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Master’s thesiscarried out at the Department of Mathematical Sciences and Technology of the
Norwegian University of Life Sciences and submitted in partial fulfilment of the
requirements for the M.Sc. degree at the Department of Mechanical Engineering of
the University of Kassel
Free decay testing of a
semisubmersible offshore floating
platform for wind turbines in
model scale
Examiners: Prof. Dr.-Ing. Martin Lawerenz Author: Felix Kelberlau
Prof. Dr.Ing. Tor Anders Nygaard
Abstract
Wind turbines can be installed on floating platforms in order to use wind resources,
which blow above the deep sea. The presented research investigates the hydro-
dynamic behaviour of the Olav Olsen Concrete Star floater in free decay motion.
The floater is a new design of a semisubmersible offshore floating platform for wind
turbines.
The thesis describes the physical free decay testing of a 1/40 plastic scale model in
a water basin as well as numerical simulations of the same test cases with the aero-
hydro-servo-elastic code 3Dfloat. Tests are performed for the heave and pitch degree
of freedom and without mooring lines. The experimental results are compared with
the simulation results in order to find adequate added mass and damping coefficients
for the numerical model and to validate 3Dfloat for the prediction of heave motions.
The overall added mass coefficient for the vertical direction is found to be CM = 2.71
and the damping behaviour is simulated by using a Morison coefficient of CD = 8.0
and a considerable amount of additional linear damping. Subsequently, the results
are discussed in order to find possible causes for discrepancies between the results.
I
“We are like tenant farmers chopping down the fence around our house
for fuel when we should be using Nature’s inexhaustible sources of
energy – sun, wind and tide. [...] I hope we don’t have to wait until oil
and coal run out before we tackle that.”
Thomas Edison (1931)
(Newton, 1989, p. 31)
II
Preface and acknowledgement
This thesis is submitted in partial fulfilment of the requirements for the Master of
Science degree in “Erneuerbare Energien und Energieeffizienz” (Renewable Ener-
gies and Energy Efficiency) at the Department of Mechanical Engineering of the
University of Kassel. It was carried out between April and September 2013 at the
Department of Mathematical Sciences and Technology of the Norwegian University
of Life Sciences in As, Norway.
I would like to express my very great appreciation to Professor Dr.Ing. Tor An-
ders Nygaard for supervising this thesis project and being helpful in all questions
concerning my stay in Norway. His support was more than one could expect.
I wish to thank Professor Dr.-Ing. Martin Lawerenz for giving me the freedom
that was needed to work on this Master’s thesis abroad.
Trond Landbø and Jose Azcona Armendariz deserve my gratitude for giving a
good introduction to the project and maintaining my work progress by providing all
needed information.
In the phase of physical model building, Bjørn Brenna was supporting me with
tools and useful advice, what I would like to acknowledge.
My special thanks go to the colleagues in our office for making the work not only
educational but also convivial.
III
Contents
List of tables VII
List of figures VIII
Nomenclature X
1 Introduction 1
2 Thesis background 4
2.1 Development of wind energy usage . . . . . . . . . . . . . . . . . . . 4
2.1.1 Early mechanical use of wind energy . . . . . . . . . . . . . . 4
2.1.2 Wind turbines for producing electricity . . . . . . . . . . . . . 7
2.1.3 Offshore technologies . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Olav Olsen Concrete Star Wind Floater . . . . . . . . . . . . . . . . . 14
2.3 Project description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Theoretical bases 17
3.1 Coordinates system and degrees of freedom . . . . . . . . . . . . . . . 17
3.2 Oscillations and damping . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Scaled model testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3.1 Scaling methodology . . . . . . . . . . . . . . . . . . . . . . . 20
3.3.2 Froude similitude . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3.3 Reynolds invariance . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Keulegan-Carpenter number . . . . . . . . . . . . . . . . . . . . . . . 24
3.5 Hydrodynamic forces . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.5.1 Morison equation . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.5.2 Linear damping . . . . . . . . . . . . . . . . . . . . . . . . . . 29
IV
4 Methodology of model testing 30
4.1 Test case description . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.1.1 General information about the performed tests . . . . . . . . . 30
4.1.2 Heave drop test case . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.3 Pitch drop test case . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Testing environment . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.1 Physical testing in water basin . . . . . . . . . . . . . . . . . . 31
4.2.2 Numerical simulation with 3Dfloat . . . . . . . . . . . . . . . 33
4.3 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.3.1 General assumptions . . . . . . . . . . . . . . . . . . . . . . . 34
4.3.2 Physical scale model . . . . . . . . . . . . . . . . . . . . . . . 35
4.3.3 Numerical scale model . . . . . . . . . . . . . . . . . . . . . . 39
5 Physical and numerical test results 45
5.1 General observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.1.1 Heave drop test case . . . . . . . . . . . . . . . . . . . . . . . 45
5.1.2 Pitch drop test case . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2 Period length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.2.1 Heave drop test case . . . . . . . . . . . . . . . . . . . . . . . 48
5.2.2 Pitch drop test case . . . . . . . . . . . . . . . . . . . . . . . . 50
5.3 Damping behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.3.1 Heave drop test case . . . . . . . . . . . . . . . . . . . . . . . 50
5.3.2 Pitch drop test case . . . . . . . . . . . . . . . . . . . . . . . . 53
5.4 Keulegan-Carpenter number . . . . . . . . . . . . . . . . . . . . . . . 53
5.4.1 Heave drop test case . . . . . . . . . . . . . . . . . . . . . . . 53
5.4.2 Pitch drop test case . . . . . . . . . . . . . . . . . . . . . . . . 55
6 Discussion of results 57
6.1 Period length and added mass . . . . . . . . . . . . . . . . . . . . . . 57
6.1.1 Heave motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.1.2 Pitch motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2 Damping coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.2.1 Heave motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
V
6.2.2 Pitch motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7 Conclusion and outlook 63
Bibliography i
Declaration iv
A Appendix v
Data sheets of sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Drop test results, single test runs . . . . . . . . . . . . . . . . . . . . . . . viii
3Dfloat input file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
Manual calculation of added mass . . . . . . . . . . . . . . . . . . . . . . . xiii
VI
List of tables
3-1 Conversion of units between translational and rotational movements . 20
3-2 Scale factors commonly used for Froude scaling . . . . . . . . . . . . 23
3-3 Influence of skin friction and form drag on the drag term . . . . . . . 25
4-1 Key figures of the OO Star floater in full scale and model scale . . . . 35
4-2 Masses of the different parts of the scale model and their ballasts . . 39
4-3 Volume of water displaced by the scale model . . . . . . . . . . . . . 39
4-4 Cross section areas of one leg of the physical and numerical model . . 44
5-1 Key figures of the results of 14 cm heave drop test . . . . . . . . . . . 47
5-2 Key figures of the results of pitch drop test . . . . . . . . . . . . . . . 49
VII
List of figures
2-1 Model of a Persian vertical axis windmill . . . . . . . . . . . . . . . . 5
2-2 Overview of the historical development of European horizontal axis
windmills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2-3 Wind turbine in Denmark, designed by Poul La Cour . . . . . . . . . 8
2-4 Common types of bottom fixed foundations for offshore wind turbines 11
2-5 Types of floating platforms for offshore wind turbines . . . . . . . . . 12
2-6 Concrete Star Wind Floater by Dr. techn. Olav Olsen AS . . . . . . 15
3-1 Coordinates system and degrees of freedom . . . . . . . . . . . . . . . 18
3-2 Polygons of forces for prototype and model . . . . . . . . . . . . . . . 21
3-3 Influence of Reynolds number on drag coefficient . . . . . . . . . . . . 24
3-4 Potential flow around a circular cylinder . . . . . . . . . . . . . . . . 26
3-5 Relative importance of drag vs. inertia forces within Morison equation
and its applicability for small vs. large structures . . . . . . . . . . . 28
4-1 Breadboard construction for moving the model in heave direction . . 32
4-2 Breadboard construction for turning the model in pitch direction . . . 33
4-3 Scale model of the OO Star platform with tower, without ballast . . . 36
4-4 Sketch of the OO Star platform in model scale . . . . . . . . . . . . . 38
4-5 Visualization of the numerical scale model in three views . . . . . . . 41
4-6 Cross section of one of three legs, divided into bucket, pontoon and
tower area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4-7 Cross section of one of three legs, divided into bucket, pontoon and
tower areas: grey and black for physical model, coloured for numerical
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5-1 Heave drop test results, experimental mean data . . . . . . . . . . . . 46
VIII
5-2 Pitch drop test results, experimental mean data . . . . . . . . . . . . 48
5-3 Heave drop test damping behaviour, experimental and numerical data 51
5-4 Heave drop test results, experimental and numerical data . . . . . . . 52
5-5 Pitch drop test damping behaviour, experimental and numerical data 54
5-6 Pitch drop test results, experimental and numerical data . . . . . . . 55
6-1 Picture of the DeepCWind 1/8 scale model . . . . . . . . . . . . . . . 61
A-1 Data sheet of Honeywell 945-L4Y-2D-1C0 ultrasonic distance sensor . vi
A-2 Data sheet of SBG IG 500-N inertial navigation system . . . . . . . . vii
A-3 Heave drop test results, single test runs . . . . . . . . . . . . . . . . . viii
A-4 Pitch drop test results, single test runs . . . . . . . . . . . . . . . . . ix
A-5 3Dfloat input file 1/4 . . . . . . . . . . . . . . . . . . . . . . . . . . . x
A-6 3Dfloat input file 2/4 . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
A-7 3Dfloat input file 3/4 . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
A-8 3Dfloat input file 4/4 . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
A-9 Manual calculation of added mass . . . . . . . . . . . . . . . . . . . . xiii
IX
Nomenclature
SymbolsSymbol Description
A Area
C Coefficient
D Characteristic Diameter/Spring rate
F Force
Fr Froude number
g Gravitational constant
K Constant
KC Keulegan-Carpenter number
L Characteristic length
λ Scale factor
m Mass
π Number Pi
Re Reynolds number
ρ Density
S Submerged length
T Period
u Velocity
u Acceleration
V Volume
x Distance in x-direction
y Distance in y-direction
z Distance in z-direction
ζ Damping ratio
X
IndicesSymbol Description
0 Undamped
A Amplitude
B Buoyancy
b Bucket
crit Critical
D Drag
d Displaced
FK Froude-Krylov
G Gravitational
H2O Water
I Inertial
l Linear
M Added mass
m Model
p Pontoon/Pressure/Prototype
res Resulting
S Spring
s Structural
t Tower
V Viscous
XI
1 Introduction
In view of the limited availability of fossil fuels and the knowledge about anthro-
pogenic climate change, it is a common goal of mankind to reduce the emission of
greenhouse gases to the atmosphere. One of the major steps to reach this goal is to
substitute the use of fossil fuels by extracting power from renewable sources. Wind
energy is supposed to be an important component of this future energy system. Al-
though in most regions there are lots of suitable locations for harvesting the wind
resources onshore, efforts in offshore technologies should also be strengthened for
the following reasons:
• The energy yield of a wind turbine, which is installed above the open seas,
is in general considerably higher than onshore due to steadier and stronger
winds.
• Many big cities are located close to a coastline and so transmission losses are
low.
• The visual and audible impact of an offshore wind park disappears with rising
distance from the coastline.
Despite these arguments only 2% of the wind energy capacity installed today is
located offshore (Sawyer, 2012, p. 15). Nearly all of these turbines are built in
shallow waters of 30 m or less and use foundations that are rigidly connected to the
seabed (Xiaojing et al., 2012, p. 304). However, in some regions no shallow waters
are found close to the coastline and to be able to profit from wind resources that
are available above deeper water, floating platforms need to be used, because the
existing methods of bottom fixed support structures are not economically applicable.
The development of those floating platforms for wind turbines is based on the
expertise of offshore oil and gas industry, but a lot of research needs to be done to
1
1 Introduction
adapt the knowledge to the smaller size of the turbine platforms and to handle the
additional wind loads. One of the central topics in many projects is the platforms’
hydrodynamic behaviour and how it can be determined by numerical simulations.
For this, free decay tests deliver information about the natural periods and the
damping behaviour of newly developed structures and are often the first tests that
are made.
This thesis gives an answer to the question, how the free decay movement in
heave and pitch of the Olav Olsen Concrete Star Wind Floater, which is a cer-
tain semisubmersible floating platform for wind turbines, can be described by the
aero-hydro-servo-elastic code 3Dfloat. 3Dfloat uses the Morison equation for the
calculation of hydrodynamic forces. This equation is often used for the determina-
tion of wave forces on circular cylindrical members of fixed offshore structures, but
little is known about its applicability on oscillating structures of other shape in a
quiescent fluid.
At first, a 1/40 plastic scale model of the floater is built and test runs are per-
formed in a water basin to supply measurement data of the actual free decay motion.
These data are then analysed in terms of periods and damping to obtain proper coef-
ficients for added mass and quadratic as well as linear damping. Then a numerical
model for 3Dfloat is generated, based on the physical properties of the plastic model
and the coefficients calculated from the obtained experimental results. The plaus-
ibility is discussed, based on previous research. As a final step the experimental
and numerical datasets of the same test cases are compared in order to find possible
reasons for discrepancies.
Chapter 2 describes the historical background that shows how floating offshore
wind turbines developed from the wind mills of ancient ages. It classifies the position
of the thesis in the overall project and gives a description of the investigated Olav
Olsen Concrete Star platform.
The following chapter 3 presents all theoretical bases, which are applied in sub-
sequent explanations. It describes the coordinates system and the degrees of freedom
that are referred to in the description of the oscillating motions of the platform.
The principle and the laws of scale model testing are presented afterwards. The
Keulegan-Carpenter number is then introduced, because it has an influence on the
hydrodynamic forces, which are presented last but not least.
