NTNU
Norwegian University of Science and Technology
Department of Marine Hydrodynamics
PROJECT THESIS
Title:
Delivered:
20.06.2002
Modelling of wave induced motions of a SPAR buoy in MOSES
Availability:
Student:
Truls Jarand Larsen
Number of pages:
94
Abstract:
This work is based on the use of MOSES (MultiOperational Structural Engineering Simulator), which is an analysis
tool for almost anything that can be placed in the water. A quite comprehensive programming language that allows
you to do coupled analysis of Spar platforms in which damping effects from mooring lines and risers are included.
The diversity of the program is further expressed trough the handling of a newly explained phenomenon, the
Mathieu instability.
Alternative hull shapes with improved heave motion characteristics are investigated, showing increased heave
damping when differ from the classical hull shape.
The effect of mooring system on the linear motion response is investigated. It is seen that even a very stiff mooring
system has small influence on the linear wave frequency response.
The results from the coupled analysis show the importance of including mooring line dynamics and riser friction
when predicting the Spar response. The response was significantly reduced and the Mathieu instability
phenomenon was suppressed. Existing Spars have deep drafts to reduce the wave loads and consequently the
heave motion. Traditionally, the mooring line dynamics and riser friction were ignored in estimating the heave
response. Since this effect is important, the draft of the Spar can be reduced while maintaining an acceptable
heave response. Reduction in Spar hull draft can reduce fabrication costs substantially and as a result the Spar
solution will be more cost effective.
Keywords:
SPAR Buoy
Wave induced motions
Advisor:
Odd M. Faltinsen
MOSES
Address:
NTNU
Department of Marine Hydrodynamics
N-7491 Trondheim
Location
Marinteknisk Senter
O. Nielsens vei 10
Tel.
Fax
+47 73 595535
+47 73 595528
Acknowledgement
This project thesis has been written under the supervision of two people that I would like to
thank, Odd M. Faltinsen, supervisor from the institute and Jon Erik Borgen, supervisor from the
company (Inocean as).
In addition I would like to thank the department of Inocean in which I have spent most of these
twenty weeks.
This work concludes my education…
OSLO , ……/…….. - 2002
Truls Jarand Larsen
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Introduction
As a termination of my Master of Science degree in Marine Technology at the NTNU
(Norwegian University of Science and Technology) in Trondheim, I am writing a thesis at the
department of Marine Hydrodynamics in co-operation with Inocean as. This thesis is a
conclusion of a 20 weeks work, starting the 28th of January with a hand-in date the 20th of June.
The assignment has the title: “Modelling of wave induced motions of a SPAR buoy
in MOSES”, and the exact wording is:
“The candidate has to be familiar with MOSES (Multioperational Structural Engineering
Simulator) and find out its limitations in relation to wave frequency motions, slowly varying
motions in 6 degree of freedom and dynamic stability (Mathieu instability) in roll and pitch. How
MOSES handles currents, wind and viscous damping are details that have to be discussed.
Further on it will be clarified how currents in the moonpool and the effect of risers and mooring
are handled. The candidate will critically indicate any possible deficiency.
As a part of the thesis a calculation of the linear wave induced motions of a spar buoy
has to be carried out. These results are compared with the calculations done by Haslum in his
Dr. Ing theses [Haslum 2000]. At the end the candidate will investigate the influence of some
changes in the hullshape.
As far as the time allows it the candidate will implement the long wavelength model for
linear wave induced motions of a Spar, as in [Haslum 2000], where currents in the moonpool
are considered. Further on the model of Haslum for dynamical instability in roll and pitch will be
implemented.”
This assignment is based on the use of MOSES, which is an analysis tool for almost
anything that can be placed in the water. It is a quite comprehensive programming language
that I first got to know during a similar assignment in Stolt Offshore in Paris. I have considerably
improved my ‘MOSES-knowledge’ by working on this thesis.
All the linear results will be compared to [Haslum 2000]. In addition a non-linear time
domain analysis has been carried out. The results have been used to point out the instability
phenomenon as well as other aspects that may be of interest in relation to the time domain,
such as the extreme response during a long lasting (2 – 3 hours) hurricane.
One of the more interesting aspects of the assignment is to see how MOSES handles
the Mathieu instability. This part has therefore been emphasised in my work.
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Institutt for hydrodynamikk
Truls Jarand Larsen
Inocean as
As said, I will compare most of my results with the one produced in the Dr. Ing. Theses
“Simplified methods applied to nonlinear motions of spar platforms”, by Haslum. I will use his
results as a reference [Haslum 2000] throughout the report and have therefor chosen the same
dimensions of the Spar buoy. This applies to the linear response, RAO, as well as the time
dependent motions and the Mathieu instability phenomenon.
In addition to the above mentioned analyses, an evaluation of the coupled effects from
mooring line dynamics and riser friction will be carried out.
A lot of effort is made in doing the actual programming and to produce every single
result. Behind every figure presented in the assignment it is hidden many days of work. Even
though only a few results have been presented, lots of analyses have been carried out without
leading to the desirable results. This is explained in the belonging chapters.
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Executive summary
After creating the hull the linear motion response were calculated. They are expressed as
RAO’s and have been compared to the linear results produced by Haslum. The agreement
between the results is good and act as verification for the MOSES model. The effect of mooring
system on the linear motion response is investigated. To increase the effect from the mooring
system, the mooring lines were modelled quite stiff. Even very stiff lines had small influence on
the linear wave frequency response.
Next part of the thesis is based on the time domain. To get the wanted level of confidence from
the results a typical three hours hurricane analysis has been carried out, showing the heave
and pitch response for a moored buoy. While the deflections in pitch are quite large, the heave
response reveals the advantages of a Spar buoy. The hurricane used is a GOM hurricane with
Hs=12.2m and T=14sec, which produces a heave response at maximum one and a half meter.
To increase the damping in heave alternative hull shapes have been tried out. When altering
the lower part of the buoy, either by adding a circular disc slightly bigger than the rest of the
Spar or by increasing the diameter at the bottom section of the Spar, the heave damping
increases.
An interesting aspect of the assignment was to see how MOSES handles the Mathieu
instability. This instability is a quite newly explained phenomenon that is testified by
complicated theory. By showing this Mathieu instability in a time domain analysis, the program
reveals its diversity.
