Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering
Proceedings of OMAE2007:
OMAE2007
26th International Conference on Offshore
Mechanics
and
Arctic
Engineering
June 10-15,
2007, San
Diego,
California,
USA
June 10-15, 2007, San Diego, California, USA
OMAE2007-29539
OMAE2007-29539
FLOW INDUCED MOTIONS OF MULTI COLUMN FLOATERS
Olaf J.Waals
MARIN
[email protected]
Amal C. Phadke
ConocoPhillips
[email protected]
Stephen Bultema
Bultema Marine
[email protected]
ABSTRACT
Evaluation of vortex induced motion (VIM) in offshore
floating structures has been largely been carried out for spars.
Classic spar, truss spar and cell spar hulls are all known to
exhibit VIV (VIM) [1], [2], [6], [7], [8], [9], [10], [12], [13],
[14], [15], [16], [19], [27], [28], [29]. [31], [32],
More recent work has indicated that in addition to spars,
both semi-submersibles and TLPs are also known to exhibit
flow induced motions [18], [24]. However, the motions of
multi-column floaters are more complex and can involve more
than one of the phenomenons listed before.
The motivation for the recent series of tow tests is confirm
the behavior and to further investigate the significance of the
response.
This work has shown low frequency response of Tension
Leg Platforms (TLP) and deep draft semi-submersibles in
steady current. The authors note that the included results
provide trends for current induced motion of semi submersibles
and TLPs. However, actual responses on a specific floater
design may vary even due to small differences in the geometry.
Based upon this work and that of others it is apparent that
current induced motion should address during the design
process for the both riser and mooring fatigue. The response in
these structures can have significant influence on the fatigue
life of steel catenary risers (SCR).
Recent years have shown an increasing interest in low
frequency response of offshore floaters in current. Spar VIM
behavior and Semi Submersible flow induced behavior is
known from calm water tow tests. Recent tow test projects have
also shown low frequency TLP response in steady current. The
motions from the model tests are used in the global analysis of
the mooring systems and risers for these platforms.
This paper discusses the dynamic behavior in current of multi
column floaters and the associated complex flow patterns.
Shielding between columns is addressed as well as the effect of
mass ratio (i.e. floater mass divided by displacement). It is
shown that lower mass ratios such as for conventional TLP's
may result in larger sway response than for deep draft semi
submersibles. The motion behavior is discussed as well as the
increase in total mean current loads due to transverse motions.
BACKGROUND
The vibration that is caused by a fluid flowing around a
bluff body is known as flow-induced vibration. A tentative list
of different types of flow-induced vibration includes [21]:
- Vortex Induced Vibrations (VIV)
- Galloping and Flutter
- Flow Interference
- Turbulence Induced Vibrations (Buffeting)
- Static Divergence
- Drag Crisis
The offshore industry has recognized the importance of
this phenomenon to the design of fixed and floating structures
in current for some time now. However, most of the effort in
the offshore arena has so far been focused on vortex induced
vibration, VIV, also referred to vortex induced motions (VIM).
INTRODUCTION
A bluff body immersed in a stream of fluid is susceptible to
vortex resonance as well as galloping instabilities. A structure
experiences vortex resonance (VIV or VIM) if its natural
frequency coincides with the vortex-shedding frequency.
Galloping is a form of self excited vibrations, where the body
generates an aerodynamic force aiding the motion, which can
build up into large-amplitude, low-frequency vibrations [22].
1
Copyright © 2007 by ASME
Second it is not self limiting. Galloping tends to increase
with increasing velocity. The structure responds to the
hydrodynamic force generated by an oscillating flow field.
Small motion of the structure can cause the flow relative to the
structure to oscillate. The hydrodynamic force generated by the
oscillatory flow can cause the amplitude of motion to grow
until limited by system nonlinearities.
Another important parameter influencing VIM response is
the mass ratio ( mr ), [3], [11], [17]. It is especially important
Several parameters are defined to help in understanding
which process is being investigated and to assist in generalizing
the results.
