandthe wayitis influenced bythe motion ofthestructure. Fromastructural point of view, no detail analysisis requiredinthe description ofthe fluid. Therefore,the effort should be concentrated on a single parameter(force coefficient) describingthefluid. Obviously,the modelshould be morerefinedthanthe coefficient function of amplitude and Renumber used in the modal analysis. The modelis solvedintime, since, evenfor a steady current,the phenomena aretime-dependent.

Severalauthors defined models whereaclassical beam equationis solvedtogether with a forcing duetothe fluid. For instance, Triantafyllouand Grosenbaugh(1995) proposeda liftcoefficientfunction oftheinstantaneousamplitude of vibration, lift coefficient which can become a damping force ifthe amplitudeislarge,to describethe self-damping mechanism of VIV. Ferrariand Bearman(2000) havea model of the in-line and cross-flow loadings with a Morison typeformulation. Guaita et al.(2001) useaspring/damper model at each node oftherisertoreproducethefluid behaviour. All these approaches neglect the fluid interactions alongtheaxis. Thespan-wisecoupling ofthe differentfluid forcesistherefore effective onlythroughthe structure.

Hartlen and Currie (1970) used an oscillator to model the fluid force and its coupling with the structure motion for an elasticallysupportedcylinder. The mainideaisto definea differentialequationfortheliftcoefficient which would be characteristic ofthe fluctuating structure ofthe near wake. A review ofthe variousequations proposedcan befoundin Facchinetti(2001).

3.1.2 A Three-Dimensional Approach

Theidea ofa wake oscillatorasfirst developed by Hartlen and Currie(1970)is based on a phenomenologicalflow modelthatsummarizesthefluctuating nature ofthe vortex

street byasingle variable, governed bya weakly nonlinear Van der Pol’s Equation. The fluid variableisthelift coefficient C_L,andthecoupledfluid-structureinteractionin two dimensionsis described bythefollowing equations:

( 5)

wherethe dot denotes atime-derivative and we usedthe following variables:

y position ofthe structure

M, R, K, D, L mass, damping,stiffness, diameterandlength ofthe structure

β linear coupling coefficient ω_vor Strouhal circularfrequency

ρ_flu, U fluid density andin-comingflow velocity α, γ coefficientscharacterizingthe nonlinearity of

the oscillator, α deals withtheself-excitation at low amplitude motion and γwith the saturation oflarge amplitude motion.

This elementary oscillator provides a self-sustained, stable and nearly harmonic oscillation,andis naturallyassociated withthe fluctuatinglift proposed bythe fluidtothe structure. The structure,forced bythisimprovedlift model,interacts on the wake oscillator by means ofits displacement andits derivatives. Such a model has been developed for VIV of an elasticallysupportedrigidstructure,successfully describing their mainfeatures, namelylock-in, qualitativelyandeven quantitatively. The pioneering work of Hartlenand Currie has beenimproved by several authors: for a historical review, see Sarpkaya (1979). Comparingto CFD models,this approach does not provideacompleteflowfieldanalysis, onlyfocusing ona description ofthefluidas“seen” bythe structure. Thisleadstofastercomputations, nevertheless, several experimental coefficients needto be properly set and thefluid mechanicsargumentsinvokedintheirevaluation are not often convincing.

A wake oscillator has been recently improved by Balasubramanianet Skop(1996)in orderto modelcellular vortex sheddingin sheared flow. When a stationary structure experiences asheared current,spanwise vortexshedding frequencyis observed as a step-like function (fig. 5),leading to vortexcells ofconstantfrequency withfrequencyjumps betweenthem.Inthe proposed model, aseries of wake oscillatorsare distributedalongthespanwiseextent ofthe structureandinteractthemselves by diffusion,reproducing qualitatively and quantitativelytheintrinsic fluidinteractions occurringinthe near wake, as computedin Figure 6. Spanwise distribution (z) ofthe power spectral density (PSD) associated withthefluid variableclearlyshowsacellular vortex pattern. My Ry Ky U DLC C C C C y L L L L L ˙˙ ˙ ˙_{˙ (} ˙ _{˙) ˙} + + = +− + + =        1 2 2 3 2 ρ αω γ ω ω β flu vor vor vor

Figure 5

Sketch ofthelock-inregions behind afixed cylinderin a

sheared current.