The results from the coupled analysis show the importance of including mooring line dynamics
and riser friction when predicting the Spar response. The response was significantly reduced
and the Mathieu instability phenomenon was suppressed. Existing Spars have deep drafts to
reduce the wave loads and consequently the heave motion. Traditionally, the additional
damping from mooring lines and risers were ignored in estimating the heave response. Since
this effect is important, the draft of the Spar can be reduced while maintaining an acceptable
heave response. Reduction in Spar hull draft can reduce fabrication costs substantially and as
a result the Spar solution will be more cost effective.
MOSES does not allow you to alter the parameters in the diffraction calculations. Consequently
to implement the long wavelength model for linear wave induced motions of Haslum (as
proposed in the introduction) is hard to accomplish.
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Table of contents
ACKNOWLEDGEMENT ............................................................................................................ 2
INTRODUCTION........................................................................................................................ 3
EXECUTIVE SUMMARY ........................................................................................................... 5
TABLE OF CONTENTS ............................................................................................................ 6
1.0 INOCEAN AS – A BRIEF PRESENTATION OF THE COMPANY ...................................... 7
2.0 MOSES – CALCULATION PROCEDURES AND GENERAL ISSUES ............................... 8
3.0 THE SPAR BUOY.............................................................................................................. 14
3.1
MOVEMENT OF THE SPAR .................................................................................................. 16
4.0 THE PROCESSES ............................................................................................................. 18
4.1
RAO- FREQUENCY DOMAIN ................................................................................................. 18
4.2
TIME DOMAIN ...................................................................................................................... 20
4.2.1 Low frequency behaviour .......................................................................................................... 20
4.2.2 The damping problem .............................................................................................................. 22
4.2.3 Hurricane analysis ................................................................................................................... 23
5.0 THE MATHIEU INSTABILITY............................................................................................ 26
6.0 COUPLING EFFECTS ....................................................................................................... 30
7.0 ALTERNATIVE HULL SHAPES ........................................................................................ 32
8.0 RECOMMENDATIONS FOR FURTHER WORK ............................................................... 35
9.0 REFERENCES................................................................................................................... 37
LIST OF FIGURES .................................................................................................................. 38
SYMBOLS AND NOMENCLATURE ....................................................................................... 38
APPENDIX ............................................................................................................................... 39
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Chapter 1
1.0 Inocean as – a brief presentation of the company
Inocean as was established in 1996 in Oslo, and also has offices in Stavanger and Houston.
Inocean is a technology company within naval architectural design, engineering and marine
operations, serving major offshore companies and ship owners at home and abroad. Inocean is
set to take part in the future development of floating structures and marine operations.
Engineering
Inocean deals with every phase of marine engineering, such as global and local structural
design and calculations, hydrodynamic and hydrostatic calculations, riser and mooring
calculations, technical drawing and documentation and the design of special tools.
Marine operations
Inocean analyses, plans, executes and leads marine operations and mobilises vessels for
offshore construction work. The company’s aim is to reduce offshore weather-related delays to
a minimum through using special tools and advanced simulations. Inocean also provides the
personnel needed to perform the actual offshore operations.
In-house design and products
Inocean offers a range of products, such as:

Lophius semi-submersible

Flexistinger

Anchor handling and stand-by design

Steel production L-riser design

3-CODS subsea drilling derrick
R&D projects
Inocean is currently engaged in joint R&D project on developing next generation propulsion
systems with industrial partners and research institutions.
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Chapter 2
2.0 MOSES – calculation procedures and general issues
As a part of this assignment it will be explained a few things about the MOSES’ calculation
procedure and the handling of some general issues in relation to analysis of the SPAR buoy.
This is important for the evaluation of the reliability in the results and in addition being able to
make a comparison with the results of the Dr. Ing thesis by Herbjørn A. Haslum. In this context
it is important to detect possible limitations regarding the program and critically indicate any
possible deficiency.
MOSES (Multi-Operational Structural Engineering Simulator) is a general-purpose simulation
program for the analysis of almost anything, which will be placed in the ocean. You can choose
the hydrodynamic theory you want to use and what kind of analyses you want to perform.
(Motions, stress, forces etc.)
An example of the syntax is shown below:
$Constants and units
&dimen –save –dimen meter m-tons
&model_def –save
&model_def –density 490 –emodulus 2.9E4
$
$Definition of the macro
Calls extern program
&insert macro
$
$Definition of the classes
~1
TUBE
42
0.75
-FYIELD 51.204
~10
TUBE
34
0.50
-FYIELD 34.136
$
$Element definition
BEAM 300
~1
*J100 *J101
BEAM 301
~10
*J101 *J102
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Geometrical properties
for the elements
Diplomoppgave NTNU
Institutt for hydrodynamikk
Truls Jarand Larsen
Inocean as
$Defines the co-ordinates for points
*J100
0.0
0.0
0.0
*J101
10.
0.0
0.0
*J102
20.
0.0
0.0
*J 10
10.
0.0
5.0
$
$Supplementary loads
Defines the
supplementary
punctual loads.
&describe load_group
MJNTS
*J101 1.75
$
&instate –loc spar 0 0 -202.5 0 0 0
Defines a position for the
Spar
Draft = 202.5 m
Trim = 0.4°
These are just a few examples from a Moses file. In addition to these commands, the specific
commands for performing the analysis and regulating the output (where and how) are many
and have to be adapted to each case.
For more details about the Moses files, see Appendix 2 and 3.
Stepwise and briefly explained, this is how MOSES function:
1.
Starting out by creating a model of a SPAR with specified degree of accuracy. This
is done by defining points at the end face of the cylinder followed by creating
panels between these points. The model is now a cylinder consisting of panels,
which has to be imparted with physical qualities that corresponds to the buoy, i.e.
mass distribution (center of gravity, partial loads etc.) and some material
properties. Further on you can model mooring and risers to include their stiffness.
The model is then ‘placed’ in equilibrium with specified draft, and all the hydrostatic
properties are then calculated.
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2.
