design, testing and validation of a scale model semisubmersible offshore wind turbine under regular...
TRANSCRIPT
Seediscussions,stats,andauthorprofilesforthispublicationat:http://www.researchgate.net/publication/265795516
Design,TestingandValidationofaScaleModelSemisubmersibleOffshoreWindTurbineunderRegularIrregularWavesandWindLoads
THESIS·AUGUST2014
DOWNLOADS
196
VIEWS
54
1AUTHOR:
LauraRolo
UniversityofStrathclyde
2PUBLICATIONS0CITATIONS
SEEPROFILE
Availablefrom:LauraRolo
Retrievedon:08September2015
DESIGN, TESTING AND VALIDATION OF A SCALE
MODEL SEMISUBMERSIBLE OFFSHORE WIND
TURBINE UNDER REGULAR/IRREGULAR WAVES
AND WIND LOADS
LAURA ROLO PÉREZ
A thesis submitted in partial fulfilment for the requirement of the degree
Master of Science
Sustainable Engineering: Offshore Renewable Energy
Under the supervision of Professor Alexander Day
Department of Naval Architecture, Ocean and Marine Engineering
University of Strathclyde
Glasgow, 2014
August 2014
DESIGN, TESTING AND VALIDATION OF A SCALE
MODEL SEMISUBMERSIBLE OFFSHORE WIND
TURBINE UNDER REGULAR/IRREGULAR WAVES AND
WIND LOADS
by
Laura Rolo Pérez
MEng in Civil Engineering
A THESIS
Submitted in Partial Fulfilment of the Requirements for
the Degree of Master of Science in Sustainable
Engineering: Offshore Renewable Energy
Under the supervision of Professor Alexander Day
Director of the Kelvin Hydrodynamics Laboratory, Glasgow
Department of Naval Architecture, Ocean and Marine Engineering
University of Strathclyde, Glasgow, UK
Copyright Declaration
This thesis is the result of the author’s original research. It has been composed by the
author and has not been previously submitted for examination which has led to the
award of a degree.
The copyright of this thesis belongs to the author under the terms of the United
Kingdom Copyright Acts as qualified by University of Strathclyde Regulation 3.50.
Due acknowledgement must always be made of the use of any material contained in,
or derived from, this thesis.
Signed: Laura Rolo Pérez
Date: 27th
August 2014
I
Abstract
Nowadays, Europe is facing an energy security challenge to satisfy its demand, as
more than the 50% of the energy consumed has to be imported. Moreover, fossil
fuels represent the vast majority of these energy resources, contributing to the
greenhouse gas emissions and their consequences. For these and many other reasons,
it is pursued a progressive shift to the renewable energies as the first solution for a
safe, secure, sustainable and affordable energy.
The offshore wind energy stands out as the most promising offshore renewable
energy for the next years and decades. Its main advantage in relation to its land-based
homogeneous technology is that its energy output is higher and steadier. In addition,
wind farms placed in deeper waters present the extra advantages of increasing power
output and reducing environmental and social impacts. However, larger water depths
require floating wind turbines whose optimal technology is still under research.
This work is focused on the performance of one of the offshore floating concepts: the
OC4-DeepCwind semisubmersible wind turbine, because of its minimal dynamic
coupling between wave-induced and turbine-induced motion and its easier and
lower-cost offshore installation. To asses this issue, a 1/80th
scale model is designed,
assembled and tested under different configurations of regular waves, sea states and
wind loads at the Kelvin Hydrodynamic Laboratory in Glasgow. The experimental
results confirm the high stability of the floating platform under the waves and wind
loads and reveals considerable hydrodynamic nonlinearities which most of the
numerical analysis does not display but might play a critical role in certain load
conditions.
Key words
Offshore, windturbine, floating, semisubmersible, platform, OC4-DeepCwind,
model, test, basin, nonlinearities
II
Acknowledgements
Firstly, I wish to express my profound gratitude to my thesis supervisor, Professor
Alexander Day, for offering his encouragement, guidance and sharing his knowledge
which allowed me to take giant steps in this topic. In particular, special thanks for
having given to me the opportunity to develop and test this floating wind turbine
model, with the great responsibility that entails. This is a great added value I
appreciate and retain for my next professional experiences.
I would like to specially thank the staff at the Kelvin Hydrodynamic Laboratory: Bill
McGuffie and Bill Wright for turning plans into reality; Charles Keay for
coordinating all procedures in model fabrication and tests; and Edward Nixon and
Grant Dunning for sharing their vast knowledge in basin testing and their company
during the long but rewarding testing hours. Special thanks also to Adil Akgül and
Steven Martin for their help with data acquisition and interpretation of results.
I would also like to send my appreciation and countless thanks to Fundación
Iberdrola and Scottish Power Foundation for the Fundación Iberdrola Scholarship I
have received, which has allowed me to join this MSc program and venture in this
new innovative direction.
Sincere thanks to the professors and rest of staff at the University of Strathclyde for
their approachability and rich share of knowledge and experiences. Special thanks
are to all my friends in Glasgow who made my time at University of Strathclyde an
unforgettable experience.
Last but not least, I extend my most special and sincerest gratitude to my loved ones
for always standing by me and supporting me at this endeavour, especially to my
parents to whom I owe everything.
III
Table of Contents
Copyright Declaration .................................................................................................. II
ABSTRACT ..................................................................................................................... I
ACKNOWLEDGEMENTS .................................................................................................. II
TABLE OF CONTENTS .................................................................................................. III
LIST OF TABLES ......................................................................................................... VII
LIST OF FIGURES ......................................................................................................... IX
LIST OF NOMENCLATURE ......................................................................................... XIII
LIST OF ABBREVIATIONS AND ACRONYMS .............................................................. XVII
CHAPTER 1 INTRODUCTION ........................................................................ 1
1.1 Outline of the Thesis .......................................................................................... 1
1.2 Aim of this Thesis .............................................................................................. 2
1.3 Introduction ........................................................................................................ 4
1.4 Present & Future of Offshore Wind Energy ....................................................... 5
1.5 Main Advantages of Offshore Wind Power ....................................................... 7
1.6 Classification of Offshore Wind Turbines ......................................................... 8
1.7 Challenges of Offshore Floating Wind Turbines (Critical Review) ................ 10
CHAPTER 2 LITERATURE REVIEW ............................................................ 13
2.1 Theory of Waves .............................................................................................. 13
2.1.1 General Waves Defining Parameters in Time Domain ............................. 15
2.1.2 Regular Waves ........................................................................................... 17
2.1.3 Irregular Waves ......................................................................................... 19
2.2 Aero-Servo-Hydro-Elastic Analysis of the Offshore Floating Wind Turbine
System .................................................................................................................... 22
IV
2.2.1 Equation of Motion .................................................................................... 23
2.3 Hydrodynamic Loads ........................................................................................ 24
2.3.1 Linear Hydrodynamics ............................................................................... 24
2.3.2 Linear Time-Domain Hydrodynamic Model ............................................. 26
2.3.3 Frequency-Domain Approach .................................................................... 28
2.3.4 Non-Linear Effects ..................................................................................... 29
2.4 Hydrostatic Properties & Stability .................................................................... 31
2.5 Damping and Natural Frequency Response ..................................................... 33
2.5.1 Free-vibration of viscous-damped 6 DOF systems .................................... 34
CHAPTER 3 DESIGN OF THE SCALE MODEL TESTS ................................... 37
3.1 Basin Specifications .......................................................................................... 37
3.1 OC4 – DeepCwind 5 MW Semisubmersible floating wind system ................. 38
3.1.1 OC4 DeepCwind OFWT System Description ........................................... 39
3.1.2 Floating Wind System Natural Frequencies .............................................. 41
3.2 Model Scaling Methodology ............................................................................ 42
3.2.1 Scaling Criteria .......................................................................................... 42
3.2.2 Established Scaling Factors ....................................................................... 47
3.2.3 Modelling of Floating Platform ................................................................. 48
3.2.4 Modelling of Mooring Lines ...................................................................... 48
3.2.5 Modelling of Environment ......................................................................... 49
3.3 Model Dimensions ............................................................................................ 49
3.3.1 Model Fidelity ............................................................................................ 51
3.4 Model Environment Loads ............................................................................... 52
3.4.1 Regular Waves ........................................................................................... 52
3.4.2 Irregular Waves .......................................................................................... 53
3.4.3 Wind ........................................................................................................... 54
V
3.4.4 Drag Disk Modelling (Rotor) .................................................................... 55
3.5 Test Matrix ....................................................................................................... 56
3.6 Tests Procedure ................................................................................................ 57
3.7 Calibration of Environment .............................................................................. 58
3.7.1 Wind assessment and calibration ............................................................... 58
3.7.2 Waves Calibration ..................................................................................... 59
CHAPTER 4 MODEL TEST RESULTS .......................................................... 61
4.1 System Identification Tests .............................................................................. 61
4.1.1 Inclining Test ............................................................................................. 61
4.1.2 Free Decay ................................................................................................. 64
4.1.3 Only Regular Waves .................................................................................. 71
4.1.4 Only Oblique Regular Waves .................................................................... 76
4.1.5 Regular Waves + Wind .............................................................................. 78
4.2 Station Keeping Test Types ............................................................................. 81
4.2.1 Sea States ................................................................................................... 82
4.2.2 Motions Significant Height........................................................................ 85
4.2.3 Frequency Domain Analysis - Spectral Analysis ...................................... 87
CHAPTER 5 NUMERICAL MODEL ........................................................... 101
5.1 Introduction .................................................................................................... 101
5.2 Data Input ....................................................................................................... 102
5.3 Results ............................................................................................................ 104
5.3.1 Response Amplitude Operators – AQWA Diffraction Tool ................... 104
5.3.2 Resultant Motion Results ......................................................................... 106
CHAPTER 6 SUMMARY AND CONCLUSIONS ............................................ 109
BIBLIOGRAPHY ...................................................................................... 113
VI
ANNEX I TEST INSTRUMENTATION ......................................................... 119
I.1 Instrumentation required for the Inclining Test ......................................... 119
I.2 Instrumentation required for test in only regular/irregular waves ............. 119
I.3 Instrumentation required for test in regular/irregular waves and wind ..... 122
I.4 Others ......................................................................................................... 124
ANNEX II LABORATORY DIARY ............................................................ 127
ANNEX III CALCULATION OF OFWT HYDROSTATIC PROPERTIES .......... 147
III.1 OFWT Centre of gravity ............................................................................ 147
III.2 Platform Hydrostatic Properties ................................................................ 148
VII
List of Tables
Table 3.1. Modelled Designs from 2005 to 2013 by the OC3 and OC4 projects ...... 38
Table 3.2. Floating Wind Turbine System Natural Frequencies (s) according to
different authors (with no wind) ................................................................................ 41
Table 3.3. Floating Wind Turbine System Natural Frequencies (s) with wind ......... 41
Table 3.4. Established scaling factors for floating wind turbine model testing ......... 47
Table 3.5. OC4-DeepCwind OWT system prototype and 1:80 scale model
dimensions ................................................................................................................. 50
Table 3.6. Difference between target and model (1:80) ............................................ 52
Table 3.7. Regular Waves Tested .............................................................................. 52
Table 3.8. Sea States Tested....................................................................................... 54
Table 3.9- NREL 5MW Wind Environment and equivalent Thrust Forces .............. 55
Table 3.10. System Identification Tests ..................................................................... 57
Table 3.11. Station Keeping Tests ............................................................................. 57
Table 3.12. Wind Flow Assessment with standard Skywatch Xplorer 2 anemometer
.................................................................................................................................... 58
Table 3.13. Wind Speed (m/s) Test Parameters ......................................................... 59
Table 4.1. Inclining test results for model without drag disk .................................... 63
Table 4.2. Inclining test results for model with installed drag disk .......................... 63
Table 4.3. Natural Periods (NP), Natural Frequencies (NF) and Damping Ratios
(DR) tested under wind and no wind loads and comparison with references in the
bibliography ............................................................................................................... 70
Table 4.4. Sea States parameters in full and model scale .......................................... 82
Table 4.5. Statistics for measured JONSWAP spectra .............................................. 84
Table 4.6. Spectral coefficients .................................................................................. 89
Table II.1 Materials used in platform scale model................................................... 128
Table II.2. Extra weight to be considered in the platform model ............................ 129
Table II.3. Spike2 Data entry for Inclining Test I-3 ................................................. 129
Table II.4. Feedback from Inclining Test I-3 ........................................................... 131
VIII
Table II.5. Components Masses of the Turbine Model ............................................ 132
Table II.6. Floating Wind Turbine System Model Weight before ballasting ........... 133
Table II.7. Floating Wind Turbine System Model Weight after ballasting ............. 133
Table II.8. Spike2 Data entry for Inclining Test I-3 ................................................. 134
Table II.9. Irregular wave configuration .................................................................. 137
Table II.10. Significant NREL 5MW wind speed conditions and correspondent thrust
forces in prototype scale and model scale ................................................................ 138
Table II.11. Mean Wind Velocities Measurements (m/s) at 5, 5.5 and 6.5 meters from
the funs position ....................................................................................................... 139
IX
List of Figures
Figure 1.1. Installed capacity – cumulative share by country (MW) (EWEA, 2014) . 6
Figure 1.2. Global offshore wind generation and projection by IEA and MTRMR
2012 (IEA, 2013) ......................................................................................................... 7
Figure 1.3 (a) Fixed Offshore Wind Turbines (b) Floating Offshore Wind Turbines
(Wiser, R. et al., 2011) ................................................................................................. 8
Figure 1.4Semisubmersible OFWT concepts: (a) DeepCwind, (b) Windfloat .......... 10
Figure 2.1. Superposition of Waves (Thurman, 1997) .............................................. 14
Figure 2.2. Ranges of validity for various wave theories (Kraineest, 2009) ............. 18
Figure 2.3. Platform modes of motion (Chen, 2012) ................................................. 25
Figure 2.4. DeepCWind Offset Column Stability Diagram ....................................... 32
Figure 2.5. Underdamped Oscillation (Rao, 2004) .................................................... 35
Figure 3.1. OC4 DeepCwind Semisubmersible Floating System (Author) ............... 40
Figure 3.2. Plan (left) and Side (right) view of the DeepCwind Semisubmersible
Platform (Robertson, et al., 2012) .............................................................................. 40
Figure 3.3. Model with drag disk installed ................................................................ 56
Figure 3.4. Wind sentry set test ................................................................................. 59
Figure 3.5. Results of the wave probe calibration...................................................... 60
Figure 3.6. Screen Capture of the wave maker software used for the irregular waves
calibration .................................................................................................................. 60
Figure 4.1. Model without drag disk during the Inclining Experiment ..................... 62
Figure 4.2. Platform motions response in Pitch Free Decay Test (without wind) ..... 65
Figure 4.3. Platform motions response in Roll Free Decay Test (without wind) ...... 65
Figure 4.4. Platform motions response in Heave Free Decay Test (without wind) ... 66
Figure 4.5. Platform motions response in Surge Free Decay Test (without wind) .... 66
Figure 4.6. Pitch Free Decay Data and Fit ................................................................. 67
Figure 4.7. Heave Free Decay data and Fit ................................................................ 68
Figure 4.8. Surge Free Decay data (Spike2 view) ..................................................... 68
X
Figure 4.9. Parameters used in the log-decrement method to obtain the damping ratio
.................................................................................................................................... 69
Figure 4.10. System configuration for only regular wave tests .................................. 71
Figure 4.11. Photography of the model during one test in only regular waves .......... 72
Figure 4.12. From Spike2 raw data representation: (a) Reflected waves, (b) Almost
broken waves, (c) Waves not yet stabilized ............................................................... 73
Figure 4.13. Pitch RAO for regular waves with wave height equal to 1, 2, 4 and 6
meters ......................................................................................................................... 74
Figure 4.14. Heave RAO for regular waves with wave height equal to 1, 2, 4 and 6
meters ......................................................................................................................... 74
Figure 4.15. Surge RAO for regular waves with wave height equal to 1, 2, 4 and 6
meters ......................................................................................................................... 74
Figure 4.16. Non-linear effects seen during test simulation ....................................... 75
Figure 4.17. System configuration for only oblique regular wave tests ..................... 77
Figure 4.18. RAO for oblique regular waves (wave incident angle 60º) with wave
height equal to 2 and 6 meters: (a) Pitch, (b) Roll, (c) Heave and (d) Surge ............. 78
Figure 4.19. System configuration for regular waves + wind tests ............................ 79
Figure 4.20. RAO for regular waves + wind with wave height equal to 2 and 6
meters: (a) Pitch, (b) Roll, (c) Heave and (d) Surge ................................................... 80
Figure 4.21. Scale model during test under wave and wind loads. It is noticeable the
increment in the heel angle due to the wind load ....................................................... 81
Figure 4.22. System configuration for the sea states’ tests ........................................ 82
Figure 4.23. Theoretical JONSWAP spectra .............................................................. 83
Figure 4.24. Significant Height of pitch for load cases with only waves and waves +
wind ............................................................................................................................ 86
Figure 4.25. Significant Height of roll for load cases with only waves and waves +
wind ............................................................................................................................ 86
Figure 4.26. Significant Height of heave for load cases with only waves and waves +
wind ............................................................................................................................ 86
Figure 4.27. Significant Height of surge for load cases with only waves and waves +
wind ............................................................................................................................ 87
Figure 4.28 Theoretical and Measured JONSWAP spectra under wind load (W)
when data available .................................................................................................... 92
XI
Figure 4.29. PSDs from test data for pitch, roll, heave and surge for an irregular wave
only case with Hs = 2 m and Tp = 7.5 sec .................................................................. 92
Figure 4.30. PSDs from test data for pitch, roll, heave and surge for an irregular wave
only case with Hs = 2.44 m and Tp = 8.1 sec ............................................................. 93
Figure 4.31. PSDs from test data for pitch, roll, heave and surge for an irregular wave
only case with Hs = 3.66 m and Tp = 9.7sec .............................................................. 93
Figure 4.32. PSDs from test data for pitch, roll, heave and surge for an irregular wave
only case with Hs = 5.49 m and Tp = 11.3 sec ........................................................... 94
Figure 4.33. PSDs from test data for pitch, roll, heave and surge for an irregular wave
only case with Hs = 9.14 m and Tp = 13.6 sec ........................................................... 94
Figure 4.34. PSDs from test data for pitch, roll, heave and surge for an irregular wave
only case with Hs = 10.5 m and Tp = 14.3 sec ........................................................... 95
Figure 4.35. Pitch RAO values for the six sea states tested ....................................... 97
Figure 4.36. Roll RAO values for the six sea states tested ........................................ 98
Figure 4.37. Heave RAO values for the six sea states tested ..................................... 98
Figure 4.38. Surge RAO values for the six sea states tested ...................................... 99
Figure 5.1. Representation of the OC4-DeepCwind OFWT system in ANSYS
AQWA ..................................................................................................................... 101
Figure 5.2. Geometry transformed in ANSYS DesignModeler ............................... 102
Figure 5.3. Mesh ...................................................................................................... 103
Figure 5.4. Pitch RAO comparison between only regular wave tests and AQWA
simulation ................................................................................................................. 105
Figure 5.5. Heave RAO comparison between only regular wave tests and AQWA
simulation ................................................................................................................. 105
Figure 5.6. Surge RAO comparison between only regular wave tests and AQWA
simulation ................................................................................................................. 105
Figure 5.7. Motions for H = 2.44 m and T = 8.10 sec ............................................. 106
Figure 5.8. Model in regular waves Hs = 2 m and Tp =8.10 sec .............................. 106
Figure 5.9. Motions for H = 5.44 m and T = 11.6 sec ............................................. 107
Figure 5.10. Model in regular waves H = 6 m and Tp =11.3 sec ............................. 107
Figure 5.11. Motions for H = 10.5 m and T = 13.16 sec ......................................... 108
Figure 5.12. Model in irregular waves Hs = 10.5 m and Tp =14.3 sec ..................... 108
Figure I.1. Inclinometer and inclining masses ......................................................... 119
XII
Figure I.2. Tank carriage .......................................................................................... 120
Figure I.3. Wave Maker ........................................................................................... 120
Figure I.4. Equipment Controls and Data Loggers mounted on the carriage ........... 121
Figure I.5. Wave Probe ............................................................................................. 121
Figure I.6. a) Qualisys Camera, b) Passive marker balls ......................................... 122
Figure I.7. Video recording camera .......................................................................... 122
Figure I.8a) Skywatch Xplorer 2 Anemometer, b) Wind Sentry Set & c) Clarke
CAM6000 Fan .......................................................................................................... 124
Figure I.9. a) Vacuum, b) Laser distance meter, c) Reference balls panel ............... 125
Figure II.1 Model being built in the workshop of the Kelvin Hydrodynamic
Laboratory ................................................................................................................ 128
Figure II.2. Weight placed on one of the offset columns’ bottom in order to achieve
the 1:80 model weight target .................................................................................... 129
Figure II.3. Inclining test for the semisubmersible platform. The different pictures
show the test procedure where the inclining masses change their position. ............ 130
Figure II.4. Calibration of the Qualysis Cameras ..................................................... 131
Figure II.5. Qualisys Track Manager Screenshot ..................................................... 132
Figure II.6. (a) wave Probe situated 10 meters away the wave maker, (b) probe slots
.................................................................................................................................. 135
Figure II.7. Model positioned and moored ............................................................... 136
Figure II.8. Roll Free Decay Test ............................................................................. 137
Figure II.9. Anemometer attached to a carbon fiber stick to measure the instant wind
speed in the turbine testing position ......................................................................... 139
Figure II.10. Floating system being tested in Irregular Waves ................................ 140
Figure II. . odel rotated and tested under H = 6 m regular waves ................. 141
Figure II.12. Free decay tests: a) Pitch and b) Surge ............................................... 143
Figure II.13. Image of the model from the Qualisys Cameras Software .................. 144
V. - Figure IV.2. DeepCWind Offset Column Stability Diagram ........................ 148
Figure IV.3. Platform dimensions in water plane .................................................... 149
Figure IV.4. Semisubmersible platform hydrostatic parameters .............................. 151
XIII
List of Nomenclature
Symbols
Latin Symbols
= Wave crest height
= Wave crest depth
( ) = Added mass matrix
= Random wave amplitudes
= Swept area of the rotor
= Wave amplitude
= Spectral normalizing
factor
= Metacentric radius
= External damping
contribution
( ) = Radiation damping matrix
= Power coefficient
= Thrust coefficient
= Restoring stiffness
( ) = Wave excitation force
= Generalized active forces
= Generalized inertia forces
= Metacentric height
= Righting lever
⁄ = Significant wave height
= Mean wave height
= Spectral wave significant
height
= Root mean squared wave
height
= Significant wave height
= Wave radiation
Retardation kernel
= Keel-center of gravity
distance
= Fluid length of travel
= Mass matrix
= Total mass of the OFWT
system
= Rotor radius
= Wave steepness
= Apparent of virtual wave
period
= Period of the damped
vibration
= Energy wave period
= Spectral zero-up-crossing
period
= Spectral mean wave period
= Peak wave period
= Statistical peak wave
period
= Total sampling time in the
spectral analysis
XIV
= Time zero-crossing period
= Ursell number
= Submerged platform
volume
= Damping constant
= Critical damping
= Group velocity
= Wave frequency
( ) = Signal data in time domain
= Sampling frequency in the
spectral analysis
= General spectral moment
= DOF velocity
= Amplitude peak
E = Average energy density
( ) = Discrete Fourier transform
in frequency domain
( ) = Fourier transform in
frequency domain
P = Energy flux
= Rotor thrust
z = Surface elevation
= Phase velocity
= Froude number
= Wave height
= Length
=
Total number of discrete
data in the spectral
analysis
= Power
= Radius
= Reynolds number
( )
( ) = Power spectral density
= Standard deviation
= Wave period
= Mean wind speed
= Wind speed
= Watt
= Acceleration due to gravity
= Wave number
= DOF displacement
= Time
= Control input
= Mean velocity of the
object relative to the fluid
XV
Greek Symbols
= Scale model factor
= Angular velocity of rotor
= Density of air
= Wave phase
Wave angular frequency
= Wave propagation direction
= Random wave phases
= Random wave angular
frequencies
= Variable time
= Non-dimensional definitions
of structure motions
ϕh = Heel angle
= Damping ratio
λ Wave length
= Apparent of virtual wave
length
= Rotor angular speed
= Angular spectral peak
frequency
= Spectral peak shape
parameter
= Spectral width parameter
= Offset
= Damped natural frequency
= Shallow water parameter
= Dynamic viscosity
= Water density
XVII
List of Abbreviations and
Acronyms
BC Base column
CB Center of buoyancy
cfm cubic feet per minute
CM centre of mass
COG centre of gravity
DFT Discrete Fourier transform
DNV Det Norske Veritas
EC European Commission
EU European Union
EWEA European Wind Energy Technology Platform
FFT Fast Fourier Transform
GHG greenhouse gases
IEA International Energy Agency
IPCC Intergovernmental Panel on Climate Change
JONSWAP Joint North Sea Wave Project
LVDT Linear variable differential transformer
MC Main column
MTRMR Medium-Term Renewable Energy Market Report
NREL National Renewable Energy Laboratory
O&G oil and gas
OC4 Offshore Code Comparison Collaboration Continuation
OFWT offshore floating wind turbine
OWT offshore wind turbine
PM Pierson Moskowitz
PSD Power Spectral Density
RAO response amplitude operator
RE renewable energies
SWL surface water level
XVIII
TLP Tension Leg Platform
TSR tip speed ratio
UC Offset column
UK United Kingdom
US United States of America
1
CHAPTER
1 Introduction
1.1 Outline of the Thesis
This work starts with a brief overview on the state of the art of the offshore floating
wind turbine systems and presents the main challenges in the deep-offshore wind
industry. Reading through those lines would make the reader to understand the need
for further research in the topic which concerns the present thesis and the reasons for
having chosen a semisubmersible platform for the offshore wind turbine.
