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7/27/2019 Reading VIV

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13.42 Lecture:Vortex Induced Vibrations

Prof. A. H. Techet

21 April 2005

Offshore Platforms


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Fixed Rigs Tension Leg Platforms

Spar Platforms


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Genesis Spar Platform

VIV Catastrophe

If neglected in design, vortex induced vibrations can prove

catastrophic to structures, as they did in the case of the Tacoma

Narrows Bridge in 1940.


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I n another city, the John Hancock tower wouldn't be anything special -- just anotherreflective glass box in the crowd. But because of the way Boston and the rest of NewEngland has grown up architecturally, this "70's modern" building stands out from therest. Instead of being colonial, it breaks new ground. Instead of being quaint, it soarsand imposes itself on the skyline. And Instead of being white like so many buildings inthe region, this one defies the local conventional wisdom and goes for black. For these

reasons and more the people of Boston have fallen in love with the 790-foot monsterlooming as the tallest building in New England at the time of its completion. In themid-1990's, The Boston Globe polled local architects who rated it the city's third bestarchitectural structure. Much like Boston's well-loved baseball team, the building hashad a rough past, but still perseveres, coming back stronger to win the hearts of itsfans. The trouble began early on. During construction of the foundation the sides of thepit collapsed, nearly sucking Trinity Church into the hol e. Then in late January, 1973construction was still underway when a winter storm rolled into town and a 500-poundwindow leapt from the tower and smashed itself to bits on the ground below. Anotherfollowed. Then another. Within a few weeks, more than 65 of the building's 10,344panes of glass committed suicide, their crystalline essence piling up in a roped-off areasurrounding the building. The people of Bean Town have always been willing to kick abrother when he's down, and started calling the tower the Plywood Palace because ofthe black-painted pieces of wood covering more than an acre of its faade. Somepeople thought the building was swaying too much in t he wind, and causing thewindows to pop out. Some thought the foundation had shifted and it was putting stressof the structural geometry. It turns out the culprit was nothing more than the leadsolder running along the window frame. It was too stiff to deal with the kind ofvibrations that happen every day in thousands of office buildings around the world. Sowhen John Hancock Tower swayed with the wind, or sighed with the temperature, thewindows didn't and eventually cracked and plummeted to Earth. It cost $7,000,000.00to replace all of those panes of glass. The good news is, you can own a genuine pieceof the skyscraper. According to the Globe, the undamaged sheets were sold off for useas tabletops, so start combing those garage sales. For any other skyscraper, thehardship would end there. But the Hancock building continued to suffer indignities.The last, and most ominous, was revealed by Bruno Thurlimann, a Swiss engineer whodetermined that the building's natural sway period was dangerously close to the period

of its torsion. The result was that instead of swaying back-and-forth like a in the windlike a metronome, it bent in the middle, like a cobra. The solution was putting a pair of300-ton tuned mass dampeners on the 58-th floor. The same engineer also determinedthat while the $3,000,000.00 mass dampeners would keep the building from twistingitself apart, the force of the wind could still knock it over. So 1,500 tons of steel braceswere used to stiffen the tower and the Hancock building's final architectural indignitywas surmounted.

Reprinted from http://www.glasssteelandstone.com/BuildingDetail/399.php

John Hancock Building

Classical Vortex Shedding

Von Karman Vortex Street

lh

Alternately shed opposite signed vortices


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Reynolds Number DependencyRd < 5

5-15 < Rd < 40

40 < Rd < 150

150 < Rd < 300

300 < Rd < 3*105

3*105 < Rd

< 3.5*106

3.5*106 < Rd

Transition to turbulence

Vortex shedding dictated bythe Strouhal number

St=fsd/U

fs is the shedding frequency, dis diameter and Uinflow speed


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Reynolds Number

subcritical (Re


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Force Time Trace

Cx

Cy

DRAG

LIFT

Avg. Drag 0

Avg. Lift = 0

Alternate Vortex shedding causesoscillatory forces which induce

structural vibrations

Rigid cylinder is now similar

to a spring-mass system with

a harmonic forcing term.