Truls Jarand Larsen
Inocean as
By using the model and the geometry beneath the water surface, the potential
distribution of the pressure on the panels is given by the linearized Bernoulli
equation
p    ( gz 

)
t
(2.1)
where
  fluid density
g  acceleration of the gravity
z  depth
  velocity potential
By integrating the pressure over the body we obtain the hydrodynamic forces on a
portion of the body. The program now calculates the added mass, damping
matrices and in addition all the hydrodynamic properties.
3.
On basis of the hydrodynamic forces the linear motions in six degree of freedom
are estimated as the RAO (Response Amplitude Operator). This is straightforward
done by using the equations of motions for a freely floating body:
 (M
6
k 1
jk

 A jk )k  B jk k  C jk k  F j (t )
(j=1,…,6)
(2.2)
where
M jk  body mass
A jk  hydrodynamic mass (added mass)
B jk  damping coefficient
C jk  restoring coefficient

body movement
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Inocean as
F j  excitation force
The RAOs are considered as transfer functions and are further found by estimating
the coefficients in the equations of motions for each period defined, and finally end
up with the corresponding RAO. These are defined as vectors in six degree of
freedom and expresses the linearized wave induced motions in the frequency
domain.
Further on it is implied that the response is linear such that the RAOs can be
multiplied with a chosen wave spectrum, to finally obtain the response spectrum
(expressed as RMS values – Root Mean Square):
S x ( )  RAO ( ) S F ( )
2
(2.3)
where
S x ( )  response spectrum
S F ( )  wave spectrum
The major disadvantage with spectral response is that this response is applicable
to a single environment and thus the post processing options are limited.
4.
So far, all the static properties have been found. Next one wishes to analyse the
movements in relation to a time series. That leads us to the strength of MOSES,
the time domain.
As a starting point it utilises the hydrodynamic properties calculated in the
frequency domain to satisfy the basic equations of motion. These equations are
integro-differential. This means that the unknown is placed in an integral
expressed as the derived. In a linear system a known deceleration function is
included in the integrand. This deceleration function is estimated from the added
mass and damping coefficients, which are dependent on the frequency. This
requires great numerical accuracy that in practice can lead to inaccuracy.
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The program will persistent calculate and bring up to date the parameters like the
centre of buoyancy, waterplane area etc. as the buoy moves and the wet surface
changes. The hydrodynamic forces are calculated at the displaced position and the
finite amplitude effect of the changing waterplane area is taken into account. The
dynamics of the system are in other words taken care of and the non-linear wave
induced motions are found, i.e. the presence of one of the Mathieu instability
phenomena will be, according to the theory, detected during a time domain
analysis. The dynamic stability can be verified in all six degree of freedom. The
calculations are based on a current environment (wave spectrum, significant wave
height and peak period).
5.
A function allows one to scale the wave excitation force in the time domain. This
means that you can (in percentage) specify the interaction from the wave
excitation force on the model. For example zero, which results in the direct wave
force not being applied to the system. By this you can investigate the low
frequency behaviour, i.e. slowly varying motions.
6.
Currents and wind can easily be modelled by specifying the characteristic area and
defining the velocity and direction of the load. As an alternative the wind can be
specified by a wind spectrum. Effects from wind and currents are however not
applied in this model.
7.
The program allows you to model the SPAR with risers and all the geometrical
gadgets inside the moonpool. It is difficult to predict how the program manages to
simulate the complexity inside the moonpool with respect to the damping and the
added mass effects, but it is likely to think that the problem will not be handled
satisfactory. Alternatively the buoy can be sealed at the bottom and regarded as a
closed cylinder. This is not far from the reality, since the actual opening in the
moonpool, between the risers and the buoyancy tanks etc., is quite small. The
model used here is therefor considered as a closed cylinder.
8.
At last in this brief MOSES ‘introduction’, a few words about the environment.
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Inocean as
It is possible to choose wave spectrum (ISSC or JONSWAP) or any sized regular
wave, represented by the direction, the wave height and peak period.
The wave is represented by a cosine wave
 =  a cos(t + kx cos + ky sin)
(2.4)
 = wave heading
R = RAO cos(t + )
 = phase lead
The environment directions are as follows:
270°
y
315°
x
O
225°
0°
180°
45°
135°
90
°
Fig. 2.1. MOSES Reference [Larsen 01]
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Chapter 3
3.0 The Spar buoy
A spar platform is a large vertical circular cylinder with a large draft that reduces the heave
response significantly and permits rigid risers and surface trees, i.e. the motion response are
crucial for the Spar buoy. Configured with oil storage and surface completed well, a spar may
be able to combine the best characteristics of the TLP (Tension Leg Platform) and FPSO
(Floating Production Storage and Offloading) for fields where the reservoir can be reached from
one drilling centre [CMPT 1998].
Fig. 3.1. Isometric view with mooring
Fig. 3.2. Front view with mooring
When creating the hull, different levels of accuracy were tried out. First a hull was created in a
program called Femgen. The model was made by horizontal panels every 10th meter and 17
panels vertically, before it was converted into a MOSES model. This gave a large number of
panels, which was unpractical to work with. To cope with this problem, MOSES has a function
that allows you to refine your model at a specified level of accuracy. All the horizontal panels
were then deleted and left a model consisting of seventeen vertical panels. This made the work
easier and not so time demanding. As explained earlier, the reproduction of the hydrodynamic
database required a lot of time. By using a quite rough mesh this was no longer a problem.
When the analysis required several different databases (different range of periods), the mesh
was chosen quite rough and a fine mesh was chosen when the database was used for the nonlinear analyses. Different accuracy in the mesh, showed however good agreement when
comparing some of the results.
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Truls Jarand Larsen
Inocean as
The main particulars of the spar used in this assignment are the same as used in [Haslum
2000], except some small adjustments in the diameter to obtain the hydrostatic properties as
correct as possible. After the impartment of the geometry, MOSES calculated a centre of
buoyancy too low, compared to the spar in [Haslum 2000]. This lead to negative GM. By adding
more buoyancy in the upper section, the centre of buoyancy ascended and the GM value
became closer to the actual one.
A lot of work has been put down to verify the MOSES model and consequently be able to
compare it to the model of [Haslum 2000]. Many of the static properties not given in the Dr. Ing
thesis, but calculated by MOSES, have been verified by means of hand calculations. MOSES
calculates most of these parameters using the input properties, and it is therefore useful to do
this verification in order to control the input as well. Here are a few examples:

By stability reasons the GZ value has to be positive during a time domain process. This is
continuously verified.

