Proceedings of the Eleventh (2001) hlternational Offshore and Polar Engineering Conference
Stavanger, Norway, June 17-22, 2001
Copyright © 2001 by The International Society of Offshore and Polar Engineers
ISBN 1-880653-51-6 (Set); ISBN 1-880653-53-2 (VoL I1); ISSN 1098-6189 (Set)
Parameter Study of Long Free Spans
Tore Soreide and Gunnar Paulsen
REINERTSEN Engineering ANS
Trondheim, Norway
Finn Gunnar Nielsen
Norsk Hydro Research Centre
Bergen, Norway
ABSTRACT
KEY WORDS
The paper deals with the extension of the present design
methodology for free spans into the regime of higher L/D-ratios.
The paper is coupled to the Ormen Lange field development,
thus major effort is given to pipelines in deeper water, for which
VIV generated fatigue comes out to be the governing design
control.
Pipeline free spans, hydrodynamic loads, vortex induced vibrations,
cable effect, multi-mode vibration.
NOMENCLATURE
A
Ai
Ao
A~
C
D
E
f
I
k
L
L~fr
m
Existing guidelines for free spans, like DNV G14, consider L/Dratios up to around 120, which for a 20-inch pipeline means span
in the range of 70 m. Typical for this range of L/D-ratio is that
the beam effect plays a dominant role on the natural frequencies
of the pipeline. However, with spans up to 200 m as in the
present study for a 20-inch pipeline, the major stiffness
contribution becomes the cable effect in which the effective
tension is the primary parameter.
The static configuration over the free span is given as the
equilibrium pattern between the net weight and the effective
tension. In the case of axial restraints from the soil at the
shoulders, the first half wave mode in cross-flow vibration may
be suppressed due to the deflected static mode combined with the
lack of axial feed-in from the shoulders. Characteristic for the
major free spans is also the occurrence of a multiple of vibration
modes, both cross-flow and in-line, within the excitation range
for VIV. The design impact from such multi-mode response is
not covered by the existing guidelines.
NE
NEFF
NrNNER
NLAY
NOUTER
NTRUE
Pi
PO
q
T
U
VIV
V~
50
~hoop
k
V
The present paper considers the installation and operational
phases of the pipeline, ending up in the static equilibrium
configuration as basis for VIV analysis. Analytical formulas are
presented covering the effect of axial restraint on the cross-flow
natural frequencies. The discussion on VIV related natural
frequencies and corresponding modes is related to practical
application by implementing the design format from relevant
guidelines.
~(x)
55
Vibration amplitude
Inner cross-section area
Outer cross-section area
Steel cross-section area
Coefficient, see (Eq. 4)
Outer diameter of pipe
Young's modulus, C-Mn steel = 207 000 MPa
Natural frequency of the pipe free span
Cross section moment of inertia
Shoulder longitudinal stiffness (kN/m)
Length of span
Effective span length
Mass of pipe, including content and external
water
Euler buckling load
Effective tension
Pi " Ai
Lay tension
P0" A0
True tension
Inner pressure
Outer pressure
Submerged weight of pipeline per unit length
Temperature
Current velocity
Vortex Induced Vibrations
Reduced velocity
Static deflection amplitude
Hoop strain (due to internal overpressure)
Sag parameter, see (Eq. 5)
Kinematic viscosity
Shape function
depicted in Figure 6. The positive effective tension for longer spans
brings the VIV exciting current velocity higher up and out of the
range of current distribution, while the negative NEFF for the short
span has the opposite effect.
INTRODUCTION
For development ofoil and gas fields in deeper water, oil companies
are facing several locations with very irregular seabed topography.
Installation of rigid pipelines within these areas might give numerous
pipeline free spans with very high L/D- ratios. The Ormen Lange
field introduces great challenges with respect to pipeline free spans,
and a separate study has been conducted by Norsk Hydro and
Reinertsen Engineering in order to investigate the possibility of
allowing free spans outside the range normally covered by existing
guidelines, i.e. DNV Guideline no.14. As far as design methodology
for long free spans is concerned, most experience up to now is gained
on shorter spans. The general formulation in DNV G14 covers longer
spans, however, the application part of the guideline handles L/Dratios below 120, while the present study aims at L/D-ratios up to
350, corresponding to a 200 m long span for a 20-inch pipeline.