The Strouhal number [5], [26]
St =
Df s
,
U
is the proportionality constant between the predominate
frequency of vortex shedding
fs =
StU
D
for TLPs. It is defined as the ratio of floater mass ( M ) to the
floater displacement ( ∆ ) as shown below. The mass ratio is
close to 1 for spars and semi-submersibles, while it is much
less than 1 for TLPs.
and the free stream velocity (U) divided by the maximum width
normal to the free stream (D). D, the maximum width normal to
the free stream, is ordinarily used because this width tends to
govern the width of the wake.
Strouhal (1878) determined the average Strouhal number
for a circular cylinder to be 0.185. Later work by Rayleigh
(1879) and others has shown this value to be 0.2.
Recent work by Sarioglu, M. and Yavuz, T, [25], for
Reynolds number range 1x104 − 2x105 determined Strouhal
numbers between 0.12 and 0.16 for the square cylinder (w=h =
1.0) having the same hydraulic diameter as that of the circular
cylinder at 0 degree incidence,
mr =
Vandiver’s work [29, 30] on riser VIV found that the mass
ratio of a submerged structure can affect the response in
current. The physical background of the increased VIM
response for low mass ratios lies in the fact that the added mass
becomes more important. VIM is generally known as a coupled
hydromechanics phenomenon. The response and exciting
forces can not be separated from each other, since the exciting
forces depend on the motion (and its history) of the structure.
This is because the flow pattern and the related forces depend
on the motion of the structure interactively. Furthermore, the
added mass adapts itself to the motion and therefore the VIM
does not only occur at one signal frequency but at a range of
frequencies around the natural frequency in calm water.
Because of its shape, the response curve is generally referred to
as the bell curve.
The ability of the added mass to adapt itself to the motion
becomes more pronounced if the added mass is larger with
respect to the mass of the floater itself. This means that the
expected response is larger at a wider frequency range for
lower mass ratios. In this paper the increase in VIM response
for lower mass ratios is discussed such as for TLPs compared
to that of deep draft semis submersibles.
Yet another variable that affects flow induced response is
the excitation length or the correlation length at which the
vortices are shedding in phase. A critical excitation length is
needed for VIM to occur.
The response of an elastically mounted cylinder in free
stream or towed can be divided into three regions, sub-critical,
critical, and post-critical. These occur at increasing velocities.
At very small speeds (sub-critical), the transverse motion is
very small and without significant periodicity. In the critical
region, lock-in can occur, a harmonic transverse oscillation
with nearly constant amplitude. Periodic transverse oscillation
can also occur under post-critical condition. It is due to
galloping phenomenon in this regime.
The flow induced response becomes much more complex
for tube arrays or multiple cylinders as in case of
semisubmersibles and TLPs. Depending on the flow direction
In addition, for the rectangular cylinders the Strouhal number
decreases with increasing width-to-height ratios.
A parameter called reduced velocity is normally defined as
Ur =
U
fD
It is used to establish a relationship between flow velocity,
amplitude of the response, and, the frequency of vibration of
the structure, f .
In this work a modified definition of Ur has been used. Instead
of the response frequency we will use the calm water natural
frequency, f N . Therefore,
Ur =
M
∆
U
fN D
VIV or VIM is the unique case where the structural
response frequency is equal to the vortex shedding frequency,
f = fs
The response of a structure at or near the vortex shedding
frequency is broad banded. However, when the two frequencies
are very close a phenomenon can occur which is commonly
referred to as lock-in. The process does not increase without
bound as it is drag limited.
Galloping is different than VIV. First, it is a low frequency
response. That is, the vortex shedding frequency is much larger
than the structural response frequency,
f s >> f
2
Copyright © 2007 by ASME
The results of configuration I and II were tested to
compare the effect of mass ratio. Both configurations have
exactly the same geometry. However, the second configuration
has 32% less mass than the first. The lower mass ratio is typical
for a TLP.
The configuration III was tested to investigate the effect of
the correlation length of the columns by comparing it to
configuration I. The third configuration was chosen such that
the free span column height was 50% smaller than for
configuration I.