Making the hydrodynamic database is time demanding and has to be done for a range of
specified frequencies. A need for different periods arises when producing different kinds of
linear results. Consequently the hydrodynamic database has to be changed and adapted.
In addition to the things mentioned, lots of extra work is required to get the wanted results. This
is mostly time demanding work, which is not explicit shown in this report.
The main particulars of the spar are shown below:
Draft (d) = 202.5m
Diameter (D) = 36.4m (Haslum D=37.5)
Radius of gyration Rxx=80 Ryy=80 Rzz=36.5
Centre of gravity (KG) = 105.25m
Metacentric height (GM) = 3.11 (Haslum GM =4.4m)
Natural period in heave TN,3= 31.3sec
Natural period in pitch TN,5= 95.9sec
The spar is moored with a 16 points taut system, as shown in fig. 3.1 and fig. 3.2. The fairleads
are situated vertically at the centre of gravity and on the outside of the spar body. The
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Inocean as
pretension in each fairlead is set to 400 kN. A discussion of the mooring lines and their
influence on the linear wave frequency motions will follow later.
In the effort of modelling the right mooring system, different parameters have been evaluated
and tried in the model. The pretension, the weight and the e-modulus of the lines are
parameters that are continuously changed and adapted. The whole process culminated in
modelling an equivalent mooring line at each fairlead.
However, to detect the Mathieu instability in section 5.0 the mooring lines are deactivated.
3.1
Movement of the SPAR
A right hand co-ordinate system is applied as illustrated in fig 3.1.1.
Heave (z)
yaw
pitch
Sway (y)
roll
Surge (x)
Fig 3.1.1.The six degrees of freedom
Existing spar platforms have deep drafts to reduce the wave loads and consequently the heave
motions. Traditionally, the damping from mooring lines and risers was ignored in heave
response analyses. By simultaneously predict the dynamic response of the spar, mooring lines
and risers one has revealed that mooring lines dynamics and riser friction can have significant
effect on the spar heave response. As a consequence the draft of the spar can be reduced and
still maintain an acceptable heave response. Reduction in spar hull draft can reduce the
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Inocean as
fabrication and transportation costs, which will result in making spar solutions more cost
effective. [OTC 12082]
Important ‘types’ of motions are the slow drift motions. They are caused by non-linear effects
from waves, wind and currents. These motions arise from resonance oscillations and appear in
surge, sway and yaw for a moored buoy. Low frequency behaviour is considered in section
4.2.3.
In addition to the slow drift motion (low frequency) a floating structure can experience wavefrequency motion, high-frequency motion and mean drift. Linear excitation forces mainly cause
the wave-frequency motion, while the high-frequency motion and mean drift are caused by
resonance oscillations [Faltinsen 90].
Damping form the risers is caused by Coulomb friction at the riser guides and the keel as well
as from hydrodynamic forces. The risers exert a normal force on the Spar that increases as the
Spar pitches or offsets laterally. If the heave response is small enough, the static friction on the
guides will prevent the Spar from moving further. If the motions are larger, the friction opposes
the heave motions and will consequently produce damping. In addition to the damping,
coupling forces between the risers and the Spar occurs in both surge/sway and pitch/roll. When
predicting the Spar response, summation of all the risers are important.
When the Spar offsets from the mean position the mooring lines will provide restoring forces.
The lines will go slack or taut as the buoy moves. This causes drag load on the lines, which
provides damping to the Spar. However, the damping is more pronounced on the heave motion
than on surge/sway or roll/pitch motions. The current induced drag on the lines can as well
change the restoring force characteristics on of the mooring lines, and are thus useful to
consider [OTC 12082]
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Chapter 4
4.0 The Processes
Both the time domain and the frequency domain process give adequate solutions in most
cases. The time domain process does properly account for all aspects of a problem but is
computationally expensive. A solution in the frequency domain is in many cases a good
alternative solution, which is much less time demanding.
The theory behind the time and frequency domain is explained in section 2.0.
4.1
RAO- frequency domain
The movements of the SPAR are expressed statically by the RAO (Response Amplitude
Operator) as a function of the six degrees of freedom (Surge, sway, heave, roll, pitch and yaw).
In the following figures, a presentation of the linearized motions in heave, pitch and surge are
given. The calculations are done with and without mooring and the results are shown in the
same diagram.
How MOSES calculates the transfer functions, are explained earlier in section 2.0.
SPAR
20
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
Pitch [deg/m]
Pitch [deg/m]
SPAR
Moored
Free floating
15
10
5
0
0
10
20
30
40
50
88
90
92
94
96
T [sec]
T [sec]
Fig. 4.1.1. Pitch RAO Two frequency intervals, to illustrate the natural period in pitch.
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98
100
102
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SPAR
0.8
16
14
12
10
8
6
4
2
0
0.7
Surge [m/m]
Heave [m/m]
SPAR
Moored
Free floating
0.6
0.5
0.4
Moored
0.3
Free floating
0.2
0.1
0
5
10
15
20
25
30
35
40
45
0
0
T [sec]
Fig. 4.1.2. Heave RAO
5
10
15
20
25
T [sec]
30
35
40
45
Fig. 4.1.3. Surge RAO
The spar is floating with a draft d=202.5m. The main particulars of the spar are given earlier in
section 3.0.
However, the transfer functions (RAO – Response amplitude operators) are defined as the
frequency dependent steady state motion response amplitude divided by the wave elevation
amplitude [Haslum 2000]:
RAOi(T) =
i
[m/m]
a
(4.1)
i = [1,2,3,4,5,6] = degrees of freedom
In the Dr. Ing thesis by Haslum, these RAO’s are calculated using two different simplified
methods (Long wavelength approximation and McCamy and Fuchs theory) and the panel
method program WAMIT [Haslum 2000]. The agreement between the three methods shown in
[Haslum 2000] is good, as well as the agreement between Haslum and the MOSES-results
presented here.