LIFT =L(t) = Lo cos (st+)

s = 2 fs

DRAG =D(t) = Do cos (2st+ )

Heave Motion z(t)

2

( ) cos

( ) sin

( ) cos

o

o

o

z t z t

z t z t

z t z t

=

=

=

&

&&


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Lock-in

A cylinder is said to be locked in when the frequency of

oscillation is equal to the frequency of vortex shedding. In this

region the largest amplitude oscillations occur.

v = 2fv = 2St(U/d)

n =k

m + ma

Shedding

frequency

Natural frequency

of oscillation

Equation of Cylinder Heave dueto Vortex shedding

Added mass term

Damping If Lv > b system is

UNSTABLE

k b

m

z(t)( )mz bz kz L t + + =&& &

( ) ( ) ( )a v

L t L z t L z t= +&& &

( ) ( ) ( ) ( ) ( )a v

mz t bz t kz t L z t L z t + + = +&& & && &

{

( ) ( ) ( ) ( ) ( ) 0a v

m L z t b L z t k z t + + + =&& &14243 14243

Restoring force


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LIFT FORCE:

Lift Force on a Cylinder

( ) cos( )o oL t L t = + vif 0 then the fluid force amplifies the motion

instead of opposing it. This is self-excited

oscillation. Cma, CLv are dependent on and a.

( ) (( , () () , ))a vL t z t L aM za t= +&& &

( )

( )

24

212

( , ) ( )

( , ) ( )

ma

Lv

d C a z t

dU C a z t

=

+

&&

&

Coefficient of Lift in Phase withVelocity

Vortex Induced Vibrations are

SELF LIMITED

In air: air ~ small, zmax ~ 0.2 diameterIn water: water ~ large, zmax ~ 1 diameter


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Lift in phase with velocity

Gopalkrishnan (1993)

Amplitude Estimation

=b

2 k(m+ma*)

ma* = V Cma; where Cma = 1.0

Blevins (1990)

a/d =1.29/[1+0.43 SG]3.35~

SG=2 fn2

2m (2)

d2; fn = fn/fs; m = m + ma

*^^

__


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Drag Amplification

Gopalkrishnan (1993)

Cd = 1.2 + 1.1(a/d)

VIV tends to increase the effective drag coefficient. This increase

has been investigated experimentally.

Mean drag: Fluctuating Drag:

Cd occurs at twice the

shedding frequency.

~

3

2

1

Cd |Cd|~

0.1 0.2 0.3

fd

U

a

d= 0.75

Single Rigid Cylinder Results

a) One-tenth highest

transverse

oscillation amplitude

ratio

b) Mean drag

coefficient

c) Fluctuating drag

coefficient

d) Ratio of transverse

oscillation frequency

to natural frequency

of cylinder

1.0

1.0


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Flexible Cylinders

Mooring lines and towing

cables act in similar fashion

to rigid cylinders except that

their motion is not spanwise

uniform.

t

Tension in the cable must be consideredwhen determining equations of motion

Flexible Cylinder Motion Trajectories

Long flexible cylinders can move in two directions and

tend to trace a figure-8 motion. The motion is dictated by

the tension in the cable and the speed of towing.


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Shedding patterns in the wake of oscillating

cylinders are distinct and exist for a certain range

of heave frequencies and amplitudes.

The different modes have a great impact on

structural loading.

Wake Patterns Behind

Heaving Cylinders

2S 2Pf , A

f , A

UU

Transition in Shedding Patterns

WilliamsonandRoshk

o(1988)

A/d

f* = fd/UVr = U/fd


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Formation of 2P shedding pattern

End Force Correlation

Uniform Cylinder

Tapered Cylinder

Hover,Tech

et,Triantafyllou(JFM1998)


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Longitudinal Vortices

C.H.K. Williamson (1992)

The presence of

longitudinal vortices leads

to rapid breakdown of the

wake behind a cylinder.