2
1 Introduction
In chapter 4, the performance of the drop tests is demonstrated. The testing
environment is presented for both, the physical experiments and the numerical sim-
ulations and also the relevant properties of both, the real and the virtual model, are
explained.
The results of the testing are described and visualized by plots in chapter 5, while
their discussion follows in chapter 6.
Chapter 7 sums up the main findings, gives an answer to the research question
and offers an outlook on the further testing campaign.
3
2 Thesis background
This chapter embeds the subject of the thesis in its surrounding. It gives a deeper
insight into the topic but is not essential to understand the testing procedure and
results. Section 2.1 gives the historical background of wind energy usage in subsec-
tions 2.1.1 and 2.1.2 and also presents the state of the art in offshore wind technology
in subsection 2.1.3. Afterwards the investigated offshore floating platform for wind
turbines is presented in section 2.2 and the overall research project is described in
the last section 2.3.
2.1 Development of wind energy usage
This thesis is about improvements for the most modern wind power plants, which
make it possible to produce electrical energy with low impact to human and nature
and at competitive costs. While the research in the field of offshore floating platforms
for wind turbines is still in an early stage, it has been a long way to get there. This
development was always driven by the human needs of the respective time. The
following chapter describes some milestones that show, how these demands were
satisfied. It is just a glimpse into the development. For further information it is
referred to Hau (2013), who delivers a comprehensive overview about the history of
wind energy.
2.1.1 Early mechanical use of wind energy
Pumping water and milling corn are two examples of activities, which were done
for centuries, before people were able to benefit from electrical energy. Since these
daily works were exhausting and inefficient, when done by muscle power, humans
were searching for ways to facilitate their physical work.
4
2 Thesis background
Figure 2-1: Model of a Persian vertical axis windmill (Deutsches Museum)
It is assumed by historians, that the first windmills were used in the orient for
irrigation as early as 1.700 B.C. (Gasch and Twele, 2012, p. 15). The first certain
information about a machine, that converts the energy of the wind into useable
power, dates back to the year 644 AD. It is from the Persian region and describes
a vertical axis windmill for the milling of grain. As shown on figure 2-1, the wind
was led through an inlet gap, where it pressed against the blades on one side of the
rotor. The resulting drag force led to a spinning movement of the vertical axis. The
disadvantage of these windmills is that they are depending on wind blowing from a
certain direction. Also the demand of the Chinese for draining rice fields may have
led to the first remarkable usage of wind energy. To create the necessary asymmetry
the Chinese windmills did not use walls for directing the air, but had flapping sails
that turn out of the wind, while moving against the wind direction. Due to a lack of
reliable evidence, there is some uncertainty about which concept was the first. One
thing that both have in common is, that they use a direct driven vertical shaft for
energy transfer.
The occidental counterpart was developed during the outgoing 12th century in
Western Europe. The main difference to the oriental origins was that they had a
horizontal axis of rotation. This different concept made it necessary to invent a
5
2 Thesis background
Figure 2-2: Overview of the historical development of European horizontal axiswindmills. (Gasch and Twele, 2012, p. 24)
completely different way of absorbing the wind energy. Like an aircraft propeller
the rotor turns in a plane perpendicular to the wind direction. The deflection of the
airstream, which flows through this plane, causes a lift force, which accelerates the
shaft in its horizontal rotation. Lantern gears were used to change the direction of
the movement, so that it is available at the bottom of the mill.
The windmills spread over the whole western world and were slightly improved
during the following centuries. Figure 2-2 shows the development of the European
types of mills. The last stage of classical windmills, which was developed in the
mid-19th century, was the so called western mill. It had more than 20 wings made
of metal sheets and was used mainly in North America for pumping water (Gasch
and Twele, 2012, p. 25).
For a long time, the only competitors for windmills were watermills, but their us-
age was limited to a few locations close to flowing waters. This situation started to
change, when the first steam engine was put into operation in 1785. Its main advant-
ages were the independency of the weather and the bigger power output. Though, it
took the 19th century to outrun the classical windmills, which experienced a short
revival during the Second World War, when fuel was scarce.
6
2 Thesis background
2.1.2 Wind turbines for producing electricity
Large-scale exploitation of electrical energy started in 1882 with the first power
plants and justifies the idea of producing electricity from wind energy. It was not
later than 1887, when the American inventor Charles Francis Brush used a western
mill for driving a generator to produce electrical energy and stored it in a battery.
One of the first, who systematically development the use of wind energy, was
Poul La Cour from Denmark (Jamison, 2012, p. 14). He performed wind tunnel
tests to improve traditional windmill technology to perfection and did pioneer work
in the field of electricity generation out of wind power. Additionally he was faced
with the problem of energy storage for delivering a constant energy supply to rural
regions. His solution was hydrogen production by electrolysis for operating gas
lamps, whenever the light is needed. His results were used for a small wind industry
in the beginning of the 20th century, which was boosted by the rising fuel prices
during the First World War. A typical La Cour wind power station is shown in figure
2-3. Its power output was approximately 30 kW with a rotor diameter of around
18 m. While La Cour’s turbine designs were closely related to the traditional and
reliable windmills, other manufacturers entered the market after the war with more
modern concepts. They benefited from the outcomes of research on airplanes, which
was adaptable to the blades of wind turbines and helped to improve them. The
new knowledge was further processed on a scientific basis by Albert Betz. In Betz
(1926) he sums up, that not more than 16/27 of the energy transported by the wind
can be converted into mechanical energy by a discoidal turbine. His findings and
summaries of previous works are an important part of the fundamentals for modern
wind energy converter design. With this theoretical background ideas for large wind
turbines came up.
Hau (2013, p. 29) gives the example of the German steel construction engineer
Hermann Honnef, who developed the concept for a 20 MW wind power plant in the
1930s, which should be operated to support conventional power plants in a large-
scale. His ideas showed the way forward, but could not be realized, as they were
too ambitious with regard to feasibility. Instead, two turbines with a rotor diameter
of 30 m and a rated power output of 100 kW were built in USSR. One of them,
called WIME D-30 was operating from 1931 to 1942 with good results in terms of
7
2 Thesis background
Figure 2-3: Wind turbine in Denmark, designed by Poul La Cour. (Hau, 2013,p. 26)
8
2 Thesis background
reliability. The plans for continuation with bigger multi-megawatt projects were
destroyed by the war.
Solely in the USA the development continued during the war and a 1.25 MW
turbine with a rotor diameter of 53 m was connected to the grid in 1941. It was
in operation until 1945 but revealed, that the costs were too high compared with
energy from conventional power plants.
After the war, there was a revival of interest in wind energy in Europe. It star-
ted with the upcoming awareness of the limited reserves of coal in the 1950s and
ended around 10 years later with the availability of cheap oil from the Middle East.
This phase was characterized by the inventions of the German company Hutter,
which used fibreglass blades and an electrohydraulic pitch control for their proto-
type W34. Another name that should be mentioned when describing this phase is
Johannes Juul, a student of Poul La Cour. For a site in Gedser, Denmark, he used
an asynchronous generator and a robust stall-regulation to demonstrate a cheap,
reliable and safe system, compared to other wind turbines.
The last uprising of wind energy that still continues to the present day was caused
by the oil price shocks in 1973 and 1979. They led to the question about alternatives
to the dependency on oil. Two different approaches should give an answer:
On the one hand the governments of several countries like the USA, Germany,
Sweden and some others invested enormous amounts of money in huge projects for
developing giant wind turbines. One of the most popular was the ’Growian’, a 3 MW
turbine with a rotor diameter of 100 m that was erected in 1983. It was not possible
to put it into a permanent operation, due to technical problems. As a result, it was
dismantled only four years later and many wind energy critics used this defeat as
an argument, that it would not be possible to serve the energy demand by anything
else than conventional sources. On the other hand, small Danish manufacturers
started to fabricate wind turbines with diameters between 12 and 15 m and a rated
power output of 30 to 75 kW (Gasch and Twele, 2012, p. 31). A market could be
established, because the Danish and later the German government granted a feed-in
tariff for electricity from wind energy. The experiences from these small installations
gave the knowledge for steady improvements and the development of larger systems.
Today the wind industry is still on this track and is able to manage projects in a
size that could not be handled before.
9
2 Thesis background
2.1.3 Offshore technologies
Based on the idea that it should be possible to erect wind turbines at sea, the world’s
first offshore wind farm was built in 1991. The Vindeby site consists of 11 turbines
with 450 kW each. They were set up in the three to five meter shallow water of the
North Sea close to the Danish coastline. Major challenges to be addressed were the
resistance of the turbines against corrosion and lightning strikes, that are a bigger
issue offshore than onshore (Prinds, 2011, p. 43). Now, more than twenty years
later, this forerunner in offshore wind energy is still in use and due to its success,
other countries mainly in northwest Europe followed with bigger projects. Outside
of Europe, China and the United States are planning to move offshore. To show the
motivation for these plans, Lynn (2012, p. 153f) mentions four arguments for using
the wind that is blowing along the open sea:
• The bigger a wind farm is, the cheaper each turbine can be produced due to
the economies of scale. This results in the need for large areas, which are
available only offshore, when looking at countries with a dense population.
• Development trends towards bigger turbine sizes with rotor diameters over
100 m. Their visual impact and space requirement can be handled by setting
it up on the open sea.
• The wind conditions are better. In general, the average wind speed over the
water is higher than onshore and the air turbulence is less. Therefore more
full-load hours can be reached.
• While the oil under the north sea is running low, the huge industry for pumping
it remains. A lot of the workforce and know-how can be adapted and used for
harvesting wind instead of oil.
It is a business case to decide whether these advantages outweigh the higher costs of
building a structure offshore. Taking into account the higher construction and also
operating costs into account, Hau (2013, p. 677) mentions that the better specific
energy yield does not necessarily lead to an improved economical balance. Anyway,
a lot of projects initiated by the big energy suppliers tend to build huge wind farms
offshore. Their order of magnitude around 1 GW is similar to the rated output of
10
2 Thesis background
Figure 2-4: Common types of bottom fixed foundations for offshore wind turbines:monopile, tripod, jacket and gravity based (STRABAG)
conventional power stations and therefore large wind farms have the potential to be
a real alternative.
Bottom based foundations and support structures
All existing offshore wind turbines are standing in water depths of less than 50 m and
have bottom fixed foundations. Figure 2-4 shows a selection of the most common
types of foundation structures that are currently in use.
The first image shows a monopile, which is the most popular kind of structure
and is used for more than 70% of all offshore wind turbines. It is a tube of 3.5 to
6 m in diameter that is rammed into the seabed at sites with rather shallow water
(<30 m). Monopiles are cheap and simple in construction.
The second image shows a so called tripod support structure, which is common
for oil and gas platforms but quite new and still unusual for being used by wind
industry. It consists of braces that connect a central column with three piles that
found the structure to the seabed. High bending moments can be derived what gives
tripods a good stability against turning and makes them suitable for installations in
deeper water (30 to 50 m). The disadvantages are the complexity of the structure
and the bigger cross section area leads to higher wave and current loads compared
to monopiles.
Beside of the tripods, jacket structures are also possible to set up in water that is
deeper than 30 m. Three or four legs are stiffened by a supporting structure. This
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2 Thesis background
Figure 2-5: Types of floating platforms for offshore wind turbines: spar buoy, TLP,semisubmersible (SFFE)
concept is also inherited from oil and gas industry and results in low loads and good
material efficiency. Unfortunately the high number of welding nodes demands for a
lot of manual work, what raises the costs.
When the water is very shallow (<10 m), gravity based foundations, like the one
depicted in the last picture, can be taken into consideration as an independent type
of structure. These are very heavy ballasts, put on the seabed. They are holding
the turbine in place by their sheer weight. A big advantage compared to piling is,
that no hammering is needed for installation. This protects fish and sea mammals
from extremely loud noise. As gravity based structures are made out of concrete,
they are very durable and can be used for more than a turbines lifetime.
Floating platforms
Most of the global wind is blowing above deep water. For example 61% of the US
American offshore wind resources are found over deep water and in Japan nearly
the complete offshore wind potential is located above the deep sea. The situation
is similar for various European countries. (Main(e) International Consulting, 2013,
p. 4)
The use of bottom based structures in more than 50 m deep water for harvesting
wind energy would be prohibited by too high cost. For these sites, floating platforms
are seen as an alternative. They are designed to swim on the ocean’s surface and are
connected to the ground solely by anchored mooring lines, that hold the installations
in their position. So it is possible to assemble these platforms onshore and tow them
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2 Thesis background
to the sites after completion, what gives a significant cost advantage. A rule of thumb
says, that any offshore work is five to ten times more expensive than the same work
on land (Gasch and Twele, 2012, p. 521). Furthermore floating platforms can easily
be decommissioned or moved to another site.
Different concepts exist and it is not yet decided, which of them is superior. Fig-
ure 2-5 gives an overview of the most promising concepts. Although all of them are
already in use for other offshore applications, a lot of tasks in research and develop-
ment have to be coped with in order to adapt the technology for supporting wind
turbines. This mainly concerns the limited knowledge about the dynamic behaviour
in wind and waves, and it has to be investigated, how the resulting movements
influence the turbines efficiency and the fatigue of the components.
The spar buoy is a long cylindrical tube reaching deep into the water. It is
ballasted by a heavy weight in its lowest point and above it is filled with air. As a
result, the center of gravity is lower than center of buoyancy. So slight deflection from
the upright position leads to a restoring moment what makes the spar buoy stable
due to its construction. The weight of the whole structure calms the movement
in all degrees of freedom and the small diameter of the tube at water level makes
it rather insensitive to the impact of waves. Catenary mooring lines are used to
hold the buoy in position, so the installation is straightforward. One disadvantage
is that spar buoys need deep water, as their draught is very high. As part of the
Hywind project, the world’s first floating wind turbine was erected on a spar buoy in
September 2009 in Norway. It has a rated power output of 2.3 MW and the draught
is 100 m, while the diameter at sea level is just 6 m. It is operated commercially by
StatoilHydro with nearly 3200 full load hours in 2010.
