vortex-induced waves along cables - École polytechnique

Vortex-inducedVortex-induced waveswaves alongalong cablescablesMatteo Luca FACCHINETTI(1,2), Emmanuel de LANGRE(1), Francis BIOLLEY(2)

(1) LadHyX – CNRS – Ecole Polytechnique (Paris) - FRANCE (2) Institut Français du Pétrole

VORTEX-INDUCED VIBRATIONS DEEPWATER OIL FIELDS

qSz

yT

zt

ym =+˜

¯

ˆÁË

Ê∂

∂

∂

∂-

∂

∂...

2

2

( )2

2

2

2

2

322

2

2

1t

yF

z

q

zt

qq

t

qq

t

qff ∂

∂=

∂

∂-

∂∂

∂-+

∂

∂-+

∂

∂cnwewFLUID MODEL STRUCTURE MODEL

• q = near wake variable ~ fluid lift

• spanwise interactions [2]

• coupled by the structure acceleration [3]

• y = transverse displacement

• coupled by the fluid lift

Strouhal law w

structure dispersion relationk

cablecm

T

k==

w

* experimental data

model prediction[Dowling (1988)]

EXPERIMENTSTHEORY

Strouhalww =

* experimental data

St(Re) law[Williamson (1998)]

wave features established by

dispersion relations intersection [5]

Strouhalww =

cablecm

T

k==

w

evidence of a travellingwave propagating

downstream

[1] FACCHINETTI, M.L. & DE LANGRE, E. & BIOLLEY, F. « Vortex-induced waves along a cable ».Proceedings of the 2001 DFD Meeting of The American Physical Society (APS).

[2] FACCHINETTI, M.L. & DE LANGRE, E. & BIOLLEY, F. « Vortex shedding modeling using diffusivevan der Pol oscillators ». Comptes Rendus Mécanique, 330 : 451-456, 2002.

[3] FACCHINETTI, M.L. & DE LANGRE, E. & BIOLLEY, F. « On wake oscillator models for 2-D vortex-induced vibrations ». Journal of Fluids and Structures, submitted for publication, 2002.

[4] FACCHINETTI, M.L. & DE LANGRE, E. & FONTAINE, E & BONNET, P.A. & ETIENNE, S. &BIOLLEY, F . « VIV of two cylinders in tandem arrangement: analytica l and numerical modeling ».Proceedings of the 2002 International Offshore and Polar Engineering Conference (ISOPE), paper 2002-JRC-05-3-14.

[5] FACCHINETTI, M.L. & DE LANGRE, E. & BIOLLEY, F. « Vortex-induced waves along cables ».Proceedings of the 2002 ASME International Mechanical Engineering Congress, paper IMECE-2002-32161.

[6] FACCHINETTI, M.L. & DE LANGRE, E. & BIOLLEY, F. « Experiments on vortex-induced wavesalong cables ». Proceedings of the 2002 Conference on Bluff Body Wakes and Vortex-Induced Vibrations(BBVIV).

REFERENCES

free-hanging cable

in water towing tank [6]

• slender structure L/D>103

• catenary geometry

• non-linear wave reflection

focusing on

travelling waves

fluid wStrouhal structure ws

w Strouhal = ws ! lock-in

Vortex shedding has a characteristic frequency defined by theStrouhal number. As it approaches a structure frequency a lock-inoccurs and this resonance leads to larger vibration amplitudes.

Vortex-Induced Vibrations (VIV) are a major cause of fatiguedamage for all structures connecting the well heads at the sea bottomto the floating facilities

LadHyXLadHyX

The numerical simulation of the entire flow field using the Navier-Stokes equations is not effective because of strong computationalrequirements. Conversely, a phenomenological wake oscillatormodel (van der Pol) is proven really useful ...

The classical mono-dimensional cable model is effective indescribing the main features of the structure dynamics. However,results of the theory extends to more general cases like beams withinternal flow …

COMPARISON