SEA CURRENT VORTEX SHEDDING INDUCED VIBRATION OF NEMO TOWER

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SEA CURRENT VORTEX SHEDDING INDUCED VIBRATION OF
NEMO TOWER
Workshop VLVnT2 Catania, November 9-12, 2005
F. Fossati, G. Fichera
Dipartimento di Ingegneria Industriale e
Meccanica (DIIM) University of Catania
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SCOPE OF WORK

• Structural Dynamic Response due to Vortex
  shedding Induced Vibration (VIV)
• Structural design optimization

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Vortex shedding induced Vibrations (VIV)

• VIV can affect flexible or moveable structures
  subjected to water flow or wind flow, such as
• Off-shore structures
• Marine risers
• Power submarine cables or overhead transmission
  lines
• Suspension Bridges
• Lattice structures

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Typical structures interested on VIV
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Typical structures interested on VIV
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Typical structures interested on VIV
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STATE OF THE ART

• Frequency domain methods energy balance
• Time domain methods (CFD, discrete vortex models)

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BACKGROUND

• Large amount of research activities on structural
  dynamic response due to Vortex shedding Induced
  Vibration (VIV) have been carried out
• Research group University of Catania
  Politecnico di Milano
• Development of numerical approach based on a time
  domain numerical model to evaluate VIV
• Consultant activity for several applications
• ENEL (Italian National Electric Board) overhead
  transmission lines
• ENI-AGIP (Italian National Petroleum Board)
  Offshore platforms drilling/production risers
• STRETTO DI MESSINA Deck/Suspension cables
• PIRELLI Submarine power transmission cables

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CONTENTS

• Vortex shedding phenomena (VIV)
• NEMO Tower Structural dynamics modeling
• Frame Finite Element Model
• Tower Multi-body Model with rigid bodies
• Tower Mixed Multi-body / flexible Model
• Vortex shedding forces mathematical model
• Work in progress

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Vortex shedding

• Vortex-Induced Vibrations (VIV) are the primary
  mode of fluid-structure interaction for bluff
  body structures
• Bluff bodies at moderate Reynolds numbers shed
  fluid vortices at regular or irregular intervals,
  producing fluctuating hydrodynamic forces

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Vortex shedding
Cross-flow oscillating force
V
Characteristic frequency
fS frequency (Hz) S Strouhal number 0.1850.2
(depending on Re) v flow velocity (m/s) d
cylinder dimeter (m)
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Vortex shedding Strouhal frequency
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Vortex shedding induced Vibrations (VIV)
m
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VORTEX SHEDDING NON LINEAR EFFECTS

• Lock-in range
• Vibration amplitude depending on fluid velocity
• Hysteretic behaviour

Lock-in range 0.75 vSt lt v lt 1.7 vSt
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Lock-in range
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Frequency lock-in
Lock-in range
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VIV
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FLUID STRUCTURE INTERACTION ANALYSIS MAIN STEPS

• NUMERICAL ANALYSIS
• Structure schematization
• Static analysis due to mean sea current induced
  forces
• Structure natural frequencies and vibration modes
  evaluation
• Vortex shedding forces modeling
• Dynamic analysis due to Vortex shedding induced
  vibrations
• EXPERIMENTAL MEASURES
• Full scale measurements on Tower Prototype

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NEMO Tower Numerical Model 1st step

• Each frame is considered as a rigid body with 6
  d.o.f.
• Frames are connected by means of Ropes modeled
  using translational spring damper element
• Aims of the model
• tower static equilibrium position calculation due
  to weight and buoyancy forces (rope forces,
  displacement at the top, etc.)
• tower static equilibrium position calculation due
  to sea current drag forces
• Tower Natural frequencies/eigenmodes calculation
  in the static equilibrium position neighborhood

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Frame FE model Inertial properties and buoyancy
Buoyancy -149.4 N
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Rigid multibody model static analysis

• Static equilibrium due to weight and buoyancy
  forces
• Calculation of rope tensions

nemo_static
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Rigid multibody model normal modes

• Calculation of global modes of the tower

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Rigid multibody model static analysis including
fluid drag forces

