vortex-induced waves along cables - École polytechnique
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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
t
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