As earlier explained, the mooring system used is very stiff to increase its effect. Despite this the
influence from the mooring is quite small and especially the heave motion that is practically
identical with the free floating spar. The RAO calculations are performed at a water depth = 700
meters. As production systems extend to water depths beyond 1000 meters, the effects of
mooring become increasingly significant when predicting the Spar’s response. For these water
depths, the viscous damping, inertial mass, current loading and restoring effects should be
included to accurately solve the system’s motion response. By coupling the mooring as well as
the riser with the Spar’s motion typically results in a reduction in extreme motion response
[OTC 12083].
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Fig. 4.1.4 show that pitch and surge
motions are in phase with each other,
Free floating SPAR
and they are 90 degrees out of phase
200
150
compared to the wave. This means
Phase [deg]
100
50
Heave
0
-50 0
10
20
30
40
50
Pitch/Surge
that they are contributing to
displacements of the deck
-100
-150
simultaneously. It is shown that the
-200
T [sec]
heave between T=11sec and T=31
sec is 180 degrees out of phase.
Fig 4.1.4. Difference of the phases
The linear frequency motion response (RAO’s) for all the six degrees of freedom are shown in
Appendix 4, presented as “motion response operators”.
4.2
Time domain
The calculations done in the time domain are quite complicated, and interpreting time series of
the Spar response may be troublesome. When the damping is low, a transient from the start
exists for a long time. The simulations done here have consequently at least a 1500 seconds
duration, where the response has reached a steady state.
Initiating a time domain simulation in MOSES is not very complicated. The decisive part to get
reliable results is to have a stable Spar that reflects the reality as best as possible before
starting the time domain calculations. After doing this calculation once, it is possible to retrieve
all kinds of results related to the time domain.
A more thorough explanation of the time domain is given in section 2.0 and is also explained in
[MOSES manual].
4.2.1 Low frequency behaviour
For a moored spar buoy low frequency motions occurs in surge, sway and yaw. Low frequency
motions are resonance oscillations exited by second order, non-linear coupled effects between
the wave and the spar [Faltinsen 90].
- 20 -
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Inocean as
For moored large structures as the Spar, the natural periods in the horizontal degrees of
freedom are much larger than the wave periods with considerable energy. The horizontal low
frequency excitation is in general larger than the linear wave frequency motions, despite the
fact that second order difference frequency forces (1) are generally an order of magnitude
smaller than linear wave frequency forces. This effect is therefore important in relation to the
design of the mooring system [Haslum 2000.]
As explained earlier, the design philosophy behind a deep draft Spar, implies that the draft is
adequately large to reduce the heave response. The natural periods in heave, pitch and roll is
significant larger than wave periods containing important energy. Consequently the second
order excitation forces may contribute to the total motion response in vertical degrees of
freedom. This motion is a limiting factor for Spar production platforms, with regard to the design
of rigid risers and for the drilling operations [Haslum 2000].
In fig. 4.2.1.1 the low frequency surge motion is illustrated as well as the air gap in fig. 4.2.1.2.
The environment used is an ISSC spectre with Hs=7m and T=12sec.
0.2
Surge [m]
0
-0.2 0
500
1000
1500
-0.4
-0.6
-0.8
-1
-1.2
-1.4
-1.6
T [sec]
Fig. 4.2.1.1. Low frequency surge motion for the 202.5m draft spar.
35
Air gap [m]
30
25
20
15
10
0
500
1000
1500
2000
T [s e c]
Fig. 4.2.1.2. Air gap, simultaneously recorded as fig. 4.2.1.1
Second order difference frequency forces occur due to bi-spectral interaction in bicromatic waves. Such second
order forces may be represented by quadratic transfer functions, which are dependent on the wave frequencies of
the two interacting waves and independent the wave amplitudes [Haslum 2000].
(1)
- 21 -
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To simulate the low frequency motions in MOSES the direct wave force has not been applied.
This simplifies the calculations by allowing investigating this effect without having to use small
time steps to cope with the high frequency behaviour.
The response of the Spar is quite complex especially because of the interaction between wave
frequency and low frequency motions in surge pitch and heave.
4.2.2 The damping problem
As a starting point MOSES uses the equations of motion. By supposing that we know the
solution at time t1 we can estimate the solution at time t2. After a few steps the equations of
motion can be written:
S[q(t2) –q(t1)] = s
(4.2)
where
S = cI + fC + K and
s = s – [aI + dC] q(t1 ) -[bI + eC] q (t1 )
a = 1 - 1/2
b = - (1/)
c = 1/2
d = (1 – /2)
e = (1 – )
f = 

How the problem is further solved is explained in [MOSES manual]. The customised
parameters for the damping problem are the Newmark parameters and  To detect the
instability phenomenon in section 5.0, the default values .25 and .5 were used. There is almost
no numerical damping with these values. In fact, for some problems, the scheme results in
small negative damping. This is of no concern here. If these values are changed from the
default to .33 and .66, then a small bit of numerical damping is induced. For problems such as
- 22 -
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decay problems in calm seas, the defaults do not work very well. The following figure illustrates
this effect for the heave decay of the Spar.
-97.14
-97.16 0
200
400
600
800
1000
Heave [m]
-97.18
-97.2
-97.22
-97.24
-97.26
-97.28
-97.3
3366
255
-97.32
T [sec]
Fig. 4.2.2.1. Effect of Newmark parameters
These results are found for the Spar at draft = 202.5 meters and no mooring. A regular wave
with H=5m and T=10 seconds was used.
4.2.3 Hurricane analysis
The length of the simulation should be chosen such that it will give a specified level of
confidence. To avoid the transient from the start of the simulation and to ensure that the
response has reached a steady state the following results are based on a three hours typical
GOM (Gulf Of Mexico) hurricane condition with Hs=12.2m and T=14seconds. An ISSC spectre
is used.
- 23 -
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Inocean as
-96.2
-96.4
0
2000
4000
6000
8000
10000
Heave [m]
-96.6
-96.8
-97
-97.2
-97.4
-97.6
-97.8
T [sec]
Fig. 4.2.3.1. Heave response for a three hours hurricane
It is quite remarkable that despite the rough environment, the heave response is no more than
one and a half meter at most. As explained earlier this is due to the large draft and probably the
taut mooring system. As opposed to the linear motions, the second order motions produced
during a time domain are clearly affected by the restoring forces from the mooring lines. In
addition one should take the damping effect of the risers in account. These would have had an
additional damping effect on the heave motions, as will be shown later in section 6.0, where a
fully coupled analysis will be carried out.