Configuration IV was a 2 pontoon version of configuration
I. This was tested to investigate the effect of different
geometries. The two pontoons can generate lift forces that
change sign for varying yaw angle. These lift effects are known
to cause instabilities in floater motions in current, such as the
fishtailing behavior of tankers in tandem offloading situations.
relative to platform heading the arrangement of the columns
can be visualized as in-line, staggered or offset.
Figure 1: Definition of column arrays
In-line
Staggered
Offset
The flow past the leading column(s) has an effect on the
flow around and between the columns. The modified flow can
be categorized as proximity interference, wake interference or
both [4]. Any interference or shielding will affect the response
of multi-column floaters. A cylinder in the wake of another can
be strongly influenced even at a distance of 20 diameters or
more [21].
Test Setup with air bearings
A test setup using air bearings was developed to be able to
model the different vertical pretensions and allow the model to
freely respond to the incoming flow. The model was equipped
with 3 ultra low friction air bearings that slide along a
horizontal plate that is mounted to the carriage (see Figure 7).
Prior to the model test the surge/sway/yaw damping due to the
friction of the air bearing was investigated and found to be less
than 1% of critical damping.
The vertical pretension for the semisubmersibles is a result
from the weight of the mooring lines and risers. For the TLP
the downward force is introduced by the pretension in the
tension legs and risers.
The vertical pretension was applied to the model by
pushing it down into the water, without restricting the
horizontal motions. The horizontal restoring is provided by two
soft springs in the tow direction.
TOW TEST CONFIGURATION
To obtain more information on the effect of draft and mass
ratio, towing tests were carried out to record the response. The
model (scale 1:70) that was used for the tests consisted of sharp
cornered building blocks that allowed for easy adjustment of
the floater shape and weight distribution. Two main shapes
were tested:
1. Four columns (14m x 14m) with two pontoons
2. Four columns (14m x 14m) with four pontoons
Figure 2: Building blocks model of a semi submersible
Figure 3: Sketch of the test setup
B
Fairbearing
Fairbearing
Tow
direction
Table 1: Tested configurations
I: Deep Draft Semi Submersible
Mass
Displacement
Mass Ratio
t
t
44000
53000
0.83
Draft
m
35
Column height
m
24.5
II: Deep Draft TLP
Mass
Displacement
t
t
Mass Ratio
Draft
m
Column height
m
0.57
35
24.5
III: Semi Submersible (4 pontoons)
Mass
Displacement
Mass Ratio
t
t
37000
44000
0.84
Draft
m
22.8
Column height
m
12.2
IV: Semi Submersible (2 pontoons)
Mass
Displacement
Mass Ratio
t
t
Draft
m
Column height
m
35
24.5
30000
34000
53000
41000
0.83
W
Test Program
To investigate the effect of flow induced motion behavior a
reduced velocity (Ur) range between 4 and 40 was tested for all
4 configurations. The tested Ur, towing velocities and projected
diameter, D, can be found in Table 4.
Tow directions
The test program included main tow directions, 0 and 45
degrees and all measurements were referenced to a basin fixed
coordinate system.
3
Copyright © 2007 by ASME
The nominal response provides the averaged motion
amplitude that may be used for fatigue analysis of the risers and
mooring system. The maximum response is based on the
highest maximum and lowest minimum excursion. By
comparing the results of the two methods a measure for the
regularity of the response signal can be obtained. If the nominal
Figure 4: Definition of motions and tow directions
0 deg
45 deg
X
Y
⎛ A⎞
⎟ response are the same then the behavior
⎝D⎠
RESULTS
and maximum ⎜
Natural periods
The natural periods of the system in calm water are given
below. The X and Y natural periods were taken in the basin
fixed reference system. Therefore, the natural periods in the 45
deg towing direction were slightly different due to small
differences in the added mass with respect to the 0 deg tow
direction. The presented U r for every configuration are based
on the Y natural periods in calm water.
would be a sinusoidal motion. The larger the difference the
more variations in the response amplitude are present. This
difference can be observed in Figure 10 and Figure 11 for the
higher U r range. This is especially true for configuration IV,
the 2 pontoon semisubmersible, therefore the response is not
very regular. An example of the time trace for U r 30 in 0 deg
flow angle is given below.
