OMAE2009-79431

A PHENOMENOLOGICAL MODEL FOR

VORTEX-INDUCED MOTIONS OF THE

MONOCOLUMN PLATFORM AND

COMPARISON WITH EXPERIMENTS

Guilherme F. Rosetti – University of São Paulo – Brazil

Rodolfo T. Gonçalves – University of São Paulo – Brazil

André L. C. Fujarra – University of São Paulo – Brazil

Kazuo Nishimoto - University of São Paulo – Brazil

Marcos D. Ferreira – CENPES - PETROBRAS

Scope of the presentation

• Phenomenological model for the VIM of Monocolumn

platforms

– General aspects and formulation;

– Results and comparison with experiments;

– Investigation of some aspects related to the phenomenon.

Modeling of VIM/VIV-Semi-Empirical Methods

•Non-linear oscillators represent the dynamics of the fluid

region during vortex-induced motions;

•Oscillators describe lift and drag;

•Fluid oscillator interacts with the structure modeled as a

linear oscillator;

•Parameters of the model must be calibrated with

experimental results;

•Tuning parameters are determined around resonance.

Premises

What should the model reproduce from the phenomenon

to be useful for engineering analysis?

•Self-excited and sustained phenomenon;

•Lock-in (synchronization of frequencies);

•Quantify amplitudes, frequencies, forces, coeficients

(such as added mass etc).

Equations

Structural Oscillator:

Cross-Flow Fluid Oscillator:

Inline Fluid Oscillator:

Displacement:

Lift Force:

Drag Force:

Model Parameters:

Tuning Parameters:

𝑟 +(2𝑚Ω𝑠𝜉 + 𝛾Ωf𝜌𝐿𝐷

2)

𝑚𝑟 +

𝑘

𝑚𝑟 =

1

2𝑚𝜌𝑉2𝐷𝐿𝐶𝑇

𝑞 𝑦 + 𝜀𝑦Ωf2 𝑞𝑦

2 − 1 𝑞 𝑦 + Ω𝑓2𝑞𝑦 =

𝐴𝑦

𝐷𝑦

𝑞 𝑥 + 𝜀𝑥Ωf2 𝑞𝑥

2 − 1 𝑞 𝑥 + 4Ω𝑓2𝑞𝑥 =

𝐴𝑥

𝐷𝑥

r = x + iy

𝐶𝐿 = 𝐶𝐿0𝑞𝑦/2

𝐶𝐷 = 𝐶0 1 +𝐾𝑞𝑥2 + 𝐶𝑖0𝑞𝑦/2

1

2𝑚𝜌𝑉2𝐷𝐿𝐶𝑇 𝜉 𝑘

𝛾 𝐴𝑦 𝐴𝑥 𝜀𝑦 𝐾 𝜀𝑥 Ω𝑓 = 2𝜋𝑆𝑉

𝐷

Model and Tuning Parameters

How to Obtain The Model Parameters?

Experiments performed in 2008 with MonoBr platform and

experiments with bare cylinders.

Strouhal Number, Lift and Drag vortex-shedding and Drag coefficients for

stationary structure, geometric characteristics.

How to Tune the Remaining Parameters?

Following the Procedures adopted and accepted by specialists such

as Facchinetti, Furnes, Blevins.

Results

Operational Draft of MonoBR

0

0.2

0.4

0.6

0.8

1

AY / D

0 2 4 6 8 10 12 14 160

0.1

0.2

Vr0 = UT

0 / D

AX / D

Fujarra A.L.C. et al. (2009)

Present data

•Cross-flow amplitudes follow the trend up to Vr=10;

•Inline amplitudes show some difference in the trend due to the

coupling of inline and cross-flow;

•Periods are well represented as of Vr=8. For smaller Vr’s, periods

follow Strouhal frequency.

0

1

2

3

4

TY / T

nY

0 2 4 6 8 10 12 14 160

0.5

1

1.5

2

Vr0 = UT

0 / D

TX / T

nY

Fujarra A.L.C. et al. (2009)

Present data

Results – Eight Shape

-2.5 -2 -1.5 -1 -0.5 0-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Inline reduced displacement

Cro

ss-f

low

reduced d

ispla

cem

ent

•Same range of reduced velocities although different reduced velocities;

Results – Added Mass and Synchronization Range

0 2 4 6 8 10 12 14 160

5

10

15

20

25

Vr0 = UT

0 / D

Ad

de

d m

as

s c

oe

ffic

ien

t

0 200 400 600 800 1000 1200 14000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Vr0 = UT

0 / D

AY / D

•Added mass follows the trend observed by other researchers and

presents asymptotic limit in zero;

•As mass ratio is low (~1), synchronization range is very wide.

Results – Hysteresis

0 500 1000 1500 20000

5

10

15

20

25

30

Time [s]

Flo

w V

elo

cit

y [

m/s

]

0 500 1000 1500 2000-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time [s]

AY / D

0 200 400 600 800 1000 1200 14000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Vr0 = UT

0 / D

AY / D

increasing velocity

decreasing velocity

Results

Low Draft of MonoBR

0

0.2

0.4

0.6

0.8

1

AY / D

0 2 4 6 8 10 12 14 160

0.1

0.2

Vr0 = UT

0 / D

AX / D

Fujarra A.L.C. et al. (2009)

Present data

•When the aspect ratio is 0.20, ocillations drop substantially;

•Oscillations are strongly dependent on aspect ratio and constant

Strouhal number may not correctly represent the vortex shedding

pattern for the entire range.

•The model was compared with experimental results showing

merits and deficiencies;

•It is necessary to reevaluate the coupling between inline and

cross-flow in order to better represent the behavior of the

structure;

•It seems that there is a reciprocal influence of inline and cross-

flow and it has to be better modeled;

•It will be useful to employ Hilbert-Huang analysis in order to

study hysteresis;

•Considering the usual Strouhal number equal to 0.2 might be

incorrect for low aspect ratio structures;

•More investigation on low aspect ratio in terms of vortex

shedding pattern and Strouhal number is required.

Discussion