Static Configuration
In an attempt to come up with a numerical scheme for simulating the
above effects, both phases of installation and operation have to be
considered, see Figure 7. The laying operation with a given tension
NLAV defines the initial configuration of the span. At bottom, the
effective tension equals the horizontal lay tension at top, and the
equilibrium on submerged weight defines the amplitude of initial
deflection. When going into the operation phase, the interaction with
soil at shoulders is established by elastic springs belbre internal
pressure with axial Poisson effect as well as temperature is activated.
The weight is now modified by including the content.
The Ormen Lange field is located outside Mid-Norway and is
developed by Norsk Hydro. Figure 1 illustrates the free span
distribution for a 20-inch pipeline along a typical route at the Ormen
Lange field.
The net effect from temperature increase and axial hoop may be a net
elongation of the pipeline, which in turn increases the deflection. For
a short span the equilibrium with submerged weight may then come
out with a reduced effective tension in the span. However, for longer
spans where cable effect is dominant in the equilibrium with net
weight, we always come out with a positive effective tension.
STRUCTURE BEHAVIOUR
Multiple Mode Vibration
General
By applying the scheme of fatigue control according to DNV G14,
the major effect to take into consideration when going from moderate
spans into longer spans with L/D-ratio above 200. is the occurrence
of a multiple of vibration modes within the range of reduced velocity
for VIV. The symmetric modes will be close in frequency for in-line
and cross- flow responses, respectively, while [br the cross-flow
asymmetric modes the sag effect may come in. especially tbr the first
half wave mode.
Figure 2 depicts the excitation ranges from DNV G14 on in-line and
cross-flow VIV, respectively. The excitation range for in-line lies
between 1.0 and 4.5 on reduced velocity Vr, with maximum in-line
amplitude of 0.15 of outer diameter. For cross-flow, the maximum
amplitude is set to 1.10 of outer diameter, with excitation range from
Vr = 3 to Vr = 16. Included is also cross-flow induced in-line
response by 50% amplitude ratio. The probability distribution for
current forms the basis for the calculation of accumulated damage. In
general, due to the difference in VIV amplitude, cross-flow is the
critical vibration mode. However, experience demonstrates that
because of no cut-off in the fatigue curve as specified by DNV G14,
the small in-line stress ranges may sum up to give a considerable
contribution to fatigue damage.
The existence of several possible vibration modes even at the same
current velocity within the range of VIV excitation calls for an
updating of the conventional single mode design procedure in the
present guideline. As the stress ranges are mode dependent, and
further the number of cycles is frequency dependent, there comes out
the need for a "worst case" philosophy on the occurrence of different
modes. For cross-flow vibration, two or three modes are relevant lbr
L/D-ratios below 350. Since also the cross-flow generated in-line
response has a major impact on fatigue, consistency must be
implemented in the design procedure between the mode shapes in the
two directions.
Figure 3 illustrates the general layout of VIV excitation as chosen in
the present study. Applying the reduced velocity in Figure 2, a
transformation is made into actual current velocities. For pure beam
behaviour, Figure 3 describes how cross-flow vibration occurs at
lower current velocities as the length of the span increases.
Cable Effect on VlV
SAG EFFECT
The major effects implemented when going from a short span with
L/D below 100 and into the longer spans are illustrated in Figure 4.
While for the short span the beam load carrying behaviour is
dominant, the cable effects take more over for higher L/D-ratios. The
change of response characteristics is followed by the possibility for
multi-mode vibration pattern within the VIV excitation range.