• Calculation of static equilibrium under weights,
  hydrostatic forces and fluid drag forces
• Drag forces calculated by using ESDU 81027 on
  Lattice Structures
• Constant flow velocity 0.1 m/s

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Rigid multibody model static analysis including
fluid drag forces

• Static equilibrium calculation at constant flow
  velocity V0.1 m/s
• Calculation of rope tensions

nemo_static_fluid
Ropes at the base of the tower
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Rigid multibody model static analysis including
fluid drag forces

• Main results with V 0.1 m/s
• Maximum displacement of the buoy along the flow
  direction 13.5 m
• Changing of tensions only in the ropes at the
  tower base
• The two windward ropes increase tension from 1800
  to 3000 N
• The two leeward ropes decrease tension from 1800
  to 700 N

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NEMO Tower Numerical Model 2nd step
Tower mixed multi-body / flexible Model

• Frame 1 and 2 structures (starting from the tower
  base) were introduced as flexible bodies using
  Component Mode Synthesis from FE results
• The ropes connecting the frames 1 and 2 were
  modeled using finite elements
• Aims of the model
• re-calculation of static equilibrium
• re-calculation of structure natural frequencies
  and vibration modes including flexible modes

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Flexible multibody model Normal modes

• The global modes of the whole tower remain the
  same

1st lateral 0.0081 Hz
1st vertical 0.2282 Hz
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Flexible multibody model Normal modes
1st mode of short ropes (4.06 Hz)
1st mode of long ropes (1.07 Hz)
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Flexible multibody model Normal modes

• Coupled modes of long ropes and short ropes

4.02 Hz
4. 20 Hz
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Flexible multibody model Normal modes

• Coupled modes of ropes and structures

4.46 Hz
4. 48 Hz
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THE EQUIVALENT OSCILLATOR
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THE EQUIVALENT OSCILLATOR

• Aerodynamic mass frequency depending on fluid
  velocity according to Strouhal relationship
• energy input capability (Raer)
• self limited vibrations
• Lock-in range

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THE EQUIVALENT OSCILLATOR
Equivalent oscillator parameters can be evaluated
using simple experimental tests using scaled
sectional model (wind tunnel/water tank)
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VIV ON COMPLETE STRUCTURE
NEMO TOWER F.E. MODEL

• Equivalent oscillators distribution
• Time domain model

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VIV ON COMPLETE STRUCTURE
FEM nodes
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ADVANTAGES

• Simple but sophisticated approach which takes
  into account all the basic topic of vortex
  shedding phenomena
• Results allow to perform structure design
  optimization in order to avoid VIV and to
  determine the proper structural damping level
  capable of avoiding lock-in
• Full scale measurements are planned on Tower
  Prototype
• Results could be also useful in order to better
  control evaluate bioluminescenza

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WORK IN PROGRESS

• Complete tower dynamic analyses simulations are
  in progress
• Results allow to perform structure design
  optimization in order to avoid VIV and to
  determine the proper structural damping level
  capable of avoiding lock-in
• Full scale measurements are planned on Tower
  Prototype
• Results could be also useful in order to better
  control evaluate bioluminescenza

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Strategy of the research 1) channel
experimentation on rigid cylinder - smooth
cylinder - cylinder with vortex suppression
devices (ropes twisted around the
cable) o different rope/cable diameter
ratio o different pitch/twisting
direction o different damping ratioes
CableDynamics 1999 slide 38
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Strategy of the research (continued) 2) physical
modelling of the vortex shedding by means of the
equivalent oscillator
k, r contain both linear and non linear
terms. These have been identified by means of
Kalman Filtering
CableDynamics 1999 slide 39
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Strategy of the research (continued) 3) simulatio
n of the real cable behaviour by means of the
equivalent oscillators with the final
purpose a) to determine the structural damping
capable of avoiding lock-in b) to eventually
find the span critical length
CableDynamics 1999 slide 40
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PROPOSTE

• Prove in galleria per valutare il n di Strouhal
  dei piani
• Valutazione della velocità critica
• Valutazione delle ampiezze di vibrazione
• Verifica delle forze dovute alla corrente
• Integrazione del modello di calcolo con il
  forzamento per distacco di vortici