Particularly, the offshore floating system chosen comprises the DeepCwind
semisubmersible platform with the 5 MW NREL wind turbine. This system
constitutes the design belonging to the Offshore Code Comparison Collaboration,
Continuation (OC4): Phase II Results of a Floating Semisubmersible Wind System,
project under International Energy Agency (IEA) Wind Task 30.
Chapter 2 presents a review of the existing literature in order to offer the essential
concepts to describe the interaction between the environmental conditions (wind and
mostly waves) and the offshore floating wind turbine (OFWT) system. Special
attention is given to the hydrodynamic analysis in time and frequency domains and
the spectral analysis.
Following, Chapter 3 brings the model and environment scale methodology to
follow for basin tests. The full scale prototype and model dimensions calculated
with Froude methodology are also presented. The chapter finishes with a summary of
all the tests carried out at the Kelvin Hydrodynamic Laboratory (Glasgow) and the
calibration of the tests environment (wind and waves).
1
2
CHAPTER 1 Introduction
The results of the environment and model tests are shown and discussed in Chapter
4, the longest chapter of the thesis. It is divided in two sections attending the nature
of the model tests: system identification tests (inclining test, free decay, only regular
waves, only oblique regular waves and regular waves + wind) and sea states’ ones.
The data is properly elaborated in order to present meaningful indicators of the
system performance under the different loads. Numerous comparisons with the
literature and other authors’ works are also included.
A brief numerical analysis of the OC4-DeepCwind semisubmersible platform is
carried out with the software ANSYS AQWA and explained in Chapter 5 in order to
compare with the experimental results and others authors’ ones.
A final Chapter 6 includes last comments, conclusions and further proposed work
about the topic particularly. After the list of References and Bibliography used in this
work, the Annexes include an interesting diary of the testing days with test
procedures, problems solving and chronological description of the tests. The
instrumentation used and calculation of hydrostatic OFWT properties are also
included in this last part of the document.
1.2 Aim of this Thesis
The aim of this MSc Thesis is to learn and contribute to the research of the most
promising offshore renewable energy for the next years and decades: the offshore
wind energy.
In particular, the research is done on one type of the floating wind turbine concepts,
the only ones which can be installed in depths greater than 50 meters. It is chosen an
existing semisubmersible wind turbine system: the DeepCwind, in order to create a
comparative to the few existing reports through hydrodynamic tank experimental
testing and numerical analysis.
Accordingly, the specific objectives of the thesis are:
3
CHAPTER 1 Introduction
- Design of a 1/80th
scale model of the OC4-DeepCwind semisubmersible wind
turbine system according to Froude number methodology
- Calculation of the platform hydrostatic and hydrodynamic properties through
system identification tests in the Kelvin Hydrodynamic Tank
- Study of the performance and determining of RAO of the floating model for
six different cases of sea states tests in the Kelvin Hydrodynamic Tank
- Comparison of the experimental results with literature, other authors’ works
and a hydrodynamic numerical analysis simulated with the software ANSYS-
AQWA
- Discuss the validation of the experimental model tests and the observed
advantages and drawbacks of the OC4-DeepCwind semisubmersible system
4
CHAPTER 1 Introduction
1.3 Introduction
The energy sector is one of the columns of growth, competitiveness and development
in our modern economy. Nevertheless, just with safe, secure, sustainable and
affordable energy a promising future for the sector can be secured.
EU is facing an energy security challenge to satisfy its demand as more than the 50%
(European Commission, 2013) of the energy consumed has to be imported, some of
the cases from countries who pose a high risk of internal instability (De Micco &
Andrés Figueroa, 2014).
Moreover, fossil fuels represent the vast majority of these energy resources, and the
energy-related emissions account for almost 80% of the EU´s total greenhouse gas
emissions (European Commission, 2013), which directly contribute to climate
change and its consequences (IPCC, 2014). In addition, this represents a Catch-22
situation: climate change is today directly affecting energy security, as it has the
potential to act as a multiplier/accelerant for conflicts and extreme weather
conditions which can cause energy disruptions (Umbach, 2009).
In contrast, energies from renewable resources (solar, thermal, wind, hydro, tidal,
wave, biomass, and geothermal energies) have an essential role to contribute to a
safe, secure, sustainable and affordable energy future. Renewable energies allow
increasing the energy autonomy of a region and therefore decreasing the sensitivity
to international fluctuating energy prices (Molho, 2013). In addition, RE do not
considerable contribute to greenhouse gases (GHG) emissions and their operating
costs are much lower than for the rest of conventional energies (ARUP, 2011).
In this context, the European Council and Parliament agreed to an integrated climate
and energy policy and adopted the “Energy Action Plan” to maintain a careful
balance between all three parameters: (i) security of supply, (ii) competitiveness and
(iii) environmental sustainability (European Commission, 2010). The three 20%
targets to achieve by 2020 are:
5
CHAPTER 1 Introduction
Reduction in GHG emissions by 20% compared to 1990 levels or by 30% if
the conditions are right
20% share of energy from renewable sources in gross final energy
consumption
20% improvement in energy efficiency
In the case of United Kingdom, the Government objective by 2020 is to reduce GHG
emissions by at least 34% compared with 1990 levels, increase the share of
renewable energy to 15% by 2020 and enhance the energy efficiency of homes,
business and transport (HM Government, 2014).
Scottish Government gives a further step, and its policy aims to reduce 42% in GHG,
generates the equivalent of % of Scotland’s gross annual electricity consumption
and 11% of its heat by renewable resources (The Scottish Government, 2011).
1.4 Present & Future of Offshore Wind Energy
Total wind energy has presently risen to 2.6% global share (IEA, 2013) and 8% share
of EU consumption (EWEA, 2014), but just an insignificant proportion comes from
offshore wind farms. Globally, just a 2% of total global installed wind power
capacity comes from offshore developments (Sawyer, 2012).
However, in the case of some European countries the situation of the offshore wind
energy is very different, where the total installed capacity across Europe has reached
6,562 MW, producing 24 TWh in a normal wind year, enough to cover 0.7% of the
EU’s total electricity consumption1. A total of 2080 offshore wind turbines are
installed and connected to the grid in 69 wind farms in eleven European countries,
mainly in the United Kingdom (3.7 GW) and Denmark (1.3 GW), with large plants
also installed in Belgium, Germany, the Netherlands and Sweden (EWEA, 2014).
1 According to Eurostat’s latest figures, the EU’S gross domestic consumption of electricity was 3,3
Twh.
6
CHAPTER 1 Introduction
Figure 1.1. Installed capacity – cumulative share by country (MW) (EWEA, 2014)
The Global Wind Energy Council (CWEC) states that the potential of offshore wind
could meet Europe’s energy demand seven times over, and the United States’ energy
demand four times over. Nevertheless, the offshore wind power progress is delayed
because it remains expensive and technically challenge.
It is known that in offshore projects the turbine accounts for less than half of the
investment cost, important difference in comparison to the three-quarters for land-
based projects. Offshore projects incur additional expenses for foundation, electric
infrastructure and installation costs, which vary with distance from shore and water
depth. However, the IEA Roadmap (2013) expects a reduction in wind power costs
of 45% offshore by 2050.
Looking to the future and according to the more ambitious projections, a total of 80
GW of offshore wind power could be installed by 2020 worldwide, with three
quarters of this in Europe (Sawyer, 2012). EC (2012) predicts a scenario of 40 GW
installed capacity by 2020 (equivalent to 4% EU electricity demand) and 150 GW by
2030 (14% EU electricity demand).
7
CHAPTER 1 Introduction
Figure 1.2. Global offshore wind generation and projection by IEA and MTRMR 2012 (IEA,
2013)
Policies are another important motive in this context. Thanks to the EU renewable
energy targets and incentives for investments such as feed-in tariffs or green
certificates, offshore wind power generation has started to expand rapidly in Europe
(European Commission, 2012) and for example, offshore wind power has become
essential in the UK strategy.
1.5 Main Advantages of Offshore Wind Power
The main advantage offshore wind power presents in relation to its land-based
homogeneous technology it is that its energy output is higher and steadier. The sea
emplacement allows greater rotor diameters, at the same time that the wind flow is
much stronger and steadily off the coasts. In addition, offshore breezes can be strong
in the afternoon, unlike wind over the continent, matching the time when people are
using the most electricity. Another plus it is the limitation by space and visual impact
of onshore wind farms or even the depletion of appropriate onshore
emplacements in some regions.
Moreover, offshore wind farms can be located near large coastal demand centres,
often avoiding long transmission lines to get power to demand, as can be the case for
8
CHAPTER 1 Introduction
land-based renewable power installations. This can make offshore particularly
attractive for countries with coastal demand areas and land-based resources located
far inland, such as China, several European countries and the US.
While needing to satisfy environmental stakeholders, offshore wind farms generally
face less public opposition and, to date, less competition for space compared with
developments on land.
Furthermore, offshore wind farms placed in deeper waters present the extra
advantages of increasing power output because of the better wind conditions,
reducing the visual pollution and the environmental impact on the seabed and
decreasing the interferences with marine activities.
1.6 Classification of Offshore Wind Turbines
Figure 1.3 (a) Fixed Offshore Wind Turbines (b) Floating Offshore Wind Turbines (Wiser,
R. et al., 2011)
Up to now, most of the current offshore wind turbines have been built in relatively
shallow water (<45 meters depth) and supported by gravity bases, jackets or
monopoles driven into the seafloor (see Figure 1.3 (a)). Larger water depths, which
increase the average wind power available, require floating wind turbines tethered to
(a) (b)
9
CHAPTER 1 Introduction
the seabed via cables instead of monopoles (see Figure 1.3 (b)). Numerous floating
support configurations are possible for use with offshore wind turbines, particularly
when considering the variety of systems in the offshore oil and gas (O&G) industry.
A classification of floating platforms in terms of how they achieve basic static
stability are:
Ballast (e.g. Spar-buoy): Platforms that achieve stability by using ballast
weights hung below a central buoyancy tank which creates a righting moment
a high inertial resistance to pitch and roll and usually enough draft to offset
heave motion.
Mooring Lines (e.g. Tension Leg Platform TLP): Platforms which achieve
stability through the use of mooring line tension.
Buoyancy (e.g. Barge): Platforms that achieve stability through the use of
distributed buoyancy, taking advantage of weighted water plane area for
righting moment.
The floating platform which concerns us in this thesis, the semisubmersible type, is
a case of hybrid concept, as it achieves stability through restoring features from the
three classes cited above. Semisubmersible floating wind turbines stand out within
the rest of floating options due to its easier and lower-cost installation because of
its construction, assembly, outfitting and commissioning can be done quay-side;
minimal dynamic coupling between wave-induced and turbine-induced motion and
the possibility of carrying more on-board systems.
10
CHAPTER 1 Introduction
Figure 1.4Semisubmersible OFWT concepts: (a) DeepCwind, (b) Windfloat
1.7 Challenges of Offshore Floating Wind
Turbines (Critical Review)
The European Wind Energy Association has set a target of reaching 14% share of
energy demand with 40 GW installed by 2020 (EWEA, 2014). As cited before ,the
most critical priority for offshore wind power is to significantly lower its cost of
energy in order to become competitive with conventional power generation by 2030
(EWEA, 2014). To achieve this, research in six topics is needed:
Sub-structures (fixed and floating ones)
Logistics, assembly and decommissioning
Electrical infrastructure
Wind turbines
Operation and maintenance
External conditions
(a) (b)
11
CHAPTER 1 Introduction
Although the oil & gas industry technology could provide the foundations for design
of the floating platforms, wind turbines scheming need to overcome extra forces
derived from the turbines interaction with the wind loads. Several studies (Jonkman,
2009) show that platform motions have little effect on power capture and rotor
loads; instead these are dominated by the aerodynamics of the rotor. However, they
also indicate that platform motions have a considerable effect on the nacelle and
the tower loads, which are dominated by inertia. As a result, the tower would have
to be strengthened and the design of the equipment would require a reassessment if
the platform motions could not be reduced.
In the case of a semisubmersible platform, it is needed a large water line restoring
moment to achieve sufficient stability, so the control of the cost based on the
materials weight make the design of braces and pontoons very challenging. In
addition, wave loads will be significant due to the large floating area, and could
induce relatively large motions of the structure (Couñago Lorenzo & Barturen
Antépara, 2011). Therefore, based on the oil & gas industry and new developments,
there is a variety of semisubmersible platforms configurations as the DeepCwind,
Windfloat, the Dutch Tri-floater or other variations in terms of number of floats,
position of the tower, etc. but none of them has stand out as the best configuration
for a semisubmersible wind turbine platform yet.
12
CHAPTER 1 Introduction
13
CHAPTER
2 Literature Review
This Chapter presents the essential concepts from the literature to allow an
understandable reading and comprehension of this thesis and its methodology and
results. The main topics covered are:
- Theory of Waves
- Numerical Simulation of the OFWT system
- Hydrodynamic Loads
- Hydrostatic Properties
2.1 Theory of Waves
The wind turbine floating system response is going to be determined by the wind
action but mostly by the sea state. Surface waves will cause periodic loads on the
structure and its response includes accelerations, harmonic displacements and
internal loads.
Ocean waves are irregular and random in shape, height, length and speed of
propagation and can be generated in many different ways (Journée & Massie, 2001):
- Wind Waves - waves generated by the interaction between wind and sea
surface
- Tides - waves generated by astronomical forces
- Tsunamis - waves generated by earthquakes of submarine landslides
- Waves generated by a floating structure which is moving
2
14
CHAPTER 2 Literature Review
Regarding the wind waves, they can be classified into two basic categories: wind
seas and swell.
- Wind Sea: train of waves generated by local winds. The waves are short-
crested, very irregular and individual wave crests propagate in different
directions. The crests are fairly sharp and sometimes even small waves can be
observed on these crests. The apparent or virtual wave period and wave
length vary continuously
- Swell: waves that have travelled out of the areas where they were generated.
They are no longer dependent upon the wind and can propagate for hundreds
of kilometres through calm winds areas
Wind waves, especially, are very irregular. Even though, they can be seen as a
superposition of many simple, regular harmonic wave components, each with its own
amplitude, length, period and direction of propagation. This concept was introduced
in hydrodynamics by St. Denis and Pierson (1953) and it is called the superposition
principle.
Figure 2.1. Superposition of Waves (Thurman, 1997)
In the case of considering structural design purposes, wave conditions may be
described either by deterministic design wave methods of by stochastic methods
15
CHAPTER 2 Literature Review
applying wave spectra. The first case is used for quasi-static response of structures
and it is characterized by wave length and corresponding wave period, wave height
and crest height.
In the other hand, structures with significant dynamic response require stochastic
modelling of the sea surface and its kinematics by time series. In this case, the sea
state is specified by a wave frequency spectrum which will be defined in the
following sections.
2.1.1 General Waves Defining Parameters in Time
Domain
- Mean Wave Height : square root of the average of the squares of all
wave heights
∑
(2.1)
- Significant Wave Height ⁄ : average height from crest to trough
of the highest third of the waves
⁄
∑
⁄ (2.2)
- Root Mean Squared Wave Height : square root of the average of
the squares of all wave heights
⁄ √∑
(2.3)
- Wave Period : time interval between successive crests passing a
particular point
16
CHAPTER 2 Literature Review
- Time Zero-Crossing Period : average time between successive
crossings of the mean water level in an up/down-ward direction
- Wave length λ[m]: average horizontal distance between two successive wave
crests
(2.4)
- Phase velocity
: also called propagation velocity of the wave form, it is
the wave speed or wave celerity and is denoted by ⁄
- Wave frequency : the inverse of wave period, ⁄
- Wave angular frequency
⁄
- Wave number
: the average horizontal distance between two
successive wave crests
⁄ (2.5)
- Surface elevation : is the distance between the still water level and the
wave surface, ( )
- Wave crest height : distance from the still water level to the crest
(highest point of the wave)
- Wave trough depth : distance from the still water level to the trough
(lowest point of the wave)
- Wave height : vertical distance from trough to crest, ⁄ .
Nonlinear regular waves are asymmetric, which means that
- Dispersion relation: relationship between wave period , wave length and
wave height for a given water depth
17
CHAPTER 2 Literature Review
- Average energy density : sum of the average kinetic and potential wave
energy per unit horizontal area
- Energy flux : average rate of transfer of energy per unit width across a
plane normal to the propagation direction of the way
- Group velocity : speed of wave energy transfer, ⁄
2.1.2 Regular Waves
Regular waves are harmonic waves which propagate with permanent form and are
characterized by their wave length , wave period and wave height . Regular
waves behaviour is defined by a different theory according to the wave steepness
parameter , the shallow water parameter , and the Ursell number in every
specific problem.
(2.6)
(2.7)
(2.8)
In this manner, regular waves can be defined by the wave theories described below
(see also Figure 2.2). This will serve to identify the waves used for this research and
apply the formulation required (Det Norske Veritas, 2007).
- Linear wave theory (Airy): it is the simplest theory and is applied when the
wave height is much smaller than both the wave length and water depth.
The wave crest height is equal to the wave trough height , and it is simply
denoted as wave amplitude
(2.9)
18
CHAPTER 2 Literature Review
The surface elevation is given by
( )
(2.10)
Where ( ) is the phase and is the direction of
propagation measured from the positive x-axis.
- Stokes wave theory: it is an expansion of the surface elevation in powers of the
linear wave height
- Cnoidal wave theory: it is applied for a periodic wave with sharp crests
separated by wide troughs
- Solitary wave theory: it is used for high Ursell numbers when the surface
elevation lies wholly above the mean water level,
- Stream function wave theory: it is a numerical procedure for approximating a
wave profile and has a broader range of validity that the wave theories
aforementioned
Figure 2.2. Ranges of validity for various wave theories (Kraineest, 2009)
19
CHAPTER 2 Literature Review
2.1.3 Irregular Waves
The irregular random waves represent a real sea state and can be modelled as a
sum of sinusoidal wave components (superposition principle). The simplest random
wave model is the linear long-crested wave model given by
( ) ∑ ( )
(2.11)
Where are random phases uniformly distributed between and , mutually
independent of each other and of the random amplitudes which are taken to be
Rayleigh distributed with mean square value:
( ) (2.12)
Where ( ) is the wave spectrum and is the difference between
successive frequencies.
Wave Spectrum
A sea state is specified by a wave frequency spectrum with a given significant
wave height , a representative frequency , a mean propagation direction and
a spreading function and is usually assumed to be a stationary random process.
Three hours has been introduced as a standard time between registrations of sea
states when measuring waves, but the period of stationarity can range from 30
minutes to 10 hours.
The wave spectrum represents the power spectral density function of the vertical sea
surface displacement and depends on the geographical area with local bathymetry
and the severity of the sea state.