During the same hurricane the pitch response was recorded, and shows relatively large
deflections, with a maximum at almost 9 degrees pitch amplitude.
6
Pitch [deg]
4
2
0
-2
0
2000
4000
6000
8000
10000
-4
-6
T [sec]
Fig. 4.2.3.2. Pitch motions during a three hours hurricane
The evaluation of forces in the four mooring lines is as well investigated. During a 1000
seconds ISSC spectrum environment, with significant wave height at 12.2 meters and a zero
- 24 -
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up-crossing period at 14 seconds, the force magnitude in the four anchor lines are recorded.
They are shown in Appendix 4, labelled “connector force magnitudes”. These results are not
discussed, they are attached to illustrate one of the possibilities in retrieving results.
- 25 -
Chapter 5
5.0 The Mathieu instability
Under certain conditions, spar platforms can be exposed to large unexpected motions. This is
explained by the Mathieu instability phenomenon, and occurs because of two specified
situations. The first and simplest case is trigged due to an abrupt change in waterplane area
and therefor a change in the heave restoring force. This is the case when the hull cross section
area changes along the height (Fig. 5.1) [Haslum 2000].
The heave response of this hull shape has been calculated in the linear frequency domain,
shown as the RAO, and by the non-linear time domain method.
Calculating the hydrodynamic exciting forces at the mean position
produces the RAO, according to the linear theory explained earlier. In
time domain, the hydrodynamic forces are calculated at the displaced
position and the effect of the changing waterplane area is taken into
account.
The unstable wave period is expected in the vicinity of
Fig 5.1
[½TN, TN, 3/2TN,…], where TN is the natural period in heave. This is
obviously dependent on the system damping. According to the theory presented in [Haslum
2000] there should be a critical wave period at ½TN = 16.5 sec. By calculating the heave
response in frequency and time domain, one should expect a disagreement between the
methods at wave periods around 16.5 sec. The model used in MOSES did not show this
difference. This kind of instability is quite sensitive when it comes to viscous damping, and the
results obtained are probably a consequence of the damping applied to the model.
The other situation that provokes the Mathieu instability is a heave/ pitch amplifying interaction.
It may occur even if the hull has a constant cross section. One should expect this instability at a
certain wave period that is a function of the natural period in heave and pitch:
TW ave 
1
1
TN , 5

1
TN , 3
where
TN ,3  natural period in heave
- 26 -
(5.1)
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TN ,5  natural period in pitch
When a wave at this frequency occurs, the heave motion will oscillate with both the natural
heave frequency and the wave frequency. This produces an envelope process. For a certain
wave period, this envelope period coincides with the natural period in pitch, and you get the
equation explained above.
For the spar used here (see fig 5.1) with a natural period in pitch TN,5=106,0 sec, and a natural
period in heave TN,3=33,0 sec, this critical wave period is:
TW ave 
1
1
1

106 33
= 25,2 sec
By calculating the heave and pitch response in both frequency and time domain, this critical
wave period is found when the two methods disagree. As fig. 5.2 and fig. 5.3 show, the
agreement between the two methods is good, except for Twave= 25,5 sec.
Pitch motions, H=10m
14
Frequency domain
Time domain
Pitch [deg]
12
10
8
6
4
2
0
0
5
10
15
20
25
30
35
40
T [sec]
Fig 5.2. Illustration of the Mathieu instability phenomenon in pitch, shown by a disagreement between the
frequency and time domain.
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Heave motions, H=10m
50
Heave [m]
40
Time domain
Frequency domain
30
20
10
0
0
5
10
15
20
25
30
35
T [sec]
Fig 5.3. Heave motions. The Mathieu instability phenomenon is shown by the disagreement between the
frequency and time domain.
To produce the time domain results, a regular wave with H=10m was used and the steady state
amplitude was measured. In order to compare the two methods the RAO’s were multiplied by
the wave height.
A great effort has been made in producing the time domain results. Since MOSES only allows
defining one period at the time, the simulation has been carried out for each period. This is a
quite time demanding task. In addition each simulation has been run with different levels of
damping, different hull shapes and different types of environment. The alteration of the
Newmark parameters (damping) is thoroughly explained in section 4.2.2.
MOSES does not calculate the exact natural periods for a system, but allows you to investigate
them by looking at the RAO’s for different degrees of freedom. This means that the natural
periods given here are manually found at the peak of the RAO curves. This is probably the
explanation why MOSES gives the highest heave amplitude at Twave=25,5 sec. Anyway, it is in
the vicinity of the period T=25.2 sec calculated from the formula (5.1).
The envelope process of the heave motion is then illustrated by the first 400 seconds, before
the instability accrues at approximately 1100 seconds. The Illustration in fig. 5.4 shows that the
envelope for the heave motion has the same period as the natural period in pitch (T=106 sec),
i.e. the heave envelope trigs the pitch instability.
- 28 -
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Fig 5.4. The envelope process of the heave motions.
T=25.5 sec. H=10m
Generally, this effect is caused by two frequencies in the signal. When these frequencies are
close, the envelope period is large and the effect is clearly pronounced. Hence the envelope
effect is reduced if the frequencies are moved apart. This effect is caused by the amplifying
pitch/ heave interaction.
The non-linear heave excitation causing the instability can also be explained if considering the
displaced position instead of the mean position. The vertical component of the horizontal 1 st
order total force when the Spar has a pitch inclination explains this effect [Haslum 2000]. See
figure 5.5.
Fig. 5.5. Second order heave force contribution due to surge and pitch interaction.
- 29 -
Chapter 6
6.0 Coupling effects
When predicting the Spar response the effect from mooring line dynamics and riser friction is
important. Their contribution to the total damping can constitute several meters in the Spar
response. Results of this coupled analysis reveal that mooring and risers have significant effect
on the Spar heave response. A characteristic feature of a Spar platform is the slow oscillatory
motion that occurs at resonant frequencies. The damping is low at resonant periods and correct
estimation of the damping is therefore important to get reliable results [OTC 12082].
Concerns about excessive heave and pitch response of Spar arising from the Mathieu
instability have been raised for long period waves (See section 5.0). This instability occurred for
the Spar shown in fig. 5.1 without mooring lines and riser effects included. A new analysis was
carried out including these effects showing the Mathieu instability being suppressed. The heave
response is shown in fig. 6.1.