Another concept is followed by tension leg platforms (TLP). In operating position,
the buoyancy of these exceeds their weight force and that is why tensioned mooring
lines, fixed to the seabed, are needed to hold them under water. These tension legs,
which may be steel pipes, give the platform stability. When the platform tends to
pitch, the tension in one of the legs increases and pulls it back in an upright position.
The cross section area attacked by wave loads is also small. Both results in small
motions. TLPs have a wide range of possible water depths and a low steel weight,
but their installation is challenging and rather expensive.
Semisubmersible and barge floaters are wide structures, which are only partly
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2 Thesis background
submerged. Their centre of gravity is above the centre of buoyancy, but when they
are tilted out of the initial position, the centre of buoyancy moves sideways and a
positive restoring moment arises, that pushes the platform upright again. Damping
plates and the huge surface area in the water are used to stabilize the platform.
Additionally the inertia coefficients are high. Anyway, the motions are relatively
large, also since the contact surface at water level is higher than for spar buoy or
TLP. A big advantage of these floaters is, that they can be fully assembled in a
dockyard and mooring remains the single work that has to be done offshore. This
makes the setup of semisubmersible and barge floaters cheap and quite independent
from the weather. Floaters are very flexible concerning water depth. The WindFloat
project has set up a 2 MW Vestas turbine on a semisubmersible platform off the coast
of Portugal.
2.2 Olav Olsen Concrete Star Wind Floater
The platform investigated within this thesis is a patent pending design by the com-
pany Dr. techn. Olav Olsen AS (OO). The development of this semisubmersible
floater was driven by the search for a cost effective alternative to fixed bottom
structures. The floater shall support huge wind turbines under harsh environmental
conditions.
The aim of low costs is reached by a simple design that is shown on figure 2-6. The
floater construction consists of three corner cylinders (buckets) that serve buoyancy,
a star-shaped pontoon and a central tower with a transition unit to the tower of the
wind turbine. The whole system including tower and turbine can be fully assembled
on a floating barge, in a dry dock or on a quay. After testing it, it will be towed to
the wind farm where it gets additionally water ballasted and connected to pre-set
mooring lines that serve station keeping. Under operating conditions the pontoon
will be fully submerged and only the upper thirds of the cylinders are visible from
above the surface.
For building the substructure, concrete is the chosen material. It offers good
stability and the material fatigue is so low, that the design life is more than a hundred
years. This makes sense, because unlike gas and oil reservoirs, wind resources are not
limited in time. During the whole lifetime no maintenance is required. The platform
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2 Thesis background
Figure 2-6: Concrete Star Wind Floater by Dr. techn. Olav Olsen AS
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2 Thesis background
is designed for mass production and the scale effects of concrete constructions are
strong.
The OO Concrete Star Wind Floater (OO Star) is intended for use in water deeper
than 50 m. It needs to have stable motion characteristics while carrying 5 to 10 MW
wind turbines. For the investigation a 6 MW Siemens wind turbine is chosen. In
the numerical simulation it will be represented by a 5 MW reference wind turbine
defined by Jonkman et al. (2009). The extension slab at the bottom of the floater is
a water entrapment plate. It damps and slows down the motions of the platform and
helps to reach the design aims concerning the allowed motion under the influence of
waves, sea current and wind.
2.3 Project description
The work on this thesis is embedded in a two-year project granted by the Research
Council of Norway. The title is “Concrete substructure for floating offshore wind
turbines” and the overall dynamic behaviour of the OO Star shall be evaluated.
Dr. techn. Olav Olsen AS is responsible for the construction of the tested platform
(see subsection 2.2). The company is an independent structural and marine technical
consultancy that was founded in 1962. The about 80 employees have their main focus
concentrated on platforms for the oil and gas industry. OO designed many of the
world’s biggest concrete offshore structures.
The Norwegian Institute for Energy Technology (IFE), Norway’s national research
company for nuclear and energy technology, is another project member. The IFE
was founded in 1948 and has about 600 employees. They developed the software tool
3Dfloat, that is used for the numerical simulation of the test cases (see subsection
4.2.2).
The Marine Renewables Infrastructure Network (MARINET) is an initiative, fun-
ded by the European Commission, which shall contribute in the development of
marine renewable energy systems by offering access to the test facilities of the part-
ner institutions without charging for it. The Ecole Centrale de Nantes (ECN) in
France offered its Hydrodynamic and Ocean Engineering Tank for MARINET. The
project gains access for two weeks of scale model testing, which will take place after
the completion of this thesis.
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3 Theoretical bases
This chapter describes the theoretical background, which the explanations and cal-
culations throughout the thesis are based on. It is divided into five sections. The
first section 3.1 defines the used coordinates system and introduces the six degrees
of freedom, in which floating platforms can move. The second section 3.2 explains
the model, which is used for the description of a damped oscillating motion in one
degree of freedom, like found in the free decay motion during the tests. In the
third section 3.3 an insight is given into scaling methodology that is applied for
scale model testing. The second last section 3.4 deals with the Keulegan-Carpenter
number, which gives some information about the relative importance of drag and
inertia forces. These and other hydrodynamic forces are the subject of interest in
section 3.5.
3.1 Coordinates system and degrees of freedom
A Cartesian coordinates system is used for the description of the platform and its
movements. Figure 3-1 shows the inertial system and the used terms for translation
along and rotation around the axes. The origin of the three axes x, y and z is the
intersection point of the central line through the tower and the still water level. The
x-z plane is a plane of symmetry of the platform. Unlike bottom fixed structures,
floating platforms move in all 6 degrees of freedom. In the chosen right handed
Cartesian coordinates system the translation in x-direction is called surge, in y-
direction sway and in z-direction heave. Rotation around the x-axis is called roll,
around the y-axis pitch and around the z-axis yaw. Without mooring lines, these
movements are independent of each other, what means that e.g. a force in z-direction,
applied to the center of gravity, leads to a pure heave motion without any movement
in the other 5 degrees of freedom.
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3 Theoretical bases
Figure 3-1: Coordinates system and degrees of freedom
3.2 Oscillations and damping
When the tested model is put into water very slowly, it will start to float, as soon
as the gravitational force FG = msg is in equilibrium with the buoyancy force
FB = gρH2OVd, that is depending on the draught of the model. While FB may
change, when the model is moved, FG remains constant. The difference between
them is the spring force FS. It is also called hydrostatic restoring force and is caused
by the change of buoyancy resulting from a changed amount of water displaced by
the model. It is proportional to the displacement and is nonzero only for the heave,
pitch and roll degrees of freedom.
All the testing described in section 4 will investigate the movement of the model,
when it is being released after forcing it into a certain position. Such a system can
be described by a simplified equivalent model consisting of a mass m that is attached
to a spring with the spring rate D. The mass m is the sum of the structural mass of
the model and the mass of a certain amount of water that is moving with the model
(see subsection about added mass in 3.5.1). For the acceleration of this summed
mass, the inertial force FI = mx needs to be applied. FS = Dx is the spring force
that is necessary for the displacement of the model, for instance to further submerge
18
3 Theoretical bases
or lift it. The sum of both forces is the resulting force
Fres = mx+Dx. (3-1)
With no external force and an initial position in equilibrium, the resulting force is
zero and the model is standing still. The very slow application of a force, leads to a
displacement of the platform to a new position, in which FS equals Fres. When this
external force Fres is then released abruptly, the mass starts to oscillate perpetually
with no damping and its natural period
T0 = 2π√m/D. (3-2)
This undamped oscillation does not represent reality, because whenever water is
forced to a motion, energy is dissipated. This dissipation decreases the inherent
energy in the mass spring system and is therefore called damping. There are several
forms of damping forces and the simplest one is the pure viscous damping. The
damping force FD is in this case proportional to the velocity of the model in the
quiescent fluid. This damping term is added to equation 3-1 to get the equation of
damped motion for the displacement of mass.
Fres = mx+ CDlx+Dx (3-3)
When the value for the damping coefficient is
CDlcrit = 2√D/m, (3-4)
one says, that the movement is critically damped, what means, that the model
returns to its initial equilibrium position as fast as possible without oscillation. The
damping ratio ζ is defined as
ζ =CDl
CDlcrit
(3-5)
A system with 0 < ζ < 1 swings periodically around equilibrium with exponentially
decreasing amplitude, whereas a higher ζ value causes a monotonous approach of the
equilibrium position. It should be mentioned that the critical damping coefficient
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3 Theoretical bases
Transl. dim. Symbol Unit Rotat. dim. Symbol Unit
Force F kgms2
Torque M kgm2
s2
Mass m kg Moment of inertia J kgm2
Distance x m Angle ϕ radVelocity u = x m
sAngular frequency ω = ϕ rad
s
Acceleration a = x ms2
Angular acceleration α = ϕ rads2
Damping Dtrankgs
Damping Drotkgms
Table 3-1: Conversion of units between translational and rotational movements
is only valid for linear damping forces that are proportional to the velocity. The
damping increases the period length T of the damped system as follows:
T =T0√
1− ζ2(3-6)
Some of the above mentioned terms are usually used only for the description of
translational movements but all formulas may be used for rotations as well. Table
3-1 shows the corresponding terms.
3.3 Scaled model testing
Before an expensive structure like the OO Star platform is built in full scale, tests on
scaled models are carried out, in order to predict the dynamic behaviour under the
influence of the prevailing loads and to validate the results of numerical simulations.
To determine the parameters of the model and testing environment, a closer look is
taken to modeling laws.
3.3.1 Scaling methodology
When physical experiments with models are performed, it is tried to realize a similar
behaviour between the model and the prototype of the investigated object. For
reaching this similitude, several conditions need to be fulfilled. One is that the
model has a similar geometry, what means that the ratio of lengths between model
and prototype has to be a constant. This value is then called the scale factor λ
20
3 Theoretical bases
?
FGp
�����������������
Fpp
@@@I FV p
JJJJJJJJ
FIp
?
FGm
������������
Fpm
@@IFV m
JJJJJJ
FIm
Figure 3-2: Polygons of forces for prototype and model
xmxp
=ymyp
=zmzp
= λ (3-7)
It follows from this definition, that areas and volumes of a scaled model compared
to the prototype are also dependent on the scale factor:
Am
Ap
=xmymxpyp
= λ2 (3-8)
VmVp
=xmymzmxpypzp
= λ3 (3-9)
Beside of the geometrical similitude, the distribution of masses of the prototype
has to be reproduced in the model, so that the centre of gravity and buoyancy, the
mass moment of inertia and the radii of gyration are identical.
Additionally the similitude of forces has to be achieved. A fluid element flowing
along a structure is subjected to several forces. Namely the gravity force FG, pressure
force Fp and viscous force FV are considered in the following explanation, while the
21
3 Theoretical bases
elastic force and the capillary force are neglected. All of them attack the fluid
element in a certain angle and their vector sum equals the resulting inertia force FI .
The similitude of forces is achieved, if the polygon of forces is similar for model and
prototype, like shown in fig. 3-2. This would mean that
FGp
FGm
=Fpp
Fpm
=FV p
FV m
=FIp
FIm
. (3-10)
Equation 3-10 is equivalent to a combination of Froude similitude
FIp
FGp
=FIm
FGm
(3-11)
and Reynolds similitudeFIp
FV p
=FIm
FV m
(3-12)
By definition, the Froude number is the ratio of the inertia force to the gravitational
force and the Reynolds number is the ratio of the inertia force to the viscous force.
Maintaining these two dimensionless numbers would be sufficient to achieve the
same dynamic behaviour between model and prototype in a fluid flow.
3.3.2 Froude similitude
The Froude number is the most important dimensionless number for the character-
isation of objects, which are washed round by a fluid with an open surface. This
could be current and waves of water close to the surface. In these cases the grav-
itational forces have to be considered. For maintaining the Froude similitude, the
following condition applies
Fr =up√gLp
=um√gLm
(3-13)
and all scale factors listed in table 3-2 are derived from this equation and can be
used to obtain the prototype values from the model data and the other way round.
22
3 Theoretical bases
Dimension Scale factorLength λArea λ2
Volume λ3
Mass λ3
Mass per unit length λ2
Moment of Inertia Area λ4
Moment of Inertia Mass λ5
Time λ12
Velocity λ12
Acceleration 1Angle 1
Angular velocity λ12
Angular acceleration λ−1
Force λ3
Tension λ3
Table 3-2: Scale factors commonly used for Froude scaling
3.3.3 Reynolds invariance
It can easily be shown, that keeping on the Reynolds number would lead to very
high resulting fluid speeds in down scaled model tests. Chakrabarti (1994, p. 19)
mentions that Reynolds similitude is quasi non-existent in scale model technology.
Nevertheless, it is possible to get good scaling results, even if the Reynolds number
is not constant between model and prototype, as long as it is high enough. Figure
3-3 shows, how the pressure coefficient depends on the Reynolds number. While the
Cp value is a function of Re in the laminar and transitional flow state, it is about
constant in turbulent flow. The constant pressure coefficient leads to a constant
ratio of inertia force to dynamic pressure force
FIp
Fpp
=FIm
Fpm
(3-14)
and coupled with Froude similitude (eq. 3-11) the equation for the similarity of the
polygons of forces 3-10 is then also fulfilled. This becomes obvious by looking at
the fact, that very high Reynolds numbers equal very short FV vectors compared
to FI in 3-2. The polygons become triangles, which are entirely defined by the
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3 Theoretical bases
Figure 3-3: Influence of Reynolds number on drag coefficient (Jirka, 2007, p. 136),modified
Froude number and the geometrical similitude. Thus, it is acceptable to use a lower
Reynolds number in the model than in the prototype, as long as it remains above
the critical value (Jirka, 2007, p. 136). This is ensured for all presented testing
throughout this thesis, because of the flow separation that occurs generally at the
sharp edges of the water entrapment plate (Newman, 1977, p. 20).