20
CHAPTER 2 Literature Review
Developed in 1964 from measurements in the North Atlantic the Pierson-
Moskowitz (PM) spectrum is one of the simplest descriptions for the energy
distribution. It assumes that if the wind blows steadily for a long time over a large
area, then the waves will eventually reach a point of equilibrium with the wind. This
is known as a fully developed sea.
In contrast, the JONSWAP (Joint North Sea Wave Project) spectrum is a fetch-
limited version of the PM spectrum, where the wave spectrum is never fully
developed and may continue to develop due to non-linear wave-wave interactions for
a very long time. Therefore, in the JONSWAP spectrum waves continue to grow
with distance or time and the peak in the spectrum is more pronounced, specified by
the gamma γ parameter.
On the other hand, a two peak spectrum as the Ochi-Hubble spectrum and the
Torsethaugen one may be used instead to account for both wind sea and swell in
open sea areas with moderate and low sea states (which are often composed of both
wind sea and swell).
Ronold (2011) states that both JONSWAP and Pierson-Moskowitz spectrum may be
insufficient for floating wind turbine structures, because floating wind turbine
structures can be excited in heave, roll and pitch by swells of 20 to 25 seconds
period. Ronold considers that for floating wind turbine structures which can be
excited by swells, a two-peaked power spectrum model would therefore be needed
for representation of the power spectral density.
Nevertheless, the JONSWAP spectrum is the one which is going to be used in
this research to preserve the hegemony with other researches on the same matter.
Sea State Parameters
The sea state parameters belong to the frequency domain and can be defined in
terms of spectral moments, where the spectral moments of general order are
defined as:
21
CHAPTER 2 Literature Review
∫ ( )
(2.13)
Where is the wave frequency, and . Correspondingly, some sea state
parameters which are used in this work are:
- Spectral Significant Wave Height : obtained from the zero order
spectral moment, it is 5-10% highest than
2 √ √ (2.14)
- Peak Wave Period : is the inverse of the frequency associated to the
biggest spectral density of the spectrum. It has much relevance in unimodal
seas
( )⁄ (2.15)
- Statistical Peak Wave Period : spectral calculation of the peak period
of the wave
(2.16)
- Spectral Zero-up-crossing Period : spectral calculation of the
average period between each up/down-crossing of the waves
√
√
(2.17)
2 To avoid confusion due to nomenclature issues, it has to be remarked that the Spectral Significant
Wave Height ( ) is usually found in the bibliography as , although it is the name of the
Significant Wave Height in the time-domain, obtained from statistics (García-Ibañez, 2014)
22
CHAPTER 2 Literature Review
- Energy Wave Period : is equal to the period of the regular wave
that has the significant height and the same power density of the sea-state
(2.18)
- Spectral Mean Wave Period The average period of the regular
waves that integrate the spectrum weighted by their spectral density
(2.19)
2.2 Aero-Servo-Hydro-Elastic Analysis of the
Offshore Floating Wind Turbine System
The hydrodynamic study of the floating platform should be combined with an
aerodynamic model to obtain a coupled aero-servo-hydro-elastic model, which
integrate wind-inflow, aerodynamic, control system (servo), hydrodynamic and
structural-dynamic (elastic) models in the time domain in a coupled simulation
environment.
The numerical analysis can solve the motions in frequency domain or time domain.
In the first case, hydrodynamic loads are calculated with linear potential flow theory.
In the case of time domain simulations, linear potential theory can also be used to
calculate hydrodynamic loads. It allows taking into account for linear hydrodynamic
radiation and linear diffraction loads. Another approach is to use Morison equation to
calculate the hydrodynamic loads..
23
CHAPTER 2 Literature Review
2.2.1 Equation of Motion
The fully dynamic coupling between the motions of the platform and the wind
turbine are very important in establishing the equation of motion for the whole
system. The next equation gives the general form of the nonlinear time-domain
equation of motion for the coupled wind turbine and support platform system.
( ) ( ) (2.20)
Here, is the (i,j) component of the inertia mass matrix nonlinearly relying on
system DOFs motions , control input u, and time t. is a forcing function of system
DOFs, velocity ( ), control input and time, as well. It is defined positive in the
support platform direction, and is also applied on the platform reference point. The
system forces are defined by the following equation:
(2.21)
where is the number of degrees of freedom (DOF). is generalized inertia forces
and comprises the generalized active forces.
Generalized inert ia forces
The generalized inertia forces comprise tower, nacelle, hub, platform and blades
forces:
(2.22)
In this work attention is given to , which is described in the following
sections.
24
CHAPTER 2 Literature Review
Generalized active forces
Generalized active forces correspond to aerodynamic, hydrodynamic, gravity,
drive train and elastic forces:
(2.23)
Hydrodynamic loads
are presented in the next stage.
2.3 Hydrodynamic Loads
Onshore and shallow-water fixed-bottom offshore turbine loads mainly are
dominated by aerodynamics. In contrast for offshore floating turbines, hydrodynamic
loads become more important. Aerodynamics and hydrodynamics are related in
terms of the long-term statistical correlation of wind speed, wave height, and wave
period as in the long term, the wind generates waves. Therefore, load cases with
high wind speeds and increased aerodynamic loads usually are accompanied by
increased wave heights resulting in greater loads on the floating platform.
Hydrodynamic loads result from the integration of the dynamic pressure of the water
over the wetted surface of a floating platform. These loads include contributions
from inertia (added mass) and linear drag (radiation), buoyancy (restoring),
incident-wave scattering (diffraction), sea current and nonlinear effects.
2.3.1 Linear Hydrodynamics
Figure 2.3 shows the 6-DOF rigid body with small rotational and translational
motions for the semisubmersible platform.
25
CHAPTER 2 Literature Review
Figure 2.3. Platform modes of motion (Chen, 2012)
Two fundamental assumptions are accepted to consider the linear, steady-state
hydrodynamic problem:
a) Incident wave propagates at a single amplitude, frequency and direction
and platform motions are oscillating at the same frequency. This permits the
use of regular wave theory (linear Airy wave theory) and the principle of
superposition, together with appropriate wave representation (JONSWAP
spectrum) to determine the incident-wave kinematics for regular and irregular
seas.
b) Small translational motions of the platform compared to its body size, which
is the basic assumption for splitting the hydrodynamic problems into three
separate and simpler problems: diffraction, radiation and hydrostatics (Matha,
2009).
Apart from these two assumptions, the potential flow theory considers the flow
around a body to be incompressible, inviscid, and irrotational, with negligible
surface-tension effects. The model is described in reference to a global coordinate
system (GCS) that is assumed to be a right-handed Cartesian system with its origin
26
CHAPTER 2 Literature Review
located at the still water level. The linear hydrodynamic problem is solved by
superposition of the independent solutions of subproblems, as it is shown in the next
section, such that the radiation, diffraction and hydrostatic problems, which can be
solved independently.
2.3.2 Linear Time-Domain Hydrodynamic Model
In the true linear hydrodynamic model in time-domain, the total external load acting
on the support platform not only include the above three separate problems, but also
accounts for the restoring forces from mooring lines, the radiation-retardation effect
( ), and fully coupled the wind turbine and supported platform through summing
the mass matrix from the complete nonlinear equation of motion with the
hydrodynamic-added-mass solutions :
( )
(2.24)
Where the hydrodynamic problem covers three separate problems cited before:
radiation, diffraction, and hydrostatic
(2.25)
where:
- Wave Excitation Load is the external load on the platform from
incident waves and related to the wave elevation (diffraction loads). It appears
when a floating structure is restrained from oscillating and incident surface
waves are present and scattered by the body. The diffraction loads are the result
of the undisturbed pressure field (Froude-Kriloff) and wave scattering
(2.26)
27
CHAPTER 2 Literature Review
- Radiation Forces are steady-state hydrodynamic forces and moments
due to forced harmonic rigid body motions with the wave excitation frequency
when there are no incident waves.
∫ ( ) ( )
(2.27)
Where is the wave radiation retardation kernel, is simulation time and, is a
user variable time. The radiation loads are obtained in the time domain with
hydrodynamic added mass and damping matrices.
- Hydrostatic Forces
are the restoring forces of a freely-moving
body. The hydrostatic load is the combined buoyancy force and restoring from
water-plane area and centre of buoyancy (CB).
(2.28)
where is the buoyancy force from the displaced fluid in the platform’s
from Archimedes’ principle, is the DOF of the platform and
is the ( ) component of the linear hydrostatic-restoring matrix
Equation assumes the structure is symmetrical around its body-fixed xz-plane
and yz-plane. Hydrostatics only provides restoring force in heave/roll/pitch
modes; restoring in the other modes therefore should be from the mooring
system.
Besides, the linearization assumptions also allow for alternative time-domain
hydrodynamic representations, such as the frequency-domain analysis of the
response of the OFWTs in irregular seas. However, it is valid only when the platform
oscillates at the incident wave frequency. A requirement for this is that all the
loading presented in the system is linear in nature, which means only the steady-
state situation can be analyzed, and not for nonlinear and transient events. Though
the frequency-domain representation cannot be direct used in the analysis of OFWTs
28
CHAPTER 2 Literature Review
prevented by above reasons, its solutions such as ( ), ( ) and ( ) are
used in the time-domain true linear hydrodynamic-loading model
2.3.3 Frequency-Domain Approach
As described in section 2.3.2 , the frequency-domain analysis can be applied in
steady-static conditions and its solutions are helpful to determine the parameters for
linear hydrodynamic equations in time domain.
The fully coupled governing equation of motion in 6x6 matrix in frequency-domain
is given by (2.29) equation, where all coefficient matrices are about the three system
components: wind turbine (WT consisting of rotor, nacelle, tower), platform and
mooring system.
( ) [ ( ) ] ( )
(2.29)
Here, the hydrodynamic coefficients including the added mass matrix, ( ), the
platform radiation damping matrix, ( ), and the wave excitation force, ( ),
are function of frequency. is the total mass of the OFWT system. is the
external damping contributions from wind turbine. is the linear hydrostatic and
gravitational matrix of the platform. is the external stiffness matrix provided
by the wind turbine as well as the mooring systems.
The non-dimensional form of the equation (2.29) is given in (2.30), where is the
non-dimensional definitions of the structure motions.
Generally, the solution to the frequency-domain problem is given in terms of a
Response Amplitude Operator (RAO), i.e. the ratio of amplitude of platform motion
to wave motion. The following equation (2.30) is the non-dimensional form of the
governing equation above, from which the RAO formulations are easily got in
equation (2.31) for mode .
29
CHAPTER 2 Literature Review
( ) ∑[ ( ) (
) (
)]
(2.30)
⁄
(2.31)
where for translational mode and for rotational mode
; is the characteristic length of the system, and is the incident wave
amplitude. By setting the dimensional parameters to unity, the s are equal to the
transfer function ( ) of equation (2.29) and the response spectrum.
( ) | ( )|
( ) (2.32)
( ) ∫ | ( )|
( )
(2.33)
2.3.4 Non-Linear Effects
Until this point, the aero-hydro-servo-elastic simulation model described for the
floating offshore turbine include only first-order hydrodynamics, which induce loads
and motions that vary with the same frequency as the incident waves. Nevertheless,
the offshore oil and gas industry has demonstrated the importance of second-order
hydrodynamics on floating system design which better approximate the nonlinear
free-surface boundary condition and wave-body interactions (Bayati, et al., 2014).
These second-order hydrodynamics induce loads at the sum- and difference-
frequencies of the incident wave components, which can lead to large strain the
mooring system or vibrations that cause fatigue damage to the structure.
These loads are proportional to the square of the wave amplitude and have
frequencies that are equal to both the sum and the difference of pairs of incident
wave frequencies. This means that, although the natural frequencies of the
30
CHAPTER 2 Literature Review
structure are designed to be outside the first-order wave-energy spectrum, the
second-order loads can excite these frequencies. Consequently, despite the second-
order hydrodynamic loads normally being small in magnitude, the resonant effect
can be significant (Bayati, et al., 2014).
Three components of second-order hydrodynamic loads can be defined:
- Mean-drift loads, which result in a mean offset of the body relative to its
undisplaced position
- Slow-varying loads, which are the result of the quadratic interactions
between separate wave components in an irregular sea state that have
different frequencies. These loads can excite large amplitude resonant motion
of the platform at low frequency
- Sum-frequency loads, which have a frequency that is higher than the wave
frequency and are also generally small in amplitude.
The aforementioned loads are the three main second-order hydrodynamic loads, but
it can be found a multitude of non-linear effects which can generate these loads or
can trigger other effects:
- Interaction between the floaters in close proximity or large ratio between
the wave height and the diameter of the columns or braces, which can
generate unexpected hydrodynamics (Faltinsen, 1990)
- Mathieu effect, which origins parametric instability concerning a coupling
between heave and pitch/roll. . The effect is triggered by an oscillation
hydrostatic stiffness in the vertical modes
- Envelope effect, which causes that the heave motion may oscillate at two
different periods, the heave natural period and the wave period
31
CHAPTER 2 Literature Review
- Vortex-induced loads derived from vortex shedding. It might cause an
increment of the mean drag force and make the platform oscillate transverse
to the current flow
- Viscous damping. Large wave periods mean low frequencies, and this means
that the wave radiation linear damping is small and large amplification of
motions occurs close to resonance, which makes viscous damping relevant.
For instance the non-estimation of viscous damping can lead to an
overestimation of motion amplitudes
2.4 Hydrostatic Properties & Stability
The DeepCwind semisubmersible platform, as any other floating platform with wind
turbines must be able to support the weight of the wind turbine and be able to
withstand all loads and motions described associated with wind and waves. These
factors make stability a major concern for OFWT systems (Vendrell, et al., n.d.).
According to all-known Archimedes Principle, a floating platform gains its buoyancy
force by the direct displacement of water. However, a correct design of ballast,
buoyancy and mooring lines is fundamental to achieve a stable platform. As cited in
chapter 1.6 an OFWT system can increase its stability using ballast weight (spar-
buoy), weighted water plane area (barge), mooring lines (TLP), other add-on
techniques or for example the combination of ballast and buoyancy, which is the case
of the semi-submergible platform.
A body is stable if it returns to its original position after being exposed to a
small angular displacement and this depends on its hydrostatic properties.
Considering the floating platform as a vessel, it is said that when a vessel is tilted, the
centre of gravity remains at the same position relative to the vessel, while the
centre of buoyancy moves to the new centre of the volume of water which the hull
displaces.
32
CHAPTER 2 Literature Review
This creates an uprighting moment that forces the vessel back to its original position,
as illustrated in Figure 2.4. The initial stability is described by the metacentric height
, and the righting lever . The metacentre is the intersection of the line of
action of the buoyancy force when the vessel is upright and the line of action of the
buoyancy force when the ship heels to an angle ϕh.
Stability is maintained as long as the metacentre is vertically above the centre of
gravity of the ship. For heel and pitch angle above metacentric height is not an
accurate measure of stability. The stability of a vessel increases with increasing .
In general, can be calculated using the equation (2.34).
Figure 2.4. DeepCWind Offset Column Stability Diagram
(2.34)
Where is the distance from the keel (K) to the center of buoyancy, is the
metacentric radius and is the distance from the keel to the center of gravity of the
float.
The metacentric radius is calculated by Equation (2.35).
33
CHAPTER 2 Literature Review
(2.35)
where is the area moment of inertia of the water plane and is the displaced
volume.
The righting moment, as defined by Euler, is an alternate method used to determine
stability when the heel angle is large. It relates the couple of the gravitational force
and the buoyancy force and as long as the couple of these two forces causes a
restoring or righting moment the ship remains stable (Kliava & Megel, 2010).
Biran (2003) defines the righting moment as the product of the distance between
the centre of buoyancy and the ship centre of gravity and the weight of the float
:
(2.36)
The theoretical hydrostatic properties for the DeepCwind floating platform are
obtained with the cited equations in Annex III. - Calculation of OFWT .
Moreover, the DeepCwind scale model stability is measured and achieved using the
aforementioned equations as described in section 4.1.1 Inclining Test and Annex II. -
Laboratory Diary.
2.5 Damping and Natural Frequency Response
The natural frequencies of the entire system are crucial to the performance because
they determine the dynamic behaviour of the floating offshore wind turbine.
The full system should avoid resonance with both the environmental and turbine-
induced excitations. For example, to avoid as much as possible the problem of
dynamic resonance with blades and tower, the 6 DOF natural frequencies are
34
CHAPTER 2 Literature Review
designed much lower than those rotor or tower-flexibility induced excitation in most
cases (Wayman, et al., 2006).
For the NREL offshore 5-MW baseline wind turbine, the cut-in and rated rotational
speeds of the rotor are 6.9 and 12.1 rpm, respectively. Therefore, the first rotor
frequency ranges from 0.115 to 0.202 Hz, and the corresponding blade-passing
frequency ranges from 0.345 to 0.606 Hz.
The natural frequencies of the combined wind turbine and floating platform system
therefore can be estimated by considering the system’s restoring and inertial
properties by equation (2.37):
√
( ) (2.37)
where the ( ) indicates the added mass; is the total mass of the system, and
is the total restoring stiffness consisted of the contributions from the wind turbine,
the platform and the tether.
From the model tests results, 5 DOF natural frequencies and damping ratio are
calculated through the free-vibration 6 DOF systems equations.
2.5.1 Free-vibration of viscous-damped 6 DOF
systems
When an undamped 6 DOF system is set into motion with an initial displacement
and/or initial velocity, that motion will continue (theoretically) indefinitely. In
actuality, all systems have some damping that dissipates energy returning to the
equilibrium ( ) , which is the case of the OFWT system.
Damping Rat io
35
CHAPTER 2 Literature Review
The damping ratio describes how oscillations in the system decay after a
disturbanceis (in any of the 6 DOF) and it is defined as the ratio of the damping
constant to the critical damping constant :
(2.38)
Where and is called the undamped circular natural frequency
⁄ .
This floating system answers to the underdamped case as the response motion is
oscillatory with a decaying amplitude which occurs when the damping factor .
Underdamped Sys tem Equa t ions
The general equation for underdamped systems considers linearity and it is written in
the form:
( ) (√ ) (2.39)
Figure 2.5. Underdamped Oscillation (Rao, 2004)
Thus it can be seen that the object oscillates, but the amplitude slowly goes down
over time with a period of the damped vibration and at an angular damped
natural frequency :
36
CHAPTER 2 Literature Review
√ (2.40)
The constants are:
√( ) (
) (2.41)
(
⁄ ) (2.42)
( ) (2.43)
√
(2.44)
Although the value of has an effect on the frequency , the most pronounced
effect of the damping is on the rate at which the motion dies out, that is, on the
term (Craig & Kurdila, 2006).
37
CHAPTER
3 Design of the Scale Model
Tests
The model tests to evaluate the motion performance of the OC4-DeepCwind 5 MW
Semisubmersible offshore wind turbine system in 1:80 scale was carried out in the
Kelvin Hydrodynamic Laboratory of the Department of Naval Architecture and
Marine Engineering of University of Strathclyde, Glasgow.
3.1 Basin Specifications
The tank dimensions of the Kelvin Hydrodynamic Laboratory are 76 m L × 4.6 m W
× 2.5 m D with a typical water depth from 0.5 to 2.3 m. It is equipped with four-
paddle absorbing wavemaker, capable of moving vertically to accommodate water
depths from 1.6 to 2.3 m. Single frequency waves and random sea-states may be
generated with wave heights exceeding 0.6 m.
The floating body motions are measured using a Qualisys infrared optical tracking
camera system or using contact-based methods (e.g. LVDTs). Resistance
dynamometers for different vessel types and model sizes are available as well as a
six degree-of-freedom load cell for force measurement.
Up to 25 wave probes may be used to determine water surface elevation in the tank.
A 3-axis fluid velocity measurement system and a 2D PIV system are also available.
Pressure distributions on model surfaces can be measured. Above-water and
underwater video systems are routinely used.
3
38
CHAPTER 3 Model Test
The data acquisition is through a PC based modular data acquisition/control system
with up to 64 input and 20 output channels, with sampling rate up to 60 kHz3.
3.1 OC4 – DeepCwind 5 MW Semisubmersible
floating wind system
In this project, the OC4 – DeepCwind Semisubmersible floating wind system with
the NREL 5-MW Offshore Baseline Turbine (Jonkman, et al., 2009) is going to be
scaled, built and tested in the Kelvin Hydrodynamic Laboratory.
This offshore floating wind system design belongs to the Offshore Code Comparison
Collaboration, Continuation (OC4): Phase II Results of a Floating Semisubmersible
Wind System, project under International Energy Agency (IEA) Wind Task 304.
Together with their predecessor projects OC4 Phase I (Jonkman, et al., 2012) and the
Offshore Code Comparison Collaboration (OC3) under IEA Wind Task 23 (Jonkman
& Musial, 2010), the aim of this collaboration is to verify the accuracy of offshore
wind turbine dynamics simulation tools or codes through code-to-code comparison
of simulated responses of various offshore structures.
Table 3.1. Modelled Designs from 2005 to 2013 by the OC3 and OC4 projects
Project Phase Description Depth
(m)
OC3
I Monopile with a rigid foundation 20
II Monopile with a flexible foundation 20
III Tripod 45
IV Floating spar buoy 320
OC4 I Jacket 50
II Floating semisubmersible 200
3 See Laboratory Website: http://www.strath.ac.uk/naome/facilities/cmh/
4 See Web Site: http://www.ieawind.org/task_30/task30_Public.html
39
CHAPTER 3 Model Test
OC4 Phase II project involves the modelling of a semisubmersible floating offshore
wind system developed for the DeepCwind project. DeepCwind is US based project
aimed at generating field-test data for use in validating floating wind turbine
modelling tools. The semisubmersible floating wind turbine was tested by the
DeepCwind project in scaled tank tests at MARIN (Marine Research Institute
Netherlands) in 2011 (Goupee, et al., 2013).
3.1.1 OC4 DeepCwind OFWT System Description
The OC4 DeepCwind semisubmersible consists of a main column attached to the
tower, and three offset columns that are connected to the main column (MC) through
a series of smaller diameter pontoons and cross members. Each offset column (UC 1-
3) starts above the SWL and continues beneath the water. At the base of the three
offset columns is a larger diameter cylinder, or base column (BC 1-3), which helps to
suppress motion (particularly in the heave direction, but also in surge, sway, roll, and
pitch) (Robertson, et al., 2012).
