A great deal of work has been developed on the spar and monocolumn vortex-induced motion (VIM) issue. However, there are very few published works concerning VIM of semi-submersible platforms, partly due to the fact that VIM studies for this type of platform recently became interesting particularly due to the increasing semi-submersible dimensions (columns diameter and height. In this context, a meticulous experimental study on VIM for this type of platform concept is presented here. Model test experiments were performed to check the influence of many factors on VIM, such as different headings and hull appendages. The results comply with in-line, cross-flow and yaw motion amplitudes, as well as with combined motions in the XY plane.

1. EXPERIMENTAL STUDY ON VORTEX-INDUCED MOTIONS (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
Rotterdam| The Netherlands | June | 2011
June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 1

2. Outline
• Introduction
• Objective
• Experimental Setup
• HHT for Signal Analysis
• Results
– Transverse Characteristic Amplitude
– Yaw Characteristic Angle
– Time History
• Conclusions
• Ongoing Results
Rotterdam| The Netherlands | June | 2011 30th 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
VIV VIM bodies with low aspect ratio, e.g.
spar, MPSO and slender buoys
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
Umbilical
submersible implies more
Slender buoy
Every slender body operating Large-volume Semi-submersible
complex VIM than that single
at offshore scenario platforms
column platforms
Rotterdam| The Netherlands | June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 3

4. Objectives
• Model test experiments
were performed to check
the influence on VIM,
such as:
– different current incidence
angles (or headings)
– hull appendages
• Hard pipes in columns
(black)
• Fairleads and mooring
chains in columns (red)
• Riser supports in pontoons
(green)
Rotterdam| The Netherlands | June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 4

5. Experimental Setup
• Experiments 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: • Different headings:
– From 0.044m/s to 0.292m/s (model-scale) – 0, 15, 30, 45, 180, 195, 210 and 225 degrees
– These velocities were suitable to investigate the
entire range of synchronization for the VIM in the y- • Measurements:
direction (cross-flow) • 6DOF motions using a commercial system for
acquiring and processing
• Forces at the 4 equivalent mooring lines
Rotterdam| The Netherlands | June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 5

6. Hilbert-Huang Method for the
Signal Analysis
E
H
E
ω
t
Time History t
ω Instantaneous
Marginal Energy Level Hilbert-Huang
EMD Spectrum Spectrum
IMFs
Hilbert Transform Characteristic
motion
amplitude
Hilbert Spectrum
H (ω,t) Characteristic
motion
See Gonçalves et al. (OMAE2010) for details frequency
Rotterdam| The Netherlands | June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 6

7. Results:
Transverse Characteristic Amplitudes
0,50 0,50
0,45 0,45
Nondimensional Amplitude (Ay/L)
Nondimensional Amplitude (Ay/L)
0,40 0,40
0,35 0,35
0,30 0,30
0,25 0,25
0,20 0,20
0,15 0,15
0,10 0,10
0,05 0,05
0,00 0,00
0,00 5,00 10,00 15,00 20,00 0,00 5,00 10,00 15,00 20,00
Reduced Velocity (Vr) Reduced Velocity (Vr)
0º 15º 30º 45º 180º 195º 210º 225º
• The characteristic amplitude is • Except for the headings of 0 and 180
nondimensionalized by the column face
length, L. This choice permits to directly degrees, all other incidences showed a
compare results from different incidence synchronization at 4 < Vr <10
conditions • It is not possible to define one
• The reduced velocity is defined as:
– Vr = (U.T0) ⁄ D oscillation frequency for Vr > 14
– T0 is the transverse natural period in calm
water
• The appendages influence on VIM can
– D=L(|sin ∅|+|cos ∅| ) be verified by comparing the headings:
– 0 and 180 degrees
• According to those results, the 30, 45, – and also 15 and 195 degrees
210 and 225 degrees showed the largest • Differences may be attributed to the
VIM amplitudes in the transverse presence and position of the hard pipes
direction
in the columns
Rotterdam| The Netherlands | June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 7