Figure 6

Diffusive coupled Van der Pol oscillators: cellular vortex

sheddingis evidentfromthespanwise distribution ofthe

power spectral density (PSD) ossociatedtothe fluid variable.

The dynamic analysis will providethe vibration amplitude ofthe riser. In orderto determinethe fatiguelife ofthe pipe, arainflowalgorithm(forinstance Lalanne, 1999) hasto be linked to the calculations, requiring a rather large simulation time. But,theresolution ofatwo-equations modelisfast, thereforesuch methodshould be ofinterestfor design applications.

3.2 Navier-Stokes Calculations

3.2.1 Description ofthe Method

The most advanced approachis a computation ofthe coupled problem, withthe beam equation forthe structure andthe full three dimensional Navier-Stokesequationsforthefluid,at verylarge Re(upto 106_{). A numerical simulation by Lucoret} al. (2001) was conducted on a flexible structurein a sheared flow at Reof order 103_{and aspect ratio (length/diameter) of} about 103_{. Thecomputer-timerequiredisstilltoolargeto} provide a usefultoolfor design.

Therefore,anotheralternativeconsists ofcomputingthe Navier-Stokes equationsinslices, neglectingthe direct influence between the different slices. The three-dimensionality of the problem is taken into account through the riser, and no empirical coefficientis required. In orderto approximatethe 3Dfluidcalculations withlesscomputer resources, additionalterms can beintroducedtolinkthe slices(Willden and Graham, 2000).

Inthe present paper,atwo-dimensional method byslice (Étienne et al., 2001)is usedtocomputetheresponse ofa riser. Thecalculationsare performed using DeepLines,the Navier-Stokessolver as well asthe coupling procedure definingthe module DeepFlow ofthis code. Aspecific numerical method has been developedtosolvethefluid problemfor an arbitrary array of cylinders. A domain decompositionisintroduced(Étienne 1999, Étienne et al. 1999).Intheinner domain, surroundingthe cylinders, thetwo dimensional Reynolds averaged Navier-Stokes equationsareformulated based on vorticity(ζ)andstream function (ψ). The turbulent effects are computed with a k-ω model. Introducingtheturbulent viscosity ν_tandthe vector k perpendiculartothe 2D slice,the equations are:

(6) Inthe outer domain,a Lagrangian methodis used where particles are convected with a fast vortex method. A coupling proceduretakesthe positionand velocity ofthestructureas inputtothe fluid code, which computesthe resulting flowfield. The externalloads provided bythefluid simulation arethenimposed onthestructuretoreevaluatethe position and velocity. This procedureis repeated until convergence at eachtime step.

3.2.2 Effect of Top Motion onthe VIV

A riserin a uniform current at 0.5 m/sis considered withthe following characteristics:

– length: 300 m – external diameter: 0.25 m – internal diameter: 0.235 m – linear weight: 157.8 kg/m – toptension: 1469 kN.

A sinusoidaltop motionisimposed with amplitude Aand circular frequency ω. The relative fluid velocity experienced bythe riser atthetopisinthe range [U – Aω,U + Aω]. We imposed A = 0.5 m, Aω = 0.4 and 0.3, leading to periods of 7.9 s and 10.5 s. For a Strouhal number of 0.2, the uniform flowisexcitingafrequency of 0.4 Hz,thefrequencyrange withtop motion Aω = 0.4is [0.08; 0.72]. The first modes of the structure are presentedin Table 6.

∂ ∂+ ⋅ = + =−      ς ψ ς ν ν ψ ψ ςt k t ( ( ) ) ( )rot grad ∆ ∆ 0 0.20.40.6₀ .8 1 1.21.4_{1.61.8 0} 0.20.4Z 0.60.8 1 Frequency PS D 0₀.05_.01 0.005 0

Sheared current Cylinder Frequencies

f1

TABLE 6

The first eight eigenfrequencies ofthe riser

Mode # Frequency (Hz) Period (s)

1 0.09 11.11 2 0.18 5.53 3 0.27 3.67 4 0.36 2.74 5 0.46 2.18 6 0.55 1.78 7 0.66 1.52 8 0.76 1.31

Thereforethefirstseven modes ofthestructure are potentially excited whenthetop motionisimposed. The numericalsimulationis performed withfortyslices. A snapshot oftherisertogether withthefluid vorticityinthe slicesis presentedin Figure 7.

