Aiming to complete the results presented before by Gonçalves et al. (2011) – Experimental Study on Vortex-Induced Motions (VIM) of a Large-Volume Semi-Submersible Platform, OMAE2011, the present work brings new experimental results on VIM of a large-volume semi-submersible platform, particularly concerning its coexistence with waves in the free surface. The VIM tests were performed in the presence of three regular waves and also three different conditions of sea state. According to the results, considerable differences between the presence of regular or irregular waves were observed. The motion amplitudes in the transverse direction decreased harshly when the regular waves were performed and no VIM was observed. In the case of sea state condition tests, the amplitudes decreased slightly but a periodic motion characterized by the VIM was observed. The results herein presented concern transverse and yaw motion amplitudes, as well as spectral analyses.

1. WAVE EFFECTS ON VORTEX-INDUCED MOTION (VIM) OF A
LARGE-VOLUME SEMI-SUBMERSIBLE PLATFORM
Rodolfo T. Gonçalves
Guilherme F. Rosetti TPN – Numerical Offshore Tank
Department of Naval Architecture and Ocean
André L. C. Fujarra Engineering
Escola Politécnica – University of São Paulo
Kazuo Nishimoto São Paulo, SP, Brazil
Allan C. Oliveira
Rio de Janeiro | Brazil | July | 2012
July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 1

2. Outline
• Introduction
• Objectives
• Experimental Setup
• Results
– Only current
– Current + Waves
• Conclusions
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 2

3. Introduction
• The VIV is usually studied for rigid and
flexible cylinders with large aspect
Analytical
ratio (L/D), for example in a riser
dynamic scenario
• VIM is investigated for rigid
bodies with low aspect ratio, e.g.
spar, MPSO and slender buoys
VIV VIM
Numerical Experimental
• The current dimensions of the
new semi-submersible platforms
have increased, therefore
VIV on: VIM on: promoting VIM
Flexible Risers Spar platforms • The geometry of the semi-
Steel Catenary Risers Monocolumn platforms
submersible implies more
Umbilical Slender buoy
Every slender body operating Large-volume Semi-submersible
complex VIM than that single
at offshore scenario platforms column platforms
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 3

4. Objectives
• Model test experiments
were performed to
verify the influence of
concomitant presence 45-degree incidence
only current
of current and waves on
VIM, such as:
– regular waves waves
– sea state conditions
45-degree incidence
current + waves
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 4

5. Experimental Setup
• Experiments were performed at the Institute
of Technological Research (IPT) at São Paulo,
Brazil
• Small-scale tests (1:100) of a Large-volume
Semi-submersible platform:
– Four rounded-square columns
– Rectangular closed-array pontoon
– Only the hydrodynamic important appendages were
represented (riser support, hard pipe and mooring
lines running above the columns)
• Equivalent mooring system:
– Approximately parallel to the water surface
– Linear and symmetric stiffness
• Current velocity emulated by the towing
carriage: • Measurements:
– Six current velocities were carried out to represent • 6DOF motions using a commercial image system for
the main reduced velocity range in which the higher acquiring and processing (Qualisys)
transverse VIM (only current) was observed;
• Forces at the 4 equivalent mooring lines
– From 0.065m/s to 0.182m/s (model-scale)
• 3 wave probes to measure the wave elevation;
– The Re range performed was 8,500 < Re < 56,000
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 5

6. Experimental Setup
• Three irregular waves (sea • Three regular waves were
conditions) represented by chosen to represent
a JONSWAP spectra were different RAO values in the
chosen to represent heave motion.
different environmental
conditions at Campos Basin
– Brazil, corresponding to
distinct levels of unit
motion;
f [Hz]
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 6

7. Results: Characteristic
Motions in the Transverse Direction
• According to the results, the motions • On the other hand, the VIM was
in the transverse direction decreased mitigated completely with the
with the presence of sea conditions; presence of regular waves;
• Another issue is that the amplitudes • The motions are similar and very low
are lower for sea conditions with for the three regular conditions.
higher significant amplitude.
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 7