3.4 Keulegan-Carpenter number
The Keulegan-Carpenter number is a dimensionless number that is used to describe
the relative influence of drag and inertia forces on objects with an oscillating relative
velocity to its surrounding fluid. It is defined as:
KC =u0T
D(3-15)
For the free decay testing described in this thesis, the characteristic diameter D
is constant. Also the period T is nearly not changing during the tests. Hence, the
amplitude of the velocity u0 is the only parameter that influences the changing KC
value during the performance of the tests.
Like visualized in figure 3-5 on page 28, a large KC number stands for a high
relative importance of the drag forces, while for a small number the inertia forces
are dominant.
24
3 Theoretical bases
pure skin friction drag
mainly skin friction drag
mainly form drag
pure form drag
Table 3-3: Influence of skin friction and form drag on the drag term Images:(Wikipedia)
3.5 Hydrodynamic forces
3.5.1 Morison equation
The simulation tool 3Dfloat uses the Morison equation for calculating the hydro-
dynamic forces. This equation was published by Morison et al. (1950) and is a semi
empirical formula describing the force exerted on a slender object in an unsteady
fluid flow. It superposes the effects of inertia force and drag force and has the form
f = KD |u|u︸ ︷︷ ︸drag
+KM u︸ ︷︷ ︸inertia
. (3-16)
The drag term is the sum of the skin friction drag, caused by the shear stress within
the viscous fluid and the form drag, caused by the pressure gradient around the
object. For a body that is not streamlined, the form drag dominates the drag term.
This is visualized in table 3-3. In experimental estimation of the drag coefficient a
combination of both effects is found as they cannot be separated without big effort.
The drag coefficient is a function of the Reynolds number, the Keulegan-Carpenter
number and the roughness of the member. The value of the drag force varies with
25
3 Theoretical bases
Figure 3-4: Potential flow around a circular cylinder (Wikimedia Commons)
the square of the velocity. For the force on a circular cylinder it applies:
FD = CDρH2OSD
2|u|u (3-17)
The inertia term is also representing two components. One is the Froude-Krylov
force on the object in an unsteady flow. It can be illustrated by looking at the
volume of water that is displaced by the object. If the object would be absent, the
mass of this fluid volume would be accelerated by the force of the surrounding flow.
FFK = mu = ρH2OSD2π
4u (3-18)
The other component is the effect of the added mass. It can be explained by the
influence of the object on the fluid flow. Figure 3-4 shows a circular cylinder in
an incompressible originally uniform flow field. The increased length of the lines in
the surrounding of the object shows, that a member in the flow cross section leads
to an increased fluid velocity. This is resulting in a higher pressure difference and
increased force. The corresponding mass is called added mass. For instance, the
velocity around a circular cylinder is twice the speed of the undisturbed flow. Thus
the inertial force is also doubled. In this case the added mass is 100% of the mass
of the object. For getting a rough idea about the quantity of added mass for a flat
plate headed against the fluid flow, a rule of thumb, which is also used by Maniaci
and Li (2011, p. 3) and many others, can be applied. It says that the added mass
of a rectangular flat plate with a certain width and infinite length equals the mass
26
3 Theoretical bases
of the water within a circular cylinder of the same diameter like the width of the
flat plate. For a round flat plate, the added mass is assumed to be equivalent to the
mass of the water in the smallest sphere around it.
In general the inertial force can be defined by
FM = (m+mM) u = CMmu (3-19)
with
CM = 1 +mM
m(3-20)
The value of the Keulegan-Carpenter number (see section 3.4) determines, which
one of the two components, inertial or drag force, is dominating. The values on the
y-axis in figure 3-5 are equivalent to the KC number. The diagram shows, that in
states with a large KC value, the turbulent drag term in the Morison equation is
dominant, while it can be neglected for low KC numbers on the y-axis.
The resulting force on a slender object of the submerged length S determined with
the Morison equation is given by:
dF =
(CMρ
πD2
4u+ CDρ
D
2|u|u
)dS (3-21)
The real added mass and drag coefficients CM and CD depend upon the state
of the fluid motion, but in the equation, they are considered as constant. Little
is known about the coefficients in accelerated systems and available numbers are
mainly about cylinders with a circular cross section. It depends on the chosen wave
model, which of them are the best to use. For linear wave theory a drag coefficient of
1.4 and an added mass coefficient of 2.0 is suggested for round cylinders in Agerschou
and Edens (1965, p. 239).
The Morison equation is only valid for members that are small compared to the
wavelength. Looking at the x-axis of figure 3-5 shows, that for large structures,
wave diffraction forces from potential flow theory have to be added to the overall
hydrodynamic force.
27
3 Theoretical bases
Figure 3-5: Relative importance of drag vs. inertia forces within Morison equationand its applicability for small vs. large structures (Chakrabarti, 2005, p. 167)
28
3 Theoretical bases
3.5.2 Linear damping
Another approach to calculate the hydrodynamic forces on a submerged member
is based on the potential flow theory. For the computation of these flow fields,
numerical methods are used. When the submerged member is large in comparison
to the wavelength, the fluid flow remains attached to the body and the water particle
movement is affected in a large area around the object (Chakrabarti, 2005, p.160).
Incident waves are diffracted due to the presence of the member. While the drag
forces represented in the Morison equation are proportional to the square of the
velocity, these diffraction forces are directly linear to the velocity.
29
4 Methodology of model testing
This chapter explains, how the physical testing and the numerical simulations through-
out the thesis are performed. It is divided into three sections that describe the test
cases, the testing environment and the used models. While the test cases, presen-
ted in section 4.1, are the same for the physical experiments and the numerical
simulations, the description of the testing environment and of the used models in
sections 4.2 and 4.3 is divided into subsections for both ways of testing.
4.1 Test case description
4.1.1 General information about the performed tests
The testing presented in this thesis, is only the first part of a comprehensive test
program, which will give information about the coupled behaviour of the OO Star
platform, carrying a wind turbine in wind and waves. Most of these tests take place
in the hydrodynamics laboratory of Ecole Centrale de Nantes (ECN) in France. Only
the first part of the test program, which is presented within this thesis, is performed
in a basin at the Norwegian University of Life Sciences (UMB) in As, Norway. It
consists of free decay tests that do not require sophisticated equipment or huge
testing facilities. The purpose of free oscillation tests is to determine the natural
periods and damping coefficients of the model (Chakrabarti, 2005, p. 1034). The
physical test results are used to find proper added mass and damping coefficients for
the numerical model. Then, numerical simulations of the same test cases are carried
out. The results of both, the physical experiments and numerical simulations are
compared in order to evaluate the suitability of the 3Dfloat tool for the prediction
of heave and pitch motions.
The free decay tests are carried out for these two degrees of freedom, while the roll
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4 Methodology of model testing
motion is neglected, because it would deliver the same results like the pitch motion.
Surge, sway and yaw motion cannot be considered, because the basin at UMB is not
big enough for the installation of the mooring system, which delivers the restoring
forces in these degrees of freedom.
4.1.2 Heave drop test case
For the heave drop tests, the floating platform is deflected from equilibrium position
downwards in negative heave direction, by applying a force. After a while, when
the surrounding water is quiescent again, the force is released and the model starts
moving upwards. It will be found out, that the motion is subcritically damped and
will therefore oscillate. This movement is a pure heave motion. The test is finished,
when no more translation in z-direction can be detected. Two sets of heave drop
tests are performed: One with an initial deflection of 14 cm and one with 8 cm.
4.1.3 Pitch drop test case
The pitch drop test starts with adding a torque around the y-axis of rotation, which
cuts the midpoint between the centre of gravity and the centre of buoyancy. When
the desired angular excursion is reached and the water is quiescent again, the torque
is released and the model starts rotating freely. It will be found out, that the motion
is subcritically damped and will therefore oscillate. This movement is a pure pitch
motion around the centre of rotation. The test is finished, when no more rotation
in z-direction can be detected. The chosen initial angular excursion is 8◦.
4.2 Testing environment
4.2.1 Physical testing in water basin
The physical experiments are executed in a round pool with a diameter of 5.8 m
and a water depth of 1.05 m. The water temperature is 15 ◦C. For the heave drop
testing the movement of the model in vertical direction is determined by distance
measurements. A Honeywell 945-L4Y-2D-1C0 ultrasonic distance sensor is installed
on the tower top and a non-moving plate is located above it. The vertical movement
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4 Methodology of model testing
Figure 4-1: Breadboard construction for moving the model in heave direction
of the tower top is measured in the time domain by the sensor output for the distance
between sensor and plate. Attachment A-1 shows the specifications of the sensor.
150 kg of steel ballast is placed on the ground in the middle of the pool. A deflection
roller is connected to this ballast and a second roller is positioned outside the pool,
so that it is possible to pull down the platform with a rope, in order to perform the
heave drop tests without the disturbance of a moving person inside the pool. Figure
4-1 gives an overview about the complete installation for the heave drop tests.
The pitch movement is recorded with a SBG IG 500-N sensor, which uses gyro-
scopes to deliver data for the absolute angles of the platform in all rotational degrees
of freedom. During the pitch drop tests, it is fixed to the tower top. See attach-
ment A-2 for the specifications of the sensor. In order to rotate the model around
its centre of rotation, two ropes are attached to the central tower: One above the
centre of rotation and one below in the same distance. One of these ropes is led
through a deflection roller, so that both lines can be pulled from one side outside of
the pool. Figure 4-2 shows the installation for the pitch drop tests.
32
4 Methodology of model testing
Figure 4-2: Breadboard construction for turning the model in pitch direction
4.2.2 Numerical simulation with 3Dfloat
The numerical tests are performed with 3Dfloat, a software tool for the modelling
of floating offshore wind turbines. Its code uses an aero-hydro-servo-elastic finite
element model to estimate the movement of a structure under the simultaneous in-
fluence of wind, waves and current. It was developed by the Norwegian University
of Life Sciences as well as the IFE and is used for analysis and comparison of con-
ceptual designs (Cordle and Jonkman, 2011). The finite element structural model
uses Euler-Bernoulli beams with 12 degrees of freedom. 6 on both end points of each
beam. Each of these end points serves as a node, where forces can be transferred.
Loads from gravity, buoyancy, water and wind attack distributed along the nodes of
the model. Additional stiffness and damping can be applied to certain nodes. For
calculation of hydrodynamics 3Dfloat uses the Morison equation, that is presented
in subsection 3.5.1. Therefore not only strength and geometrical properties but also
added mass and damping coefficients need to be given for all structural elements.
The standard beam elements are round cylinders, but it is also possible to add rect-
angular shaped box members to the model. 3Dfloat calculates a water particle flow
field for current and waves, but the structure and its movement do not interfere with
33
4 Methodology of model testing
the flow field. Hence, the linear damping due to wave diffraction needs to be added
manually.
3Dfloat is text based for all input and output. The best way to work with it, is
to prepare a .txt file including all model definition data and simulation parameters.
This Input file will then be processed by the program, which can write the desired
simulation results in text based output files for post processing.
4.3 Model description
4.3.1 General assumptions
Figure 2-6 on page 15 shows the investigated floater with a 6 MW Siemens wind
turbine in full scale. The mooring lines that are necessary for station keeping and
that have considerable influence on the hydrodynamic behaviour in wind, waves and
current, are not shown. For model testing a scale factor of 1/40 was chosen as a
compromise between low cost and handling efforts on the one hand as well as good
scaling results on the other hand.
Several simplifications were made for modelling. In the first phase of the tests
that is presented in this thesis, the rotor nacelle assembly on the top of the tower is
represented by a clump mass. No aerodynamic effects are considered. Likewise, no
mooring lines were used for the drop tests, due to the limited dimensions of the test
basin. This can be accepted because the influence of the mooring system on added
mass and damping is assumed to be low for semisubmersible floaters of this size.
The influence of the mooring lines might be taken into account afterwards, when
their effect is investigated in further tests that are not part of this thesis.
The concrete central tower of the platform and the steel tower of the real wind
turbine have a decreasing diameter with increasing height. The diameter of the
tower in the model is constant along z-axis. The location of mechanical outfitting
like working platforms, ladders, fairleads and so on is not taken into account in the
models, only its overall mass is respected.
Table 4-1 lists the key figures of the floating wind turbine in full scale and the
representative values for the scale models. The stiffness matrix, shown in equation
4-1, is defined by the buoyancy and the geometry of the model. With g = 9.81m/s
34
4 Methodology of model testing
Full scale ScaledTower weight 350 t 5.469 kgRNA weight 310 t 4.844 kgMechanical outfitting 200 t 3.125 kgMooring tension1 2.354 ∗ 106N 36.79 NDisplacement 9870 t 154.2 kgCentre of buoyancy2 7.046 m 0.176 mCentre of gravity2 10.342 m 0.259 mInterface platform/tower2 30 m 0.75 mTower height2 102 m 2.55 mDraught 20 m 0.5 m
1 in a downwards direction2 from bottom of platform
Table 4-1: Key figures of the OO Star floater in full scale and model scale
and ρH2O = 1000 kg/m3 it accounts:
C =
0 0 0 0 0 0
0 0 0 0 0 0
0 0 1743.75N/m 0 0 0
0 0 0 155.277Nm/rad 0 0
0 0 0 0 155.238Nm/rad 0
0 0 0 0 0 0
(4-1)
4.3.2 Physical scale model
For the tests in the basin, a physical model of the OO Star floater had to be built. For
this 1/40 scale model, polycarbonate was the material of choice. This thermoplastic
polymer is not brittle and nearly unbreakable. It can easily be cut by sawing and
several different types of glue are available to bond polycarbonate. For this model,
ACRIFIX R© 1R 0192 was used. It is a light curing 1-component polymerization
adhesive with some gap-filling capability. The application of this glue makes the
resulting compound brittle.