The mass, including ballast, of the floating platform is 1.3473E+7 kg. This mass is
calculated such that the combined weight of the rotor-nacelle assembly, tower, and
platform, plus the weight of the mooring system in water, balances with the
buoyancy of the undisplaced platform in still water. The CM of the floating platform,
which includes everything except the tower, rotor nacelle assembly, and moorings, is
located at 13.46 m along the platform centreline below the SWL.
The tower used for the OC4 DeepCwind semisubmersible is the NREL offshore 5-
MW baseline wind turbine (Jonkman, et al., 2009), which is a representative utility-
scale, multi-MW turbine. The base of the tower is coincident with the top of the main
column of the semisubmersible and is located at an elevation of 10 m above the still
water level (SWL). The top of the tower is coincident with the yaw bearing and is
located at an elevation of 87.6 m above the SWL. The resulting overall (integrated)
tower mass is 249,718 kg and is centred (i.e. the centre of mass [CM] of the tower, is
40
CHAPTER 3 Model Test
located) at 43.4 m along the tower centreline above the SWL. This is derived from
the overall tower length of 77.6 m (OC4, 2012).
Figure 3.1. OC4 DeepCwind Semisubmersible Floating System (Author)
Figure 3.2. Plan (left) and Side (right) view of the DeepCwind Semisubmersible Platform
(Robertson, et al., 2012)
41
CHAPTER 3 Model Test
The OFWT system dimensions are listed in Table 3.5. OC4-DeepCwind OWT
system prototype and 1:80 scale model dimensions
3.1.2 Floating Wind System Natural Frequencies
In the following table, the natural frequencies of all the system are presented
according to different authors from scale model tests and numerical analysis:
Table 3.2. Floating Wind Turbine System Natural Frequencies (s) according to different
authors (with no wind)
Numerical Analysis Model
Average
(s)
Average
(Hz) DOF
(Coulling,
et al.,
2013)
(Robertson,
et al.,
2014)
(Bayati,
et al.,
2014)
(Koo,
et al.,
2012)
(Luan,
et al.,
2013)
Surge 107 ≈ .53 100.0 107 115.9 107.49 0.009
Sway 113 ≈ . - 112 117.3 113.66 0.009
Heave 17.3 ≈ .24 18.18 17.5 17.1 17.46 0.057
Roll 26.7 ≈ 2 .32 - 26.9 26 26.48 0.038
Pitch 26.8 ≈ 2 .32 25.0 26.8 25.8 26.14 0.038
Yaw 82.7 ≈ 8 . - 82.3 80.2 81.30 0.012
Just one reference in the existing literature is found which presents the value of the
experimental system natural frequency under wind load:
Table 3.3. Floating Wind Turbine System Natural Frequencies (s) with wind
DOF (Koo, et al., 2012)
Surge 102.0
Sway -
Heave -
Roll -
Pitch 26.9
Yaw -
42
CHAPTER 3 Model Test
3.2 Model Scaling Methodology
Appropriate scaling of a floating wind turbine system and environmental conditions
for scale model testing is indispensable to carry out a reliable and valid test.
Modelling of floating moored system is difficult since complete modelling at a
reasonable scale is a difficult task. Although there are certain scaling laws, there is
a major challenge in overcoming the inability to simultaneously maintain Froude
and Reynolds numbers for a scaled floating wind turbine test.
On one hand, Reynolds number is commonly used to establish model parameters in
wind turbine testing in order to properly represent the relationship of viscous and
inertial forces for a fluid flow (Çengel & Cimbala, 2006). On the other hand, Froude
number is customary for offshore structural experiments as this preserves the
relationship between the gravitational and inertial forces of the waves. (Chakrabarti,
1994).
In the case of floating wind turbine testing, Froude number is maintained as all wave
forcing and inertial effects are properly scaled, however Froude scaling is not well
suited for performing the simultaneous wind turbine portion of the experiment. This
is due to the fact that a Froude scale model generates very low Reynolds numbers
and the lift and drag coefficients are very dependent of these numbers (Fowler, et al.,
2013).
Therefore, it is desirable to have a model wind turbine that closely matches the
performance of the full scale design, where the right emulation of the thrust force
is the most important as it drives most of the wind-induced global response of the
floating wind turbine (Martin, et al., 2012).
3.2.1 Scaling Criteria
Following the aforementioned scaling issues, the common employed scaling
relationships for floating offshore wind turbine models are described below. Notice
43
CHAPTER 3 Model Test
that in order to achieve similitude between the model and the real floating
system, the following must be satisfied:
Geometric similitude
Hydrodynamic similitude (Froude, Strouhal and Reynolds)
Structural similitude (Cauchy) –not in the objectives of this work-
The scaling criteria considerations are presented as:
1. Froude number similitude used to scale model
Froude number and geometric similarity is used to scale the model. However, there
are some parameters that cannot be properly scaled, nevertheless the dominant factor
in the wave mechanics problem, the inertia, is well scaled (Chakrabarti, 1994). As
aforementioned, Froude scaling does not scale the aerodynamic wind forces.
The Froude number for a free surface wave is:
√ (3.1)
where is the wave celerity, is the local acceleration due to gravity and L is a
characteristic length. Assuming a model scale of and geometry similarity, the
Froude model must satisfy the following relationship:
(3.2)
where refers to full scale prototype and to scale model. According to geometric
similarity, the model linear dimensions will be scaled linearly with the scale factor
:
(3.3)
2. Froude scaled wind is employed during basin model testing
44
CHAPTER 3 Model Test
Froude scaling can be used if aerodynamic turbine features are insensitive to
Reynolds number, and thus the wind force to wave force ration from prototype to
model scale is maintained.
3. The wind turbine tip speed ratio (TSR) is to be maintained
The tip speed ratio is a non-dimensional measure of rotor angular speed and is
defined as:
(3.4)
Where is the rotor angular speed, is the rotor radius and is the mean wind
speed. The relationship between the prototype and model is given by:
(3.5)
The principal parameters defining the performance of a wind turbine are the thrust
coefficient and the power coefficient , which vary with the tip speed ratio TSR
(de Ridder, et al., 2014).
(3.6)
(3.7)
where is the thrust and is the power.
The main objective is to achieve a similar variation of the thrust coefficient as
function of the tip speed ratio TSR for the model scale turbine. One of the other
objectives is to approach the rotor performance coefficient as much as possible to
the full scale model (and hence torque). Maintaining ensures that the rotor
45
CHAPTER 3 Model Test
rotational speed as well as any system excitation frequencies will scale properly
(Martin, 2011).
Many other issues have to be taken into account when considering modelling a wind
turbine regarding the forces on the blade, airfoil shape, rotor rotational frequency,
gyroscopic moments, structural dynamics behaviour, axial stiffness, control devices,
etc. However, for this research these elements are not under consideration, so the
rest modelling considerations are going to be left aside.
4. Reynolds Number Effect
Reynolds number quantifies the viscous and inertial qualities of fluid flow and is
expressed as:
(3.8)
Where is the mean velocity of the object relative to the fluid, is the dynamic
viscosity and is the fluid length of travel of interest. This similitude is used
where maintaining the viscous and inertial properties of fluid flow is critical.
However, when Froude number similitude is used instead of Reynolds number
similitude, the Reynolds number for the hydrodynamic and aerodynamic flows are
greatly diminished for the model (Martin, et al., 2012). For the platform-fluid
interaction flows, this is not a major concern as evidenced. Nevertheless, for wind
turbines, the drastic reduction in Reynolds number yields a major impact on wind
turbine performance mainly translated in major alterations to the lift and drag
coefficients of the airfoil sections and lower torque and thrust generation (Martin,
2011).
To address this issue, several approaches have been previously applied:
Utilize a properly sized drag disk loaded with a wind generation system to
simulate wind turbine aerodynamic loading (Roddier, et al., 2010). This
46
CHAPTER 3 Model Test
method is suitable for applying the gross wind turbine loads, but no for
incorporating the impact of wind turbine controls (e.g. variable rotor speed or
blade pitch actuation)
Increase the model wind speed to compensate for the low model
and achieve the correct prototype thrust forces although TSR between the
prototype and model will not be maintained (Martin, et al., 2012). Test data
and simulations indicate that it does not greatly affect the wind turbine
damping resulting from a fixed blade rotor. This is translated into more costs,
high-output wind generation systems and causing undesirable excess drag on
non-rotor structures (Goupee, et al., 2013).
Adjust the model blade pitch angle to match the thrust coefficient at a
specified tip-speed ratio (Fowler, et al., 2013).
Roughen the leading edge of the model blade to trip the boundary layer
transition from laminar to turbulent flow around the airfoil, reattaching the
flow and improving the airfoil’s lift and drag coefficients at model scale. This
method may result in erratic wind turbine rotor behaviour so it is
recommended to be used just as a fine tuning adjustment (Martin, et al.,
2012).
Design a low-Reynolds number specific model wind turbine blade
geometry that, while may not resemble the prototype blade with regard to
surface geometry, will yield appropriate thrust performance when subjected
to an unmodified Froude scale environment. This method will better capture
wind turbine damping effects and is best suited to experiments where the
impact of active blade pitch control on global motions are of interest (Martin,
et al., 2012).
According to Martin, et al. (2012), the best option is to redesign the rotor and use the
other techniques sparingly (excepting the first one) to fine tune the model thrust
forces. Nevertheless, the first approach of the listed above is the one selected for this
47
CHAPTER 3 Model Test
research, because of its appropriate simplicity for this study and due to the fact that
the impact of wind turbine control is not considered in this study and thrust force is
considered as is the most important as it drives most of the wind-induced global
response of the floating wind turbine (see drag disk dimensioning in 3.4.4 Drag Disk
Modelling).
3.2.2 Established Scaling Factors
According to the previous relationships, the following table presents most of the
established scaling factors for floating wind turbine model testing (Chakrabarti,
1994).
Table 3.4. Established scaling factors for floating wind turbine model testing
Parameter Unit Scale
Factor
Length (e.g. displacement, wave height and length)
Area
Volume
Density ⁄ 1
Mass
Time (e.g. wave period)
Frequency (e.g. rotor rotational speed)
Velocity (e.g. wind speed)
Acceleration 1
Force
Moment (e.g. rotor torque)
Power
Stress
Mass moment of inertia
Area moment of inertia
48
CHAPTER 3 Model Test
3.2.3 Modelling of Floating Platform
The geometry of the floater is scaled dimensionally correct for the scale factor (see
Table 3.4). All the dynamic properties, (e.g. displacement, moment of inertia, GM,
natural periods) are properly scaled using Froude’s law. According to Chakrabarti
(1998) , the structural properties (e.g. elasticity) are not necessary to scale. Even at a
small scale, this scaling can provide reasonable results. Many of the details, e.g.,
appendages and small members, have been omitted.
3.2.4 Modelling of Mooring Lines
The three main parameters for the floating system response in terms of the mooring
line behaviour are:
Mooring line pretension
Stiffness of the mooring with respect to the environmental load
The load experienced by the structure at the fairlead from the mooring line
under various loading
However, the mooring lines effect on this scaled model semisubmersible platform is
not going to be considered. Instead, exceptionally elastic mooring lines are used in
the model just to maintain its floating position. It is understood that the interaction of
these mooring lines in the platform response behaviour is irrelevant at all, due to the
large mooring expected response.
49
CHAPTER 3 Model Test
3.2.5 Modelling of Environment
Waves
Both irregular and regular waves height and period are modelled according to Froude
similitude using the scale factors exposed in Table 3.4.
Wind
As explained in section 3.2.1 , wind should be scaled by Reynolds number similitude
but due to the aforementioned constrains, the wind environment will be also Froude
scaled using the correspondent scale factor exposed in Table 3.4.
According to the wind environment quality, it has to have little evidence of fan
generated swirl and low turbulence intensity. This requires a dedicated wind
generator consisting of a series of fans, screens, as well as a contracting nozzle. In
addition, the output area of the nozzle should cover the entire wind turbine rotor in
quality wind even as the floating system moves through its expected range of motion
(Martin, et al., 2012).
3.3 Model Dimensions
According to the OC4-DeepCwind semisubmersible offshore wind turbine system
dimensions, presented in Chapter 1 - and the scaling factors shown in Table 3.4, the
corresponding dimensions for the 1:80 scale model are calculated and presented in
the following table.
50
CHAPTER 3 Model Test
Table 3.5. OC4-DeepCwind OWT system prototype and 1:80 scale model dimensions
Item Full Scale Unit Factor
Scale
Model
Target
Platform Height 32 m λ 0.4
Depth of platform base below SWL (total
Draft) 20 m λ 0.25
Elevation of main column (tower base)
above SWL 10 m λ 0.125
Elevation of offset columns above SWL 12 m λ 0.15
Platform Mass, including ballast 1.3473E+07 kg λ3 26.314
Upper (offset) Column Diameter 12 m λ 0.15
Upper Columns Length 26 m λ 0.325
Base Column Diameter 24 m λ 0.3
Base Columns Length 6 m λ 0.075
Pontoons and Cross Braces Diameter 1.6 m λ 0.02
Main Column Diameter 6.5 m λ 0.081
Platform CM location below SWL 13.46 m λ 0.168
Depth to top of base columns below SWL 14 m λ 0.175
Platform roll inertia about CM 6.788E+09 kgm2 λ5 2.083
Platform pitch inertia about CM 6.788E+09 kgm2 λ5 2.083
Platform yaw inertia about CM 1.190E+10 kgm2 λ5 3.741
Number of Mooring Lines 3 u 1 3
Angle between adjacent lines 120 ° 1 120
Depth to anchors below SWL (Water
depth) 200 m λ 2.5
Depth to fairleads below SWL 186 m λ 2.325
Radius to anchors from platform centreline 837.6 m λ 10.47
Radius to fairleads from platform
centreline 40.868 m λ 0.511
Unstretched mooring line length 835.5 m λ 10.444
Mooring line diameter 0.0766 m λ 0.001
Equivalent mooring line mass density 113.35 kg/m λ2 0.018
Equivalent mooring line mass in water 108.63 kg/m λ2 0.017
Equivalent mooring line extensional
stiffness 7.536E+08 N λ3 1471.875
Equivalent mooring line extensional
stiffness 7.536E+08 N λ3 1471.875
51
CHAPTER 3 Model Test
Item Full Scale Unit Factor
Scale
Model
Target
Rotor Mass 110000 kg λ3 0.215
Rotor Diameter 126 m λ 1.575
Hub Mass 56780 kg λ3 0.111
Blade Mass (1EA) 17740 kg λ3 0.035
Nacelle Mass 240000 kg λ3 0.469
Tower Height 77.6 m λ 0.97
Tower Mass 249718 kg λ3 0.488
Tower Top Diameter 3.87 m λ 0.048
Tower Base Diameter 6.5 m λ 0.081
Tower CM (from tower base) 43.4 m λ 0.5425
Draft 20 m λ 0.250
Platform KG 6.54 m λ 0.112
Roll Gyration - kxx 31.61 m λ 0.395
Pitch Gyration - kyy 32.34 m λ 0.404
Yaw Gyration - kzz* 32.17 m λ 0.402
3.3.1 Model Fidelity
As cited before, many of the details, e.g., appendages and small members have had to
be omitted due to the high difficulty to recreate them in 1:80 scale, apart from the
fact that their contribution to the hydrodynamic system response is irrelevant. In
addition, the rotor and nacelle are replaced by a flat disk which is further discussed in
3.4.3 and 3.4.4 although it maintains their mass properties.
Due to the difficult task of recreate the model mass properties in the Froude scale
similitude, where the scale factor for length is but for mass is , the model mass
distribution is not exactly the same than the model expected, so some extra ballast
has been added to achieve the correct position of the model water line.
Table 3.6 clarifies that the model weight is lightly greater than the target, but this
difference is just of 1%, so it is acceptable. However, the achievement of the system
KG target is more complicated, due to the model building constraints and more
52
CHAPTER 3 Model Test
ballast is needed in the really platform base, which cannot be performed once the
model is built. Nevertheless, free decay tests reveal that the platform natural
frequencies are similar to the expected ones.
Table 3.6. Difference between target and model (1:80)
Item Full Scale Model Target Model Difference
OFWT Mass (kg) 1.347E+07 26.314 26.81 +1.02%
OFWT KG (m) 9.45 0.1121 0.1302 + 16.09%
3.4 Model Environment Loads
3.4.1 Regular Waves
The response of the OFWT to regular waves with/without under wind load is tested
under wave heights of 1, 2, 4 and 6 meters and period of 7.45- 30 seconds (prototype
scale) as follows. Special dedication was given to the heave and pitch peaks regions.
Table 3.7. Regular Waves Tested
Full Scale Model Scale
( ) ( ) ( ) ( )
1 7.45-30 12.5 0.83-3.35
2 7.45-30 25.0 0.83-3.35
4 7.45-30 50.0 0.83-3.35
6 7.45-30 75.0 0.83-3.35
5 There is little controversy between the existing literature about the DeepCwind prototype’s KG. For
example, Koo, et al., (2012) gives a platform’s KG of 5.60 meters, meanwhile Shin, et al., (2013)
gives a value of 6.54 m or Goupee, et al., (2013) cites a value of . for the system’s K . Therefore,
the value of KG system presented in Table 3.6 has been manually calculated by the author. The author
agrees with the value of 6.54 m for the platform.
53
CHAPTER 3 Model Test
3.4.2 Irregular Waves
As cited in 2.1.3 Irregular Waves, the JONSWAP spectrum is used to characterize
the irregular waves spectrum of this research. Its power spectral density ( ) is:
( ) ( ) ( (
)
)
(3.9)
where ( ) is the Pierson-Moskowitz spectrum,
( )
(
(
)
) (3.10)
where ⁄ is the angular spectral peak frequency
is the non-dimensional peak shape parameter, ( ) is a
normalizing factor and is the spectral width parameter which:
The average values for the JONSWAP experiment data are , and
. However, as no particular values are given for the peak shape parameter
, the following formulation is going to be used to obtain our value:
for
√
(
√ ) for
√ (3.11)
for
√
(3.12)
54
CHAPTER 3 Model Test
The values for significant wave height and peak period which characterizes
the irregular waves for the OC4-DeepCwind semisubmersible floating system are
shown in the Table 3.8. In addition, it is shown the correspondent value according
to the
√ relation.
Table 3.8. Sea States Tested
Full Scale Model Scale
Sea
State (m) (s) √ ⁄ (mm) (s)
1 2.44 8.10 5.185 1.000 30.500 0.906
2 3.66 9.70 5.070 1.000 45.750 1.084
3 5.49 11.30 4.823 1.226 68.625 1.263
4 9.14 13.60 4.498 1.780 114.250 1.521
5 10.50 14.30 4.413 1.964 131.250 1.599
According to DNV (2007), the JONSWAP spectrum is expected to be a reasonable
model for
√ and should be used with caution outside this interval.
Looking to Table 3.8 it can be observed that the previous statement is not satisfied
for the first two cases as
√ but is reasonable close.
3.4.3 Wind
The following table shows the various environmental and operating conditions for
the NREL 5MW wind turbine considered in this work, which has a cut-in velocity of
3 m/s, a rated velocity of 11.4 m/s and a cut-out velocity of 25 m/s. It is considered
one extreme environment with a parked wind turbine and a mean wind speed of 30.5
m/s corresponding to a 100-year event in the Gulf of Maine (University of Maine and
James W. Sewall Company, 2007).
55
CHAPTER 3 Model Test
Table 3.9- NREL 5MW Wind Environment and equivalent Thrust Forces
Mean Wind Speed Thrust Force
Full Scale
(m/s)
Model Scale
(m/s)
Full Scale
(kN)
Model Scale
(N)
7.32 0.82 102.6 0.200
8.94 1.00 143.4 0.280
11.23 1.26 247.2 0.483
16.11 1.80 413 0.807
21.8 2.34 779.3 1.522
30.5 3.41 153.2 0.299
Unfortunately, the equipment required to achieve the previous mean scaled wind
speeds is not yet available in the Kelvin Hydrodynamic Laboratory, as well that it is
not possible to achieve any reliable mean velocity value with the existing funs.
However, this fact is not an obstacle to analyse the response of the OWFT under the
wind thrust load, as the wind environment under operating conditions range is
achievable by the existing lab equipment.
As cited before in 3.2.1 Scaling Criteria, the model rotor is recreated with a drag
disk which conserves the thrust force and mass properties of the rotor and nacelle in
the model. The drag disk is dimensioned according to the worst case of thrust force,
which corresponds to (Coulling, et al., 2013) (see Table 3.9).
3.4.4 Drag Disk Modelling (Rotor)
It is important to note that generation of the proper thrust forces was considered
critical as it directly affected the response and global motions of the floating model.
To address this issue, a properly sized drag disk loaded is used in replacement of the
rotor, although a wind generation system to simulate the wind turbine aerodynamic
loading is not going to be recreated, as this work only does not cover the turbine
aerodynamic response.
56
CHAPTER 3 Model Test
The purpose of the flat disk is to simulate the thrust developed on the wind turbine,
which, in the worst case, it is when and in model
scale is when (see Table 3.9). Using the Thrust
Coefficient equation (3.6) for and and a drag coefficient for a flat disk
of 1.17 according to (Clift, et al., 1978) (Binder, 1973):
(
)
⁄
(
)
⁄
Figure 3.3. Model with drag disk installed
3.5 Test Matrix
A large array of tests was performed at the Kelvin Hydrodynamic Laboratory to
characterize the behaviour of the floating system in a variety of conditions. It has to
be remarked that all tests without wind were carried out without the drag disk
dimensioned in 3.4.4 A summary of the identification and station keeping tests are:
57
CHAPTER 3 Model Test
Table 3.10. System Identification Tests
Test Type Measurements Characteristics (full scale
terms)
Free decay System natural periods and
total damping Pitch, Heave, Surge and Roll
Regular Wave Linear response characteristics
(RAOs)
Frequency Range: 0.03 – 0.13Hz
Wave Heights: 1, 2, 4 & 6
meters
Regular
Oblique Wave
Linear response characteristics
(RAOs)
Frequency Range: 0.03 – 0.13Hz
Wave Heights: 2 & 6 meters
Free decay +
Wind
Damping contribution from
wind Pitch, Heave, Surge and Roll
Regular Wave
+ Wind
Linear response characteristics
include wind (RAOs)
Frequency Range: 0.03 – 0.13Hz
Wave Heights: 2 & 6 meters
Table 3.11. Station Keeping Tests
Test type Description Characteristics (full scale
terms)
Wave only Head seas Number of different sea states: 6
Running time: 3 hours
Wind only Wind test Running time: 1 hour
Wave + Wind Operation wave and Design
wave with wind
Number of different sea states: 6
Running time: 3 hours
The sampling frequency is 137 Hz at model scale, corresponding to a Froude-scaled
sampling frequency at full scale of roughly 15 Hz. All data from the tests were
converted to full scale using Froude scaling prior to analysis.