Suppression of Cross-Flow
Having established the static configuration for the phase of
operation, Figure 8 illustrates the deflection amplitude 80 for which
the effective tension in combination with deflected geometry keeps
equilibrium with the submerged weight. This stage now forms the
basis for the vibration analysis. The characteristics of vibration are
now different foi" in-line and cross-flow motion, respectively. The
major contribution to this difference is the combined influence from
sag ~) and longitudinal stiffness k at shoulders, which affects the
symmetric vibration modes. Based on modal shape assumption:
Figure 5 illustrates the conventional design philosophy for short
spans. Given the current distribution, as well as the VIV excitation
ranges, the scheme of span design is now to shorten the span so as to
increase the natural frequency and thereby move the excitation
velocity out of the range of current distribution. Installation of mid
span supports, for instance by rock dumping is one solution, as
indicated in Figure 5.
The effect from effective tension NEFFon the natural frequencies for
similar modes for short and long spans, respectively, is further
~(x)
56
=
sin(--~-)
L
(Eq. 1)
Fhe effect from k and 80 on the single half wave mode in cross-flow
direction (vertical) comes out as:
),).c/.= I _ ~ / N / ' : F F / I +
2LV m ~
NF. + :,r2 kSo 2)
NI,:H., 4L NFH..
(11_7)(Eq. 2)
The first two terms in (Eq. 2) represent cable and bending effects,
respectively', in accordance with existing DNV G14, while the
additional effect from static deflection and longitudinal stiffness goes
into the last term. Note that k now represents the stiffness at each
shoulder.
CF-3
337,0
337.0
337.0
609,6
872.1
58t4.1
29070.3
5814.1
0.140
0.295
0.622
0.204
0.167
0.167
0.168
0.201
0.320
0.339
0.315
0.363
To illustrate the effect of bending stiffness and sag on the natural
frequency of the free span, we have computed the first natural
frequency using several analytical approximations. By the first
natural frequency is here meant the frequency corresponding to the
first symmetric mode of oscillation. For a straight cable this
corresponds to a half sine wave. As will be demonstrated in the
following, this first symmetric mode of oscillation not necessarily
corresponds to the lowest frequency of oscillation.
As part of the present study on long free spans, a systematic
numerical analysis scheme has been made on the sensitivity of
fatigue capacity of longer free spans to vital structure parameters as
lay tension, effective tension, temperature, shoulder stiffness and sag.
The numerical studies have been related to expected spans for the
Ormen t,ange project. From these analyses the input for model
testing on multiple mode VIV has been generated.
The simplest approximation is the pure cable equation, without sag
and bending effects, i.e. including the first term inside the parenthesis
of (Eq. 2) only. This provides a lower limit for the natural frequency.
By using the two first terms of (Eq. 2), the bending stiffness is
included. This estimate on the natural frequency is valid for the inline response, as there is no sag effect in the in-line direction. The
full (Eq. 2) is valid for moderate sag values, i.e. as long as the mode
shape may be approximated by a half sine wave. The cable
approximation according to Triantafyllou ignores the bending
stiffness but accounts for finite sag values. The finite sag will cause
the first natural mode to be different from a pure half sine mode
shape deflection. I.e. forcing the mode shape to be a half sine will
give a too high natural frequency. In Figure 11 the first natural
frequency is computed using the different approximations discussed
above. The case considered is ease four (last line) of Table 1. The
length of the span is varied, and a pinned - pinned boundary
condition at the ends of the span is assumed.
Finite Element Analysis, L/D=350
The present section presents a span for a 20-inch pipeline. The case
of a slender pipeline is depicted through the span of 195 m,
corresponding to L/D=350, for which cable effect and multiple mode
bchaviour emerge.
In the following some results from the finite element analyses for
extremely long spans will be discussed. The combined effect of sag
and axial stiffness on the beam - cable equations will be discussed
from an analytical point of view
Figures 9 and 10 illustrate the soil interaction effect. In Figure 9 there
is no axial restraint applied to the tensioned pipe, while in Figure 10
an axial spring is introduced at each end simulating shoulder
restraints. Comparing the two cases, it is seen how the first half wave
mode in cross-flow, denoted CF1, moves along the current velocity
axis and out of the actual current distribution. The effect on the
higher cross-flow modes, as well as on in-line modes, is seen to be
negligible. Natural frequencies and corresponding mode shape
numbers for the span of 195 m are shown in Table 1 and 2, assuming
added mass coefficient of 1.0.