Figure 4-3 shows the plastic model of the OO Star platform with tower. A sketch
35
4 Methodology of model testing
Figure 4-3: Scale model of the OO Star platform with tower, without ballast
36
4 Methodology of model testing
of the model of the platform is shown in figure 4-4. The three buckets and the
central tower are manufactured from of pipes with a diameter of 250 mm and 200 mm
respectively and a wall thickness of 3 mm. All other plastic elements are built out of
1.5 mm thick plane sheet. The three pontoon legs are completely flooded with water
during the tests. Holes were drilled through the base and roof slab and the bulkheads
in order to let water in and all air out, when the model is put into the water. There
are three water inlets on the bottom of each pontoon (�10 mm) and air outlets on
the opposite (�5 mm). The holes in the lower area of the bulkheads (�5 mm) let
the water flow between the compartments, in the case of different water levels. The
bonds between the pipes and the base slab are the only connections, which need to
be watertight, because the central tower and the buckets are only partly filled with
water and additionally ballasted by sandbags in order to achieve the correct scaled
values for masses, centre of gravity and buoyancy as well as moments of inertia. The
manufacturing met the requirements for tolerances of DIN ISO 2768 T1 class c, but
the real diameter of the buckets is 248 mm and therefore 2 mm less than intended.
This results in a slightly decreased buoyancy of around 0.5% for the complete model
and has minor influence on its hydrodynamic behaviour. Table 4-2 lists the masses
of all parts of the platform and table 4-3 shows, how much water is displaced by
the model, when it is submerged to the designed draught of 0.5 m. The difference of
3.754 kg between the sum of masses and the sum of the displaced water is caused by
the missing mooring lines in the model. This mass equals a reduction of draught of
0.021 m, but the effect is partly eliminated by the before mentioned lower diameter
of the outer columns. The real draught of the model is 0.483 m.
While the pontoons and the pipes are quite stiff, the extensions of the base slab
(water entrapment plates) can be deformed by hand. So some minor deformation
will result also from the forces exerted by the fluid flow.
The dimensions of the base slab are so large, that it was not possible to build
the whole platform in one piece. Hence, the construction was divided into two
components: Component 1 with two buckets and the central tower and component
2 with the third bucket. For testing, the two pieces are connected with overlapping
joints and glue. The position of the interface between the two components is shown
as a red line on the sketch of the base slab. This division makes transportation less
complex.
37
4 Methodology of model testing
748.5
Figure 4-4: Sketch of the OO Star platform in model scale
38
4 Methodology of model testing
Plastic mass Water ballast Solid ballast SumPontoons1 3 X 1.313 3 X 20.663 - 65.928Buckets 3 X 2.171 3 X 12.465 3 X 5.845 61.443Central tower 1.668 7.560 3.695 12.923Tower 4.221 - 1.270 5.491Rotor nacelle assembly - - 5.000 5.000Sum 16.341 106.944 27.500 150.7851 including water entrapment plates
Table 4-2: Masses of the different parts of the scale model and their ballasts in kg
Volume SumPontoons1 3 X 21.823 65.468Buckets2 3 X 24.470 73.410Central tower2 15.661 15.661
154.5391 including water entrapment plates2 to still water line at elevation 0.5 m
Table 4-3: Volume of water displaced by the scale model in litre (10−3m3)
The tower is 1800 mm long and has the same outer diameter and wall thickness
like the central tower of the platform. Both components are connected by an inner
overlapping joint and tape. The tower top is equipped with a mounting device for
the sensors.
4.3.3 Numerical scale model
The numerical 3Dfloat scale model is a simplified model, which represents the phys-
ical scale model during all simulations. The input file is printed in figures A-5 to
A-8 in the appendix. Figure 4-5 shows a plot of the numerical scale model. Round
objects are not shown.
The input file defines four connected bodies. The first body represents the tower
and the rotor nacelle assembly. It consists of two circular beams, which are composed
of several stacked beam elements. These elements may be imagined as pieces of
pipes, with a start and an end point, a diameter, wall thickness and the respective
material parameters. All beam elements that are used in the model have a vertical
39
4 Methodology of model testing
or horizontal orientation. The first beam, described in the input file, is representing
the tower and the other is defined to correspond to the mass of the rotor nacelle
assembly at the tower top.
The second body contents beam elements to represent one of the outer buckets
and a box member for one pontoon. This body is rotated twice by 120◦ to generate
the third and fourth body for completing the model by adding a second and third
bucket and pontoon.
The beams for tower and buckets start in the same vertical depth. And their
overall height, diameter and wall thickness equal the values of the respective elements
in the physical model. The highest and lowest of these beam elements are closed
by a massless lid, so that there will be no water flow between the inside of the
pipes and the surrounding. In their lower area, the box member with a horizontal
orientation is located between the beams. It has a cuboid shape with given length,
width and height. While the length between the two beams and the height in z-
direction equal the values from the physical model, the width is a constant value,
which is equivalent to the changing width with length in the physical model. The
beams and the box members are connected by massless beam elements, which have
no influence on buoyancy and hydrodynamic forces and are so thick, that they are
considered to be rigid.
The densities, set in the geometry definition, are calculated from the real material
values, so that the mass of the polycarbonate and its respective sand or water filling
will be concentrated in the wall area.
Unlike the physical model with its extended base and roof slab, the numerical
model uses no explicit water entrapment plates. The influence of these plates on
added mass and damping is taken over by the lowest beam elements of tower and
buckets and the box member elements of the pontoons.
Added mass
The added mass for movement in z-direction, that is applied in the Morison equation
(see 3.5.1), is represented in the CM coefficients of the pontoons and the lowest beam
elements of buckets and tower. All other elements have only a physical mass due to
their density and no added mass in z-direction.
40
4 Methodology of model testing
Figure 4-5: Visualization of the numerical scale model in three views. Objects,that should have a round shape in the respective view, are not shown
In order to estimate the distribution of the added mass to buckets, pontoons and
tower, a closer look is taken at the wetted surfaces of the physical model. Figure 4-6
shows the cross section of one of the three legs of the platform in z-direction. The
dark grey area in the middle between the red lines has a surface of 0.1864 m2. It is
surrounded by water from two sides and therefore counts twice. The light grey area
on the left is 0.0917 m2. This value is also multiplied by two but then reduced by
the circular area of the bucket, whose top end is located above sea level and thus has
only half of the impact of a fully submerged section. The black surface on the right
has an area of 0.0173m2 and is also only partly submerged because of the tower.
This comparison of surfaces results in the conclusion that 70.2% of the added mass
should be set to the pontoons, 25.3% to the lowest bucket elements and 4.5% to the
lowest tower element.
The absolute value of the model mass plus added mass will be derived from the
results of the physical heave drop tests. The scale model behaves like a damped
spring pendulum with low damping after some periods. When a damping ratio of
ζ = 0.15 is assumed for late periods the influence of the remaining damping increases
the period length by around 1%. This influence is neglected in the calculation of
added mass. With the measured period T and the spring rate D, obtained from the
C33 element of the stiffness matrix (see eq. 4-1), the total mass equals:
m =
(T
2π
)2
D (4-2)
This total mass is then divided into the three parts for the pontoons, buckets
41
4 Methodology of model testing
Figure 4-6: Cross section of one of three legs, divided into bucket, pontoon andtower area
and the tower. With the masses of water, displaced by the considered elements
mdp = 64.52 kg, mdb = 9.20 kg and mdt = 1.96 kg the added mass coefficients are:
CMp = 1 + 0.702m− (mdp +mdb +mdt)
mdp
, (4-3)
CMb = 1 + 0.253m− (mdp +mdb +mdt)
mdb
(4-4)
and
CMt = 1 + 0.045m− (mdp +mdb +mdt)
mdt
. (4-5)
In section 5.2 it is shown, that the period of the oscillation of the physical scale
model in heave direction is T0 = 3.04 s. With this number, the total mass is
calculated to 408.199 kg. With a structural mass of 150.785 kg, the overall added
mass coefficient in heave motion is CM = 2.71. Distributed on the three relevant
elements, the coefficients are:
42
4 Methodology of model testing
Pontoon: CMp = 4.61
Bucket: CMb = 10.18
Tower: CMt = 8.63The CM values for movement in x and y-direction are set to 2 for all circular
elements according to Agerschou and Edens (1965, p. 239). For the pontoon the
added mass is set to 1.38 for y-direction (see A-9 in the appendix) and to 1 for
x-direction.
Damping
In order to achieve the damping coefficients for the numerical model, the cross
sections of the physical model with its damping plates are compared to the cross
sections of the 3Dfloat model. Figure 4-7 reveals, that the real cross section is
bigger than the numerical. Therefore the CD values need to be adjusted. The
physical values are overtaken from the calculations for the added mass. The values
for the numerical model are 0.1434m2 for one pontoon, 0.0491m2 for one bucket and
0.0105m2 for a third of the tower. All of them count twice, because the elements are
fully submerged. By dividing the real areas by the numerical, the following factors
result:Pontoon: 1.30
Bucket: 1.37
Tower: 1.15The assumed damping coefficients need to be multiplied by these factors to achieve
the intended damping behaviour.
It follows from the application of strip theory for heave motions and small angles in
pitch motion, that the hydrodynamic damping effects are the same for all movement
in z-direction, no matter whether they are caused by heave or pitch motions. Thus,
the same damping coefficients can be used for the simulation of the free decay
behaviour in the heave and pitch degree of freedom. This is done for the Morison
damping values and would be possible for linear damping also, if the damping would
not be added to one central point of the numerical model, but to the same elements in
bucket, pontoon and tower that are used for Morison damping. For the simulations
presented in this thesis, separate values for linear damping in heave and pitch are
applied only to the point of origin, instead of distributing the linear damping forces
43
4 Methodology of model testing
Figure 4-7: Cross section of one of three legs, divided into bucket, pontoon andtower areas: grey and black for physical model, coloured for numerical model
to different nodes.
Physical Top Bottom SumBucket 0.0426 0.0917 0.1343Pontoon 0.5591 0.5591 1.1182Tower 0.0068 0.0173 0.0241
Numerical Top Bottom SumBucket 0.0491 0.0491 0.0982Pontoon 0.1434 0.1434 0.2868Tower 0.0105 0.0105 0.0209
Table 4-4: Cross section areas of one leg of the physical and numerical model in m2
44
5 Physical and numerical test results
The following chapter shows the test results obtained from both, the physical exper-
iments and the numerical calculations of the same test cases. It is divided into the
four sections 5.1 to 5.4 for general observations, period length, damping behaviour
and the Keulegan-Carpenter number. Within each section two subsections for the
heave and pitch drop test case are found.
The chosen coefficients for the 3Dfloat simulations and all other assumptions
are only presented, while the arguments for choosing them are given in the next
chapter 6. Likewise, the discussion of the observations follows in chapter 6.
5.1 General observations
5.1.1 Heave drop test case
For the physical heave drop tests several test runs with a drop height of -14 cm and
a decreased initial position at -8 cm were performed. The measured signals of five
of these runs are plotted in time domain in figure A-3 in the appendix. It is visible,
that the signal is distorted by noise. This noise has a frequency of around 1.1 Hz
and an amplitude of around 24 mV. Effective filtering with a low-pass has severe
damping impact on the signal and cancellation by overlaying of a regular sine was
not successful because of a slightly varying frequency in the noise. The best practice
to cope with this issue, is to calculate the average over several test runs. This was
done for the plot in figure 5-1. It shows the free decay of the movement for the
heave drop tests with both heights. The graph is oscillating around equilibrium
with damping. In table 5-1, the time and displacement values are listed for all
extremes reached after each half period for the 14 cm drop. Only the first five
periods are considered to deliver reliable values for the displacement because of the
45
5 Physical and numerical test results
−40 −30 −20 −10 0 10 20 30
−14
−12
−10
−8
−6
−4
−2
0
2
4
6
8Heave drop test 14cm vs. 8cm
Z−
posi
tion
in 1
0−2 m
Time in s
14 cm8 cm
Figure 5-1: Heave drop test results, experimental mean data
above mentioned distortion in the sensor’s signal.
The 3Dfloat output graphs, plotted in figure 5-4, are undisturbed and show no
conspicuousness in their shape. In the moment of release, the acceleration is higher
in the 3Dfloat simulation than the acceleration of the physical model. This results
in a phase shift between the numerical and experimental results.
5.1.2 Pitch drop test case
For the pitch drop test, several test runs with an initial rotation angle of around 8
degrees were performed. The measured signal of three of these runs is plotted in
time domain in figure A-4 in the appendix. The signal is of a higher quality than
the heave signal with no relevant noise. Thus, a longer time span can be used for
determining the free decay behaviour. Anyway, an average is calculated over the
46
5 Physical and numerical test results
No. of t in s T in s extreme value abs. valueperiod in cm in cm
0 0 -14.29 14.290.5 2.24 7.21 4.16 4.16 -2.78 2.78
1.5 5.81 1.732 7.32 3.16 -1.09 1.09
2.5 9.04 0.863 10.64 3.32 -0.62 0.62
3.5 12.12 0.624 13.58 2.94 -0.41 0.41
4.5 14.96 0.415 16.34 2.76 -0.28 0.28
5.5 18.38 0.286 19.68 3.34 -0.28
6.5 21.10 0.377 22.44 2.76 -0.23
7.5 24.56 0.348 25.90 3.46 -0.27
8.5 27.38 0.399 28.80 2.9 -0.18
Table 5-1: Key figures of the results of 14 cm heave drop test
47
5 Physical and numerical test results
0 20 40 60 80 100 120 140−10
−8
−6
−4
−2
0
2
4
6
8
Time in s
Ang
le in
deg
Pitch drop test 8deg
Experimental mean data
Figure 5-2: Pitch drop test results, experimental mean data
single test runs for minimizing the small drift of the equilibrium position that is
recognizable throughout the signal. The averaged displacement is plotted over time
in figure 5-2. It shows the free decay of the movement from the moment of release
and on. The graph is oscillating around equilibrium with damping. In table 5-2,
the time and displacement values are listed for all extremes reached after each half
period for the pitch drop.