3.6 Tests Procedure
Best description of each of the performed tests from Table 3.10 and Table 3.11 can
be found in Annex II Laboratory Diary.
58
CHAPTER 3 Model Test
3.7 Calibration of Environment
3.7.1 Wind assessment and calibration
A standard anemometer and a contact closure anemometer are used to identify the
wind resource generated by the three drum funs of the Kelvin Hydrodynamic
Laboratory (see Figure II.9). The standard Skywatch Xplorer 2 anemometer is used
for an early assessment of the wind flow. Continued instant wind speed
measurements are taken from 4, 5 and 6 meters from the generation of the wind.
Table 3.12. Wind Flow Assessment with standard Skywatch Xplorer 2 anemometer
Fun
Distance
(m)
Fun Velocity Program
1 2 3
Wind Speed Range (m/s)
4 0.3 – 1.1 0.3 - 1.8 0.4 – 3.4
5 0.2 – 1.4 0.3 - 1.8 0.3 – 3.1
6 0.3 – 1.3 0.2 - 1.8 0.3 – 3.2
As observed in Table 3.12, the standard anemometer proves evidence of unsteady
wind and does not show correlation for the distance between the fans and the
anemometer. Moreover, the anemometer shows instant wind speeds which change
drastically in fractions of a second.
For a more accurate measure of the wind flow in the model position, a wind sentry
set is placed in the model position (4 meters from the fans) and two tests run for at
least 2 minutes.
59
CHAPTER 3 Model Test
Figure 3.4. Wind sentry set test
The wind speed parameters for the two tests are shown in the following table:
Table 3.13. Wind Speed (m/s) Test Parameters
Test Mean Max Min SD
1 2.174 2.859 1.411 0.227
2 2.084 2.800 1.249 0.231
As cited in Table 3.9- NREL 5MW Wind Environment and equivalent Thrust Forces,
the model scale wind environment range is [0, 3.41] m/s, which corresponds to the
range [0, 30.5] in full scale. As it can be observed in Table 3.13, the maximum wind
speed in the test does not achieve the maximum operational wind velocity but it does
with the wind speed worst case: when thrust force is the highest (2.34 m/s in model
scale and 21.8 m/s in full scale).
3.7.2 Waves Calibration
Both regular and irregular waves are calibrated prior to installation of the model in
the basin (open sea tests).
Wave Probe Calibration
The wave probe is placed 10 meters away the wave maker. As it is considered that
the regular waves maintain the same characteristics along the basin, there may not
have difference between this point and the model position.
0
0.5
1
1.5
2
2.5
3
3.5
4
0 50 100 150 200 250 300 350 400
Win
d S
pee
d (
m/s
)
Time (sec)
60
CHAPTER 3 Model Test
The maximum difference in standard deviation between the target waves and
measured waves was less than 1%.
Figure 3.5. Results of the wave probe calibration
Irregular Waves Calibration
The wave spectrum should be calibrated for a duration corresponding to the test
duration, which is 20 minutes in Froude similitude. The target of the wave calibration
is the JONSWAP spectrum (see Table 3.8. Sea States Tested). The acceptance
criteria, which is the percentage deviation from target significant wave height and
peak period from spectral and zero crossing analysis, is 2% for this project. This has
been achieved after fourteen tests, where the greatest number of repetitions was for
the highest wave value of 10.5 m.
Figure 3.6. Screen Capture of the wave maker software
y = 0.010666x + 0.001839
R² = 0.999926 -0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
-80 -60 -40 -20 0 20 40 60 80
Mea
sure
d V
olt
age
(V)
Vertically Moved Distance of the wave probe (mm)
fixed probe Linear (fixed probe)
61
CHAPTER
4 Model Test Results
Chapter 4 presents the results of the OC4-DeepCwind OFWT system model tests
carried out in the Kelvin Hydrodynamic Laboratory. The data acquired in the tests is
processed and presented as indicators which can transmit significant information
about the performance of the model. The results are divided according two blocks:
System Identification tests and Station Keeping tests.
4.1 System Identification Tests
Prior to the tests in sea states, various system identification tests are performed with
the model, in order to verify the hydrostatic and hydrodynamic properties of the
system.
4.1.1 Inclining Test
The inclining experiment consists of several relatively simple steps in order to
determine the craft actual vertical centre of gravity. For more information about the
followed procedure please see Annex II Laboratory Diary.
Firstly, the weight of the full model is determined by reading drafts and comparing
with the known properties. Secondly, the model is placed in a small still calm water
tank and free of mooring restraints. In this case, the actual waterline does not
correspond exactly to the correct one and 400 g extra ballast is distributed among the
offset columns bases. It means that in order to achieve the floating model properties
4
62
CHAPTER 4 Model Test Results
the model weight is 1.02% greater than the target scale model weight (see 3.3.1
Model Fidelity).
The GM position is determined by moving two 100 g weights transversely
to produce a known overturning moment (see Figure II.3. Inclining test for the
semisubmersible platform. The different pictures show the test procedure where the
inclining masses change their position.. When calculated the restoring properties
(buoyancy) of the vessel from its dimensions and floating position and measuring the
equilibrium angle of the weighted vessel, the KG can be calculated. When
corresponded, the ballast is moved down or up to achieve the required KG and
floating stability.
The full inclining experiment is carried out twice for the cases of the model without
and with the drag disk installed. The model without the drag disk is used for all only
wave tests and free decay tests without wind thus the model with the drag disk is
used for only wind tests, waves and wind and free decay with wind.
Figure 4.1. Model without drag disk during the Inclining Experiment
63
CHAPTER 4 Model Test Results
Table 4.1. Inclining test results for model without drag disk
Results Full Scale Model Scale
GM measured 6.614 m 82.7 mm
KG measured 10.586 m 132.3 mm
KG corrected 10.413 m 130.2 mm
GM corrected 6.787 m 84.8 mm
Abs KG Error -1.013 m -12.66 mm
% KG Error -10.77 % -10.77 %
Move ballast by -400 mm
Table 4.1 displays the final results for the inclining test for the model without the
drag disk. As aforementioned, the ballast was moved down or up in order to achieve
the required KG and floating stability, but due to building constraints, the target KG
has not been able to be achieved and the actual one is 400 mm above. No solution
has been found without modifying the platform geometry below the actual keel,
which has been discarded as it may have important influence on the platform
motions. A quick natural frequency test has been carried out to compare the results
with exciting bibliography and no considerable differences have been found, so the
model floating characteristics are accepted.
Table 4.2 presents the inclining test final results for the model with the drag disk.
The ballast has been moved to achieve the KG position correspondent to the model
without the drag disk.
Table 4.2. Inclining test results for model with installed drag disk
Results Full Scale Model Scale
GM measured 6.538 m 81.7 mm
KG measured 10.662 m 133.3 mm
KG corrected 10.490 m 131.1 mm
GM corrected 6.710 m 83.9 mm
Abs KG Error -0.077 m -1.0 mm
% KG Error -0.742 %
64
CHAPTER 4 Model Test Results
4.1.2 Free Decay
The natural periods/frequencies and associated damping of the floating
platform system are obtained from free decay tests.
Two types of free decay tests are carried out. The first type is calm water free decay
that measures system natural periods of the system without and with the drag disk.
The second type is free decay with steady wind that measures aerodynamic damping
from the wind turbine. Each of these tests includes pitch, roll, heave and surge free
decay tests.
For all the tests, the platform is pulled from its original equilibrium position and then
released. In the case of free decay tests with wind, the pulling force was applied once
the wind fans run for at least 1 minute. The instantaneous OFWT model system
position was determined by the Qualisys Cameras and given with a sampling rate of
0.0073 seconds. Each test was repeated at least three times. In Annex II Laboratory
Diary the procedure followed for the free decay tests is described.
Data for the 4 DOF are presented in Figure 4.2, Figure 4.4, Figure 4.5 and Figure 4.3
from the pitch, roll, heave and surge free decay tests for the model without the drag
disk (No Wind data) and the model with the drag disk under wind load (With Wind
data).
65
CHAPTER 4 Model Test Results
Figure 4.2. Platform motions response in Pitch Free Decay Test (without wind)
Figure 4.3. Platform motions response in Roll Free Decay Test (without wind)
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 50 100 150 200
Pit
ch (
deg
)
Time (sec)
No Wind With Wind
-1.2
-0.8
-0.4
0
0.4
0.8
1.2
0 50 100 150 200Ro
ll (
deg
)
Time (sec)
No Wind With Wind
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0 50 100 150 200
Hea
ve
(m)
Time (sec)
No Wind With Wind
-4
-2
0
2
4
6
8
10
0 100 200 300 400
Su
rge
(m)
Time (sec)
No Wind With Wind
-3
-2
-1
0
1
2
3
4
0 50 100 150 200Pit
ch (
deg
)
Time (sec)
No Wind With Wind
-8
-6
-4
-2
0
2
4
6
8
0 50 100 150 200Ro
ll (
deg
)
Time (sec)
No Wind With Wind
-1
-0.5
0
0.5
1
0 50 100 150 200Hea
ve
(m)
Time (sec)
No Wind With Wind
-6
-3
0
3
6
0 50 100 150 200 250 300 350 400Su
rge
(m)
Time (sec)
No Wind With Wind
66
CHAPTER 4 Model Test Results
Figure 4.4. Platform motions response in Heave Free Decay Test (without wind)
Figure 4.5. Platform motions response in Surge Free Decay Test (without wind)
-2.5
-1.5
-0.5
0.5
1.5
2.5
0 50 100 150 200
Pit
ch (
deg
)
Time (sec)
No Wind With Wind
-1.5
-1
-0.5
0
0.5
1
0 50 100 150 200
Ro
ll (
deg
)
Time (sec)
No Wind With Wind
-6
-4
-2
0
2
4
6
0 50 100 150 200Hea
ve
(m)
Time (sec)
No Wind With Wind
-3
-2
-1
0
1
2
3
0 50 100 150 200Su
rge
(m)
Time (sec)
No Wind With Wind
-6
-4
-2
0
2
4
0 50 100 150 200 250
Pit
ch (
deg
)
Time (sec)
No Wind With Wind
-1
-0.5
0
0.5
1
0 50 100 150 200Ro
ll (
deg
)
Time (sec)
No Wind With Wind
-1
-0.5
0
0.5
1
0 50 100 150 200Hea
ve
(m)
Time (sec)
No Wind With Wind
-55
-45
-35
-25
-15
-5
5
15
0 50 100 150 200 250 300 350 400
Su
rge
(m)
Time (sec)
No Wind With Wind
67
CHAPTER 4 Model Test Results
Natural Frequencies and Damping Ratio Calculation
In order to obtain the natural periods and damping ratio for each of the degree of
freedoms, equations described in section 2.5.1 Free-vibration of viscous-damped 6
DOF systems are used.
Thus each DOF motion data for each test is fit according the general equation for
underdamped 6 DOF systems (2.39):
( ) (√ )
Where is the offset from the zero real position. Then, a solve equation is used to
obtain the undamped natural frequency and damping ratio .
It is necessary to set the range of cycles taken into the account to do the fit for each
of the tests. The first cycle has to be rejected due to the first disturbance from the pull
force. In most of the cases, after 4-5 cycles, data presents noise and time between
cycles extends due to non-linearity, so these cycles are also rejected.
Figure 4.6. Pitch Free Decay Data and Fit
Moreover, there are some cases that a considerable smooth fit might be applied for
just 1-2 cycles (see Figure 4.7) or that free-vibration equation fit is not possible due
to weak platform response, as it the case of surge free decay. Therefore, in these
-5
-2.5
0
2.5
5
0 10 20 30 40 50Pit
ch (
deg
)
Time (sec)
Pitch No Wind fit
Noise Non-linear effects Range for final fit
68
CHAPTER 4 Model Test Results
cases, to obtain the natural frequency is preferable to do it with the software Spike2’s
tool “Peak to Peak time”.
Figure 4.7. Heave Free Decay data and Fit
Figure 4.8. Surge Free Decay data (Spike2 view)
To obtain the damping ratio in these circumstances, the log-decrement method is
used. It is shown in standard texts (Chopra, 1995) that the corresponding damping
ratio is given by:
(4.1)
-5
-2.5
0
2.5
5
0 2 4 6 8 10 12 14
Hea
ve
Am
pli
tud
e (m
)
Time (sec)
Heave No Wind fit
Non-linear effects
3 4 5 6
69
CHAPTER 4 Model Test Results
Where in which , , etc, are successive amplitude peaks at times , , etc. (see
Figure 4.9).
To avoid the possibility of a zero off-set influencing the result it is advisable to base
the calculation on peak-to-peak values. The formula is readily shown to apply
equally well to peak-to-peak measurement as follows (Butterworth, et al., 2004).
(4.2)
Figure 4.9. Parameters used in the log-decrement method to obtain the damping ratio
Finally, Table 4.3 shows the natural periods and damping ratios obtained
experimentally through the methods explained.
70
CHAPTER 4 Model Test Results
Table 4.3. Natural Periods (NP), Natural Frequencies (NF) and Damping Ratios (DR) tested
under wind and no wind loads and comparison with references in the bibliography
DOF
No Wind With Wind
Measured Biblio_
graphy6
Measured Biblio-
graphy7
NP (s) NF
(Hz) DR% NP (s) NP (s)
NF
(Hz) DR % NP (s)
Pitch 26.50 0.037 4.18 0.038 27.49* 0.036 29.76* 0.037
Roll 27.23 0.037 4.94 0.038 26.50 0.038 4.18 -
Heave 18.73 0.0548 9.77 0.057 18.73 0.054 8.28 -
Surge 166.61*9 0.006 1.62* 0.009 124.16* 0.008 5.40* 0.010
The analysis of the free decay tests shows that steady wind substantially increases
pitch damping and slightly increases its natural period (as also occurs for Koo, et al.,
(2012)). In the cases of heave motion, the wind does not meaningfully affects the
natural period or the damping coefficient, as it can be visually perceived in Figure
4.4. In reference to roll rotation, both natural period and damping ratio are slightly
lower when wind load is affecting the system.
The case of surge translation is singular. The only restoring in surge comes from the
mooring system, which does not give reliable information as lines just maintain the
floating platform in position but are not scale modelled from the original DeepCwind
mooring parameters. Nevertheless, it can be seen the larger-motion response of the
platform and that natural period under wind load decreases and damping as well.
Reference has to be done with existing bibliography about the DeepCwind system
data. As seen in Table 4.3 the natural periods’ results are slightly greater than the
average made from the bibliography data of four different reports. In the case of
Pitch rotation, the closest existing result corresponds to Robertson, et al., (2013)
6 See Table 3.2. Floating Wind Turbine System Natural Frequencies (s) according to different authors
(with no wind) 7 See Table 3.3. Floating Wind Turbine System Natural Frequencies (s) with wind
8 In 4.2.3 Frequency Domain Analysis - Spectral Analysis it will be assumed that a most appropriate
experimental value for heave frequency is 0.056 Hz instead of 0.054 Hz. 9 The symbol ‘*’ refers when the Free-vibration of viscous-damped 6 DOF systemsequations cannot
be used to obtain the system natural period and damping ratio and the second explained method of
“Peak to Peak” is used
71
CHAPTER 4 Model Test Results
which is 26.32 seconds. Qvist, J. and Froyd, L. in (Robertson, et al., 2013) give the
closest value for heave, which is around 18.18 seconds. Koo, et al., (2012) provides
the closest model test result for roll, which is 26.9 seconds. In the case of surge,
Luan, et al., (2013) offers the closer experimental result of 115.9 seconds, but it is
still significantly far. However, this difference in surge natural period is not upsetting
as the mooring line modelling is non-existent.
4.1.3 Only Regular Waves
In the only regular wave tests, the tested frequencies comprise from 0.3 Hz to 1.2 Hz
in model scale, which corresponds to 0.03 – 0.13 Hz range in full scale. Wave
heights tested are 1, 2 4 and 6 meters in full scale terms, as shown in the Test Matrix
(Table 3.10). The wave heading angle is 0º. For test validation purposes, each wave
height at one frequency value (close to the peak) is tested four times.
Figure 4.10. System configuration for only regular wave tests
To compare the response behaviour achieved by the OFWT model system
experiencing regular wave loads only, the Response Amplitude Operators (RAOs)
are shown to be a adequate way to examine offshore structure response
characteristics across a range of wave conditions (Robertson, et al., 2013).
Wave Direction
x
y
z
CG
72
CHAPTER 4 Model Test Results
Previously described in 2.3.3 Frequency-Domain Approach, it is considered that
the form of analysis is consistently linear, so it is supposed that RAOs will not
depend on the wave height (however this is a point which is going to be further
discussed).
Figure 4.11. Photography of the model during one test in only regular waves
From the experimental data, the RAO for each platform translation or rotation DOF
is obtained from the following equation:
(4.3)
Where is the amplitude (mm or deg) for each degree of freedom studied
(pitch, roll, heave and surge) and the amplitude of the waves generated. Both
amplitudes are obtained from the sinusoid fit processed by the software Spike2. For
this purpose, just a region of all the data recorded is selected, where waves are seen
to be stabilized but no to be reflected yet and without broken waves.
73
CHAPTER 4 Model Test Results
Figure 4.12. From Spike2 raw data representation: (a) Reflected waves, (b) Almost broken
waves, (c) Waves not yet stabilized
This analysis generates a wave-period dependent RAO curve for each degree of
freedom which is shown in full scale prototype terms.
Figure 4.13, Figure 4.14 and Figure 4.15 show the results for pitch, heave and surge
RAOs. Yaw and roll RAO results are omitted due to their non-significant
contribution to the platform motion in only regular waves load case.
RAO pitch values remain considerably constant up to a wave period of 21 seconds,
where it exponentially increases until a peak around 27 seconds, which in principle is
outside the real wave-excitation region for the DeepCwind system: 4 – 20 seconds
(Robertson, et al., 2012).
In contrast, heave RAO peak is found in the limit of the real wave-excitation region
for the DeepCwind system, and corresponds to a period of around 18 - 21.0 seconds
depending on the wave height. Surge’s peak is known to be at seconds
(Robertson, et al., 2014), which is outside the real wave-excitation region and the test
range as well.
Both the peak value and the curve inflexion points for wave height in the
cases of pitch, heave and surge RAO agree with Luan, et al., (2013) RAO results.
Robertson, et at., (2014), Robertson, et al., (2013) and Gueydon & Weller (2012)
present a similar results overview but derived from banded white noise tests.
(a) (b)
(c)
74
CHAPTER 4 Model Test Results
Figure 4.13. Pitch RAO for regular waves with wave height equal to 1, 2, 4 and 6 meters
Figure 4.14. Heave RAO for regular waves with wave height equal to 1, 2, 4 and 6 meters
Figure 4.15. Surge RAO for regular waves with wave height equal to 1, 2, 4 and 6 meters
0
0.05
0.1
0.15
0.2
0.25
5 10 15 20 25 30
Pit
ch (
deg
/deg
)
Period (sec)
h=1m h=2m h=4m h=6m
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
5 10 15 20 25 30
Hea
ve
(m/m
)
Period (sec)
h=1m h=2m h=4m h=6m
0
0.25
0.5
0.75
1
1.25
1.5
1.75
5 10 15 20 25 30
Su
rge
(m/m
)
Period (sec)
h=1m h=2m h=4m h=6m
75
CHAPTER 4 Model Test Results
However, the most interesting fact of these regular waves RAO results is the
non-linear effects observed. Contrary to what is exposed at the beginning of the
chapter, nonlinear phenomenon is captured and RAO values are slightly drifted to the
left and magnitude decreased mostly in the pitch and heave figures (see 2.3.4 Non-
Linear Effects to find the possible non-linear effects which affect the OFWT model).
The experiments show that when regular waves approach to approximately 18
seconds and 25 seconds, the model undergoes to less heave and pitch motions
respectively when was under higher wave amplitudes.
In addition, comparing the three RAO figures, it can be seen a coupling effect
around the 26 seconds of wave period, where it is found the peak in pitch for wave
height equal to 1 meter. It is seen how this affects the heave motion which
experiments a second peak in the same wave period at the expense of surge motion.
This fact also reinforces the idea that non-linear effects also affect the platform
motions under small wave motions and not only under high wave amplitudes.
Figure 4.16. Non-linear effects seen during test simulation
Some other authors have also found non-linear effects consequences in their OFWT
scale model tests, mostly when compared with numerical simulations which in most
of the cases pay no heed to second-order hydrodynamics.
76
CHAPTER 4 Model Test Results
It is the case of Huijs, et al., (2013), who found that heave motions in the model tests
for higher wave conditions were smaller than in the simulations, and attributed to
non-linear effects, such as viscous damping.
An investigation from the MIT (2012) also found out that their OFWT scale model
underwent in addition to the wave-frequency motions, large amplitude natural
frequency heave and pitch period motions from certain wave periods. They
concluded that coupled heave-pitch resonant motions of the floating platform in
waves resulted from the second order difference frequency interactions between
surface waves and body motions (and not from the Mathieu instability).
However, it is found some contradiction to some authors about non-linear effects.
For example, Herbjᴓrn (1999) found that the higher the incoming wave amplitude,
the stronger the instability and larger excitations and his non-linear analyses showed
approximately 10 times larger motions than in an ordinary frequency domain
analysis. The results of this work agree with the fact that for higher wave amplitudes
stronger the instabilities are, but as seen in the previous RAO figures, motions are of
the same magnitude for all the wave amplitudes, unless for larger wave periods,
which cause lower pitch and heave motions.
4.1.4 Only Oblique Regular Waves
In order to test the floating platform facing oblique waves the model has been rotated
and the actual wave heading angle is 60º. In this manner, the model faces the waves
with two of the offset columns instead of one. Mooring lines have changed their
position accordingly and just three lines have been required instead of four.