8. Results: PSD of the
Motions in the Transverse Direction
4 fN Cross-Flow 4 fN Cross-Flow 4 fN Cross-Flow
x 10 x 10 x 10
fN Yaw fN Yaw fN Yaw
15 4 4
fP Sea Condition fRW Regular Wave
3 3
PSD [mm .s]
PSD [mm2.s]
PSD [mm2.s]
10
2
2 2
5
1 1
0 0 0
20 20 20
15 0.3 15 2 15 2
10 0.2 10 1.5 10 1.5
1 1
5 0.1 5 0.5 5 0.5
Reduced Velocity [Vr] 0 0 Reduced Velocity [Vr] 0 0 Reduced Velocity [Vr] 0 0
Frequency [Hz] Frequency [Hz] Frequency [Hz]
Only current Current + sea condition Current + regular wave
• The energy is considerable in the • VIM behavior for sea conditions • PSD for the motions in the
range of reduced velocities 5.0≤𝑉𝑟 tests occurs but with smaller transverse direction only confirms
≤9.0. amplitudes or energy density that no VIM is evidenced for
• The energy is concentrated around around the transverse natural regular waves.
the natural frequency of frequency.
transverse direction, which
corroborates the assumption that
the VIM is a resonant behavior.
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 8

9. Results: PSD of the
Motions in the In-Line Direction
fN Cross-Flow fN Cross-Flow 4 fN Cross-Flow
x 10
fN Yaw fN Yaw fN Yaw
15000 10000 6
fP Sea Condition fRW Regular Wave
8000
PSD [mm2.s]
PSD [mm2.s]
PSD [mm2.s]
10000 4
6000
4000
5000 2
2000
0 0 0
20 20 20
15 0.3 15 2 15 2
10 0.2 10 10 1.5
1 1
5 0.1 5 5 0.5
Reduced Velocity [Vr] 0 0 Reduced Velocity [Vr] 0 0 Frequency [Hz] Reduced Velocity [Vr] 0 0
Frequency [Hz] Frequency [Hz]
Only current Current + sea condition Current + regular wave
• The results showed no • The energy in the presence of sea • The energy for this degree-of-
considerable energy in the in-line condition is higher and freedom is concentrated in the
direction. concentrated around the natural frequency of the regular waves
frequencies at the free surface performed, with no considerable
plane, in-line; energy in other frequencies.
• This is a resonant behavior in low
frequencies caused by the
irregular characteristics of the sea
conditions.
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 9

10. Iwagaki & Asana (1984)
procedure for forced motions
• It is possible to consider
the in-line motion due to
0.5 45 degrees
no waves
regular wave
0.4 fRW = 0.91Hz H = 43.87mm
the wave excitation as the 0.3
regular wave
fRW = 0.59Hz H = 78.91mm
Ay / L
regular wave
imposed oscillatory 0.2
fRW = 0.38Hz H = 116.64mm
sea condition (JW)
fP = 0.67Hz Hs = 65.23mm
motion and calculate the 0.1
sea condition (JW)
fp = 0.56Hz Hs = 58.71mm
sea condition (JW)
respective Keulegan-
fp = 0.54Hz Hs = 51.80m
0
0 5 10 15 20
Reduced Velocity (V r)
Carpenter number: 1
SS - Sea Conditions
𝑈 𝑀 0.9
– Regular wave: 𝐾𝐶 =
SS - Regular Waves
0.8
𝑓 𝑊 𝐷
Predominantly Inertia
0.7
2𝜎 𝑈
– Sea condition: 𝐾𝐶 𝑟 =
0.6
𝑓𝑃 𝐷 
0.5
• The effect of current and
0.4
Predominantly Drag
0.3 (Viscous)
waves is calculated using
𝜎𝑈
0.2
the ratio 𝛼 =
0.1
0
𝜎 𝑈 +𝑈 0 1 2 3 4
KC
5 6 7 8
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 10