5.2 Period length
5.2.1 Heave drop test case
The first outcome that is regarded in the experimental heave drop test, is the os-
cillation period. Only full periods are considered. The first full period, listed in
48
5 Physical and numerical test results
No. of t in s T in s extreme value abs. valueperiod in deg in deg
0 0 -8.214 8.2140.5 2.12 6.4731 4.3 4.30 -4.974 4.974
1.5 6.48 3.6662 8.62 4.32 -2.671 2.671
2.5 10.68 2.1923 12.82 4.20 -1.789 1.789
3.5 14.88 1.5674 16.94 4.12 -1.315 1.315
4.5 18.98 1.2555 21.08 4.14 -0.966 0.965
5.5 23.18 1.0046 25.3 4.22 -0.815 0.815
6.5 27.28 0.7867 29.58 4.28 -0.730 0.729
7.5 31.54 0.6498 33.64 4.06 -0.608 0.608
8.5 35.6 0.5899 37.72 4.08 -0.575 0.575
9.5 39.8 0.42810 41.88 4.16 -0.474 0.474
10.5 43.96 0.39511 46.02 4.14 -0.411 0.411
11.5 48.08 0.34312 50.12 4.10 -0.403 0.402
12.5 52.16 0.35413 54.36 4.24 -0.337 0.337
13.5 56.32 0.31814 58.42 4.06 -0.302 0.302
14.5 60.42 0.29615 62.6 4.18 -0.256 0.255
Table 5-2: Key figures of the results of pitch drop test
49
5 Physical and numerical test results
the third column of table 5-1, is longer than all others. The other values vary from
2.76 s to 3.46 s with no obvious systematics. A damped signal has a period T , which
is longer than the period T0 of the undamped oscillation. In section 5.3 it will be
shown, that the damping of the oscillation is low after a number of periods. Hence,
the period of the 5th to 9th period is averaged, in order to get a value close to the
undamped period. This mean value is 3.04 s, which equals a frequency of 0.33 Hz.
The 8 cm drops deliver a similar mean value of 3.08 s.
The period length in the numerical simulations is about constant after the first
two periods. Its mean value for 5th to 9th period is 3.17 s.
5.2.2 Pitch drop test case
The numbers in the third column in table 5-2 show full period lengths of between
4.06 s and 4.32 s for the physical pitch drop test. The standard deviation is lower
than for the heave drop test results. The tendency to shorter periods in the later
oscillations is the same. With period number 8 to 15 taken into account, the average
period length is 4.13 s. If this period length is compared with the 3Dfloat simulations,
a deviation is detected. It is visible in figure 5-6, that the oscillations in the numerical
simulation have a longer period. Its value of 4.55 s is 10% higher.
5.3 Damping behaviour
5.3.1 Heave drop test case
The numbers for the extreme values in table 5-1 show, that the movement in the
downwards direction is damped stronger than the movement in positive z-direction.
In the periods 4 to 6 even no damping could be measured for the upwards movement.
Thus, only full periods will be considered. The absolute values of the locations of the
lower turning points are listed in the last column of the table. They correlate linearly
to the remaining energy, that is still inherent in the oscillating system and not yet
dissipated by any damping effects. The damping behaviour will be investigated for
the first five full periods only, because the signal becomes unclear in later periods.
In figure 5-3, the corresponding points are plotted as black circles on a logarithmic
50
5 Physical and numerical test results
0 1 2 3 4 510
−3
10−2
10−1
100
101
102
Heave drop test damping behaviour
No. of period
Z−
posi
tion
in 1
0−2 m
Experimental dataPure linear damping (445 kg/s)Pure Morison damping (CD=11.4)3Dfloat data (CD=8, lin: 120 kg/s)
Figure 5-3: Heave drop test damping behaviour, experimental and numerical databetween linear and quadratic damping
y-scale. For getting a first impression about what effect dominates the damping
characteristic, pure linear damping and pure Morison damping is also plotted. In
both cases, the damping coefficients were adjusted to achieve the correct damping
after the first full period. For linear damping, this needs 445 kg/s, which is about
53% of the value for critical damping. The Morison coefficient for achieving the same
damping after one period is 11.4. A combination with a Morison coefficient of 8.0
and linear damping of 120 kg/s delivers the best approximation for the simulation of
the real damping behaviour. The 3Dfloat results with these parameters are plotted
as red asterisks. The maximum deviation between simulation and experiments is
13.8% after the 2nd period. The plot in figure 5-4 shows the experimental and
numerical results for both drop heights in displacement over time.
51
5 Physical and numerical test results
−40 −30 −20 −10 0 10 20 30
−14
−12
−10
−8
−6
−4
−2
0
2
4
6
8Heave drop test experimental vs. 3Dfloat, 14cm
Time in s
Z−
posi
tion
in 1
0−2 m
Experimental data3Dfloat data (CD=8, lin: 120 kg/s)
−40 −30 −20 −10 0 10 20 30
−14
−12
−10
−8
−6
−4
−2
0
2
4
6
8Heave drop test experimental vs. 3Dfloat, 8cm
Time in s
Z−
posi
tion
in 1
0−2 m
Experimental data3Dfloat data (CD=8, lin: 120 kg/s)
Figure 5-4: Heave drop test results, experimental and numerical data for both dropheights
52
5 Physical and numerical test results
5.3.2 Pitch drop test case
In figure 5-6, the angular displacement over time is plotted for the experimental and
numerical pitch drop test. The angular displacement can also be understood as the
amount of potential energy that is still inherent in the system. The trigonometric er-
ror for this assumption is less than 0.7% for 8 deg and moves towards zero for smaller
angles. For the assessment of the damping behaviour, the first 15 oscillation periods
are regarded. Subsequently, the graph shows much deviation from the expected sine
wave form and too much changing of the equilibrium position to rely on the posi-
tion of the extreme values. The experimental data is compared with the results of
3Dfloat simulations. For these the CD value of 8.0 is taken over from the heave drop
simulations and a linear damping value of 6 kgm2/s was chosen to reach the best
approximation between the experiment and the simulation. Figure 5-5 shows the
angular displacement after each full period for experimental and numerical results.
The highest deviation of 23,7% is found after the 15th period. Before, the deviation
is always lower.
The damping of pitch movement is way lower than the damping of heave move-
ment. For example, after two full periods 7.6% of the energy is remaining for heave,
but 32.5% for pitch.
At last, it is observed carefully what might happen in the last oscillations, which
were not considered for the approximation. One notices, that it could be, that the
oscillations calculated by 3Dfloat come to a standstill, while the physical model
might still be moving.
5.4 Keulegan-Carpenter number
5.4.1 Heave drop test case
The KC number in the heave drop test is decreasing with the amplitude of the
oscillation. For calculating it, the characteristic diameter is set to the width of the
base slab of the pontoons, which is around 0.38 m. The period is around 3 s. The
vertical velocity reaches its maximum when crossing the equilibrium position. In the
first period it is 0.18m/s and in the second 0.075m/s. With these values, the KC
53
5 Physical and numerical test results
0 5 10 15
100
Pitch drop test damping behaviour
No. of period
Ang
le in
deg
Experimental data3Dfloat data (CD=8, lin: 6 kgm²/s)
Figure 5-5: Pitch drop test damping behaviour, experimental and numerical data
54
5 Physical and numerical test results
−20 0 20 40 60 80 100 120 140−10
−8
−6
−4
−2
0
2
4
6
8
Time in s
Ang
le in
deg
Pitch drop test 8deg
Experimental mean data3Dfloat data (CD=8, lin: 6 kgm²/s)
Figure 5-6: Pitch drop test results, experimental and numerical data
number becomes 1.4 for the first period, 0.6 for the second and → 0 subsequently.
5.4.2 Pitch drop test case
The KC number in the pitch drop test is decreasing with the amplitude of the
oscillation. Like in the heave drop, the characteristic diameter is set to the width
of the base slab of the pontoons, which is around 0.38 m and the period is 4.13 s.
For obtaining values for the vertical velocity, the angular velocity is multiplied by
0.688 m, the distance between the central tower and the bucket that is located in
positive x-direction. The angular velocity, when crossing zero is 0.186 rad/s in the
first period and 0.107 rad/s in the second. With these values, the KC number for
the outer position is 1.0 for the first period, 0.6 for the second and→ 0 subsequently.
Looking at the flow velocity in x-positions between the bucket and the tower, the
55
5 Physical and numerical test results
KC number is decreasing linearly from the mentioned values to zero. The Keulegan-
Carpenter number for the two other buckets in negative x-direction is 50% lower,
since the shorter levers result in lower translational velocities.
56
6 Discussion of results
The results that were presented in the previous chapter 5 will be discussed in the
following. All assumptions that were made are justified here and possible reasons
are given for deviations from the expected results. In section 6.1 the results in terms
of period length are used to find the correct added mass of the model and section 6.2
deduces the damping coefficients from the displacement data. Within the sections,
the discussion is split into two subsections for the heave and the pitch degree of
freedom.
6.1 Period length and added mass
6.1.1 Heave motion
The first full period measured in the heave drop tests, is longer than all others.
A possible reason could be that the process of releasing the platform might have
been not suddenly enough. Therefore this first value is ignored. The latter values
are also not constant, what might be explained by the influence of remaining fluid
movement from previous periods and also by the inaccuracies of the sensors signal.
Theoretically, the undamped heave period is strictly depending on the total mass
that is composed of the structural mass plus added mass. The 14 cm heave drop
experiments deliver an averaged period of 3.04 s. This corresponds to a total mass
of 408.2 kg and an added mass of 257.4 kg, when the structural mass of 150.8 kg is
excluded. For getting a rough idea about whether this value is realistic, the rule of
thumb, presented in 3.5.1 is used to calculate the added mass manually. With the
assumptions shown in appendix A-9, this delivers a value of 244.8 kg, which is close
to the experimental results, although the influence of the not submerged areas atop
of the buckets and tower are neglected.
57
6 Discussion of results
A WAMIT1 analysis for the OO Star in full scale delivers a scaled value of 245.7 kg
for added mass. Therefore, the experimental value is accepted and will be used for
the added mass in the definition of the numerical model.
6.1.2 Pitch motion
For the period of heave motion, only the total quantity of added mass is important,
but for the pitch motion it is crucial in order to achieve the correct moment of inertia,
in what distance from the center of rotation the added mass comes into effect. The
3Dfloat simulations show a 10% longer period than the experiment. Hence, it can
be assumed, that the chosen distribution of the added mass to the bucket and
pontoon explained in subsection 4.3.3 is not exact. Less mass should be added to
the buckets and more to the pontoons or tower in order to achieve a lower moment
of inertia with the same amount of mass. The deviation can be partly explained
by the simplifications that were made in the subsection about added mass in 4.3.3.
The applied procedure for distributing the added mass is lacking in just looking at
the wetted surface areas and not on the actual shape of the added water masses
above and below them. It was assumed, that the upper areas of bucket and tower
elements that end above still water level might be linearly excluded from the added
mass calculation. But in reality this procedure underestimates the influence of these
non-wetted surfaces on the added mass, because central areas move a higher amount
of added mass, compared to areas close to the boundary of the elements. The bigger
effect of subtracting areas, which are positioned in the centre of elements, could
be considered by a more sophisticated approach, which uses spheres and cylinders
instead of just areas for the circular beam and box member properties. Such a more
complex approach could be justified for future investigations, when no experimental
reference data (and no WAMIT analysis) is available. Tests were made with a
1“WAMIT is a computer program based on the linear and second-order potential theory foranalyzing floating or submerged bodies [...]. The boundary integral equation method (BIEM)[...] is used to solve for the velocity potential and fluid pressure on the submerged surfaces ofthe bodies. Separate solutions are carried out simultaneously for the diffraction problem [...]and the radiation problems for each of the prescribed modes of motion of the bodies. Thesesolutions are then used to obtain the relevant hydrodynamic parameters including added-massand damping coefficients, exciting forces, response-amplitude operators (RAO’s), the pressureand fluid velocity, and the mean drift forces and moments.” (WAMIT Inc.)
58
6 Discussion of results
reduced added mass of 20% less on the buckets, which was added to the pontoon
elements. The simulation showed a decreased period of 4.45 s which is still 8%
too much. Likewise, a reduction of the pontoon’s axial CM value has only minor
influence on the period length. Thus, there must be another unknown effect. The
WAMIT calculations for the full scale platform deliver a down scaled moment of
inertia of 28.84 kgm2, what leads to a gyration radius of 0.343 m. This value cannot
be reached, because the distance between the centre of rotation and the centre of
the pontoon is already 0.396 m. So even adding all added mass to the pontoon that
was previously attached to the bucket would result in a higher moment of inertia,
but performed simulations for this scenario showed, that the period will be 4.00 s
then. This is too low and adding no mass to the buckets would be unrealistic. Thus,
for the presented testing, it is adhered to the original values and the longer period is
accepted, although it might have a slight impact on the damping behaviour. Further
testing needs to be done in order to find the cause of this deviation.
6.2 Damping coefficients
6.2.1 Heave motion
During the experimental free decay in heave motion, the half periods in which the
physical model is moving upwards are less damped than the downwards movement.