872.1
5814.1
29070.3
5814.1
N~ural frequencies (Hz)
CF-2
Analytical estimates on natural frequencies.
General
337.0
337.0
337.0
609.6
CF-I
Table 2 demonstrates the dependency of cross-flow natural
frequencies on both static effective axial force, as well as on shoulder
stiffness. While the in-line frequencies in Table 1 regularly increase
by increased tension, the first cross-flow mode shows a more
irregular pattern. It emerges that the static sag deflection in
combination with shoulder restraint, also is a vital parameter in
addition to the geometric effect from tension itself.
NUMERICAL STUDIES
Shoulder
restraint
k
(kN/m)
Shoulder
mstmint
k
(kN/m)
Table 2. Cross-flow natural frequencies. Span = 195 m.
The lbrmula (Eq. 2) does not account for the axial flexibility L/EAs
of the pipe span. This effect may be taken in by a modification of the
end restraints. Trianta~llou et al. (1985) considers the axial restraint
effects also on the higher order symmetric modes.
Axial
force
N
(kN)
Axial
force
N
(kN)
IL-1
Natural 9equencies(Hz)
IL-2
IL-3
IL-4
IL-5
IL-6
0.068
0.068
0.068
0.088
0.170
0.170
0.170
0.202
1.11
1.I1
1.11
1.16
0.320 0.526
0.320 0 . 5 2 8
0.320 0.528
0.361 0.572
0.790
0.790
0.790
0.836
From Figure 11, we observe that for moderate span length
(L/D<100), the combined beam - cable formulation gives a good
approximation of the first natural frequency. However, as L/D
increases beyond 150, care must be taken while estimating the
natural frequencies. Firstly, we observe that the beam effect now
diminishes rapidly. I.e. the straight cable approximation and the
beam - cable formulation gives asymptotically the same result.
However, the sag effect becomes important for such long spans. The
sag (the deflection at the mid span), 8o may for the pinned-pinned
boundary condition be estimated from:
80
Table 1. In-line natural frequencies. Span = 195 m.
57
qL2
8
other end is instrumented for axial force measurement. At the active
end, the arm of the pretension regulator governs the axial stiffness.
Here q is the submerged weight of the pipeline per unit length and:
e
=
,/,,~H,
As indicated in Figure 13, four different spans were modelled,
namely L = 4.7m, 7.0m, 9.0m and finally 11.4m. By the model scale
of 17.05, these spans in full-scale range from 80 m to 195 m, thereby
representing Leer/D-ratios from 100 to 350. The shortest span is close
to the length up to which DNV G14 presently is applicable.
(Eq. 4)
~t E1
As the sag of the span increases, the natural frequency based upon
(Eq. 2) may overestimate the frequency, as this approach assumes a
half-sine deflection, which may not be a valid approximation. If the
axial stiffness is high, the symmetric eigen-modes will be suppressed
as the axial deflection of the pipeline is restricted. However, if the
axial stiffness is low, either due to low shoulder (soil) stiffness or
interaction with neighbouring spans, the symmetric sine-shaped first
mode may still exist. The case of high shoulder stiffness is illustrated
in Figure 12, corresponding to case three of Table 1.
The variation of the span is practically solved in the model set up by
adding support points along the two end parts of the 11.4 m span.
The boundary condition simulated for the shorter free spans is
thereby closer to a partially clamped end condition, while for the
11.4m span, rotationally free end supports are simulated.
