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Vortex Induced Vibrations

By:Abhiroop J ayanthi

Indian Institute of Technology , Delhi


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Some Questions ! What is VIV?

What are the details of a steady approachflow past a stationary cylinder?

How and why does VIV occur? What kind of body shapes experience

VIV? What kinds of VIV are there?

How do you eliminate VIV?17/12/2007 Abhiroop J ayanthi IIT Delhi


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17/12/2007 Abhiroop J ayanthi IIT Delhi

Contents

Introduction to Fluid flows

(Instabilities and Bifurcations)1

Bifurcation of flow around a cylinder(Karman Vortex Street)2

Galloping Vs VIV

3 Vortex Induced Vibrations.

4


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Flow around a circular cylinder?

At very low Reynolds numbers (based on

the diameter of the circular member) thestreamlines of the resulting flow isperfectly symmetric as expected frompotential theory. However as the Reynoldsnumber is increased the flow becomes

assymetric.



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Introduction to Fluid Flows:

Regimes of external flow.



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Profile Drag

When a body is immersed in a fluid and is

in relative motion with respect to it , thedrag is defined as that component of theresultant force acting on the body which isin the direction of the relative motion.

Profile Drag = Pressure drag + Skin frictiondrag.



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Flow past a circular cylinder :

Re < 0.5

Inertia effects are negligible pressure recovery is nearly complete.



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2


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Further increase of Re

Tends to elongate the eddies which thenbegin to oscillate until at about Re=90

depending on free stream turbulence level.They break away from the cylinder.



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This process is further intensifies by

further increase of Re leads to VortexStreet

( Von Karman Vortex Street.)



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Up to Re values of 2 x 105 the boundary

layer is laminar but at that valueapproximately depending on the intensityof the free stream turbulence, it changesto turbulence before separation .

The effect of this is that separation points movefurther back and hence there is a marked drop inthe value of CD



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Further



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At Re > 107 the value of CD appears to be

independent of Re but there areinsufficient experimental data available forthis end of the range.



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For higher Re Numbers Vortices disappear

because of high rate of shear and are thenreplaced by a highly turbulent wake.

This produces an increase in the value of CD

and here pressure drag is nearly responsible forall drag.



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Separation of Boundary Layer



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Cp

vs Angular position



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Separation angle with Reynolds Number


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Fluid Structure interaction



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Vortex Shedding

Vortex shedding is an unsteady-flow that

takes place in special flow velocities(according to the size and shape of thecylindrical body).

In this flow, vortices are created at theback of the body and detach periodically

from either side of the body.



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Vortex shedding is caused when air flows

past a blunt object. The airflow past the object creates

alternating low-pressure vortices on thedownwind side of the object.

The object will tend to move toward the

low-pressure zone.

Vortex Shedding



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Vortex Shedding



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Karman Vortex Street.

Von Krmn

vortex street isa repeatingpattern ofswirling vorticescaused by theunsteadyseparation offlow over bluffbodies



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Some points to note : The frequency of vortex shedding is definite andis related to the Reynolds number (flow velocity,

viscosity of fluid, and the diameter of the cylinder). The frequency of vortex shedding is the sameas the vibrating frequency of the cylinder induced

by the flow. If the density and viscosity of the fluid areknown and the diameter of the cylinder is given,the frequency measured at the cylinder can beused to represent the flow velocity.



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Karman Vortex Street



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What is VIV ?

Vortex-induced vibrations (VIV) are

motions induced on bodies facing anexternal flow by periodical irregularities onthis flow.

The classical example is the VIV of anunderwater cylinder.



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How and why VIV ?

When the vortices are not formed symmetrically aroundthe body (with respect to its mid plane), different lift

forces develop on each side of the body, thus leading tomotion transverse to the flow.

This motion changes the nature of the vortex formation

in such a way as to lead to a limited motion amplitude.(differently from what would be expected in a case ofresonance).



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Strouhal instability

The Strouhal number relates the frequency of

shedding to the velocity of the flow and acharacteristic dimension of the body (diameter inthe case of a cylinder).

fv -vortex shedding frequency of a body at rest

(Strouhal frequency)

Dc is the diameter of the circular cylinder

V is the velocity of the ambient flow.



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The phenomenon of lock-in happens when

the vortex shedding frequency becomesclose to a natural frequency of vibration ofthe structure. When this happens large

and damaging vibrations can result.

Strouhal instability


Strouhal Number Vs Reynolds


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Strouhal Number Vs Reynolds

number for cylinder..



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Types of VIV:

Self-excited oscillations - this type of VIV is whatoccurs naturally, i.e., when the vortex-shedding

frequency and the natural frequency areapproximately the same. (This is the real VIV this isvortex-induced vibration)

Forced oscillations occurs at velocities andamplitudes which are preset and can be controlled

independently of fluid velocity. (This is not the realVIV this is vibration-induced vortices).



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Need to understand VIV ?

VIV manifests itself on many different

branches of engineering, from cables toheat exchanger tube arrays.

Vortex-induced vibration (VIV) is animportant source of fatigue damage ofoffshore oil exploration and production

risers.


E l


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Example.



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Map of VortexSynchronization

patterns



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Map of VortexSynchronization

patterns


Elastically mounted cylinder


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Elastically mounted cylinder.(High Mass Ratio)


Classical definition Vs New


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Classical definition Vs New

findings. Classical definition of lock-in or synchronization is

often perceived as the regime where thefrequency of oscillation (f), as well as the vortexformation frequency (fV), are close to the natural

frequency (fN) of the structure throughout theregime of large-amplitude vibration

However, recent studies show a dramatic

departure from this classical result; bodies canconceivably vibrate with large amplitude, athundreds of times the natural frequency!


i di


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Findings

The phenomenon of lock-in, or synchronizationtraditionally means that the ratio f*=f/f

Nremains

close to unity for high mass ratio.

However, for light bodies in water, for m*= 2.4

the body oscillates at a higher frequency (f*=1.4).

Therefore, one might define synchronization as

the matching of the frequency of the periodicwake vortex mode with the body oscillationfrequency.


H d d VIV ?


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How do we reduce VIV ?

This is the important question!

It may be best to design around VIV. In otherwords, lets learn how to predict VIV and thenavoid the situations that will produce VIV. The

circular cylinder will always be the preferredshape and the fluctuating lift will always bethere, VIV or no VIV.

Since we cant avoid the shedding of vortices,lets try to learn to avoid the situations thatproduce VIV


S f hi i thi


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Some ways of achieving this.


U f C t l C li d


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Use of Control Cylinders.

G ll i V VIV


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Galloping Vs VIV

Two well-known phenomena in the problems of fluid/structureinteraction are vortex-induced vibration (VIV) and galloping.

VIV is associated with synchronization, or lock-in of the structuraloscillation frequency with the vortex-shedding frequency, Lock-inoccurs at reduced velocities where the vortex shedding frequency iscomparable to the natural frequency of the structure.

Galloping is driven by a time-averaged fluid force which develops inphase with the structural velocity and has a frequency many timeslower than that of vortex shedding. galloping is prevalent at higherreduced velocities where the frequency of oscillation is lower thanthe vortex-shedding frequency.


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