This behaviour can partly be explained by the shape of the platform, because it can
be assumed that the real drag coefficient is higher for a fluid streaming around the
model in upwards than downwards direction. But another effect must be superim-
posed to these different coefficients, because a differing drag does not explain why
the damping in upwards direction comes to a complete standstill in several periods.
A possible effect that could cause this might be the influence of the history of the
motion. It could be for example that the first fast upwards movement after releasing
the model, might have accelerated the water so vastly that its remaining motion in-
fluences the damping effects in subsequent period. This cannot be validated without
further investigation.
Faltinsen (1987, p. 63) explains, that there is a significant influence of the sea
bed on the damping characteristics, when the water depth to draft ratio is less than
59
6 Discussion of results
two. In this experiment it is a little more than two, but possibly the basin bed still
has a considerable but unknown influence. Also the limited stiffness of the plastic
model, especially in the area of the water entrapment plates, due to the thin material
thickness might have an influence that is not investigated here. It could influence
the damping coefficients, especially for fast motions, compared to a completely stiff
model.
The heave damping coefficients, applied to the 3Dfloat model, were chosen so
that it emulates the models movement in the experiment. Therefore the CD value of
Morison equation was set to 8.0. Faltinsen (1990, p. 238f.) mentions that findings
of Graham (1980) may be used for explaining experimental results, when the KC
number is in a range of 0 to 10. His experiments show, that the CD value is then
8∗KC− 13
for a flat plate. This implies that for a KC number above 1, the CD value
is less than 8.0 and the other way round. The Keulegan-Carpenter numbers in the
experiment are in this order of magnitude for the first periods, but then they move
towards zero. That means that the CD values rise. As this cannot be considered in
the 3Dfloat model, the chosen values are supposed to be intermediate.
The 8.0 value is relatively high compared to the CD value of 4.8 that was chosen
to match DeepCWind tank-test data with numerical simulation results (Robertson
et al., 2012). Figure 6-1 shows the semisubmersible floating platform that was
investigated in the DeepCWind project. Unlike the OO Star, it has no thin flat
water entrapment plates attached. Thus, the DeepCWind floater is assumed to
have a lower Morison damping than the OO Star. The above mentioned value of
4.8 is also suggested for the second phase of OC4 simulations, but no experimental
reference data is available yet.
From the visualization in figure 5-3, it becomes clear, that the real damping is
characterized rather by quadratic Morison damping but does also need some amount
of linear viscous damping from diffraction forces for getting enough damping, while
moving with low velocity. Hence, in order to complete the damping forces, linear
damping coefficients were added to the 3Dfloat model. To simulate the heave motion
a linear damping coefficient of 120 kg/s was selected. This equals 14.2% of critical
damping. IT shoudl be kept in mind that this value for critical damping is only
for the linear damping. The sum of Morison and linear damping delivers higher
amounts.
60
6 Discussion of results
Figure 6-1: Picture of the DeepCWind 1/8 scale model (Bangor Daily News)
The above mentioned damping coefficients were chosen to fit only the first five
oscillation periods of the physical model. This was done, because the subsequent
measurement signal does not deliver reliable numbers for the remaining energy in
the system. But when the later sensors’ signal and the simulation results in figure
5-4 are compared qualitatively, it seems like the oscillation of the simulation results
come to a standstill, before the physical model does. Therefore, it might be that
the linear damping coefficient is too high to represent reality in low amplitudes.
Another effect that could cause the continuous motion in the physical tests can be
the influence of waves reflected from the basin walls. These returning waves excite
small movements of the platform.
6.2.2 Pitch motion
The pitch motion has a lower damping in general, what can be explained by the
shape of the floater. While pitching, the relative velocities between model and fluid
are higher for points with a big distance from the centre of rotation than for points
61
6 Discussion of results
close to it. Therefore and because of the long corresponding levers the effect of a
damping element is big, when it is located far from the central tower. By looking at
the shape of the floater on figure 4-4, one can see that exactly in these outer areas,
the damping is reduced by the buckets ending out of the water. The huge extensions
of the base slab close to the central tower seem to have a big impact on damping in
vertical direction. That cannot effect the pitching a lot.
The simulations with a Morison damping of 8.0 and linear damping of 6 kgm/s,
chosen for the pitch degree of freedom, deliver matching results with the experi-
mental data. The value for linear damping equals only 2.9% of critical damping
and is therefore less than for the heave degree of freedom. This nearly 80% lower
value compared to heave damping makes sense, because the overall damping of pitch
is also i.e. 77% lower, when the remaining energy after the first two oscillations is
compared.
A qualitative comparison of the last amplitudes shown in figure 5-6 reveals the
possibility of over damping the small motions in 3Dfloat. This might be due to too
much linear damping but needs to be further investigated.
62
7 Conclusion and outlook
It was the objective of this research to find out, if the 3Dfloat code is capable
of simulating the movement of the OO Star semisubmersible floater in heave and
pitch free decay motion and what parameters have to be used in the numerical
model. The measurement data of a plastic model in 1/40 scale in a water basin of
limited size therefore serve as a reference. Although reflections from the basin walls
and bed might influence the free decay, it is presumed, that these experimental data
represent the models behaviour in open waters. The measurements show oscillations
with periods that correspond to added masses, that are close to the expectations.
Some deviations from the expected behaviour, concerning the varying period lengths,
suggest that the experimental results were influenced by the history of the fluid
motion, especially while performing the heave drop tests. Further testing with more
sophisticated measuring equipment will show, if this is the reason or if the poor
sensors signal in heave tests causes the mentioned effect.
The distribution of the added mass to the buckets, pontoons and tower of the
model led to a deviation of about +10% in the period length of the pitch motion,
when the numerical data is compared with the experimental results. This is for an
unknown reason and can be corrected by measuring the moment of inertia for the
physical model, what is part of the subsequent testing campaign at ECN.
With regard to the damping characteristics, simulation results show good agree-
ment with the experimental data, when a CD value of 8.0 is applied in the Morison
equations and linear damping of 120 kg/s in heave and 6 kgm/s in pitch degree of
freedom is added to the numerical model. The water entrapment plates at the bot-
tom of the platform seem to contribute a high amount of the overall damping forces.
The damping of heave motions is stronger than the pitch damping. Further testing
should be done with additional plates in the bucket area to find out more about
their effect.
63
7 Conclusion and outlook
It also needs to be investigated, if the numerical model represents the damping
of very small motions properly. This can be done in the further testing campaign
at ECN. There the model’s motion will be recorded with a laser tracking system,
which will deliver more accurate measurement data.
It can be summarised, that the 3Dfloat code is suitable for simulating the motion
of the OO Star in heave and pitch, when the hydrodynamic forces achieved from
Morison equations are supplemented by linear damping forces. The further progress
of testing will show, if the results remain valid for coupled motions with other degrees
of freedom and under the influence of wave and wind loads. There is also a need
to further investigate, to what extent mooring lines influence the motion of the
platform.
64
Bibliography
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ph240/pratt1/docs/50543.pdf; visited on July 24th 2013.
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http://www.deutsches-museum.de/sammlungen/maschinen/kraftmaschinen/
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Faltinsen, O. M. (1990). Sea loads on ships and offshore structures. Cambridge
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iii
Declaration
I herewith declare, that I have completed the present thesis independently making
use only of the specified literature and aids. Sentences or parts of sentences quoted
literally are marked as quotations; identification of other references with regard to
the statement and scope of the work is quoted. The thesis in this form or in any other
form has not been submitted to an examination body and has not been published.
As, 2nd October 2013
Felix Kelberlau
iv
A Appendix
v
A Appendix
Figure A-1: Data sheet of Honeywell 945-L4Y-2D-1C0 ultrasonic distance sensor
vi
A Appendix
IG-500N - Specifications
Rev
2.3
Sp
ecii
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on
s a
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ub
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ho
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013
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© 2
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SB
G S
yste
ms
SBG Systems EMEA (Headquarters) Phone: +33 1 80 88 45 00 E-mail: [email protected] www.sbg-systems.com
SBG Systems North America Phone: +1 (773) 754 3272 E-mail: [email protected]
MECHANICAL DRAWINGAll dimensions are in millimeters
Side view
Top view
PRODUCT CODE: standard product options
IG-500N-G#A#P#-#
PACKAGING B: Box small size S: Box with SyncOut O: OEM version
PROTOCOL MODE 1: RS-232 2: Serial TTL3: CAN 2.0A/B4: RS-422
ACCELEROMETERS 1: 2 g 2: 5 g 3: 18 g
GYROSCOPES 2: 75 °/s 3: 150 °/s 4: 300 °/s 5: 600 °/s6: 1200 °/s
22
36,40
635,80
M3
49,40
PARAMETER SPECIFICATIONS REMARKS
Performance Aerospace Ground Marine / Subsea
Roll/Pitch (Dynamic) 1.0° RMS 0.8° RMS 0.35° RMS Under good GPS availability
Heading (Dynamic) 1.0° RMS 0.5° RMS 1.0° RMS Depends on heading aiding source
Resolution < 0.05° < 0.05° < 0.05°
Velocity (RMS) < 0.1 m/s < 0.1 m/s < 0.1 m/s Under good GPS availability
Position (SEP) < 2 m < 2 m < 2 m Under good GPS availability
Heave - - 10 cms or 10 % Whichever is greater
Sensing range 360° in all axes, no mounting limitation Solid state sensors
Inertial Sensors Accelerometers Gyroscopes Magnetometers
Measurement range ± 5 g ± 300 °/s ± 1.2 Gauss Refer to sensors options table
Non-linearity < 0.2 % < 0.05 % < 0.2 % % of full scale
Initial bias error ± 5 mg ± 0.5 °/s ± 0.5 mGauss Over temperature range
Bias in-run stability ± 0.06 mg 20 °/hr - Allan variance - constant temperature
Scale factor stability < 0.1 % < 0.05 % < 0.5 % Over temperature range
Noise density 0.25 mg/√ Hz 0.05 °/s/√ Hz 0.01 mG/√ Hz
Alignment error < 0.05° < 0.05° < 0.1°
Bandwidth 250 Hz 240 Hz 500 Hz 1 k Hz gyroscopes coning integrals
Sampling rate 10,000 Hz 10,000 Hz 1,000 Hz Advanced anti-aliasing FIR ilters
GPS Receiver
Receiver type L1 frequency, C/A Code, 50 Channels, SBAS, 4 Hz
Acquisition time < 1.0 s / 29 s Hot start / Cold start
Tracking sensitivity -160 dB
Pressure Sensor
Resolution 2.5 Pa / 20 cms / < 1 feet
Pressure accuracy ± 50 Pa / ± 150 Pa Relative / Absolute
Sampling rate 50 Hz
Communication
Available data Euler angles, quaternion, rotation matrix, velocity, position, heave, calibrated sensor data, delta angles, barometric data, device status, raw GPS data, UTC time reference, etc.
Each output can be enabled or disabled by the user. Output rate is user selectable
Output rate 100 Hz for orientation, velocity and position 500 Hz in IMU mode only
Serial interface RS-232, RS-422, TTL 3.3V or USBBinary proprietary protocol and NMEA/ASCII
RS-422 only for S and O packagesUSB using an external adapter
CAN interface CAN 2.0A/B up to 1 Mbit/s Only available for S and O packages
Physical
Dimensions OEM 27 x 30 x 14 mm, 1.1 x 1.2 x 0.6”
Dimensions box 36 x 49 x 22 mm, 1.4 x 1.9 x 0.9” B package
36 x 49 x 25 mm, 1.4 x 1.9 x 1” S package
Weight OEM 10 grams, 0.02 pounds
Weight box 44 grams, 0.1 pounds B package
48 grams, 0.1 pounds S package
Speciied temperature -40 to 85°C, -40 to 185°F Non-condensing environment
Shock limit 1,000 g (Powered); 2,000 g (Unpowered) Shocks can afect performance
Operating vibration 3 g RMS (20 Hz to 2 k Hz per MIL-STD 810G) Valid for 18g accelerometers
Electrical
Operating voltage 3.3 V to 30 V
Power consumption 800 mW @ 5.0 V High eiciency DC/DC converter
SyncOut, Trigger Open drain pull-up voltage -0.3 to 25 V Open drain, use a pull-up resistor
Start-up time < 1 s Valid data
OEM VERSION
Figure A-2: Data sheet of SBG IG 500-N inertial navigation system
vii
A Appendix
−40 −30 −20 −10 0 10 20 30
−14
−12
−10
−8
−6
−4
−2
0
2
4
6
8Heave drop test 14cm
Z−
posi
tion
in 1
0−2 m
Time in s
1st2nd3rd
−40 −30 −20 −10 0 10 20 30
−14
−12
−10
−8
−6
−4
−2
0
2
4
6
8Heave drop test 8cm
Z−
posi
tion
in 1
0−2 m
Time in s
1st2nd
Figure A-3: Heave drop test results, single test runs
viii
A Appendix
0 20 40 60 80 100 120
−8
−6
−4
−2
0
2
4
6
Pitch drop test 8deg
Ang
le in
deg
Time in s
1st2nd3rd
Figure A-4: Pitch drop test results, single test runs
ix
A Appendix
! 1:40 Scale model of OOStar concrete floater for test at ECN in September 2013
!
set_environment
gravity: on
buoyancy: on
hydro_force: morison
wind_force: ndrg
waves: extrapolated_airy
norder: -1
wind: no_mean_profile
rho_water: 1000.
rho_air: 1.29
nu_water: 1.e-5
nu_air: 1.e-6
wave_amplitude: 0.
wave_direction: 0.
current_speed: 0.
current_direction: 0.
wind_speed: 0.
wind_ref_height: 90.
wind_exponent: 0.
wind_direction: 0.
wave_ramps: 0.
wave_rampe: 20.