In Figure 8,theamplitude of vibrationinthecross-flow directionis plottedalongthelength oftheriser. Thecase Aω = 0.4 exhibits a decreaseinthe vibration amplitude. For a uniformflow,thestructurecanimposeitsfrequencytothe fluid, creating alock-in with alarge amplitude of vibration.If the currentistime-dependant,thelock-inis destabilized, and the vibrationtendsto decrease. Similarresults have been obtainedforacable withatime-dependant modalapproach (Le Cunffet al., 1999).

Figure 7

Snapshot ofthe riser andthe fluid slices att= 40 s, only half

the slices are presented.

Figure 8

Amplitude of vibration with and withouttop motion.

4 MEASUREMENTS

A projectfortheacquisition of VIV data waslaunchedin 1998entitled“Hydlines”, withthefinancialsupport ofthe Comité d’études pétrolièreset marines(CEPM)as wellas the Club pourles actions derecherchesurles ouvragesen mer(CLAROM),andthe participation ofseveralcompanies (Principia R.D., Doris Engineering, Sirenha, Stolt Offshore, TotalFinaElf)together with Institutfrançais du pétroleand École supérieure desingénieurs de Marseille.The objectives wereto obtainlarge Reynolds data onatowedcylinder,to studythe effect of anti-vibration devices, andfinallyto observe a multimodal response for a cable. In this paper, we will presentthelatter part ofthe project.

4.1 Experimental Setting

Theexperiments werecarried outatthe“bassin de génie océanique First” (BGO First)in La Seyne-sur-Mer. The basin has a useful testing area of 24 × 16 m. The maximum speed velocityis 0.5 m/s. The depthisadjustable upto 5 m. A conceptualstudy wasconducted by Molin(1999)and Le Cunff (1999) to define the geometry and observable frequencies. Resultsforeachconfigurations were monitored duringtheexperimentsto verifytheiraccuracy(Pluvinet, 1999).

A 3 m depth is used, with a velocity ranging from 0.2 to 0.4 m/s. Thecableisfixedatthe bottom ofthe basinand tensioned atthetop.(Fig. 9).

The cable hasthefollowing characteristics:

– length betweenthefixed point andthe pulley: 20.9 m – diameter: 0.5 mm

– mass: 0.103 kg/m

– tension: between 200 N and 800 N.

0.32 0.28 0.24 0.2 0.16 0.12 0.08 0.04 0 0 100 200 300 A mp lit ud e ( m)

Length alongthe riser (m)

Utop

0.0

0.3

Figure 9

Sketch ofthe experimental setting.

Figure 10

Examples of cable configuration.

4.2 Experimental Results and Comparisons

Variouscableconfiguration werestudiedandfour ofthem arerepresentedin Figure 10. Thefirst one(C2) has a constant diameterin water,thesecond one(C5) hasthree diameters andthethird one (C7),two diameters. The first 12 m ofcable,startingfromthefixed point,areindicated. The rest ofthe structureisthe bare cable with a 5 mm diameter.

The Reynolds number for all the cases considered is less than 104_{. Measurementsto verifytheaccuracy ofthe} in-comingflow velocityalongthecable wereconducted by Kimmoun et al.(2000)forthree different positions.

Figure 11

Comparison between DeepVIVandexperimentalresultsfor

the RMS amplitude of vibration.

Comparisons with DeepVIV are presentedin Figure 11 on configuration C4 withatoptension of 800 Nandacurrent velocityrequirement of 0.4 m/s. The RMS amplitude of vibrationsinthecross-flow directionis plottedalongthe cablelength. It showsthatthe agreementis very goodinthe case of multi-modal excitation.

CONCLUSION

Areview ofthe work conducted at Institutfrançais du pétrolein collaboration withÉcole supérieure desingénieurs de Marseilleand École polytechniqueon vortex-induced vibrationsis presented. Severalapproachesarestudiedin orderto provide a reliable methodto computethe fatiguelife ofriserssubmittedtocurrents. Therangeextendsfroma simple modal approachto Navier-Stokes calculations. A “middle oftheroad”techniqueis developed based onthe time-dependantsolution ofthestructuralequationcoupled with a model equation forthe fluid forcing. Itis expectedthat such a method will provide a powerfultoolforriser design.

Detailed experiments have also been conducted in collaboration withindustrial partnersto gather data on a wide range ofconfigurations. They provide benchmarkstestfor the various numericaltools at our disposal.

