VIV II Notes

8/6/2019 VIV II Notes

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13.42 Lecture

VIV II

Alex Techet

March 18, 2003

Vortex Induced Forces

Due to unsteady flow, forces, X(t) and Y(t), vary with time.

Force coefficients:

Cx = Cy =X(t)

1/2 U2 dY(t)

1/2 U2 d

Force Time Trace

Cx

Cy

DRAG

LIFT


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3/15


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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

*^^

__

Three Dimensional Effects

Shear layer instabilities as well as longitudinal (braid)

vortices lead to transition from laminar to turbulent flow in

cylinder wakes.

Longitudinal vortices

appear atRd= 230.

Longitudinal Vortices

C.H.K. Williamson (1992)

The presence of

longitudinal vortices leads

to rapid breakdown of the

wake behind a cylinder.


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Longitudinal Vortices

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 from

40:1 Tapered Cylinder

Techet,etal(JFM1

998)

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

sheddingmodes along

the cylinder.

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

z/d=22.9

z/d=7.9

Evolution of the

Hybrid Shedding Mode

2P 2S

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

z/d = 22.9z/d = 7.9


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Evolution of the


2S2P

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

z/d = 22.9z/d = 7.9

Evolution of the


2S2P

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

z/d = 22.9z/d = 7.9

Evolution of the


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

VIV Suppression by Helical Strakes

Helical strakes are a

common VIV suppresion

device.


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Trip Wire Experiments

Trip wires cause the shear layer totransition early and thus retards separation.The wires can reduce amplitude of vibration

but this reduction is very dependant onangle on incoming flow.

Lift Characteristics of Rigid Cylinder

a) mean lift coefficientb) phase angle between oscillating lift force and cylinder motion.

Tandem Rigid Cylinders-Amplitude

Leading cylinder

Trailing cylinder

10D

Trailing cylinder

5D

-single cylinder

-no offset

-1D lateral offset


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-single cylinder

-no offset

-1D lateral offset

Leading cylinder

Trailing cylinder

10D

Trailing cylinder

5D

Tandem Rigid Cylinders-Frequency

Leading cylinder

Trailing cylinder

10D

Trailing cylinder

5D

-single cylinder

-no offset

-1D lateral offset

Tandem Rigid Cylinders-Drag

Tandem Flexible Cylinders-Amplitude

A - Leading Cylinder B-Trailing Cylinder

-single inline -tandem inline-single transverse -tandem transverse


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Forced Oscillation in a Current

U

y(t) = a cos t

= 2 f = 2 / T

Parameters: a/d, , ,

Reduced velocity: Ur= U/fd

Max. Velocity: Vm = U + a cos

Reynolds #: Re = Vm d /

Roughness and ambient turbulence

Wall Proximity

e + d/2

At e/d > 1 the wall effects are reduced.

Cd, Cm increase as e/d < 0.5

Vortex shedding is significantly effected by the wall presence.In the absence of viscosity these effects are effectively non-existent.

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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Lift Force, Y()

Y(t)

V

Cy =Y(t)

1/2 U2 Ap

Cy Stable

Unstable

Galloping motion

m

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

U

-y(t).

V

b k

a my + by + ky = Y(t).. .

Y(t) = 1/2 U2 a Cy - ma y(t)

..

Cy() = Cy(0) + Cy (0)

+ ...

Assuming small angles, :

~ tan = - yU

.

= Cy (0)

V ~ U

Instability Criterion

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

2 a )y + ky = 0.. .

U~

b + 1/2 U2 a

U

< 0If

Then the motion is unstable!

This is the criterion for galloping.


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is shape dependent

U

1

1

12

1

2

1

4

Shape Cy (0) -2.7

0

-3.0

-10

-0.66

b

1/2 a ( )

Instability:

= Cy (0)

Cy (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.

Documents

VIV II Notes