11. Iwagaki & Asana (1984)
procedure for forced motions
• The results showed the regular wave
condition and the sea condition incidence
at a distinct behavior region, predominant
1
inertia and predominant drag (viscous), SS - Sea Conditions
0.9
respectively. SS - Regular Waves
0.8
• It is possible to infer that the possibility of Predominantly Inertia
VIM existence depends on the imposed in- 0.7
line motions due to the wave incidences 0.6
to be at the predominantly drag (viscous) 0.5

region, where the viscous forces or lift 0.4
Predominantly Drag
forces due to vortex shedding are 0.3 (Viscous)
considerable.
0.2
• The fact that VIM is not verified for
0.1
regular wave tests is justified because
0
imposed in-line motions due to waves are 0 1 2 3 4 5 6 7 8
KC
located at the predominant inertia region,
i.e. the inertia forces are greater than the
forces due to vortex shedding.
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 11

12. Gonçalves et al. (2010)
VIM of monocolumn platform
1
base case
• The same procedure was applied 0.8 T = 14.00 s
H = 4.00 m
to the results presented in 0.6
T = 16.00 s
AY / D
H = 5.22 m
Gonçalves et al. (2010) for a 0.4
T = 18.00 s
H = 6.68 s
monocolumn platform subjected 0.2
to current and regular wave
incidence. 0
0.2
• Even for regular waves, the
AX / D
0.1
monocolumn platform
experimented VIM, lower than 0
0 5 10
Vrn = UTn / D
15 20
with current incidence only, 1
differently from the semi- 0.9
Monocolum
Regular Waves
Gonçalves et al. (2010b)
submersible platform; 0.8 Predominantly Inertia
• However, the imposed in-line
0.7
0.6
motion due to wave was located 
0.5
at the predominantly drag 0.4
Predominantly Drag
(viscous) force, as can be seen, in 0.3 (Viscous)
which VIM can be verified. 0.2
0.1
0
0 1 2 3 4 5 6 7 8
KC
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 12

13. Conclusions
• The results for SS showed that, in regular wave tests, the VIM was
completely mitigated. Motions in the transverse direction were not
observed and the energy around the natural frequency of
transverse motions could not be found;
• Differently, the SS results for the sea condition tests showed lower
VIM when compared with the case without waves, but the PSD
showed considerable energy levels around the natural frequency of
transverse motion;
• This behavior is better understood by making plot 𝛼 vs 𝐾𝐶 using
the in-line motions due to waves as the imposed oscillatory motion;
• The in-line response due to waves may be conjectured as the
responsible to the possibility of VIM existence and not the wave
nature (regular or irregular). However, the VIM amplitude also
depends on the motion amplitudes of the other DOF, mainly heave,
roll and pitch; as firstly discussed in Gonçalves et al. (2010).
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 13

14. Conclusions for the SS case
studied
• The velocity ratio 𝛼 for the regular wave incidence is
located at the predominantly inertia region, where the
forces due to the vortex shedding are small and the VIM
does not occur;
• However, the sea condition incidences are located at
predominantly drag (viscous) region, where the forces due
to vortex shedding are significant and the VIM may occur,
but the VIM amplitudes also depend on the heave, roll and
pitch motions;
• This assumption must be confirmed with more tests and
studied in depth with fundamental experiments on
simplified geometries such as bare cylinders, which has
been done by the authors.
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 14

15. THANKS
rodolfo_tg@tpn.usp.br
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 15

16. References
• Gonçalves, R. T., Fujarra, A. L. C., Rosetti, G. F., &
Nishimoto, K. (2010). “Mitigation of Vortex-
Induced Motion (VIM) on a Monocolumn
Platform: Forces and Movements”. Journal of
Offshore Mechanics and Arctic Engineering, Vol.
132(4), p. 041102.
• Iwagaki, Y., & Asano, T. (1984). “Hydrodynamic
Forces on a Circular Cylinder due to Combined
Wave and Current Loading”. Proceedings of the
International Conference on Coastal Engineering,
No. 19.
Rio de Janeiro | Brazil | July | 2012 31th International Conference on Ocean, Offshore and Arctic Engineering 16