Table 2: Natural periods for 0 deg towing direction
Config I
Config II Config III Config IV
Tx [s]
132
123
118
111
Ty [s]
205
189
184
180
Tyaw [s]
49
43
42
47
Figure 5: Y response for Config 4 (0 deg angle, Ur =30).
10
Y [m]
5
0
-5
-10
Table 3: Natural periods for 45 deg towing direction
Config 1
Config 2
Config 3
Config 4
Tx [s]
132
122
117
117
Ty [s]
205
187
184
187
Tyaw [s]
49
43
41
47
0
500
1000
1500
2000
2500
time [s]
3000
3500
4000
4500
5000
At U r of 7 for the 45 deg tow direction we observed much
more regular response:
Figure 6: Y response for
Config
deggtow angle, Ur =7).
p
g 1 (45
g
10
5
Y [m]
Drag
⎛ A⎞
⎝ D⎠
Figure 8 Cc vs ⎜ ⎟ and Figure 9 – Drag force vs. tow
-10
speed for 45 degree platform heading present results similar to
that found by Rijken, et al [24] showing an increase of the total
drag on the platform with increasing tow velocity with a
dependency on both forward speed as well as the amplitude of
oscillation.
⎛ A⎞
=
⎟
⎝ D ⎠ nomimal
0
2000
4000
6000
8000
time [s]
10000
12000
14000
16000
Table 4 shows the observed transverse motion (Y) periods
and the vortex shedding periods for Strouhal numbers of 0.14,
0.16 and 0.2. It also shows that the platform motion period
varies considerably with towing speed. This can be attributed to
the increase in added mass. The shift in period away from the
vortex shedding frequency indicates that the response is not
VIV but more likely due to galloping or a combination of
vortex shedding and galloping. The change in response
frequency and monotonic increase in response with velocity is
attributed to variation in added mass and lift coefficient and a
visibly modified flow between and around the cylinders which
can be categorized as proximity interference, wake
interference.
Test results are presented in Figures 10, 11, 12 and 13 for
platform transverse and torsional response, all 4 configurations
and the 2 tow headings. The response at 45 degree tow
Flow Induced Vibration
The results from the towing tests are analyzed by taking
the statistics from the time traces as follows.
nominal response : ⎜
0
-5
2 × σ (Y (t ))
D
where σ = standard deviation of Y (t )
max (Y ( t ) ) − min (Y ( t ) )
⎛ A⎞
=
⎟
D
⎝ D ⎠maximum
maximum response: ⎜
4
Copyright © 2007 by ASME
direction has larger transverse response which is again
consistent with what Rijken, et al [24].
In the 45 degree towing angle the vortex shedding period
is close to the observed motion period for Ur = 6, 7 and 8 which
indicates that the shedding vortices are the most likely driver
for the motion for these velocities. The peak response is found
at a Ur between 5 and 8.
Figure 11 also shows that the nominal sway response for
the 0 deg current angle is limited to an A/D value between 0.25
and 0.3 at Ur 8. (Please note that the reference diameter is a
factor 1.41 smaller than for the 45 degree tests). However, the
response is not reducing for higher Ur as is the case for the 45
degree tow direction. The vortex shedding frequencies are not
close to the motion periods, therefore the motions are not
driven by shedding vortices, but they are driven by lift effects
on the hull.
Figure 12 shows that the galloping (at Ur >10) seems to be
more pronounced for the 2 pontoon semi submersible. It is
likely that this because the 2 pontoons are directed into the
undisturbed flow and not shielded by the foremost transverse
pontoon. Therefore 2 pontoons can generate larger lift forces
and consequently the response at the higher Ur (Ur >10) is the
largest for configuration 4 in 0 and 45 deg current angles.
The conventional semisubmersible, configuration III,
shows much less flow induced transverse and yaw response
when compared to configurations I, II and IV. This may be a
result of the smaller column height. This would be consistent
with reduced length of the column resulting in a smaller forcing
length.