77
CHAPTER 4 Model Test Results
Figure 4.17. System configuration for only oblique regular wave tests
The model is tested under wave heights of 2 and 6 meters in frequency ranges of 0.03
– 0.13 Hz (in full scale terms). RAO results for pitch, heave and surge DOF are
presented in the following figures together with the results for the only regular
waves.
0
0.05
0.1
0.15
0.2
0.25
5 15 25
Pit
ch (
deg
/deg
)
Period (sec)
h=2m h=2m 120° h=6m h=6m 120°
0
0.05
0.1
0.15
0.2
5 15 25
Ro
ll (
deg
/deg
)
Period (sec)
h=2m h=2m 120° h=6m h=6m 120°
Wave direction
x
y
z
CG
78
CHAPTER 4 Model Test Results
Figure 4.18. RAO for oblique regular waves (wave incident angle 60º) with wave height
equal to 2 and 6 meters: (a) Pitch, (b) Roll, (c) Heave and (d) Surge
The most relevant output of this system identification test is the verification that
when the platform faces oblique waves, significant roll motions appear at the
expense of pitch rotation. Moreover, roll motions become more important than pitch
ones. In contrast, RAO heave and surge results do not seem to be modified when
different wave heading angle.
It is noticed that in this test, the non-linearity effects are also observed in the case of
pitch, heave and roll DOFs, as RAO values for 6 meters wave height are lower than
for 2 meters for the same frequency.
Bagbanci (2011) presents similar behaviour results for another semisubmersible
OFWT when the wave heading angle is 30º.
4.1.5 Regular Waves + Wind
In regular waves + wind tests, the tested frequencies also comprise 0.03 – 0.13 Hz
range in full scale terms and wave heights tested are 2 and 6 meters. Wave heading
angle is 0º.
0
0.25
0.5
0.75
1
1.25
1.5
1.75
5 15 25
Hea
ve
(m/m
)
Period (sec)
h=2m h=2m 120° h=6m h=6m 120°
0
0.25
0.5
0.75
1
1.25
1.5
1.75
5 15 25
Su
rge
(m/m
) Period (sec)
h=2m h=2m 120° h=6m h=6m 120°
79
CHAPTER 4 Model Test Results
The three wind generators are placed on a carriage 4 meters ahead the model. The
mean wind speed next to the rotor is approximately 2.1 m/s - 18.7 m/s in full scale -
(see 3.7.1 Wind assessment and calibration). Before the activation of the wave
maker, the model is subjected to the wind load at least for 20 seconds to allow a
stabilization of the model motion after activation of the fans (mostly for surge
translation). More details of the test procedure can be found in Annex II. -
Laboratory Diary.
Figure 4.19. System configuration for regular waves + wind tests
Wave direction
x
y
z
CG
80
CHAPTER 4 Model Test Results
Figure 4.20. RAO for regular waves + wind with wave height equal to 2 and 6 meters: (a)
Pitch, (b) Roll, (c) Heave and (d) Surge
In general terms, the action of the wind on the model does not significantly affect the
heave and surge RAO. Just a slight decrease of heave and surge RAO for wave
height of 2 meters can be seen.
In contrast, the wind load makes the pitch rotation grows in the real wave period
range (4 - 20 seconds) and dampens it for wave periods higher than 25 seconds. In
the case of roll rotation, the load case of regular waves + wind slightly increase the
RAO for 2 meters wave height during the real wave period range and considerably
rise for wave periods higher than 20 seconds. RAO for 6 meters wave height also
0
0.05
0.1
0.15
0.2
0.25
5 15 25
Pit
ch (
deg
/deg
)
Period (sec)
h=2m h=2m W h=6m h=6m W
0
0.004
0.008
0.012
0.016
0.02
5 15 25
Ro
ll (
deg
/deg
) Period (sec)
h=2m h=2m W h=6m h=6m W
0
0.25
0.5
0.75
1
1.25
1.5
1.75
5 15 25
Hea
ve
(m/m
)
Period (sec)
h=2m h=2m W h=6m h=6m W
0
0.25
0.5
0.75
1
1.25
1.5
1.75
5 15 25
Su
rge
(m/m
)
Period (sec)
h=2m h=2m W h=6m h=6m W
81
CHAPTER 4 Model Test Results
experiments greater values for high wave periods in comparison to loads without
wind.
Figure 4.21. Scale model during test under wave and wind loads. It is noticeable the
increment in the heel angle due to the wind load
4.2 Station Keeping Test Types
The station keeping test types can recreate different real sea states in the test tank.
This section presents the different sea states tested and the correspondent measured
spectra, the motions significant m/deg amplitude and the spectral analysis for all the
station keeping tests.
82
CHAPTER 4 Model Test Results
Figure 4.22. System configuration for the sea states’ tests
4.2.1 Sea States
As described in 3.4.2 Irregular Waves, the model is tested in real sea state simulation
following the Joint North Sea Wave Observation Project (JONSWAP) spectrum,
with the following wave configurations (from Table 3.8. Sea States Tested):
Table 4.4. Sea States parameters in full and model scale
Full Scale Model Scale
Sea
State (m) (s) (mm) (s)
1 2 7.5 1.000 25.000 0.839
2 2.44 8.10 1.000 30.500 0.906
3 3.66 9.70 1.000 45.750 1.084
4 5.49 11.30 1.226 68.625 1.263
5 9.14 13.60 1.780 114.250 1.521
6 10.50 14.30 1.964 131.250 1.599
83
CHAPTER 4 Model Test Results
Each of these waves is applied at 180 degrees (x-axis), which means 0 degrees of
incident wave angle, and is aligned with the wind direction in the cases the model is
under wind load too.
It is easy to see that for lower wave significant heights and peak period , the
spectra is wider and the greatest energy density is found in the wave energy range
around 0.13 Hz. As the and are increased, the spectra is getting narrower but
higher and moving right to lower wave energy ranges. As an example, energy density
peak for sea state 1 is 2.53 m2/Hz and corresponds to 0.12 Hz, and for sea state 6 it is
215.73 m2/Hz and corresponds to 0.068 Hz.
Figure 4.23. Theoretical JONSWAP spectra
The statistics in time domain for the measured 6 sea states, consisting of standard
deviation, maximum amplitude, minimum amplitude, maximum crest height,
maximum trough and maximum wave height, are presented in Table 4.5. As it can be
seen in the table, the maximum crest heights are around 1.5 times larger than the
value of , while the maximum wave heights are more than the double and
slightly double for the greatest values.
0
10
20
30
40
50
60
70
0 0.1 0.2 0.3 0.4 0.5 0.6
PS
D (
m2/H
z)
Frequency (Hz)
Sea State 1
Sea State 2
Sea State 3
Sea State 4
Sea State 5
Sea State 6
0
50
100
150
200
250
0 0.2 0.4
84
CHAPTER 4 Model Test Results
Table 4.5. Statistics for measured JONSWAP spectra
Theoretical Measured
Sea
State Wind
(m)
(sec) SD
Maximum
Amp.(m)
Minimum
Ampl.(m)
Max
Crest
(m)
Max
Trough
(m)
Max
Wave
(m)
1 No 2 7.5 0.49 2.87 -2.35 3.22 -1.98 5.22
2 No 2.44 8.1 0.58 2.84 -2.64 3.13 -2.34 5.48
Yes 2.44 8.1 0.58 3.23 -2.40 3.56 -2.04 5.63
3 No 3.66 9.7 0.90 5.59 -3.62 5.83 -3.59 9.21
4 No 5.49 11.3 1.32 7.30 -6.51 7.38 -5.28 13.81
Yes 5.49 11.3 1.33 6.19 -6.44 7.14 -4.92 12.64
5 No 9.14 13.6 2.20 12.41 -7.76 12.18 -7.95 20.17
6 No 10.5 14.3 2.52 12.73 -8.39 11.69 -9.16 21.12
Yes 10.5 14.3 2.42 13.49 -8.09 11.87 -9.21 21.58
Where:
- Standard Deviation (SD) – If there are data
points, and the sum of the squares of the
differences between the points and the mean
value is ∑ ( )
, the result is calculates
as √
∑ ( )
- Maximum/Minimum – the value is the
maximum/minimum value found in the time
range
- Maximum Crest – maximum value found in the time range measured relative to
a baseline formed by joining the two points where the cursors cross the data.
This is always greater than or equal to 0
- Maximum Trough - minimum value found
between the cursors measured relative to a
85
CHAPTER 4 Model Test Results
baseline formed by joining the two points where the cursors cross the data. This
is always less than or equal to 0
- Maximum Wave – maximum difference
between crest and trough
4.2.2 Motions Significant Height
The motion of the OFWT system in certain sea states is expressed in terms of a
significant height as a representative value which is defined in 3.4.2 Irregular Waves
by the average of the 1/3 highest that is, four times the square root of the zeroth-order
of the response spectrum.
To obtain a significant height from measured date, the motion spectrum from FFT
(Fast Fourier Transform) has been used.
The model presents similar significant motion height under wind loads for heave
motion, slightly higher for pitch and double for roll. For surge motion, the difference
between no wind and wind load performance is greater for lower significant wave
height.
Shin et.al (2013) also tested the DeepCwind OFWT scale 1:80 in sea states 2, 3, 4
and 5 and their results for significant height behave similar to this report’s ones.
There is not difference at all in heave motions under wind and no wind and pitch is
incremented under wind loads. Remarkably, Shin et. al.’s shows considerable
experimental yaw (most probably due to gyroscopic moment induced by their
rotating rotor), but their numerical analysis and this report`s model test evidence no
yaw significant height at all. Roll performance is not shown in Shin et. al.’s.
Heave significant height is nearly the same for wind and no wind cases with the
exception of sea state 5, where the results of this work are 1.5 greater the magnitude
than Shin et. al.’s. In contrast, the significant height of pitch in this work is much
higher than in the other report, being double in the case or sea sates 4 and 5. No close
86
CHAPTER 4 Model Test Results
similitude in surge magnitude is found between the two reports (notice that the
mooring lines in this work are not modelled).
Figure 4.24. Significant Height of pitch for load cases with only waves and waves + wind
Figure 4.25. Significant Height of roll for load cases with only waves and waves + wind
Figure 4.26. Significant Height of heave for load cases with only waves and waves + wind
0
2
4
6
8
1 2 3 4 5 6
Sig
nif
ican
t H
eigh
t o
f
Pit
ch (
deg
)
Sea State
Waves Waves + Wind
0
0.2
0.4
0.6
1 2 3 4 5 6
Sig
nif
ican
t H
eigh
t o
f
Ro
ll (
deg
)
Sea State
Waves Waves + Wind
0
1
2
3
4
5
6
1 2 3 4 5 6
Sig
nif
ican
t H
eigh
t o
f H
eave
(m)
Sea State
Waves Waves + Wind
87
CHAPTER 4 Model Test Results
Figure 4.27. Significant Height of surge for load cases with only waves and waves + wind
4.2.3 Frequency Domain Analysis - Spectral Analysis
Response spectra and statistical results are provided to illustrate the relative motion
performance of the system in irregular seas with and without wind loads according to
the wave frequencies.
To build up the response spectra in the frequency domain from the raw data in the
time domain, discrete Fourier transform is used. Its particularity is that it uses
exponentials and complex numbers instead of sines and cosines as Fourier series
does. The Fourier transform for a signal ( ) is defined as:
( ) ∫ ( )
(4.4)
And the inverse Fourier transform is:
( )
∫ ( )
(4.5)
where ( ) ( ) (4.6)
Particularly, discrete Fourier transform (DFT) is used for analysing the frequency
content of discrete signal. Its expression is:
0
5
10
15
1 2 3 4 5 6
Sig
nif
ican
t H
eigh
t o
f
Su
rge(
m)
Sea State
Waves Waves + Wind
88
CHAPTER 4 Model Test Results
( ) ∑ ( ) ( )( )
(4.7)
Where
- ( )is the discrete Fourier transform output, which gives one complex
value for each discrete frequency, that provides information about the relative
contribution to the signal by each discrete frequency.
- is the frequency increment or resolution of the DFT output, is
the total number of discrete data points taken, is the total sampling time
and is the time between data points
The frequency increment of a DFT is analogous to the fundamental frequency of
a Fourier series, in that the DFT provides information about the relative contribution
of the harmonics of , just as the Fourier series coefficients provide information
about the relative contribution of the harmonics of the fundamental frequency.
- For ( ) is the DFT at the first harmonic frequency
- For ( ) is the DFT at the second harmonic frequency
- For ( ) is the DFT at the third harmonic frequency , etc.
In DFT analysis, the Nyquist criterion has to be taken into account, as reliable
frequency information is only obtained for frequencies less than , where
is the sampling frequency.
Regarding the previous statements, it can be calculated at what value of the
frequency equals :
( ⁄ )
(4.8)
89
CHAPTER 4 Model Test Results
Therefore, the maximum useful frequency from a DFT output, also called the
folding frequency , is:
(4.9)
To process these calculations on a computer, the Fast Fourier Transform (FFT) is
used to simplify a DFT. The FFT function of Microsoft Excel has been used to do the
analysis and checked with Matlab and the power results of the wave maker software.
The frequency of test sampling is 137.02 Hz, which corresponds to 15.32 Hz in
full scale. The number of data points sampled has to be a power of 2, in this case is
212
, so
The spectral analysis described here is used to calculate spectral coefficients; Power
Spectral Density (PSD) for the generated waves spectrum and pitch, roll, heave and
surge motions; and Response Amplitude Operator (RAO) for the DOFs are analysed.
Spectral Coefficients
According to the spectral moments equations described in 2.1.3 Irregular Waves, the
correspondent spectral moments are calculated to know the sea spectral coefficients:
Table 4.6. Spectral coefficients
Sea
State Wind
Hs
(m)
Tp
(s) m2 m1 m0 m1 m2
Hmo
(m)
Te
(s)
Tm
(s)
Tp
(s)
1 No 2 7.5 13.68 1.04 0.14 0.02 0.00 1.47 7.70 7.04 7.04
2 No 2.44 8.1 22.12 2.10 0.29 0.04 0.01 2.15 7.25 6.56 7.23
Yes 2.44 8.1 19.51 2.57 0.36 0.06 0.02 2.41 7.06 6.07 7.43
3 No 3.66 9.7 51.47 5.48 0.63 0.08 0.01 3.17 8.74 8.17 10.70
4 No 5.49 11.3 156.11 14.32 1.49 0.17 0.03 4.88 9.61 8.71 9.90
Yes 5.49 11.3 262.15 23.07 2.21 0.24 0.04 5.95 10.43 9.26 12.15
5 No 9.14 13.6 1587.15 59.98 4.51 0.43 0.08 8.50 13.28 10.58 10.70
6 No 10.5 14.3 1424.05 93.24 6.70 0.54 0.08 10.35 13.93 12.37 14.85
90
CHAPTER 4 Model Test Results
Yes 10.5 14.3 1384.52 89.05 6.45 0.53 0.09 10.16 13.81 12.14 13.37
Where is the spectral significant wave height, is the peak wave period, is
the energy wave period and is the spectral mean wave period and, obtained
according the equations (2.14), (2.15), (2.18) and (2.19) respectively.
Power Spectral Density
Power Spectral Density (PSD) is presented in the following figures for wave
spectrum, pitch, roll, heave and surge motions for the different sea states tested.
When available, it is also presented the comparative with the wind cases. The PSD is
calculated as
( ) ( ( )
)
(4.10)
where ( ) is equal to the modulus of the Fast Fourier Transform from
the wave amplitude and DOF motions in time domain:
( ) | ( )| (4.11)
Wave Spectrum PSD
A comparison of the theoretical and measured spectra is shown in Figure 4.28 where,
at first sight, it can be seen as a not very close agreement. In fact, the measured
JONSWAP data shown in the figure are calculated with the Fast Fourier Transform,
which might be affected by leakage, which occurs when the input signal does not
repeat periodically and the periodic length is not equal to the length of the actual
input. A better Fourier Transform fit or the application of a Hanning window would
91
CHAPTER 4 Model Test Results
enhance the results’ impression. However, the total energy captured is approximately
the same, as spectral coefficients show in Table 4.6. Spectral coefficientsso no
further data enhancement is required for this thesis aim.
In Figure 4.28 it is also remarkable the effect of the wind in the wave spectra. This
variation in the wave spectra is due to the wind waves caused by the interaction
between wind and sea surface during a significant period of time. It is reminded that,
in contrast to the regular wave tests, the tests in sea states were performed during 20
minutes (3 hours in model scale).
0
1
2
3
4
5
6
7
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
PS
D (
m2/H
z)
Frequency (Hz)
Theoretical
Jonswap
Measured
Jonswap
0
2
4
6
8
10
12
14
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
PS
D (
m2/H
z)
Frequency (Hz)
Theoretical
Jonswap
Measured
Jonswap
Measured
Jonswap W
0
2
4
6
8
10
12
14
16
18
20
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
PS
D (
m2/H
z)
Frequency (Hz)
Theoretical
Jonswap
Measured
Jonswap
0
10
20
30
40
50
60
70
80
90
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
PS
D (
m2/H
z)
Frequency (Hz)
Theoretical
Jonswap
Measured
Jonswap
Measured
Jonswap W
92
CHAPTER 4 Model Test Results
Figure 4.28 Theoretical and Measured JONSWAP spectra under wind load (W) when data
available
Rotational and Translational Motions PSD
Figure 4.29. PSDs from test data for pitch, roll, heave and surge for an irregular wave only
case with Hs = 2 m and Tp = 7.5 sec
0
20
40
60
80
100
120
140
160
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
PS
D (
m2/H
z)
Frequency (Hz)
Theoretical
Jonswap
Measured
Jonswap
0
50
100
150
200
250
300
350
400
450
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
PS
D (
m2/H
z)
Frequency (Hz)
Theoretical
Jonswap
Measured
Jonswap
Measured
Jonswap W
0
5
10
15
20
0.03 0.06 0.09 0.12 0.15 0.18
PS
D (
deg
2/H
z)
Frequency (Hz)
Pitch NW
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.03 0.06 0.09 0.12 0.15 0.18
PS
D (
deg
2/H
z)
Frequency (Hz)
Roll NW
0.00
0.02
0.04
0.06
0.08
0.10
0.03 0.05 0.07 0.09 0.11 0.13 0.15 0.17
PS
D (
m2/H
z)
Frequency (Hz)
Heave NW
0.0
0.2
0.4
0.6
0.8
1.0
0.03 0.08 0.13 0.18
PS
D (
m2/H
z)
Frequency (Hz)
Surge NW
93
CHAPTER 4 Model Test Results
Figure 4.30. PSDs from test data for pitch, roll, heave and surge for an irregular wave only
case with Hs = 2.44 m and Tp = 8.1 sec
Figure 4.31. PSDs from test data for pitch, roll, heave and surge for an irregular wave only
case with Hs = 3.66 m and Tp = 9.7sec
0
50
100
150
200
0 0.1 0.2 0.3
PS
D (
deg
2/H
z)
Frequency (Hz)
Pitch NW
Pitch W
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 0.1 0.2 0.3
PS
D (
deg
2/H
z)
Frequency (Hz)
Roll NW
Roll W
0.0
0.1
0.2
0.3
0.4
0 0.1 0.2 0.3
PS
D (
m2/H
z)
Frequency (Hz)
Heave NW
Heave W
0
50
100
150
200
250
300
0 0.1 0.2 0.3
PS
D (
m2/H
z)
Frequency (Hz)
Surge NW
Surge W
0
5
10
15
20
0 0.1 0.2 0.3
PS
D (
deg
2/H
z)
Frequency (Hz)
Pitch NW
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.1 0.2 0.3
PS
D (
deg
2/H
z)
Frequency (Hz)
Roll NW
0.0
0.2
0.4
0.6
0.8
0 0.1 0.2 0.3
PS
D (
m2/H
z)
Frequency (Hz)
Heave NW
0
50
100
150
200
0 0.1 0.2 0.3
PS
D (
m2/H
z)
Frequency (Hz)
Surge NW
94
CHAPTER 4 Model Test Results
Figure 4.32. PSDs from test data for pitch, roll, heave and surge for an irregular wave only
case with Hs = 5.49 m and Tp = 11.3 sec
Figure 4.33. PSDs from test data for pitch, roll, heave and surge for an irregular wave only
case with Hs = 9.14 m and Tp = 13.6 sec
0
10
20
30
40
50
60
70
80
0 0.1 0.2 0.3
PS
D (
deg
2/H
z)
Frequency (Hz)
Pitch NW
Pitch W
0
2
4
6
8
0 0.1 0.2 0.3
PS
D (
deg
2/H
z)
Frequency (Hz)
Roll NW
Roll W
0
2
4
6
8
10
12
0 0.1 0.2 0.3
PS
D (
m2/H
z)
Frequency (Hz)
Heave NW
Heave W
0
200
400
600
800
0 0.1 0.2 0.3
PS
D (
m2/H
z)
Frequency (Hz)
Surge NW
Surge W
0
10
20
30
40
50
60
70
80
0 0.1 0.2 0.3
PS
D (
deg
2/H
z)
Frequency (Hz)
Pitch NW
0
1
1
2
2
3
3
4
0 0.1 0.2 0.3
PS
D (
deg
2/H
z)
Frequency (Hz)
Roll NW
0
20
40
60
80
100
0 0.1 0.2 0.3
PS
D (
m2/H
z)
Frequency (Hz)
Heave NW
0
200
400
600
800
1,000
0 0.1 0.2 0.3
PS
D (
m2/H
z)
Frequency (Hz)
Surge NW
95
CHAPTER 4 Model Test Results
Figure 4.34. PSDs from test data for pitch, roll, heave and surge for an irregular wave only
case with Hs = 10.5 m and Tp = 14.3 sec
Response Amplitude Operators (RAO)
Figure 4.35, Figure 4.36, Figure 4.37, Figure 4.38 and show the RAO results for roll,
heave and surge for the different sea states tested. RAO for each degree of freedom is
obtained as
( )
( )
( ) (4.12)
The main advantage of representing the RAOs is that it allows to clearly seeing the
natural frequencies in the graph, as the very high magnitude should correspond to
these frequencies (considering only linear hydrodynamics). From the free decay
tests, pitch, roll, heave and surge associated natural frequencies are 0.037 Hz,
0.037 Hz, 0.054 Hz and 0.006 Hz respectively (Table 4.3). Under wind loads, the
model showed to have associated natural frequencies of 0.036 Hz, 0.038 Hz, 0.054
Hz and 0.008 Hz for pitch, roll, heave and surge respectively.