ACKNOWLEDGEMENTS

We wouldliketoacknowledgethefinancialsupport ofthe CEPM and CLAROM through grant M.02117/98 and M.7502/99. The Hydlines projectincludedthefollowing CLAROMmembers: Principia R.D., Institutfrançais du pétrole, Doris Engineering, École supérieure des ingénieurs de Marseille, Sirenha, Stolt Offshore, TotalFinaElf. The modeltestsat BGO First were made possible byfunding

Length alongthe cable (m)

0 5 10 15 20 25 0 2 4 6 8 RUN G461 calculations experiment R MS a mp lit ud e ( m m)

Configuration C2:

Configuration C5:

Configuration C4:

Configuration C7:

12 m 1.5 m 3 m 7.5 m 4 m 3 m 1 m 2 m 2 m 4 m 2 m 6 m ∅ = 21 mm ∅ = 21 mm 14 mm 10 mm ∅ = 10 mm 21 mm 10 mm ∅ = 10 mm 21 mm 10 mm 21 mm 10 mm Cable with

silicontubes _Measuring

area

Pulley

Tension

fromthe Hydlines project’s members. Thesetests were carried out under The GISHYDRO research program witha partial financial support from Conseil général du Var. Finally, we would like to thank the partners of the Hydlines project for permission to publish a comparison with experimentalresults.

REFERENCES

Balasubramanian, S. and Skop, R. A. (1996) A Nonlinear Oscillator Model for Vortex Shedding from Cylinders and Cones in Uniform and Shear Flows. J. of Fluids and Structures,10, 197 -214.

Bearman, P.W.(1984) Vortex Sheddingfrom Oscillating Bluff Bodies. Ann. Rev. Fluid Mech.,16, 195-222.

Blevins, R.D. (1990) Flow-Induced Vibration, Van Nostrand Reinhold, Co.

Bokaian, A. (1993) Lock-in Prediction of Marine Risers and Tethers. J. Sound and Vibrations,175, 607-623.

Bruschi, R.,Jacobsen, V., Simantiras, P. and Vitali, L.(1996) Vibration Suppression Devices for Long, Slender Tubulars. Proc. OTC, 71-80.

Chen, S.S.(1987) Flow Induced Vibration of Circular Cylindrical Structures, Hemisphere Publishing Corp., Spr inger-Verlag, Chap 7.

DeepLinesTM_{(2000) Keywords Manual, IFP/PRD Report V2r2.}

DNV(1996) Rulesfor Submarine Pipeline Systems, Section 5, C509/C510.

Étienne, S., Scolan, Y.M. and Biolley, F.(1999) Modélisation numérique de l’écoulement de fluide visqueux autour d’un faisceau deriser.7e_{Journées del’hydrodynamique, Marseille,}

France, 57-72.

Étienne, S. (1999) Contribution àla modélisation del’écoulement defluide visqueuxautour defaisceaux decylindrescirculaires. Thèse de doctorat de l’université de la Méditerranée, Aix -Marseille II - École supérieure d’ingénieurs de Marseille.

Étienne, S., Biolley, F.,. Fontaine, E., Le Cunff, C. and Heurtier, J.M. (2001) Numerical Simulations of Vortex Induced Vibrations of Slender Offshore Structure. Proc. ofISOPE Conference, 3, 419-425.

Every, M.J., King, R.and Weaver, D.S.(1982) Vortex-Induced Vibrations of Cylinders and Cables andtheir Suppression, Ocean Engineering,9, 135-157.

Facchinetti, M.L.(2001) Vibrationsinduites dansles courants non uniformes. Rapport IFPn° 55815.

Ferrari,J.A. and. Bearman, P.W(2000) A Three-Dimensional Modelfor Wave and Vortex-Induced Vibration of Deepwater Riser Pipes. Flow-Induced Vibrations, 3-10.

Guaita, P., Fossati, F. and Resta, F. (2001) Development and Test of a Time-Domain VIV Prediction Model. Proc. of Offshore Mediterranean Conference, Paper No 61.

Griffin, O.M.(1985) Vortex-Sheddingfrom Bluff Bodiesin a Shear Flow: a Review. Transactions ofthe ASME, 298-306. Hartlen, R.T. and Currie,I.G.(1970) Lift-Oscillator Model of Vortex-Induced Vibration. J. of the Engineering Mechanics Division, 577-591.

Hopper, C.T (1983) Vortex-Induced Oscillations of Long Marine Drilling Risers. Proc. of DOT, 97-109.