Test Results
For large sag and axial stiffness values, the natural frequency of the
single half wave (first symmetric mode) may be higher than the
frequency of the two half wave (first anti symmetric mode). The anti
symmetric modes are not affected by the sag. For a pure cable, the
combined effect of sag and axial stiffness on the natural frequency is
expressed through the parameter ~, which is given as:
=
qL .[. k
NEFF ~2NEFF
In the following a few examples are given on the measured dynamic
response of a very long free span were multimodal response can be
expected. The results are preliminary, as the analyses are not yet
completed. The example presented corresponds to case four in Table
1 and 2.
In Figure 14, the in-line results for a case with a low current velocity
is shown. The velocity corresponds to 0.2 m/see in full scale. We
observe a small in-line VIV response at the second in-line mode (ref.
Table 1). This frequency corresponds to a reduced velocity of 1.8.
The first in-line mode has a reduced velocity of 4.2. We should thus
expect this mode to be outside the in-line excitation range. No in-line
response is observed at this frequency.
(Eq. 5)
Here the axial stiffness of the pipeline is to be included in the
shoulder stiffness, k. As L--~ 0% the symmetric modes of oscillation
shifts to higher frequencies, while the anti- symmetric modes are not
affected by X. According to Triantafyllou, the frequency of the first
symmetric mode becomes higher than the first anti-symmetric mode
for X > 2n. The frequency of the second symmetric mode becomes
higher than the second anti-symmetric mode for L > 47t. The effect of
frequency shift is illustrated in Table 3, where the frequencies for X =
0 and ~.---~oo for the cases three and four of Table 1 and 2 are given.
Comparing the values of Table 3 with Figures 11 and 12, we observe
that f~ from the L = 0 case corresponds to the cable solution with no
sag and thus represents the first in-line natural frequency, fl for k--~
ov is close to the first natural frequency in cross-flow direction as
obtained by the finite sag approach. In Figures 11 and 12 the natural
frequencies as given in Table 1 and 2 are included. We observe the
good correspondence between the analytical and numerical results
for the first in-line and cross-flow natural mode. In addition we
observe the large amount of higher harmonics.
(Eq. 5)
k=0
X=0
NEFF
(kN)
337
337
610
610
f~
(sym)
0.061
0.183
0.082
0.246
f~
I
f3
I
f~
(asym) [ [ ( s y m ) (asym)
0.122
0.183
0.244
0.122
0.305
0.244
0.164
0.246
0.328
0.164
0.410
0.328
The cross-flow response for the current velocity of 0.2 m/see is
illustrated in Figure 15. We observe response at the frequency
corresponding first cross-flow frequency. Indeed, there are two
modes of oscillation at almost the same frequency in this case. The
response is, however, one order of magnitude less than the in-line
response. The small response at f=0.08 Hz, seems to be related to a
coupling to the in-line response at this frequency.
In Figures 16 and 17 the responses at a current velocity of 0.7 m/see
is shown. The spectra of the responses depend now on position along
the span. This demonstrates that higher modes of response are
involved. Figures 16 and 17 show the responses close to L/4. In
Figure 16 the in-line response is shown. We now observe that the inline response has shifted to about 0.45Hz. This seems to be crossflow induced in-line response, as the dominating cross-flow response
occurs at about 0.22Hz, Figure 17. From Figure 17 we also observe
that higher modes have a significant response. Work remain to
analyse these responses to identify if they are natural modes directly
excited by VIV, or if they are related to coupling effects between inline and cross-flow response. A close examination of the peak
frequencies of response reveals that the natural frequencies seem to
increase as the reduced velocity increases. This seems to be related to
two phenomena: As the velocity increases, the drag on the span
increases and thus the effective tension increases, causing higher
natural frequencies. Secondly, experience from 2D tests has shown
that in the lock-in range of reduced velocity, the added mass of the
cylinder may be significantly reduced, also causing an increase in
natural frequency. These effects will be investigated in more detail in
the ongoing work.
f,
(sym)
0.305
0.426
0.410
0.574
Table 3. Natural frequencies for zero and infinite k values. L/D =
350. Cable assumption.
MODEL TESTS
Test Arrangement
Figure 13 shows the test set-up. A truss girder of length 12m serves
as the support structure for the pipe. At one end there is the
mechanism for pretension and axial stiffness variation, while the
58
~-
o
r
CONCLUSION
The present paper has highlighted the need for an extension of
existing design guidelines on VIV induced fatigue into regimes of
higher L/D-ratios. As the structure stiffness goes from beam
dominated and into cable behaviour, also the implementation of
multiple modes must be given special attention.
