Vortex-Induced Motions (VIM) of floating structures is a very relevant subject for the design of mooring and riser systems. In the design phase, Spar VIM behavior as well as Semi Submersible and Tension Leg Platform (TLP) flow-induced motions are studied and evaluated. This paper discusses flow-induced behavior on the Monocolumn concept by presenting a phenomenological model and comparing its results with a set of experiments that took place in the IPT Towing Tank - Brazil (September 2008). The experimental results have shown some fundamental differences from previous VIM tests on other units such as Spars. This numerical model attempts to identify these disparities in order to better understand the mechanics of this phenomenon. The model is based on a time-domain, two degree-of-freedom structural model coupled with a van der Pol type wake oscillator. The comparison was performed in order to calibrate the model, to study and better understand the tests results, and finally to identify important aspects to investigate in further experiments.

1. 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

2. 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.

3. 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.

4. 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).

5. Equations
(2𝑚Ω 𝑠 𝜉 + 𝛾Ωf 𝜌𝐿𝐷2 ) 𝑘 1
Structural Oscillator: 𝑟+ 𝑟+ 𝑟= 𝜌𝑉 2 𝐷𝐿𝐶 𝑇
𝑚 𝑚 2𝑚
𝐴𝑦
Cross-Flow Fluid Oscillator: 𝑞 𝑦 + 𝜀 𝑦 Ω2 𝑞 2 − 1 𝑞 𝑦 + Ω2 𝑞 𝑦 =
f 𝑦 𝑓 𝑦
𝐷
𝐴𝑥
Inline Fluid Oscillator: 𝑞 𝑥 + 𝜀 𝑥 Ω2 𝑞 2 − 1 𝑞 𝑥 + 4Ω2 𝑞 𝑥 =
f 𝑥 𝑓
𝐷
𝑥
Displacement: r = x + iy
Lift Force: 𝐶 𝐿 = 𝐶 𝐿0 𝑞 𝑦 /2
Drag Force: 𝐶 𝐷 = 𝐶0 1 + 𝐾𝑞 2 + 𝐶 𝑖0 𝑞 𝑦 /2
𝑥
1
Model Parameters: 𝜌𝑉 2 𝐷𝐿𝐶 𝑇 𝜉 𝑘
2𝑚
𝑉
Tuning Parameters: 𝛾 𝐴𝑦 𝐴𝑥 𝜀𝑦 𝜀𝑥 𝐾 Ω 𝑓 = 2𝜋𝑆
𝐷

6. 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.

7. Results
Operational Draft of MonoBR
•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.
1
4
Fujarra A.L.C. et al. (2009) Fujarra A.L.C. et al. (2009)
0.8 Present data 3 Present data
nY
T /T
0.6 2
AY / D
Y
1
0.4
0
0.2
2
0
1.5
0.2
TX / TnY
1
AX / D
0.1
0.5
0
0 2 4 6 8 10 12 14 16 0
0 2 4 6 8 10 12 14 16
Vr0 = UT0 / D
Vr0 = UT0 / D

8. Results – Eight Shape
•Same range of reduced velocities although different reduced velocities;
0.8
0.6
Cross-flow reduced displacement
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-2.5 -2 -1.5 -1 -0.5 0
Inline reduced displacement

9. Results – Added Mass and Synchronization Range
•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.
25 1
0.9
20 0.8
Added mass coefficient
0.7
15 0.6
AY / D
0.5
10 0.4
0.3
5 0.2
0.1
0
0 0 200 400 600 800 1000 1200 1400
0 2 4 6 8 10 12 14 16
Vr0 = UT0 / D
Vr0 = UT0 / D

10. Results – Hysteresis
30
1
0.8
25
0.6
Flow Velocity [m/s]
20 0.4
0.2
A /D
15
0
Y
-0.2
10
-0.4
5 -0.6
-0.8
0
0 500 1000 1500 2000 -1
0 500 1000 1500 2000
Time [s]
Time [s]
1
increasing velocity
0.9 decreasing velocity
0.8
0.7
0.6
AY / D
0.5
0.4
0.3
0.2
0.1
0
0 200 400 600 800 1000 1200 1400
Vr0 = UT0 / D

11. Results
Low Draft of MonoBR
•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.
1
Fujarra A.L.C. et al. (2009)
0.8 Present data
0.6
AY / D
0.4
0.2
0
0.2
AX / D
0.1
0
0 2 4 6 8 10 12 14 16
Vr0 = UT0 / D

12. Discussion
•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.