0
20
40
60
80
100
0 0.1 0.2 0.3
PS
D (
deg
2/H
z)
Frequency (Hz)
Pitch NW
Pitch W
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 0.1 0.2 0.3
PS
D (
deg
2/H
z)
Frequency (Hz)
Roll NW
Roll W
0
50
100
150
200
250
300
350
0 0.1 0.2 0.3
PS
D (
m2/H
z)
Frequency (Hz)
Heave NW
Heave W
0
500
1,000
1,500
2,000
0 0.1 0.2 0.3
PS
D (
m2/H
z)
Frequency (Hz)
Surge NW
Surge W
96
CHAPTER 4 Model Test Results
Regarding the pitch RAOs in Figure 4.35, it can be seen that the pitch rotations
occur with the exactly same characteristics for sea states 1 and 2 without wind and
their RAO peaks are found on the 0.0374 Hz frequency, which perfectly agrees with
the system’s natural frequency in pitch. For the sea state 3, the RAO peak is also
found on the same frequency but its magnitude is more than the double. Unexpected,
pitch RAO for sea states 4 and 5 drop drastically and their peak start to shift to lower
frequencies, as progressively happens to the highest sea states. Finally, RAO for sea
state increases immediately and its peak’s frequency decreases until . 3 Hz.
The effect of the wind in pitch RAOs is not easy to evaluate although what it is clear
for all the cases it is that it increases the pitch rotations. The case of wind in sea state
6 draws particular attention to the high magnitude of a peak correspond to a very
small frequency of 0.0037 Hz.
When looking to roll RAOs in Figure 4.36 the first fact observed is the low response
of the OFWT in roll, with an average of [0-2] deg/m for most of the cases, which is
one of the characteristics and advantages of the semisubmersible platforms. The
RAO peak is found in 0.0374 Hz for sea states 1, 2, 3, and 5, which coincides with
the roll natural frequency. RAO peak for sea state 6 is placed on 0.030 Hz.
In contrast to the roll and pitch cases, the heave RAO peaks for low significant wave
heights are not found exactly on the natural frequency obtained in the free decay
tests. Specifically, the frequency which corresponds to the peaks is 0.056, while the
natural frequency experimentally obtained was 0.054. As seen in Figure 4.7 Heave
Free Decay data and Fit, considerable non-linear effects are shown when trying to
achieve the natural frequency with the underdamped equation (2.39). Therefore, it is
assumed that a most appropriate value for heave natural frequency is 0.056 Hz
instead 0.054 Hz, which is even closer to the values from bibliography (Table 4.3).
It is recalled that this model’s mooring lines are not properly scale dimensioned
because their main function is to maintain the model in its testing position, so this
representation of surge RAO is just for orientation. It can be observed that for sea
states , 2 and 3 the RAO peaks’ frequency is placed on . 3 Hz, which is
97
CHAPTER 4 Model Test Results
considerably lower than the measured natural frequency in the free decay tests. For
the rest of sea states, this value is reduced until almost the 0 Hz frequency.
Finally, it can be said that in general terms, the effect of the wind for the lower
significant wave heights is considerable, as it increases the RAO values for all the
DOF studied and also increase the number of RAO peaks in the rotational motions
pitch and roll. In contrast, in the sea state 6 the effect of the wind shift the peak of all
the DOF considered to very low frequencies (approx. 0.0037 Hz) and decrease the
motions in all the cases but pitch.
The results of this work follow the same line than the RAO comparisons which the
Offshore Code Comparison Collaboration (Robertson, et al., 2014) presented in June
of this year. Notice that their RAO are calculated from 0.05 Hz and ours from 0.03
Hz, so the range [0.03-0.05 Hz] has not been able to compare.
Figure 4.35. Pitch RAO values for the six sea states tested
0
10
20
30
40
50
60
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17
Pit
ch R
AO
(d
eg/m
)
Frequency (Hz)
Sea State 1 NW
Sea State 2 NW
Sea State 2 W
Sea State 3 NW
Sea State 4 NW
Sea State 4 W
Sea State 5 NW
Sea State 6 NW
Sea State 6 W
0
100
200
300
400
500
600
0 0.1
98
CHAPTER 4 Model Test Results
Figure 4.36. Roll RAO values for the six sea states tested
Figure 4.37. Heave RAO values for the six sea states tested
0
2
4
6
8
10
12
14
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17
Ro
ll R
AO
(d
eg/m
)
Frequency (Hz)
Sea State 1 NW
Sea State 2 NW
Sea State 2 W
Sea State 3 NW
Sea State 4 NW
Sea State 4 W
Sea State 5 NW
Sea State 6 NW
Sea State 6 W
0
1
2
3
4
5
6
7
8
9
10
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17
Hea
ve
RA
O (
m/m
)
Frequency (Hz)
Sea State 1 NW
Sea State 2 NW
Sea State 2 W
Sea State 3 NW
Sea State 4 NW
Sea State 4 W
Sea State 5 NW
Sea State 6 NW
Sea State 6 W
0
20
40
60
80
0 0.1
0
10
20
30
40
0 0.1
99
CHAPTER 4 Model Test Results
Figure 4.38. Surge RAO values for the six sea states tested
In conclusion, it is clearly observed from PSD and RAO figures that although it is
said that the second-order loads are quite small compared to the first-order loads, this
loading results in non-negligible responses with respect to first order, mostly for sea
states 4, 5 and 6. This might results from the excitation of system natural frequencies
(as observed in the experimental results) and a small amount of damping. Bayati, et
al., (2014) state that the very small amount of radiation damping at these frequencies
results in large resonant motion, and although the sum-frequency contribution is not
playing an important role for the OFWT system, the difference-frequency
contribution is.
Also, it has been seen for all the cases that the pitch, roll, heave and surge natural
frequencies are lower than the first-order wave spectrum frequency range.
Nevertheless, it is understood that second-order hydrodynamics are responsible for
exciting the natural frequencies of the platform, mostly in the cases of heave and roll.
The results agree with the second-order hydrodynamics results made by Bayati, et
al., (2014), who compared them to first-order simulation for the same platform
concept.
0
100
200
300
400
500
600
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Su
rge
RA
O (
m/m
)
Frequency (Hz)
Sea State 1 NW
Sea State 2 NW
Sea State 2 W
Sea State 3 NW
Sea State 4 NW
Sea State 4 W
Sea State 5 NW
Sea State 6 NW
Sea State 6 W
0
500
1,000
1,500
0 0.05
100
CHAPTER 4 Model Test Results
101
CHAPTER
5 Numerical Model
5.1 Introduction
Figure 5.1. Representation of the OC4-DeepCwind OFWT system in ANSYS AQWA
Besides the comparison of this work’s experimental results to others authors’, it is
also included a brief numerical analysis based on the literature concepts included in
Chapter 2. For the analysis, the software ANSYS AQWA, which is very similar to
WAMIT, is used.
What it is interesting from ANSYS AQWA for this work it is that it provides an
engineering toolset for the investigation of the effects of wave, wind on floating
offshore structures. The tools AQWA Hydrodynamic Diffraction, AQWA
Hydrodynamic Time Response and ANSYS DesignModeler have been chosen for
this analysis.
5
102
CHAPTER 5 Numerical Model
AQWA Hydrodynamic Diffraction provides an integrated environment for
developing the primary hydrodynamic parameters required for undertaking motions
and response analyses. Three-dimensional linear radiation and diffraction analysis
may be undertaken with multiple bodies, taking full account of hydrodynamic
interaction effects that occur between bodies. Computation of the second-order wave
forces via the full quadratic transfer function matrices permits use over a wide range
of water depths (ANSYS, 2012).
AQWA Hydrodynamic Time Response provides dynamic analysis capabilities for
undertaking global performance assessment of floating structures in the time domain.
It allows the sea-keeping simulation with the inclusion of forward speed effects.
5.2 Data Input
As it is aforementioned, the tools AQWA Hydrodynamic Diffraction, AQWA
Hydrodynamic Time Response and ANSYS DesignModeler are used in this work.
The first step for the analysis is to import the CAD geometry into the DesignModeler
and continue with all necessary actions to convert the geometry into a surface body
and match the XY plane with the still water level plane (draft). In this point, it is also
necessary to split the structure into the diffracting and non-diffracting parts.
Figure 5.2. Geometry transformed in ANSYS DesignModeler
103
CHAPTER 5 Numerical Model
Then, the geometry output from DesignModeled is imported into the Hydrodynamic
Diffraction tool. According to the project information, water depth is 200 m and a
mass point is added for each of the structure parts with their correspondent mass
centre (from SWL), mass and moments of inertia. A drag disk is also included at this
point.
In this paper, only quasi-static drag force, which occurs in the wings of wind turbine,
is considered and aerodynamic load is not considered. Since we calculated the
motion of floating body, modeling is conducted without wind turbine wings.
The mesh is simulated with a defeaturing tolerance of 0.4 m, and 18 m of maximum
element size (none of the mesh elements closely reach this dimension). The number
of nodes is 3167 from which 2018 are from diffracting bodies.
Figure 5.3. Mesh
For the hydrodynamic analysis, the tower and the nacelle are excluded in structure
selection. The analysis is just done with on single wave direction (180º which means
0º incident wave angle) and under the same Jonswap spectrum and 6 sea states used
in the rest of this thesis (same parameters of Hs, Tp and γ). Interval frequency of
0.002 Hz is used between a wave frequency range of [0.03-1.2] Hz.
Finally, the entire diffraction model is exported to the Hydrodynamic Time Response
tool and time testing range is added.
104
CHAPTER 5 Numerical Model
5.3 Results
A summary of the results from the Hydrodynamic Diffraction and Time Response
results are presented below.
5.3.1 Response Amplitude Operators – AQWA
Diffraction Tool
The RAO graphs illustrate how the amplitude of the structure response changes with
wave frequency in this case. The following figures include the experimental results
for the wave heights in only regular wave tests and the results of the simulations in
AQWA Diffraction Tool.
Two remarks and differences are seen when comparing experimental and simulated
results. The most evident one it is that the AQWA simulations for all the significant
wave height yield the same results. Linear hydrodynamics theory states that RAO
results are independent of wave amplitude, but it can be clearly seen in the
experimental graphs that it is not (or at least it is what the scale tests show). AQWA
Diffraction tool includes second order hydrodynamics (2.3.4 Non-Linear Effects) in
its analysis but it is seen that other nonlinear effects exert a distinct influence on the
dynamic responses of the semisubmersible platform.
The second main difference between the experimental and simulated results is the
different platform natural frequencies which the peaks in the rotational graphs show.
Roll is not shown as its contribution to platform motion is almost neglected in no
wind load cases. In the pitch case, the peak is displaced to lower wave period and
there is no similitude in the results at all, most probably due to neglected viscous
damping. As it was cited in 2.3.4 Non-Linear Effects: “the non-estimation of viscous
damping can lead to an overestimation of motion amplitudes”, which is the case. In
contrast, the agreement for translational motions is very satisfactory, mostly for the
standard wave period range, with a noticeable higher peak in the case of heave RAO.
105
CHAPTER 5 Numerical Model
Figure 5.4. Pitch RAO comparison between only regular wave tests and AQWA simulation
Figure 5.5. Heave RAO comparison between only regular wave tests and AQWA simulation
Figure 5.6. Surge RAO comparison between only regular wave tests and AQWA simulation
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
7 9 11 13 15 17 19 21 23 25 27 29 31
Pit
ch (
deg
/deg
)
Period (sec)
h=1m h=2m h=4m h=6m AQWA
0
1
2
3
4
5
6
7 9 11 13 15 17 19 21 23 25 27 29 31
Hea
ve
(m/m
)
Period (sec)
h=1m h=2m h=4m h=6m AQWA
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
7 9 11 13 15 17 19 21 23 25 27 29 31
Su
rge
(m/m
)
Period (sec)
h=1m h=2m h=4m h=6m AQWA
106
CHAPTER 5 Numerical Model
5.3.2 Resultant Motion Results
In this section it is presented the resultant platform motion for the hydrodynamic
diffraction simulation simulations. Figures are shown for just some of the different
combinations of wave height and frequency in regular waves. In addition, each of
this graphic it is accompanied with a photography of the platform in the experiment
with the same test characteristics.
Figure 5.7. Motions for H = 2.44 m and T = 8.10 sec
Figure 5.8. Model in regular waves Hs = 2 m and Tp =8.10 sec
107
CHAPTER 5 Numerical Model
Figure 5.9. Motions for H = 5.44 m and T = 11.6 sec
Figure 5.10. Model in regular waves H = 6 m and Tp =11.3 sec
108
CHAPTER 5 Numerical Model
Figure 5.11. Motions for H = 10.5 m and T = 13.16 sec
Figure 5.12. Model in irregular waves Hs = 10.5 m and Tp =14.3 sec
109
CHAPTER
6 Summary and Conclusions
The performance of this experimental thesis concludes with satisfactory results and
some novelties regarding most of the existing literature on the experimental research
of the semisubmersible offshore floating wind turbine platform concept.
The main conclusions drawn from the data processing, discussion of the results and
comparison to others authors’ work and the numerical analysis run with ANSYS-
AQWA are schematically presented beneath these lines.
Conclusions regarding the Scale Modelling
Dimensioning of the main semisubmersible platform elements lengths and
diameters was not a tough task in comparison to the assignment of scaling the
mass properties due to the restraints that the materials impose. Although some
extra ballast was added and the model KG did not totally agree with the
prototype’s one, the natural frequencies of the system agreed with the intended
values
Assessment and modelling of the wind environment was not an easy task due to
the nature of the existing wind generator system in the laboratory. Wind
generator consisting of a series of fans, screens and contracting nozzle is
recommended for accurate testing of the performance of the offshore floating
wind turbine system under wind loads. Nevertheless, the wind speed range
achieved in the laboratory matched the operating wind loads of the OC4-
DeepCwind prototype
6
110
CHAPTER 6 Summary and Conclusions
Conclusions regarding the System Identification Tests
It is considered that the form of Response Amplitude Operator (RAO) analysis is
consistently linear, so it is supposed that RAOs will not depend on the wave
height. However, the experimental results throw very different information.
Nonlinear phenomenon is captured from the fact that RAO scattering is
noticeable drifted to greater wave periods and peaks magnitude is reduced
mostly in pitch and heave motions for highest wave amplitudes
In addition, it can be observed significant coupling effects between pitch and
heave for wave height equal to 1 meter. This fact also strengthens the idea that
non-linear effects also affect the platform motions under small wave motions
and not only under high wave amplitudes
The first fact contradicts some authors who state that the higher the incoming
wave amplitude, the larger the excitations; which have been proved that does not
happen for determined wave periods
The most relevant output of the test under oblique waves is that significant roll
motions appear at the expense of pitch rotation. Moreover, roll motions become
more important than pitch ones. In contrast, RAO heave and surge results do not
seem to be modified
In general terms, the action of the wind in system identification tests does not
significantly affect the translational heave and surge RAOs. In contrast, the wind
load makes the pitch rotation considerably increases in the real wave period
range (4 - 20 seconds) and dampens it for wave periods higher than 25 seconds.
In the case of roll rotation, the wind loads increase the rotation just in some
cases
111
CHAPTER 6 Summary and Conclusions
Conclusions regarding the Tests in Sea States
Not a perfect agreement is found between theoretical and measured JONSWAP
spectra. This difference is attributed to the fact that measured JONSWAP
spectrum in this work is calculated with the Fast Fourier Transform, which
might be affected by leakage. Another Fourier Transform fit or the application of
windows is recommended for next analysis
RAO results from the floating model tests in sea states clearly indicates again the
presence of non-linearity effects in all cases, and not just in higher significant
wave cases
The graphics show the agreement between the peaks in RAO and the natural
frequencies of the different degrees of freedom for the lowest energy sea states.
Then, the peaks start to shift to lower wave frequencies, as also happened in the
system identification tests
The sea state tests show once more one of the advantageous characteristic of the
semisubmersible platform: the low response concerning the roll motions
The effect of the wind for the lower significant wave heights is considerable, as
it increases the RAO values for all the DOF studied (mostly pitch) and also
increase the number of RAO peaks in the rotational motions pitch and roll. No
significant influence in the case of the highest energy sea state
Wind causes slight variation in the wave spectra due to the wind waves caused
by the interaction between wind and water surface during a significant period of
time
In conclusion, it is clearly observed from PSD and RAO figures that although it
is said that the second-order loads are quite small compared to the first-order
loads, this loading results in non-negligible responses with respect to first order.
112
CHAPTER 6 Summary and Conclusions
This might results from the excitation of system natural frequencies and
damping
Also, it has been seen for all the cases that the pitch, roll, heave and surge
natural frequencies are lower than the first-order wave spectrum frequency
range, which confirms the correct design of the DeepCwind semisubmersible
platform
Conclusions regarding the comparison of the experimental results with the numerical
analysis and others authors’ research
In contrast to the experiment results, AQWA simulations throw the same RAO
results for all the regular wave tests. AQWA Diffraction tool includes second
order hydrodynamics in its analysis but it is seen that other nonlinear effects
exert a distinct influence on the dynamic responses of the semisubmersible
platform
AQWA simulations indicates different platform natural frequencies for
rotational motions pitch and roll, most probably due to the non-estimation of
viscous damping
Although multiple comparisons of the experimental results with others authors’
works are presented in this thesis, what definitely have to be highlighted is the
vast importance of the nonlinear effects shown. This contrasts to other thesis
about the same floating concept, mostly the ones based just in numerical
analysis. Most probably, this is thanks to the high number of wave frequencies
tested, significant wave heights and sea states in more than 200 tank
experiments. However, it should be further researched if the fact of the reduce
1/80 scaling affects these statements.
113
Bibliography
ANSYS, 2012. AQWA User Manual. Canonsburg, PA: SAS IP, Inc..
ARUP, 2011. Review of the generation costs and deployment potential of renewable
electricity technologies in the UK, London: Department of Energy and Climate
Change.
Bagbanci, H., 2011. Dynamic Analysis of Offshore Floating Wind Turbines. Lisbon:
Instituto Superior Técnico Universidade Técnica de Lisboa.
Bayati, I., Jonkman, J., Robertson, A. & Platt, A., 2014. The effects of second-order
hydrodynamics on a semisubmersible floating offshore wind turbine. Journal of
Physics: Conference Series 524 - The Science of Making Torque from Wind 2014
(TORQUE 2014).
Binder, R. C., 1973. Fluid Mechanics. 5th ed. NJ: Upper Saddle.
Biran, A., 2003. Ship Hydrostatic and Stability. Oxford: Elsevier.
Butterworth, J., Lee, J. H. & Davidson, B., 2004. Experimental determination of
modal damping from full scale testing. Vancouver, B.C., Canada, s.n.
Çengel, Y. A. & Cimbala, J. M., 2006. Fluid Mechanics: fundamentals and
applications - 1st ed.. New York: McGraw-Hill.
Chakrabarti, S., 1998. Physical Model Testing of Floating Offshore Structures. s.l.,
Dynamic Positioning Commitee. Marine Technology Society.
Chakrabarti, S. K., 1994. Offshore Structure Modeling, Singapore: World Scientific
Publishing Co. Pte. Ltd.
Chen, J., 2012. Coupled Dynamic Analysis of Large-Scale Mono-Column Offshore
Wind Turbine with a Single Tether Hinged in Seabed, Texas, USA: Texas A&M
University.
Chopra, A. K., 1995. Dynamics of structures. s.l.:Prentice Hall Inc..
114
Bibliography
Clift, R., Grace, J. R. & Weber, M. E., 1978. Bubbles, Drops and Particles.
Cambridge: Academic Press.
Coulling, A. J. et al., 2013. Validation of a FAST semi-submersible floating wind
turbine numerical model with DeepCwind test data. Journal of Renewable and
Sustainable Energy, Volume 023116.
Couñago Lorenzo, B. & Barturen Antépara, R., 2011. Parque Eólico Marino
Flotante, Madrid: Escuela Técnica Superior de Ingenieros Navales (UPM).
Craig, R. R. & Kurdila, A. J., 2006. Fundamentals of Structural Dynamics. Second
ed. New Jersey, USA: John Wiley and Sons.
De Micco, P. & Andrés Figueroa, S., 2014. The prospect of Eastern Mediterranean
gas production: An alternative energy supplier for the EU?, Brussels: European
Parliament. Directorate-General in External Policies.
de Ridder, E.-J.et al., 2014. Development of a Scaled-Down Floating Wind Turbine
for Offshore Basin Testing. San Francisco, California, USA, s.n.
Det Norske Veritas, 2007. Environmental Conditions and Environmental Loads,
Norway: DNV.
European Commission, 2010. Europe 2020. A European strategy for smart,
sustainable and inclusive growth, Brussels: s.n.
European Commission, 2012. Blue Growth - opportunities for marine and maritime
sustainable growth. Communication from the Commission to the European
parliament, the Council, the European Econonomic and Social Committee and the
Committee of the Regions, 13 September, p. 494 final.
European Commission, 2013. EU Energy in Figures. Statistical Pocketbook 2013,
Brussels: Directorate-General for Energy.
EWEA, 2013. The European offshore wind industry - key trends and statistics 1st
half 2013, s.l.: s.n.
EWEA, 2014. Strategic Research Agenda / Market Deployment Strategy, s.l.:
European Wind Energy Technology Platform.
115
Bibliography
EWEA, 2014. The European offshore wind industry - key trends and statistics 2013,
s.l.: The European Wind Energy Association.
Faltinsen, O. M., 1990. Sea loads on ships and offshore structures. UK: Cambridge
University Press.
Fowler, M. J., Thomas III, D. A., Kimball, R. W. & Goupee, A. J., 2013. Design and
Testing of Scale Model Wind Turbines for Use in Wind/Wave Basin Model Tests of
Floating Offshore Wind Turbines. Nantes, France, s.n.
García-Ibañez, J., 2014. A cost-efficient method for the resource assessment and
performance optimization of offshore wave energy converters, Glasgow, UK:
University of Strathclyde.
Goupee, A. J. et al., 2013. Experimental comparison of three floating wind turbine
concepts. Journal of Offshore Mechanics and Arctic Engineering, 13 January.