Huse, E., Kleiven, G. and. Nielsen, F.G (1998) Large Scale Model Testing of Deep Sea Risers. Proceedings of OTC, 44-61. Iwan, W.D. (1981) The Vortex-Induced Oscillations of Nonuniform Structural Systems.J. of Sound and Vibrations, 79, 291-301.

Kimmoun O., Molin, B. and Zucchini, B.(2000) Mesures par film chaud de la vitesse du courant dans le bassin de génie océanique First. Rapport ESIMdu 27 mars 2000, Projet CLAROM HydLines.

Lalanne, C. (1999) Vibrations et chocs mécaniques, Hermès Science Publication, Paris.

Larsen, C.M.and. Halse, K.H(1995) Comparison of Models of VortexInduced Vibrations of Slender Marine Structures. Flow Induced Vibrations, 467-482.

Le Cunff, C. (1999) Note de calculs sur les essais 3D. Note externe IFPn°I4455066-1.

Le Cunff, C., Biolley, F. and Durand, A. (1999) Prediction ofthe Response of a Structure to Vortex-Induced Vibrations: Comparison of a Modal and a Wave Aproach. Proc. 18th OMAE Conference, St John’s, Canada, 1-8.

Lucor, D., Imas, L. and Karniadakis, G.E. (2000) Vortex Dislocationsand Force Distribution of Long Flexible Cylinders Subjectedto Sheared Flows. J. Fluids and Structure, 15, 641-650.

Lyons, G.J. and Patel, M.H.(1989) Application of a General Techniquefor Prediction of Riser Vortex-Induced Responsein Waves and Current. J. of ASME,111, 82-91.

Marris, A.W. (1964) A Review on Vortex Sreets, Periodic wakes, and Induced Vibrations Phenomena. J. of Basic Eng., 185-196. Moe, G.(1991) An Experimentally Based Modelfor Prediction of Lock-in Riser Motions. Proc. of OMAE Conference,1-B, 497-506.

Molin, B. (1999) Personal Communication.

Morison,J.R., O’Brien, M.P.,Johnson,J.W. and Schaaf, S.A. (1950) The Forces Exerted by Surface Waves on Piles. Petroleum Trans.,AIME,189, 149-157.

Naudascher, E.(1987) Flow-Induced Streamwise Vibrations of Structures. J. of Fluids and Structures,1, 265-298.

Naudascher, E. and Rockwell, D.(1994) Flow-Induced Vibrations – An Engineerin Guide, Balkema A.A.

Nedergaard, H., Ottesen Hansen, N.-E. and Fines, S. (1994) Response of Free Hanging Tethers. Proc. of BOS 94, 315-332. Pantazopoulos, M.S. (1994) Vortex-Induced Vibrations Parameters: Critical Review. Proc. of OMAE,1, 199-255. Pluvinet, F. (1999) HydLines essais 3D : rapport d’essais, Document Principia, n° RET.95.304.01.

Sarpkaya, T.(1979) Vortex-Induced Oscillations- A Selective Review. J. of Applied Mech.,46, No. 2.

Sheppard, R.M. and Omar, A.F. (1992) Vortex-Induced Loading on Offshore Structures: a Selective Review of Experimental Work. Proc.of OTC, 183-112.

Torum, A., Moe, G., Johansen, J.V and Katla, E. (1996) On Current Induced In-Line Oscillation in Pipelines Free-Spans. Proc. of OMAE Conference,5, 459-469.

Triantafyllou, M.S. and Grosenbaugh, M.A. (1995) Prediction of Vortex-Induced Vibrations in Sheared Flow. Flow-Induced Vibrations, Bearman (Ed.) Rotterdam.

Vandiver, J.K. (1987) The Relationship between In-Line and Cross-Flow Vortex-Induced Vibration in Cylinder. J. of Fluids and Structures, 1, 381-399.

Willden, R.H.J. and. Graham, J.M.R (2000) Vortex Induced Vibrations of Deep Water Risers. Flow-Induced Vibrations, 29-36.

Williamson, C.H.K. (1996) Vortex Dynamics in the Cylinder Wakes. Ann. Rev. Fluid Mech., 28, 477-539.

Zdravkovich, M.M. (1981) Review and Classification of Various Aerodynamic and Hydrodynamic Means for Suppressing Vortex Shedding. J. Wind Eng. And Industrial Aerodynamics, 7, 145-189.