8. Results:
Yaw Characteristic Angles
5,00 5,00
4,50 4,50
4,00 4,00
Yaw Amplitude [degree]
Yaw Amplitude [degree]
3,50 3,50
3,00 3,00
2,50 2,50
2,00 2,00
1,50 1,50
1,00 1,00
0,50 0,50
0,00 0,00
0,00 5,00 10,00 15,00 20,00 0,00 5,00 10,00 15,00 20,00
Reduced Velocity (Vr) Reduced Velocity (Vr)
0º 15º 30º 45º 180º 195º 210º 225º
• Considering the TRANSVERSE-T0, a • Again, it is possible to observe the
synchronization range of the yaw is appendages influence by comparing
identified for Vr > 10 the 0 and 180 degrees, and also 15
• Possible existence of “Vortex- and 195 degrees heading
induced Yaw Motion (VIY)” • In previous work, Waals et al. (2007)
proposed that the yaw oscillation
was a consequence of a galloping
phenomenon
• The same behavior has not been
observed in the present work
Rotterdam| The Netherlands | June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 8

9. Yaw Characteristic Angle
5,00
• By using the natural period of yaw 4,50
(model test value), T6, to calculate the 4,00
Yaw Amplitude [degree]
3,50
reduced velocity, a typical VIM 3,00
behavior, for this degree of freedom, is 2,50
observed 2,00
1,50
– Vr=U T6 / D 1,00
• The largest yaw angles occur in Vr = 8, 0,50
0,00
a very similar result to that usually 0,00 5,00 10,00 15,00 20,00
obtained for VIM in the transverse Reduced Velocity (Vr=U T6 / D)
0º 15º 30º 45º 180º 195º 210º 225º
direction
• The amplitudes decrease for a high
value of Vr, characterizing a auto-
controlled phenomenon, like VIV
Rotterdam| The Netherlands | June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 9

10. Comparing Time Histories
Vr=3.78 Vr=6.76 Vr=12.06
• Time history of motions in the in-line (x/L), transverse direction (y/L) and yaw motion for the heading
of 45 degrees
• Vr=3.78 corresponds to a region at the beginning of the transverse synchronization
• Vr=6.76 corresponds to the peak of oscillation inside the region of the transverse synchronization. The
yaw motion presents frequency similar to the transverse oscillation
• Vr=12.06 corresponds to the peak of yaw motion, i.e. in the region of the yaw synchronization. The
frequency of the yaw motion is clearly defined
Rotterdam| The Netherlands | June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 10

11. Conclusions
• The VIM phenomenon was experimentally observed
for a Large-volume Semi-submersible Platform
• The largest VIM in the transverse direction was
observed at 30, 45, 210 and 225 degrees of heading
• In general, the VIM in the transverse direction occurs in
a range of 4.0<Vr<14.00 with peaks around
7.0<Vr<8.0. The largest amplitudes obtained were
Ay/L=0.4 (where L is the characteristic dimension of
the rounded-square column)
Rotterdam| The Netherlands | June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 11

12. Conclusions
• Considering the headings, an important asymmetry
was observed by comparing the 0 and 180 degrees
incidences. Among other appendages, the hard pipes
may be the reason for the differences observed
• Considerable yaw motion oscillations were verified in
these tests and a synchronization region could be well
identified, herein named as “Vortex-Induced Yaw
Motion (VIY)”
• The largest yaw motions were verified for the 0 and
180 degrees of incidence, corresponding to angles
around 4.5 degrees.
Rotterdam| The Netherlands | June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 12

13. Ongoing Results
• How do the waves concomitant with current influence the
VIM?
• What is the procedure to consider the VIM (current + waves)
in the fatigue analysis?
PRELIMINARY RESULTS
Regular waves
Sea conditions
Rotterdam| The Netherlands | June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 13

14. See you in RIO next year!!
THANKS
rodolfo_tg@tpn.usp.br
Rotterdam| The Netherlands | June | 2011 30th International Conference on Ocean, Offshore and Arctic Engineering 14