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Distacco di Vortici Parametri significativi
Reynolds
Strouhal
Scrouton
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Il numero di Scrouton
m massa lineare del cilindro h smorzamento
adimensionale r densità del fluido D diametro
del cilindro
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Modalità di distacco vibrazioni in-line
Modo di distacco 2Salternati
Modo di distacco 2P simmetrici
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Forzamento In-line ampiezze di oscillazione
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Cilindro libero nello spazio
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Oscillatore equivalente equazioni del moto

• Le costanti KAcc, KAer etc. sono funzione di
  velocità della corrente, lunghezza, diametro e di
  parametri numerici identificati sulla base di
  prove sperimentali

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IDENTIFIED SYSTEM
Natural frequency 3Hz, damping factor h 0.1
U/D
Hz
v/vs
v/vs
h
v/vs
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Loscillatore equivalente

• La massa aerodinamica MAer è identificata in
  modo da vibrare, a cilindro fermo, alla frequenza
  di Strouhal
• Lelemento dissipativo Raer è negativo in modo da
  introdurre energia nel sistema
• Gli elementi elastici e dissipativi sono
  non-lineari in modo da riprodurre le
  caratteristiche non lineari del forzamento
• Le forze sono locali, variano quindi da sezione a
  sezione in funzione della velocità della corrente
  e del diametro
• Utente non deve prevedere il lock-in del riser o
  di parte di esso

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Nel caso della struttura NEMO

• Si mettono in eccitazione I primi modi di
  vibrare delle funi corte
• Si mettono in eccitazione dal terzo al sesto
  modo delle funi lunghe
• Si mettono in eccitazione I primi modi
  flessionali dei piani accoppiati a quelli di fune
• Se la corrente fosse di minore intensità potrebbe
  eccitare I primi modi di fune lunga

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Nel caso della struttura NEMO

• NON SAPPIAMO NULLA SUL COMPORTAMENTO DEL PIANO
• IPOTESI

• SI METTEREBBE IN ECCITAZIONE UN MODO GLOBALE DI
  SBANDIERAMENTO
• NECESSITA DI VALUTARE LA RISPOSTA AL DISTACCO DI
  VORTICI DEL SINGOLO PIANO
• VIBRAZIONI IN-LINE ???

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THE EQUIVALENT OSCILLATOR
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Risposta in frequenza di un sistema ad un grado
di libertà
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Distacco di Vortici Strutture interessate
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Distacco di Vortici Strutture interessate
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Distacco di Vortici Strutture interessate
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Component Mode Synthesis Normal modes of the
condensed structure
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FE model Free-Free Modal Analysis
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NEMO Tower Numerical Model

• Several steps have been followed
• Single Frame FE model (beam elements) in order
  to have a detailed model able to
• Calculation of inertial and stiffness
  distribution
• Calculation of material volume and fluid volume
• Static analysis and natural frequencies/eigenmodes
  calculation
• Modal condensation using Component Mode Synthesis
  based on Craig-Bampton method in order to take
  into account frames flexibility effects into
  multi-body model of the Nemo tower with 16 floors

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NEMO Tower Numerical Model

• Linear FE model made of beam elements with rigid
  connections and concentrated masses
• Light model requiring short time simulation
• Aims of the model
• Calculation of inertial and stiffness
  distribution
• Calculation of material volume and fluid volume
• Static analysis and natural frequencies/eigenmodes
  calculation
• Modal condensation using Component Mode Synthesis
  based on Craig-Bampton method in order to take
  into account frames flexibility effects into
  multi-body model of the Nemo tower with 16 floors

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Multibody model of the Nemo tower using rigid
bodies

• Each frame is considered as a rigid body with 6
  dof in the space
• Ropes modeled using translational spring damper
  element with preload
• Aims of the model
• static calculation of the all tower under weight
  and hydrostatic forces (rope forces, displacement
  at the top, etc.)
• static calculation including fluid drag forces
  due to different constant flow velocities
• eigenmode calculation starting from static
  equilibrium

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Natural frequencies of the ropes under static
tensions

• Calculation of natural frequencies of the ropes
  under static tensions using rope theory