-80
500
-85
1000
1500
2000
2500
3000
Heave [m]
-90
-95
-100
-105
-110
-115
-120
moored with risers
free floating
T [sec]
Fig. 6.1. Heave response. Two cases: 1) free floating and 2) coupling effects included. Regular wave, H=10m and
T=25.5sec
Two cases are presented in the figure. The heave response for a free floating Spar, i.e. no
additional damping and coupling effects from mooring and risers included. The mooring lines
used are described earlier in section 3.0, and the riser system consists of 16 risers each with a
diameter= 346mm and a pretension= 100 kN. As tried with the mooring system, the risers were
modelled as one equivalent riser with pretension equal the sum of the 16 risers. The problem
arising with the introduction of an equivalent riser, was the adaptation of the stiffness and
- 30 -
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weight and attachment to the seabed. With 16 separate risers, the separation of the
attachment points at seabed gives a certain effect, which is probably not taken care of by one
equivalent riser.
The results show the importance of including all the damping effects in predicting the response
Pitch [deg]
under resonance conditions. This type of
8
6
4
2
0
-2500
-4
-6
-8
analysis is conservatively done by
excluding the damping from mooring and
700
900
1100
1300
1500
1700
1900
moored, with risers
free floating
risers and does often lead to Spars with
hull draft greater than necessary. A
reduction in the draft will reduce the costs
significantly [OTC 12082].
T [sec]
Fig. 6.2. Pitch response. Coupled and uncoupled with
mooring and risers.
As well as the heave motions, the
resonant pitch response is substantially
reduced by including the effects from mooring and risers. Fig. 6.2 shows the
pitch response from the same analysis as in fig. 6.1. The uncoupled pitch response shown is
the Mathieu instability response. According to analysis done [OTC 12082] the coupled effect
gets even more important when operating in deep sea.
The response characteristics for a Spar are fairly complex due to the interaction of wave
frequency and low frequency motions. When coupling the effects from mooring and risers with
the vessel response, large reductions in extremes are obtained. As explained, these reductions
are important to take into the design of the mooring lines and risers in an early stage.
Finally, there is a role for coupled analysis in the validation of the design, in particular when
designing deep water Spars where lack of experience is a problem. The limitations of model
basins to access the full vessel/ riser/ mooring system in very deep water makes the ability to
accurately simulate coupled effects practically a requirement for new systems [OTC 12083].
Not many computer programs can handle these effects. Coupled results from MOSES in
relation to a Spar buoy, as presented here, are therefore useful and have a certain commercial
value.
- 31 -
Chapter 7
7.0 Alternative hull shapes
It is because of its relatively low damping in resonant motions and low natural period in heave
the classical spar (hull I, Fig. 7.1) may experience the large heave motion explained. According
to [Haslum 2000] some measures are possible to reduce the heave response:
1.
Increase the damping in heave
2.
Increase the natural heave period out of the wave energy region
3.
Reduce the linear heave excitation force
Fig. 7.1 shows alternative hull shapes to cope with these three points. The first point is in
theory dealt with by adding a circular disk at the
bottom of the spar (hull II). The heave response
for hull shape II from a time domain analysis is
illustrated in Fig. 7.2. The time domain shows
small deviations from the classical spar (hull I).
The RAO’s were also calculated without
Fig. 7.1. Alternative hull shapes
showing any major differences between the two hulls. It is however uncertain whether or not
the results are comparable. The physical properties are changed as a consequence of the
geometrical differences and the results compared here are the actual heave motion for each
spar.
heave [m]
-96
500
-96.5
700
900
1100
1300
1500
-97
-97.5
-98
hull shape I
-98.5
hull shape II
T [sec]
Fig. 7.2. Heave response from an ISSC spectrum with Hs=10 m and T=14 sec. Two different hull shapes are
considered.
- 32 -
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Especially hull shape III has major differences in centre of gravity, metacentric height etc. To
deal with this problem in a different manor, the damping coefficients in heave for the three hull
shapes have been compared. They are shown in fig. 7.3.
The second point, increasing the natural heave period, is done by adding a pontoon at the keel,
i.e. hull shape III has a natural period in heave higher than the classical spar.
An increase in the added mass increases the diffraction term and thus reduces the heave
excitation force. For example adding a disk at the keel will in theory increase the added mass,
but practical tests shows that the disk has to be very large to have an important effect on the
heave excitation force. It is practical troublesome to construct spars with large disks [Haslum
2000]. Hull shape III however, shows large added mass coefficients in heave for a given
Damping coeff. [-]
interval of periods compared to hull I and II.
0.0016
0.0014
0.0012
0.001
Hull shape III
Hull shape II
Hull shape I
0.0008
0.0006
0.0004
0.0002
0
0
5
10
15
20
25
30
35
40
T [sec]
Fig. 7.3. Heave damping coefficients for three different hull shapes
The damping coefficients are normalized by the mass of the buoy and express the linear heave
damping (exclusive of added mass effects).
This figure confirms the theory explained. Hull shape III produces at the most fifteen times the
damping of hull I and II (T=20sec), and hull shape II has a few percent more damping than hull
I. This difference is slightly expressed in the heave response during a time domain analysis,
shown in fig. 7.2. In addition to these structural changes, increasing the draft can reduce the
heave response. This is an expensive measure and is seldom the solution used for a spar
buoy.
The three hulls shown in fig. 7.1 are the same as used in [Haslum 2000]. Hull shape I is the
classical spar shaped as a cylinder. Hull shape II is the same cylinder with a cylindrical disk at
bottom. The disk diameter is 1.32D, where D is the cylinder diameter and the thickness=0.2m.
- 33 -
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The last hull shape consists of two cylinders. The upper is the same as hull I and the bottom
cylinder has a diameter=2.596D and height=30m.
The idea behind the increased heave damping, together with the use of this enormous hull is
that due to the counteracting diffraction force and the large draft, the motion response of the
platform should be adequately low to permit installation of rigid risers with dry wellheads.
Therefore, the motion response (in particular heave and pitch) is crucial for the concept.