depth: 200.
spectral_peak: 10.
seed: .3
nfreq: 64.
tshift_waves: 800.
tshift_wind: 0.
tsweeps: 0.
tsweepe: -1.
stretch: 0.
wavelength: 156.07768226721353
pre_computed_waves_file: off
random_mode: write_file
random_file: irreg_waves.txt
!Global Morison coefficients are applied, if not specified elementwise
wave_forces cm_morison: 2.0 cd_morison: 0.7
! Geometry definition
define_material name: plast rho: 1225.0 e: 2.7e9 g: 0.97e9 ! real rho: 1154.4
define_material name: plast_sand_tower rho: 33065.94754 e: 2.7e9 g: 0.97e9 ! taking sand fill into account
define_material name: plast_water_tower rho: 17145.473773 e: 2.7e9 g: 0.97e9 ! taking water fill into account
define_material name: plast_sand_bucket rho: 41397.739541 e: 2.7e9 g: 0.97e9 ! taking sand fill into account
define_material name: plast_water_bucket rho: 21311.3697705 e: 2.7e9 g: 0.97e9 ! taking water fill into account
define_material name: plast_water_pontoon rho: 34141.84901 e: 2.7e9 g: 0.97e9 ! taking water fill into account
define_material name: plast_rna rho: 10185.39066 e: 2.7e9 g: 0.97e9 ! adjusted to 5 kg RNA
define_material name: plast_tower rho: 1636.37254 e: 2.7e9 g: 0.97e9
new_keypoints ! node # x y z [m]
1 0. 0. -.5 ! center column bottom
2 0. 0. -.4375 ! sand ballast upper level 2ton/m**3
3 0. 0. -.425 ! center column attachment
4 0. 0. -.2 ! water ballast upper level, also high-res area for elements -.2 to .2m
5 0. 0. 0. ! center still water node
6 0. 0. 0.2 ! high-resolution (wave forces) up to here
7 0. 0. .375 ! tower base
8 .1 0. -.425 ! center pontoon attachment
9 .5625 0. -.425 ! column 1 surface pontoon attachment
10 .6875 0. -.425 ! column 1 center pontoon attachment
11 .6875 0. -0.18625 ! water level
12 .6875 0. .0 ! column 1 swl
13 .6875 0. -.4375 ! sand level
14 .6875 0. -.5 ! column 1 bottom
new_boxmember_properties ! Pontoon, see python script for calculations
iprop: 1 ! Property set no
material: plast_water_pontoon
connect_mode: auto
btype: beam_lid1_lid2
ea1: 3701700.0 ea2: 3701700.0 ! axial stiffness at keypoints 1 and 2
eiy1: 48440.7 eiy2: 48440.7 ! EIyy bending stiffness, STIFFNESS FOR BENDING ABOUT Z AXIS !
eiz1: 15988.05 eiz2: 15988.05 ! EIzz bending stiffness, STIFFNESS FOR BENDING ABOUT Y AXIS !
lx1: .4625 lx2: .4625 ! equiv section length for use in drag calculations
ly1: .31 ly2: .31 ! section width for use in drag calculations
lz1: .15 lz2: .15 ! section height for use in drag calculations
m1: 46.808475 m2: 46.808475 ! mass per unit length at keypoint 1 and 2
ab1: 0.0465 ab2: 0.0465 ! area for buoyancy calculation
pre_strain_long: .0 ! longitudal pre-strain. optional keywords from here
pointmass1: 0. pointmass2: 0.
cdx: 0. cdy: 1. cdz: 10.4 ! drag coefficients
cmx: 1. cmy: 1. cmz: 4.61 ! inertia coefficients
Figure A-5: 3Dfloat input file 1/4
x
A Appendix
new_body
reftype: inertial
name: center_column
parent: inertial
axes: normal
! Central tower
!
new_elements_beam1 nelem 1 material plast_sand_tower connect_mode auto ! bottom to upper level sand
x1 0. 0. -.5 dcyl1 .2 tcyl1 0.003 pre_strain_long 0.
x2 0. 0. -.4375 dcyl2 .2 tcyl2 0.003 btype beam_lid1 cda 9.2 cma 8.63
new_elements_beam1 nelem 1 material plast_water_tower connect_mode auto ! upper level sand to pontoon attachment
x1 0. 0. -.4375 dcyl1 .2 tcyl1 0.003 pre_strain_long 0.
x2 0. 0. -.425 dcyl2 .2 tcyl2 0.003 btype beam cda 0. cma 0.01
new_elements_beam1 nelem 1 material plast_water_tower connect_mode auto ! pontoon attachment to upper level water
x1 0. 0. -.425 dcyl1 .2 tcyl1 0.003 pre_strain_long 0.
x2 0. 0. -.18174 dcyl2 .2 tcyl2 0.003 btype beam cda 0. cma 0.01
new_elements_beam1 nelem 1 material plast connect_mode auto ! upper level water to SWL
x1 0. 0. -.18174 dcyl1 .2 tcyl1 0.003 pre_strain_long 0.
x2 0. 0. .0 dcyl2 .2 tcyl2 0.003 btype beam cda 0. cma 0.01
new_elements_beam1 nelem 1 material plast connect_mode auto ! SWL to upper level high resolution
x1 0. 0. .0 dcyl1 .2 tcyl1 0.003 pre_strain_long 0.
x2 0. 0. .2 dcyl2 .2 tcyl2 0.003 btype beam cda 0. cma 0.01
new_elements_beam1 nelem 1 material plast connect_mode auto ! upper level high resolution to tower base
x1 0. 0. .2 dcyl1 .2 tcyl1 0.003 pre_strain_long 0.
x2 0. 0. .25 dcyl2 .2 tcyl2 0.003 btype beam cda 0. cma 0.01
! Tower
!
new_elements_beam1 nelem 1 material plast_tower connect_mode auto ! SWL to tower base
x1 0. 0. .25 dcyl1 .2 tcyl1 0.003 pre_strain_long 0.
x2 0. 0. 2.05 dcyl2 .2 tcyl2 0.003 btype beam cda 0. cma 1.
! Rotor nacelle assembly
!
new_elements_beam1 nelem 1 material plast_rna connect_mode auto ! SWL to tower base
x1 -.125 0. 2.05 dcyl1 .05 tcyl1 0.025 pre_strain_long 0.
x2 0. 0. 2.05 dcyl2 .05 tcyl2 0.025 btype beam
new_elements_beam1 nelem 1 material plast_rna connect_mode auto ! SWL to tower base
x1 0. 0. 2.05 dcyl1 .05 tcyl1 0.025 pre_strain_long 0.
x2 .125 0. 2.05 dcyl2 .05 tcyl2 0.025 btype beam
new_body
name: pontoon_1
reftype: refnode
xfind: 0. 0. 0.
rotorder: 123
rotation: 0. 0. 0.
axes: normal
parent: center_column
new_elements_beam1 nelem 1 material massless connect_mode auto ! attachment inside cylinder
x1 0. 0. -.425 dcyl1 .2 tcyl1 0.03 pre_strain_long 0.
x2 .1 0. -.425 dcyl2 .2 tcyl2 0.03 btype beamwb
new_elements_beam1 nelem 1 material massless connect_mode auto ! attachment inside cylinder
x1 .5625 0. -.425 dcyl1 .2 tcyl1 0.03 pre_strain_long 0.
x2 .6875 0. -.425 dcyl2 .2 tcyl2 0.03 btype beamwb
! bucket_1
!
new_elements_beam1 nelem 1 material plast_sand_bucket connect_mode auto ! bottom to upper level sand
x1 .6875 0. -.5 dcyl1 .25 tcyl1 0.003 pre_strain_long 0.
x2 .6875 0. -.4375 dcyl2 .25 tcyl2 0.003 btype beam_lid1 cda 10.96 cma 10.18
new_elements_beam1 nelem 1 material plast_water_bucket connect_mode auto ! upper level sand to pontoon
x1 .6875 0. -.4375 dcyl1 .25 tcyl1 0.003 pre_strain_long 0.
x2 .6875 0. -.425 dcyl2 .25 tcyl2 0.003 btype beam cda 0. cma 0.01
new_elements_beam1 nelem 1 material plast_water_bucket connect_mode auto ! pontoon to upper level water
x1 .6875 0. -.425 dcyl1 .25 tcyl1 0.003 pre_strain_long 0.
x2 .6875 0. -0.17524 dcyl2 .25 tcyl2 0.003 btype beam cda 0. cma 0.01
new_elements_beam1 nelem 1 material plast connect_mode auto ! upper level water to SWL
x1 .6875 0. -0.17524 dcyl1 .25 tcyl1 0.003 pre_strain_long 0.
x2 .6875 0. 0. dcyl2 .25 tcyl2 0.003 btype beam cda 0. cma 0.01
new_elements_beam1 nelem 1 material plast connect_mode auto ! SWL to top of bucket.
x1 .6875 0. 0. dcyl1 .25 tcyl1 0.003 pre_strain_long 0. ! lid2 will take water on deck into account
x2 .6875 0. .25 dcyl2 .25 tcyl2 0.003 btype beam_lid2 cda 0. cma 0.01
new_boxmembers nelem_default: 2 ! member_no keypoint_1 keypoint_2 Property_Set optional nelem
1 8 9 1 nelem: 1
Figure A-6: 3Dfloat input file 2/4
xi
A Appendix
new_body
name: pontoon_2
reftype: refnode
xfind: 0. 0. 0.
rotorder: 123
rotation: 0. 0. 120.
axes: normal
parent: center_column
copy_elements
from_body: pontoon_1
to_body: pontoon_2
new_body
name: pontoon_3
reftype: refnode
xfind: 0. 0. 0.
rotorder: 123
rotation: 0. 0. -120.
axes: normal
parent: center_column
copy_elements
from_body: pontoon_1
to_body: pontoon_3
! Just for station keeping, check of level
add_node_stiffness find 0. 0. 0.
f_lin 0. 0. -46.532754 0. 0. 0.
1 1 1.
2 2 1.
6 6 1.
!for linear damping
add_node_damping find 0. 0. 0.
3 3 120 ! i.e. 100 eq. 71% of last periods Amplitude, 445 for pure linear damping, 844 for critical damping
5 5 29 ! i.e. 8, 20 for pure linear damping
! Initial conditions
! Heave drop
apply_nodal_bc find: 0. 0. 0. apply_displ idofs: 1 idofe: 6 displ: 0. 0. -.1429 0. 0. 0. tstart: 0. tramp: 10. tend: 20.
! or Pitch drop
!apply_nodal_bc find: 0. 0. 0. apply_displ idofs: 1 idofe: 6 displ: 0. 0. 0. 0. -0.14336 0. tstart: 0. tramp: 10. tend: 20.
! Sensorer inn her
! sensor 18 to 23 platform displacements swl
!
monitor_element_b1 type orientation file turb1_swl.txt nmonitor 5 find 0. 0. 0. node 2 body_name inertial
label PtfmSurge PtfmSway PtfmHeave Ptfm_xx Ptfm_xy Ptfm_xz Ptfm_yx
! plotting with Python script plot_geo.py
monitor_element_b1 type: plot nmonitor: 100 file: turb1.plot
! Tecplot
monitor_element_b1 type: tecplot nmonitor: 1000 file: turb1.dat
! adjustment of sensor position above
monitor_element_b1 find 0. 0. -20 nmonitor 5 node 1 type gather
file sensor_outputs.txt label oc4_gather toffset 0.
sensors:
nfact: 1 source: PtfmSurge scale: 1. unit: [m] ! rel. inertia
nfact: 1 source: PtfmSway scale: 1. unit: [m] !
nfact: 1 source: PtfmHeave scale: 1. unit: [m] !
nfact: 1 source: Ptfm_xy scale: -57.295779513082323 unit: [deg] header: PtfmRoll
nfact: 1 source: Ptfm_xx scale: 57.295779513082323 unit: [deg] header: PtfmPitch
nfact: 1 source: Ptfm_yx scale: -57.295779513082323 unit: [deg] header: PtfmYaw
print_nodes
nodes.txt
-1 -1
newmark dt: 0.01 nassemble: 1 nnewton: 10 nsubmin: 2 rwilson: 0.9
relax: 0.0 resid_newton: 1e-06 nmonitor: 100
!material damping
damping type ratio2rayl ratio_1 .01 ratio_2 .01 omega_1 0.1 omega_2 1.
! Simulation length in ms
! 6000 for heave, 15000 for pitch
step nstep 6000 method gen_alpha
Figure A-7: 3Dfloat input file 3/4
xii
A Appendix
!printing and plotting to outputfile
!print_nodes
nodes.txt
-1 -1
!print_b1_elements
elements.txt
-1 -1
3 2 3 2
print_solution
solution.txt
END
!_______________________________________________________________________________
Figure A-8: 3Dfloat input file 4/4
Manual calculation of added mass for z-direction according to areas shown in fig. 4.6
Bucket area considered as a rectangular plate
Pontoon and tower areas considered as round plates
Calculation based on rule of thumb presented in 3.5.1
Bucket: given area=0.1864m, length=0.4625m
->width=0.403m
->cylinder: 59.00kg
Pontoon: given area=0.0917m
->radius=0.171m
->sphere: 20.89kg
Tower: given area=0.0173m
->radius=0.074m
->sphere: 1.71kg
total added mass: 81.6kg
times 3: 244.8kg
This approach neglects the influence of the dry areas of buckets and tower
Manual calculation of added mass for pontoon y-direction
Mass of displaced water from volume of pontoon (0.15m*0.31m*0.4625m)
Mass of added mass from circular cylinder with radius and length
mass of displaced water=21.506kg
length=0.4625m
radius=0.075m
added mass=8.173kg
The real added mass is higher because of the influence of the water entrapment plate
Figure A-9: Manual calculation of added mass
xiii