Figure 15 shows the response spectra for the 45 deg tow
tests versus Ur. The largest response can be found around Ur 6
and Ur 7. In Figure 16 for the 0 deg tow direction the response
is less narrow banded and response is observed at a wider
frequency range, especially at lower frequencies and higher Ur.
water. A complex coupling between Y and yaw may be
affecting the platform response.
Yaw motion of multi-column floaters induced due to
steady current could due to galloping phenomenon as the data
in Figure 13 suggests. This figure shows that the yaw amplitude
is not self limiting but rather increases almost monotonically
with tow speed, a characteristic of galloping induced response.
The yaw motion is likely the result of moments generated due
to disturbances in oscillating flow field induced by motion of
the floater. Further research is required to better understand this
behavior.
CONCLUSIONS
The largest motions were observed for the 45 deg towing
direction. At this heading an increasing drag coefficient was
found due to the motions. These findings were similar as from
previous papers, although the observed Y response is smaller
than in [24].
The effect of mass ratio for floater VIM is consistent with
that of VIV on risers. A lower mass ratio causes a wider range
of response that is slightly higher.
The correlation length of the column is important for the
amount of response. With 50% of the column height of the
deep draft floater, almost no flow induced motions could be
observed.
At higher Ur a combination between galloping and VIM
occurs. The motion behavior seems to be less regular compared
to VIM response only. Larger yaw motions were observed for
the galloping in high currents.
Further work should include variations such as column
corner shape (sharp vs. rounded) and column spacing. Also
further work is required on the yaw motions in 0 deg towing
angle.
Finally, the authors note that the included results provide
trends for flow induced vibrations for semisubmersibles. Actual
responses on a specific floater design may vary due to small
differences in the geometry. It is recommended during design
process that testing and analysis be conducted to address the
possibility of any flow induced vibration and its effect on the
riser and mooring fatigue.
Mass Ratio
Furthermore, the lower mass ratio of the TLP results in a
higher maximum response at a wider Ur range. This is because
the TLP added mass represents a larger part of the total mass
that is moving and therefore the changing added mass effect
results in relatively larger response at a wider Ur range (i.e. the
added mass adaptation effect is stronger). Based on these
results it is recommended to model the mass ratio correctly for
a towing test with a TLP.
Yaw
The measured yaw motion for the 45 deg tow direction is
small (< 1 deg). However, the yaw response for the 0 deg
towing direction is considerable. The maximum measured yaw
amplitude was 6.79 deg for the 2 pontoon configuration at a Ur
of 40. Figure 13 shows the analysis of the yaw signal for
configuration I. The behavior is very complex, especially at the
higher Ur. There are motion response peaks at the same
frequencies as for the transverse (Y) motion. Furthermore,
there is energy close to the natural period for yaw in calm
5
Copyright © 2007 by ASME
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Copyright © 2007 by ASME
Figure 7 Towing test setup with air bearing plate (see inserts for detail of air bearing)
Table 4 Y Motion periods and responses for configuration 1
Ur
4
5
6
7
8
10
11
15
20
30
40
4
5
6
7
8
10
15
20
angle
[deg]
0
0
0
0
0
0
0
0
0
0
0
45
45
45
45
45
45
45
45
Vtow
[m/s]
0.272
0.340
0.408
0.476
0.544
0.680
0.748
1.020
1.360
2.041
2.721
0.385
0.481
0.577
0.673
0.770
0.962
1.443
1.924
D
[m]
14
14
14
14
14
14
14
14
14
14
14
20
20
20
20
20
20
20
20
Y motion
period [s]
209.2
289.7
334.8
292.0
256.5
233.6
218.1
182.0
211.2
160.6
109.4
224.3
288.1
211.1
187.6
177.3
173.9
173.5
289.9
Y response
Max [A/D]
0.05
0.11
0.21
0.30
0.42
0.45
0.48
0.40
0.39
0.42
0.42
0.06
0.08
0.37
0.41
0.38
0.16
0.16
0.16
Vortex (St=0.14)
period [s]
367.5
294.0
245.0
210.0
183.8
147.0
133.6
98.0
73.5
49.0
36.8
367.5
294.0
245.0
210.0
183.8
147.0
98.0
73.5
Vortex (St=0.16)
period [s]
321.6
257.3
214.4
183.8
160.8
128.6
116.9
85.8
64.3
42.9
32.2
321.6
257.3
214.4
183.8
160.8
128.6
85.8
64.3
Vortex (St=0.2)
period [s]
257.3
205.8
171.5
147.0
128.6
102.9
93.6
68.6
51.5
34.3
25.7
257.3
205.8
171.5
147.0
128.6
102.9
68.6
51.5
NOTE: The presented U r are based on the Y natural periods in calm water.