{
~
NO
~
/
CFI~'"-~
CF~I,-.------.~, C F I ~
1-
0.5-
As part of the Ormen Lange field development, a systematic study on
VIV response for long free spans has been carried out, involving
numerical analysis, as well as laboratory tests. Consistency between
the two different approaches has to be verified. It is concluded that
there is a realistic potential for modifcation of existing guidelines in
order to allow longer spans for rigid pipelines, thereby reducing free
span intervention work.
O-
o~
0.4
o.e
o.0
1
1.2 U I,~t'm"'
Figure 3. VIV excitation in terms of current velocity.
FIGURES
SHORT SPAN
L/Ds 1 0 0
Typical Free Span Distribution, 20*inch pipeline
,.....
182
162
14.2
122
~
~
40
10.2
8.2
62
42
22,
0.2
•
•
:'..
•
•
•
".,*:"
4. . . . . . . . .
.
•
. .
•
DEAM BENAVIOUR
•
SINGLE
•
EXISTING
.
,
HALF WAVE
DNV-
...
.
GOVERNING
MODE
014
j
......
LONG SPAN
IdD ~ 2 0 0
130
30
230
Span
330
Length
430
•
•
•
530
[m]
Figure 1. Typical free span distribution for the Ormen Lange field.
CABLE DOMINATEDIBENAVIOUR
MULTIPLE MODE EXCITATION
NOT COVERED BY EXISTING DNV • G 1 4
Figure 4. Major parameters for short and long spans.
A/D
A/D
t.1
1o21"
CF1
Ib
CURRENT~
DISTR.
0.8"
0.6"
0,4-
~
0.2"
A/D
2
4
6
8
10
12
14
ROCKDUMPING
SPAN REOUCTION
16
U
VR = . . . .
f'D
O.1s r ~ / , , ~
DNV Guidelines No. 14
~. ~
~
U(n~s)
Figure 2. VIV requirements according to DNV Guidelines No. 14.
Figure 5. Design philosophy for conventional spans.
59
SHORT
SPAN
LONG
SPAN
, k f (H=)
L
AID
N=~,<
0
I¢~F
>0
CF1
~
C F ~
CF3o ~ . J ~ - ' e
1
~
,~,
0.5
~
.
.
/
.
"~"~" ~
0.2
~
j
~
.
C
F
4
e--~../-..j,
~"'--'~'-~~~r'--'-r~n,
0.4
0.6
0.S
1
1.2
U
(m/s)
Figure 6. Effect from NEF F o n VIV excitation regime.
Figure 9. VIV excitation, tensioned cable and no restraint.
Span = 195m. NEFF=610 kN. k =0 kN/m.
•
N~v
AID
N m
"N~I
+p,A,
INky
CWRRS~T
.......
O.5
aummm~
Nm
- N ~
Nm
,N~
,N~
N m
+peA.-pIA
>0
~0
. . . . .
wuo~
q
LO~IO SPAN
uHowr
0
SpAN
0.2
1.
0.9.
'
%
~..
"~
...
~ .,,.
• ~*
....
.
•
.
-I.
.
.
"
°
.
.
.
.
0.8 ;
-
.
.
,
.
,
.
". :.
.
.
.
~
o.e
1.z
~" ( m / s )
Sagging c~;bJe(Triantaf'~iou)
Cable w/o s a g
Equalion 2
Equation 2 w/o b e a m e f f e c t
Equation 2 w/o s a g e f f e c t
FEM vaJues, IL
FEM values, CF
o.7i ....