- 34 -
Chapter 8
8.0 Recommendations for further work
Wave induced motions on a Spar buoy are presented. Motions in frequency and time domain
are calculated and illustrated. An analysis including mooring line dynamics and riser friction is
also presented. In addition, there are some issues in relation to wave induced motions on a
Spar that are not treated in this thesis. These issues are useful to consider in an overall
evaluation.
Effects produced by wind forces and currents are not applied to the MOSES model. They will in
some cases affect the Spar motions. Especially low frequency motions can be caused by wind
gusts with significant energy at periods at the order of magnitude of a minute. This is due to the
high natural periods of the Spar [Faltinsen 90].
A well known phenomenon in many fields of engineering is resonance oscillations caused by
vortex shedding, typical for cylindrical shaped structures as the Spar. To avoid these vortexinduced oscillations, helical strakes are often used (see the illustration in Appendix 1). To
control the instability in pitch that is discussed, more pitch damping is required. Helical strakes
contribute to this kind of damping and will consequently play a part in suppressing this
instability [Faltinsen 90]. An analysis with helical strake should be carried out.
In section 7.0 alternative hull shapes have been tried out, in the effort to increase the damping
in heave. By further investigating the effect of different hull shapes, one should be able to find
an optimisation of the Spar hull with respect to the heave motion. By optimising the hull with
respect to one degree of freedom, it will probably affect the motion characteristic of the buoy in
the other modes. To which extend this geometrical change will affect the motions of the buoy,
should be investigated,
The flooded centerwell of the Spar called moonpool, may have some effects on the motion
characteristics. For the classical Spar the natural period of the vertical fluid motion is close to
the natural period of the platform in heave. This makes it sometimes difficult to simulate. In
cases where the moonpool is constructed for large equipment to be lowered through it, the
passage between the risers is quite large. The simplified method of considering the Spar as
closed at the keel, is in such cases probably too simple. The resonance response of the water
column could be important [Haslum 2000].
- 35 -
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The Mathieu instability phenomenon could as well be studied more carefully. The effect of
altering the wave amplitudes and the wave periods on the instability, could be examined. This
problem is treated in [Haslum 2000], where the results are presented as a 3-D chart, to
illustrate the influence from the wave amplitude at the range of periods where the instability
occurs.
In addition to the mentioned means, there are a lot of possibilities in the use of MOSES. Once
the time domain simulation has been turned successfully, several results have been produced
and stored in a database. It is then possible to specify the result wanted, everything from
evaluation of the forces in the risers to stability verifications of the buoy.
- 36 -
Chapter 9
9.0 References
1.
The Centre for Marine and Petroleum Technology (CMPT) (1998). Floating Structures:
a guide for design and analysis, Volume One.
2.
The Centre for Marine and Petroleum Technology (CMPT) (1998). Floating Structures:
a guide for design and analysis, Volume Two.
3.
Faltinsen, Odd M. (1990). Sea loads on ships and offshore structures. Cambridge
University Press.
4.
Haslum, Herbjørn A. (2000). Dr. Ing thesis: Simplified methods applied to nonlinear
motions of Spar platforms.
5.
OTC 12083 (Offshore Technology Conference - 2000). Coupling effects for a
deepwater Spar.
6.
OTC 12082 (Offshore Technology Conference – 2000). Effects of Spar coupled
analysis.
7.
OTC 12085 (Offshore Technology Conference – 2000). Deepwater nonlinear coupled
analysis tool.
8.
Larsen, T. J. Projet de fin d’etudes (2001). Motion and stability analysis of a pipelay
vessel (barge and stinger). Stability verifications of a buoy launch from a barge.
9.
MOSES manual. Ultramarine Inc. Offshore Engineering Software
(www.ultramarine.com)
- 37 -
List of figures
Figure 2.1
Figure 3.1
Figure 3.2
Figure 3.1.1
Figure 4.1.1
Figure 4.1.2
Figure 4.1.3
Figure 4.1.4
Figure 4.2.1.1
Figure 4.2.2.1
Figure 4.2.2.1
Figure 4.2.3.1
Figure 4.2.3.2
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 6.1
Figure 6.2
Figure 7.1
Figure 7.2
Figure 7.3
MOSES reference
Isometric view with mooring
Front view with mooring
The six degrees of freedom
Pitch RAO. Two frequency intervals, to illustrate the natural period in
pitch
Heave RAO
Surge RAO
Difference of the phases
Low frequency surge motion for the 202.5m draft Spar
Air gap, simultaneously recorded as fig. 4.2.1.1
Effect of Newmark parameters
Heave response for a three hours hurricane
Pitch motions during a three hours hurricane
Spar platform
Illustration of the Mathieu instability in pitch, shown by the
disagreement between the frequency and time domain
Heave motions. The Mathieu instability phenomenon is shown by the
disagreement between the frequency and the time domain
The envelope process of the heave motion, T=25.5sec, H=10m
Second order heave force contribution due to surge and pitch
interaction
Heave response. Two cases: 1) free floating and 2) coupling effects
included. Regular wave, H=10m and T=25.5sec
Pitch response. Coupled and uncoupled with mooring and risers
Alternative hull shapes
Heave response from an ISSC spectrum, with Hs=10m and T=14sec.
Two different hull shapes are considered
Heave damping coefficients for three different hull shapes
Symbols and nomenclature
MOSES
RAO
GOM
RMS
ISSC
TLP
FPSO
d
D
KG
GM
TN
MultiOperational Structural Engineering Simulator
Response Amplitude Operator
Gulf of Mexico
Root Mean Square
International Ship and Offshore Structures Congress
Tension Leg Platform
Floating Production Storage and Offloading
Draft
Diameter
Vertical centre of gravity
Metacentric height
Natural period
- 38 -
Appendix
Appendix 1
Illustration of a moored SPAR with helical strake and risers
Appendix 2
MOSES files
Appendix 2a
Command file: Spar6.cif (*)
Appendix 2b
Geometry file: Spar6.dat
Appendix 3
MOSES files, alternative hull shapes
Appendix 3a
Hull shape, fig. 5.1
(Spar8.dat)
Appendix 3b
Hull shape II
(Spar7.dat)
Appendix 3c
Hull shape III
(Spar9.dat)
Appendix 4
(*)
(Hull shape I)
MOSES file, output (Spar6.out)
This command file applies to all the geometry files.
- 39 -