7
Copyright © 2007 by ASME
Figure 8
Drag vs Vtow for the 45 deg tow direction
8000
Deep Draft Semi(4 pontoon)
TLP (4 pontoon)
Conventional Semi (4 pontoon)
Deep Draft Semi (2 pontoon)
7000
Fdrag [kN]
6000
5000
4000
3000
2000
45
Y
1000
0
0
0.5
1
1.5
Vtow [m/s]
2
2.5
3
Figure 9
Drag vs A/D for the 45 deg tow direction
2
Cdrag [-]
1.5
1
0.5
Deep Draft Semi(4 pontoon)
TLP (4 pontoon)
Conventional Semi (4 pontoon)
Deep Draft Semi (2 pontoon)
Trend
45
Y
0
0
0.05
0.1
0.15
0.2
0.25
A/D [-]
8
0.3
0.35
0.4
0.45
0.5
Copyright © 2007 by ASME
Figure 10 Maximum Y-Response for 45 deg tow direction
Figure 11 Nominal Y-Response for 45 deg tow direction
0.5
0.4
Deep Draft Semi (4 pontoon)
TLP (4 pontoon)
0.4
0.3
Conventional Semi (4 pontoon)
Deep Draft Semi (2 pontoon)
0.3
A/D [-]
A/D [-]
Deep Draft Semi (4 pontoon)
TLP (4 pontoon)
Conventional Semi (4 pontoon)
Deep Draft Semi (2 pontoon)
0.35
0.2
0.25
0.2
0.15
0.1
0.1
Y
0
0
2
4
6
8
10
Ur [-]
12
14
Y
0.05
16
18
0
0
20
2
4
6
8
10
Ur [-]
12
14
16
18
20
NOTE: The presented U r are based on the Y natural periods in calm water.
Figure 12 Maximum Y-Response for 0 deg tow direction
Figure 13 Nominal Yaw-Response for 0 deg tow direction
0.8
A/D [-]
0.6
Deep Draft Semi (4 pontoon)
TLP (4 pontoon)
Conventional Semi (4 pontoon)
3
Deep Draft Semi (2 pontoon)
2.5
std(yaw) [deg]
0.7
3.5
0.5
0.4
0.3
2
1.5
1
0.2
5
10
15
20
Ur [-]
25
30
Y
0.5
Y
0.1
0
0
Deep Draft Semi (4 pontoon)
TLP (4 pontoon)
Conventional Semi (4 pontoon)
Deep Draft Semi (2 pontoon)
35
40
9
0
0
5
10
15
20
Ur [-]
Copyright © 2007 by ASME
25
30
35
40
Figure 14 configuration 1
Y response spectrum for 0 deg
Figure 15 configuration 1
Y response spectrum for 45 deg
10000
10000
Y
8000
Sy [m2/s]
6000
4000
6000
4000
0
20
0
40
10
20
Ur [-]
Y
2000
2000
0 0
0.1
0.1
0.05
Ur [-]
0.05
0 0
ω [rad/s]
ω [rad/s]
NOTE: The presented U r are based on the Y natural periods in calm water.
Figure 16 configuration 1
Yaw response spectrum for 0 deg
1000
900
800
700
600
Sy [deg2s]
Sy [m2/s]
8000
500
400
300
200
100
ωn yaw
0
40
35
0.2
30
25
0.15
20
15
0.1
10
0.05
5
Ur [-]
0
0
10
ω [rad/s]
Copyright © 2007 by ASME