vortex-induced vibrations - petroleumstilsynet 2012/konstruksjon 29-8... · eurocode en...

VORTEX-INDUCED VIBRATIONS

PHYSICAL ASPECTS AND PREDICTION TOOLS

1 KONSTRUKSJONSSEMINAR 29. AUGUST 2012

Vortex-induced vibrations - bending vibrations


Vortex shedding on circular cylinders


Critical wind velocity

Stnb

v yiicrit

,,

⋅=

b: cross-wind dimension ni,y: natural frequency St: Strouhal number


6

ee

aa nm

cπ

ζ4

=eee

ee

ee

aa m

bdmn

bndbnmn

yF ρρζ ==∝

)/(/ 22

−−=

2

1bam

bdKL

y

eaGa

σρζ

KONSTRUKSJONSSEMINAR 29. AUGUST 2012

Odense, Denmark. Height 75 m, diameter 2.4 m


Aarhus, Denmark. Height 56 m, diameter 2.2 m


Influence of turbulence

0 200 400 600Measuring time. [sec.]

ymax / d

-0.75

0

0.75

-0.75

0

0.75

-0.75

0

0.75vm ≈ 0.96 vr

vm ≈ vr

vm ≈ 1.05 vr


Eurocode EN 1991-1-4:2005

• Approach 1: Vortex-resonance model • Approach 2: Spectral model


Approach 1 versus approach 2

• Approach 2 allows for the consideration of different turbulence intensities, which may differ due to meteorological conditions.

• For regions where it is likely that it may become very cold and stratified flow condition may occur (e.g. in coastal areas in Northern Europe), approach 2 may be used.


Vortex-shedding action – inertia forces – approach 1 and 2

max,2

, )()2()()( ysnsmsF yiyiw ⋅Φ⋅⋅⋅⋅= π

py ky ⋅= σmax


Inertia forces – approach 1 and 2


Scruton number – approach 1 and 2

2,2

bm

Sc eis

⋅⋅⋅

=ρδ

δs: structural damping – logarithmic decrement mie/(ρ·b2): mass ratio


Approach 1 – deflection from vortex shedding

latw cKKScStb

y⋅⋅⋅⋅=

112

max


Approach 2 – deflection from vortex shedding

hb

mb

abKSc

CStb e

L

ya

cy2

22

14

1 ρ

σπ

σ

⋅

−−⋅

=

aL: determines the amplitude of large vibrations Cc: determines the amplitude of small vibrations Ka: determines the critical Scruton number between large and small vibrations


Approach 2 Aerodynamic damping as function of turbulence intensity

)()Re(),Re( max, vvava IKKIK ⋅=

vv IK 31−=


Approach 2 – circular cylinders

0 5 10 15 20 25Scruton number, Sc.

0.00

0.15

0.30

0.45

σy / d

Re = 105

Re = 106

Re = 5 ∙ 105


0.00

0.15

0.30

0.45

σy / dSmooth flow, Iv = 0%

Iv = 0%

Re = 105

Iv = 10%

Iv = 20%


0.00

0.15

0.30

0.45Re = 106


0.00

0.15

0.30

0.45

σy / d

σy / dRe = 5 ∙ 105

Iv = 0%

Iv = 10%

Iv = 20%

Iv = 0%

Iv = 10%

Iv = 20%


Approach 2 – full scale measurements

0.0

0.5

1.0

( ymax / d )observed

( ymax / d )predicted

0.1 1 10 100Reynold number, Re∙10-5.


Influence of temperature gradient


New data – turbulence intensity as function of mean wind


30

Analysis for various structural elements Approach 2, Eurocode:

hd

md

daKSc

CStd e

L

ya

cy2

2max,

2

14

1 ρ

σπ

σ

−−

=

aL: determines the amplitude of large vibrations Cc: determines the amplitude of small vibrations Ka: determines the critical Scruton number between large and small vibrations


31

Figure:The aerodynamic parameters Cc,max and Ka,max for circular cylinders in smooth flow. Due to uncertainty of Strouhals number minimum values at 0.0075 and 0.75 for Cc,max and Ka,max, respectively, are used.



32

Figure: The response for elements on which damages have been observed is shown in red, and the response for elements on which no damages have been observed is shown in green. The special cases of Statfjord and Gullfaks are shown in black. The dashed lines show upper and lower limits of the responses as function of the Scruton number Sc divided by 4πKa, where Ka is the aerodynamic damping parameter.



33

Approach 2 – code calibration


38

Wind-tunnel tests

Vortex-induced vibrations of spanbreakers

• 1:1 scale of spanbreakers in a bay

• Influence of structural damping

• Determination of aerodynamic damping (Ka)

• Influence of Reynolds number

• Influence of incoming turbulence

Full-scale tests to determine the structural damping


39

Jack-up


40

Spanbreakers – filter 11-13 Hz


41

Spanbreakers with 23 kg ekstra mass – filter 10-13 Hz


42

Spanbreakers with 46 kg ekstra mass – filter 9.5-11.5 Hz


43

Parametric excitation

Force

1/n1

F

Time


44


1.02.03.0

6.05.04.0

7.08.0

10.09.0

Vibration amplitude [-]

Force frequency n [-]n1 12n 2n F


n : First natural frequencyn : Second natural frequency

1

2


45

What is the problem?

Main engine and/or wind • Main engine - induced vibrations: Not the only source • Wind – induced vibrations: Not only source

Conbined effect of main engine and wind


46

The end


vortex-induced vibrations - petroleumstilsynet 2012/konstruksjon 29-8... · eurocode en...

Documents