..
o.s
Figure 10. VIV excitation, tensioned cable and shoulder restraints
Span = 195 m NEFF=610 kN. k =5814 kN/m.
Figure 7. Laying and operation phases.
N~,lw|
ql
0.4
•
.
°
".
°
•
.
.
.
"
-•,
.
.
-
,
4-
L
N=F~ • N~u = + Nountx * N = ~
HIFp = I¢IUI.IRRIUM |QUIVALIB4T IFOROll
N~u I = F~JIIQN F O R C E
1
Nt~
N~
" "
¥
0,6 .
.
.
~
0.5-
.
0.3:
.-
.
.
.
-~-.i " 7 ~
0.2i . . . . .
o.11
t
N ~
N r
.
.
n =
:':= ~i-~...
k,~o:
00
50
100
150 "
200
250
360
350
400
LID
Figure 11. Natural frequency of free span as function of span length.
Computed according to various approximations. Tension
and stiffness values according to case four of Table 1.
Figure 8. Effect from longitudinal soil stiffness on natural
frequencies.
60
1
0.9
0.8
o.7
"G
Saggifig c al~Je"(Tfi anta Jyllou)
Cable w/o sag
E¢~Jation 2
.. EqJJa~On2 w/o beam effect
... Equation 2 wlo sag effect
. FEM values, IL
FEM values, CF
iI
. . . .
•
Spectrum, toO= 7.8522e-011
xl0 °
....
..
-r ......
T.........
/
P
i
l
0.6
~o.5
~o.~t
"--- 0,4
0.3
0.2
---..::: .......
0.1
00
100
-1"~>0
200
250
360"
"3,~0 "
~-0-(}-
"-
L/D
Figure 12. Natural frequency of free span as function of span length.
Computed according to various approximations. Tension
and stiffness values according to case three of Table 1.
0
0.1
0.2
0.3
0.4
0.5
0.6
Frequency (1/sec)
0.7"
0.8
0.9
Figure 15. Spectrum of measured cross-flow curvature close to the
end of the free span. Full scale current velocity 0.2 m/sec.
Case four of Table 1 (L/D=350).
Spectrum, toO= 4.8809e-008
x 104
~" A X I A l . S T I F F N E S S
~
PiPE
2.5
PRElrlENSlON
REGUtJkTO~t
Mr=ASUREMEWr
11413
/
12000
2
A
.... ? X ~ ~
"L
A
A
~
A1.5
= 4.7m. 7 . 0 m . 9.0m, t t . 4 m
LEI,~O : lOO, tso~ ~oo, ~SO
1
Figure 13. Test arrangement.
Spectrum, toO= 1.1354e-009
x I 0 "s
0.5
i
0.1
,A
0.2
0.3
J
0.4
0.5
01.6
Frequency (I/see)
0.7
0.8
A
0.9
i
4
Figure 16. Spectrum of measured in-line curvature close to the end of
the free span. Full scale current velocity 0.7 m/sec. Case
four of Table 1 (L/D=350).
3
2
\
C
0.1
--0.2
0.3
0.4
0.5
0.6
Frequency (l/see)
0 7
0 8
0.9
Figure 14. Spectrum of measured in-line curvature close to the end of
the free span. Full scale current velocity 0.2 m/sec. Case
four of Table I (L/D=350).
61
Spectrum, toO= 1.1297e-008
x 10"~
2.5
2
1.5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Frequency(llsec)
Figure 17. Spectrum of measured cross-flow curvature close to the
end of the free span. Full scale current velocity 0.7 m/sec.
Case four of Table 1 (L/D=350).
REFERENCES
DNV Guidelines-No. 14. "Free Spanning Pipelines", June 1998.
Paulsen, G., Soreide, T.H., and Nielsen F.G. "Submerged Floating
Pipeline in Deep Water", ISOPE 2000-HM-05. Seattle 2000.
Triantafyllou, M.S., Bliek, A. and Shin, H. "Dynamic analysis as a
tool for open-sea mooring system design". SNAME annual meeting
New York, Nov 1985.
62