Longitudinal Vortices


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Strouhal Number for the taperedcylinder:

St = fd / U

where d is the average

cylinder diameter.

Oscillating Tapered Cylinder

x

d(x)U(x)=Uo

Spanwise Vortex Shedding from40:1 Tapered Cylinder

Techet,etal(JFM1998)

dmax

Rd= 400;

St = 0.198; A/d = 0.5

Rd= 1500;

St = 0.198; A/d = 0.5

Rd= 1500;

St = 0.198; A/d = 1.0

dminNo Split: 2P


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Flow Visualization Reveals:

AHybridShedding Mode

2P pattern results at

the smaller end

2S pattern at the

larger end

This mode is seen to

be repeatable over

multiple cycles

Techet, et al (JFM 1998)

DPIV of Tapered Cylinder Wake

2S

2P

Digital particle image

velocimetry (DPIV)

in the horizontal plane

leads to a clear

picture oftwo distinct

shedding modes alongthe cylinder.

Rd = 1500; St = 0.198; A/d = 0.5

z/d=22.9

z/d=7.9


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Evolution of the

Hybrid Shedding Mode

2P 2S

Rd = 1500; St = 0.198; A/d = 0.5

z/d = 22.9z/d = 7.9

Evolution of theHybrid Shedding Mode

2S2P

Rd = 1500; St = 0.198; A/d = 0.5

z/d = 22.9z/d = 7.9


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Evolution of the

Hybrid Shedding Mode

2S2P

Rd = 1500; St = 0.198; A/d = 0.5

z/d = 22.9z/d = 7.9

Evolution of theHybrid Shedding Mode

2S2P

Rd = 1500; St = 0.198; A/d = 0.5

z/d = 22.9z/d = 7.9


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NEKTAR-ALE Simulations

Objectives: Confirm numerically the existence of a stable,

periodic hybrid shedding mode 2S~2P in the

wake of a straight, rigid, oscillating cylinder

Principal Investigator:

Prof. George Em Karniadakis, Division of Applied

Mathematics, Brown University

Approach:

DNS -Similar conditions as the MIT experiment

(Triantafyllou et al.)

Harmonically forced oscillating straight rigid

cylinder in linear shear inflow

Average Reynolds number is 400

Vortex Dislocations, Vortex Splits & Force

Distribution in Flows past Bluff BodiesD. Lucor & G. E. Karniadakis

Results:

Existence and periodicity of hybrid mode

confirmed by near wake visualizations and spectral

analysis of flow velocity in the cylinder wake and

of hydrodynamic forces

Methodology:

Parallel simulations using spectral/hp methods

implemented in the incompressible Navier- Stokes

solverNEKTAR

VORTEX SPLIT

Techet, Hover and Triantafyllou (JFM 1998)

VIV Suppression

Helical strake

Shroud

Axial slats

Streamlined fairing

Splitter plate

Ribboned cable

Pivoted guiding vane

Spoiler plates


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VIV Suppression by Helical Strakes

Helical strakes are a

common VIV suppresion

device.

GallopingGalloping is a result of a wake instability.

m

y(t), y(t).Y(t)

U

-y(t).

V

Resultant velocity is a combination of the

heave velocity and horizontal inflow.

Ifn


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Instability Criterion

(m+ma)z + (b +1/2 U

2 a )z + kz = 0.. .

U~

b + 1/2 U2 a

U

< 0If

Then the motion is unstable!

This is the criterion for galloping.

is shape dependent

U

1

1

1

2

1

2

1

4

Shape Cl (0) -2.7

0

-3.0

-10

-0.66


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b

1/2 a ( )

Instability:

= Cl (0)

Cl (0)

Torsional Galloping

Both torsional and lateral galloping are possible.FLUTTER occurs when the frequency of the torsional

and lateral vibrations are very close.


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Galloping vs. VIV

Galloping is low frequency

Galloping is NOT self-limiting

Once U > Ucritical then the instability occurs

irregardless of frequencies.

References

Blevins, (1990) Flow Induced Vibrations,

Krieger Publishing Co., Florida.

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