Gueydon, S. & Weller, S., 2012. Study of a Floating foundation for Wind Turbines.
Rio de Janeiro, Brazil, s.n.
Herbjᴓrn, A. H., 1999. Alternative Shape of Spar Platforms for Use in Hostile Areas.
s.l., s.n.
HM Government, 2014. Europe 2020: UK National Reform Programme 2014,
London: Crown.
Huijs, F., Mikx, J., Savenije, F. & de Ridder, E.-J., 2013. Integrated design of
floater, mooring and control system for a semi-submersible floating wind turbine,
The Netherlands: EWEA.
IEA, 2013. Medium-Term Renewable Energy Market Report 2013 - Market trends
and projections to 2018, Paris: IEA/OECD.
IEA, 2013. Technology Roadmap - Wind energy, s.l.: s.n.
IEA, 2013. Wind Power seen generating up to 18% of global power by 2050, s.l.: s.n.
IPCC, 2014. Climate Change 2014. Mitigation of Climate Change, Berlin: IPCC
Working Group III Contribution to AR5.
116
Bibliography
Jonkman, J., Butterfield, S., Musial, W. & Scott, G., 2009. Definition of a 5-MW
Reference Wind Turbine for Offshore System Development., s.l.: Golden.
Jonkman, J. K., 2007. Dynamics Modeling and Loads Analysis of an Offshore
Floating Wind Turbine. s.l.:NREL National Renewable Energy Laboratory.
Jonkman, J. M., 2009. Dynamics of Offshore Floating Wind Turbines - Model
Development and Verification. Wiley Interscience.
Jonkman, J. & Musial, W., 2010. Offshore Code Comparison Collaboration (OC3)
for IEA Task 23 Offshore Wind Technology and Deployment, s.l.: Golden, CO.
Jonkman, J. et al., 2012. Offshore Code Comparison Collaboration Continuation
(OC4), Phase I-Results of Coupled Simulations of an Offshore Wind Turbine with
Jacket Support Structure. s.l.:NREL National Renewable Energy Laboratory.
Journée, J. M. & Massie, W. W., 2001. Offshore Hydromechanics. First ed.
s.l.:University of Delft.
Kliava, J. & Megel, J., 2010. Stability, Metacenter and Ship. American Journal of
Physics, Volume 78, pp. 738-747.
Koo, B., Lambrakos, K., Goupee, A. J. & Kimball, R. W., 2012. Model Tests for a
Floating Windturbine on Three Different Floaters. Rio de Janeiro, Brazil, s.n.
Luan, C., Gao, Z. & Moan, T., 2013. Modelling and Analyisis of a Semi-Submersible
Wind Turbine with a Central Tower with Emphasis on the Brace System. Nantes,
France, s.n.
Lui, Y., Yan, H. & Yung, T. W., 2012. Nonlinear Resonant Response of Deep Draft
Platforms in Surface Waves. s.l., s.n.
Martin, H. R., 2011. Development of a Scale Model Wind Turbine for Testing of
Offshore Floating Wind Turbine Systems, Maine, USA: University of Maine.
Electronic Theses and Dissertations.
Martin, H. R., Kimball, R. W., Viselli, A. M. & Goupee, A. J., 2012. Methodology
for Wind/wave Basin Testing of Floating Offshore Wind Turbines. Rio de Janeiro,
Brazil, s.n.
117
Bibliography
Matha, D., 2009. Model Development and Loads Analysis of an Offshore Wind
Turbine on a Tension Leg Platform, with a Comparison to Other Floating Turbine
Concepts, Colorado, USA: NREL.
Molho, N., 2013. Going green & energy security, s.l.: University of Oxford, The
Economist.
OC4, 2012. Website for OC4 project. [Online].
Philippe, M., Barbarit, A. & Ferrant, P., n.d. Hydro-Elastic Simulation of a Semi-
Submersible Floating Wind Turbine. Nantes, s.n.
Rao, N. N., 2004. Mechanical Vibrations. Fourth ed. NJ, USA: Pearson Education,
Inc..
Robertson, A. et al., 2012. Definition of the Semisubmersible Floating System for
Phase II of OC4, s.l.: OC4.
Robertson, A. et al., 2013. Offshore Code Comparison Collaboration, Continuation:
Phase II Results of a Floating Semisubmersible Wind System, s.l.: s.n.
Robertson, A. et al., 2014. Offshore Code Comparison Collaboration Continuation
within IEA Wind Task 30: Phase II Results Regarding a Floating Semisubmersible
Wind System. San Francisco, USA, s.n.
Robertson, A. N. et al., 2013. Summary of Conclusions and Recommendations drawn
from the DeepCwind scaled floating offshore wind system test campaign. Nantes,
France, s.n.
Roddier, D., Cermelli, C., Aubault, A. & Weinstein, A., 2010. WindFloat: A Floating
Foundation for Offshore Wind Turbines. Journal of Renewable and Sustainable
Energy, Issue 033104.
Ronold, K. O., Landet, E., Jorgensen, E. R. & Sandberg, J., 2011. Design Standards
for Floating Wind Turbine Structures. s.l., European Wind Energy Association.
Sawyer, S., 2012. Global Offshore: Current Status and Future Prospects. Energy and
Environment Management Magazine, October.
118
Bibliography
Shin, H., Kim, B., Dam, P. T. & Jung, K., 2013. Motion of OC4 5MW Semi-
Submersible Offshore Wind Turbine in Irregular Waves. Nantes, France, s.n.
The Scottish Government, 2011. 2020 Routemap for Renewable Energy in Scotland,
Edinburgh: Crown.
Thurman, H. V., 1997. Introductory Oceanography. Eigth Edition ed. s.l.:Prentice
Hall, Inc., Upper Saddle River, N.J..
Umbach, F., 2009. Global energy security and the implications for the EU, Munich-
Berlin: Centre for European Security Strategies (CESS).
University of Maine and James W. Sewall Company, 2007. Maine Deepwater
Offshore Wind Report, s.l.: s.n.
Vendrell, L., Susheelkumar, C., Redkar, S. & Montgomery Jr., J. W., n.d.
Hydrostatic Analysis of a Suction-Stabilized Float. Journal of Offshore Mechanics
and Arctic Engineering.
Wayman, E. et al., 2006. Coupled Dynamic Modeling of Floating Wind Turbine
Systems. Houston, Texas, USA, s.n.
Wiser, R. et al., 2011. Wind Energy in IPCC Special Report on Renewable Energy
Sources and Climate Change Mitigation, Cambridge and New York: Cambridge
University Press.
119
ANNEX I
I. - Test Instrumentation
I.1 Instrumentation required for the Inclining
Test
Annex Square Tank (4.572 m Large × 2.150 m Depth)
Schaevitz LSOP/LSOC Gravity-Referenced Inclinometer
- Connected to a DC power source and a
readout
- Range: ± 30º
Inclining masses
- Weight: 100 g each
I.2 Instrumentation required for test in only
regular/irregular waves
Kelvin Hydrodynamic Tank
- Tank Dimensions: 76 m long, 4.6 m wide and 2.5 m deep
- Typical water depth: 0.5 – 2.3 m
- Depth during tests: 2.1 m
Figure I.1. Inclinometer and inclining
masses
120
ANNEX I Instrumentation
Carriage
- Computer-controlled digital drive
- Max speed 5m/s, max acceleration
1m/s2
- Speed accuracy and regulation
exceeding ITTC standards
- Equipped with digitally-controlled
sub-carriage for unsteady forward
speed testing
- (Carriage was stop in the same position
during all tests run in this thesis and
just moved for specific issues out of
the tests duration)
Waves maker
- Variable-water-depth, computer-controlled for flap absorbing wavemaker
- Generates regular or irregular waves over 0.5m height (subject to water
depth)
Figure I.3. Wave Maker
Beach
- High quality variable-water-depth sloping beach
- Reflection coefficient typically less than 5% over frequency range of interest
Figure I.2. Tank carriage
121
ANNEX I Instrumentation
Data acquisition
- PC based modular data acquisition/control system
- Up to 64 input and 20 output channels, sample rate up to 60kHz
Figure I.4. Equipment Controls and Data Loggers mounted on the carriage
Wave Probe
- Determine surface elevation
Figure I.5. Wave Probe
Qualisys Cameras and marker balls
- Oqus Qualisys optical 6 DOF real-time motion capture camera system
- 5 light-weighted passive reflective semispherical markers. Made of
polystyrene hemispheres covered in special retro-reflective tape
122
ANNEX I Instrumentation
Figure I.6. a) Qualisys Camera, b) Passive marker balls
Video Recording Camera
Figure I.7. Video recording camera
I.3 Instrumentation required for test in
regular/irregular waves and wind
Skywatch Xplorer 2 Anemometer
- Measures balanced instant
windspeed and maximum
windspeed
- Maximum reading: 150 km/h, 42
m/s, 81 knots, 97 mph, 138 fps
- Resolution: 0.1 units
(a) (b)
123
ANNEX I Instrumentation
- Measuring cycle: 2 measurements
per second
- Accuracy: +/- 3%
- Operation temperature: -20°C to
70°C
Wind sentry set
a) W200P Potentiometer Windvane
- Meet the requirements of the IEC61400-12-1 standard
- Incorporates a precision wire-wound potentiometer as a shaft angle transducer
- (The windvane has not been connected to the data logger in this thesis)
b) A100R Contact Closure (Switching) Anemometer
- Rotor: 3-cup R30S (standard)
- Threshold: 0.2m/s
- Maximum windspeed: over 75m/s
- Temperature Range: -30 to +70 °C
operating
- Accuracy: 1% of reading between
10 and 55m/s, 2% above 55m/s.
0.1m/s for 0.3..10m/s
- Mode of work: calibrated 3-cup
series rotor drives an actuator in a
carefully balanced magnet system
with the resulting varying field
operating a reed switch (contact
opens and closes once per rotor
revolution)
c) Dual Mounting Arms (Cross-Arms) Type 405-1
3 Clarke CAM60000 Drum / Barrel Fans
- Fully enclosed 3 blade impellor
- Dimensions: 900 L x 330 W x 990
H (diameter 3 ’’), 27.6 kg weight
- Input Power: 350 watt, 230 v, 50
Hz
- Motor with variable 3 speed
control
- Airflow: massive, 6600 to 8000
cfm
ANNEX I Instrumentation
124
Figure I.8a) Skywatch Xplorer 2 Anemometer, b) Wind Sentry Set & c) Clarke CAM6000
Fan
I.4 Others
Water Vacuum
- Necessary for vacuuming water that rarely entered inside the model offset
columns during tests
Laser distance meter Leica Disto Classic5a
- Range of measurement: 0.2 up to 200 m, Accuracy: +/-1.5mm
Calibrating reference balls to calibrate the six Qualisys cameras previous to
place the model in the basin
Weights for ballast, used during the inclining tests
Crain + weight + slings to weight the full model mass
(a) (b) (c)
ANNEX I Instrumentation
125
Figure I.9. a) Vacuum, b) Laser distance meter, c) Reference balls panel
(a) (b) (c)
ANNEX I Instrumentation
126
127
ANNEX II
II. - Laboratory Diary
A description of all steps taken in the decision making, problem solving and testing
procedures in the two weeks of model testing are presented in the following pages.
All the experiments were carried out in the Kelvin Hydrodynamic Laboratory,
Glasgow from 23rd
June to 4th
July 2014.
1st day, Monday 23
rd June 2014
i) Inclining Test (Test I-1, I-2, I-3)
ii) Calibration of the Qualisys Cameras
During the past weeks, the OC4-Deepcwind semisubmersible platform 1:80 scale
model has been built and assembled in the workshop of the Kelvin Hydrodynamic
Laboratory. The model dimensions are obtained from Table 3.5 regarding very
carefully the mass properties, although it has been a difficult task due to the
considerable thin thicknesses that with a 1:80th
scale are calculated and are not
possible to manufacture in reality.
ANNEX II Laboratory Diary
128
Figure II.1 Model being built in the workshop of the Kelvin Hydrodynamic Laboratory
The materials used for each of the parts of the model are:
Table II.1 Materials used in platform scale model
Item Material
Offset Columns Acrilic
Main Column Foam Divinycell H60, PVC and plastic
Braces Acrilic
Pontoons Foam Divinycell H60
Reference Ball Supporters Stainless Steel
i) Inclining Test
Today, the model has been placed in a small water tank to carry out the Inclining test
in order to determine its stability and rest of hydrostatic properties.
The total weight of the assembled platform rises to 21.52 kg, but the model target
weight is 26.314 kg, according to Table 3.5. Before adding extra weight to each
column, we have to take into account the extra weight corresponding to:
ANNEX II Laboratory Diary
129
Table II.2. Extra weight to be considered in the platform model
Item Weight (kg)
3 × Marker balls 0.13
Domy Inclinometer 0.345
Total 21.995
Therefore, it is needed an extra weight of to adjust
our model to the target weight. It means that an extra weight of
has
to be added to each offset column. This has been achieved distributing this extra
weight on the bottom of the columns as shown in Figure II.2.
Figure II.2. Weight placed on one of the offset columns’ bottom in order to achieve the 1:80
model weight target
Then, the data recording software, Spike2, has been configurated with the
correspondent test data. The data entry for the third and last test of the day (Test I-3)
is presented in the following table:
Table II.3. Spike2 Data entry for Inclining Test I-3
Date 23/06/2014
Water Temperature 18.4ºC
Scale 80
Variable Unit Full Scale Model
ANNEX II Laboratory Diary
130
Draft m 20 0.25
Displacement kg 13809825 26.97231
Volume m3 13556.76 0.026478
KG m 6.54 0.08175
KM m 17.12 0.214
Model Mass kg - 26.314
Set-up
Inclining Masses g - 2*200
Inlining Mass KG m - 0.4265
Inclining Mass
Movement m
- 0.475
Movable Ballast
Mass kg
- 1
Before running the test, the Domy inclinometer and the two inclining masses are
placed at the ends of a foam platform that has been installed on the y axis for the test.
Then, with a graduated ruler, the inclining mass KG and movement are measured.
Figure II.3. Inclining test for the semisubmersible platform. The different pictures show the
test procedure where the inclining masses change their position.
After running the test, the feedback from the software has been the following:
ANNEX II Laboratory Diary
131
Table II.4. Feedback from Inclining Test I-3
Variable Value
% KG Error -18.040%
Move ballast by -388 mm
As it can been observed from the previous table, the inclining test is showing that we
have to displace the ballast by 388 mm below the position it is currently placed.
Nevertheless, the 1.4 kg ballast weight that each of the three offset columns has on
its bottom is sitting about 100 mm above the keel. From the incline, with the
amended values, the movable mass would have to been moved by
, which would put it right at the bottom of the floater. However, this adjust
will light vary the shape and thus the displacement.
- Calibration of the Qualisys Cameras
On the other hand, the calibration of the 6 Qualisys Cameras has been carried out
today. A platform with four reference balls is placed at the same position in the tank
where the 1:80 scale model is going to be tested. Then, with a wand with two extra
reference balls, all the system is calibrated in an enough wide area in the tank with
the software Qualisys Track Manager.
Figure II.4. Calibration of the Qualysis Cameras
ANNEX II Laboratory Diary
132
Figure II.5. Qualisys Track Manager Screenshot
2nd
day - Tuesday 24th
June 2014
a) Inclining Test
b) Calibration of the Wave Probe
a) Inclining Test
According to the feedback of the last Inclining test I-3 of the previous day, the ballast
has to be moved down, but it has been considered to carry out a new Inclining test
with the full system (platform + turbine) and study the new feedback. A rigid plastic
bar has been assembled on the platform main column which has two centered masses
that can be moved along it in order to facilitate the adjustment of the KG and the
radius of gyration.
Table II.5. Components Masses of the Turbine Model
Item Mass (kg)
Bar 0.23
Moving Mass 1 0.47
Moving Mass 2 0.47
Total Turbine Model 1.17
Model Target 1.1713
ANNEX II Laboratory Diary
133
Moreover, we have realized that the mass of the three bars which hold the reference
balls had not been considered. Therefore, we have quitted them and attached the
reference balls directly on the model.
As the system weight and distribution have changed, the model weight has to be
measured again in order to have certainty about the actual weight. Then, the model is
taken out from the small tank and when got dried, it is weighted with the help of a
wooden board, a crane and some slings. This has allowed adjusting the total mass
until the target model weight.
Table II.6. Floating Wind Turbine System Model Weight before ballasting
Item Target Weight
(kg)
Actual Weight
(kg)
Platform + Turbine 26.312 21.99
Platform + Turbine
+ Extra mass 26.312 26.41
error +0.37%
The model is placed back in the small tank, and the correct draft is supposed to be
achieved after having reached the target weight. Nevertheless, the actual floating line
is founded lower than the correct draft and therefore ballast has to be adjusted. 200 g,
150 g and 50 g is added on the bottom of columns 1, 2 and 3 respectively. It means
that the final model weight is:
Table II.7. Floating Wind Turbine System Model Weight after ballasting
Item Target Weight
(kg)
Actual Weight
(kg)
Platform + Turbine + Extra
mass + Ballast 26.312 26.81
error +1.51%
The specific data entry for the full system is:
ANNEX II Laboratory Diary
134
Table II.8. Spike2 Data entry for Inclining Test I-3
Date 24/06/2014
Water Temperature 18.2 ºC
Scale 80
Variable Unit Full Scale Model
Draft m 20 0.25
Displacement kg 13809825 26.97231
Volume m3 13556.76 0.026478
KG m 6.54 0.08175
KM m 17.12 0.214
Model Mass kg - 26.314
Set-up
Inclining Masses g - 2*200
Inlining Mass KG m - 0.4265
Inclining Mass
Movement m
- 0.475
Movable Ballast Mass kg - 1
The test feedback shows a remaining KG greater than 15%, so adding extra ballast
underneath the model continues to be the best solution.
b) Calibration of the Wave Probe
The wave probe is placed 10 meters away from the wave maker. It is calibrated
measuring its accuracy when it is vertically displaced along its own vertical axis,
which has multiple slots. The vertical displacements generated in the wave probe
were 4, 8, 12, 28, 20, 40 and 60 mm and the calibration performed with less than a
0.5% error.
ANNEX II Laboratory Diary
135
This wave probe is made by stainless steel and works on the principle of measuring
the electrical conductivity between two parallel wires and is placed 10 meter away
from the wave maker.
Figure II.6. (a) wave Probe situated 10 meters away the wave maker, (b) probe slots
3rd
day - Wednesday 25th
June 2014
a) Inclining Test
b) Launch the model in the tank
c) Regular wave tests
a) Inclining Test
The inclining test has been done again with just the semisubmersible platform and
without the turbine. The feedback of the test shows a KG error of -10.77% and a
recommendation of moving the ballast by -400 mm. Nevertheless, the natural
frequency of the model is highly close to the one expected, so we have decided to
proceed to the rest of the tests without doing any other physical change to the model.
b) Launch the model in the tank
The model has been taken out from the small tank and placed on a board. There, the
distance between the reference balls have been measured to then introduce this data
ANNEX II Laboratory Diary
136
in the Qualisys Track Manager software. Finally, the model has been launched in the
main tank, positioned at the testing place and moored.
Figure II.7. Model positioned and moored
c) Regular wave tests
Model tests have started with the tests from the Regular wave matrix. With wave
height of 1 meter (12.5 mm in model scale), frequencies from 0.3 Hz to 1.2 Hz
(model scale) have been programmed.
Each of the tests runs for around 100 seconds, enough time to allow stabilizing the
motions of the model. Then, the pitch, heave and surge RAOs are plotted with
special attention to the peak regions in order to run new tests with the correspondent
frequencies close to the actual peak one.
4th
day - Thursday 26th
June 2014
a) Validation Regular Wave Result
b) Free Decay Tests
c) Calibrate wave probe for irregular waves
d) Wind Velocity Test
a) Validation Regular Waves Result
To check how repeatable the regular waves results are, we do again one of the tests
correspondent to the frequency of one of the pitch peak values, . This
ANNEX II Laboratory Diary
137
test is repeated three more times and it is seen that the difference between the results
is less than , so the test data acquisition can be validated.
b) Free Decay Tests
Free Decay Tests have been done for surge, heave, pitch and roll motions. At least
three repetitions have been done for each DOF to ensure the validity of the results.
Figure II.8. Roll Free Decay Test
c) Calibrate wave probe for irregular waves
To calibrate the wave probe for the irregular waves spectra, the model has been taken
out from the tank. Then, the waves maker is configured with the and matrix
parameters and each of these configurations runs for 20 minutes (equivalent to 3
hours waves in full scale). It is important to remark that for the irregular waves, the
wave probe has been positioned next to the model place (29.020 m away from the
wave maker) as the wave properties are variable along the tank.
Table II.9. Irregular wave configuration
Irregular Waves
Full Scale Model Scale
( ) ( ) ( ) ( )
ANNEX II Laboratory Diary
138
2.44 8.1 30.5 0.906
3.66 9.7 45.75 1.085
5.49 11.3 68.625 1.263
9.14 13.6 114.25 1.521
10.5 14.3 131.25 1.599
To validate the test, the error of the following relationship has to be less than 3%:
where , and is the input wave height from the
irregular waves matrix configuration. Then, to refine the calibration, we change the
calibration as follows:
where is the new input value of significant wave in the software data
entry. Finally, we have achieved an error less than 2% for all the cases.
d) Wind Testing
In order to design the drag disk, first it is calculated the drag coefficient of a disk and
do measurements about the mean wind speed in the floating system testing rotor
position. In addition, it is essential to know the turbine key wind velocities and the
correspondent thrust forces.
Table II.10. Significant NREL 5MW wind speed conditions and correspondent thrust forces
in prototype scale and model scale
Mean Wind Speed Thrust Force
Description
Full
Scale
(m/s)
1:80 Model
(m/s)
Full Scale
(kN)
1:80 Model
(N)
ANNEX II Laboratory Diary
139
Rated Wind 11.4 1.275 247.2 0.483
Design Maximum 21.0 2.348 413.0 0.807
Survival 30.5 3.410 749.8 1.522
Looking at Table II.10, we would like to achieve in the scale model mean wind speed
of 3.14 m/s which correspondent to survival conditions. Nevertheless it is important
to remark that by the moment the Kelvin Hydrodynamic Laboratory does not have a
proper wind generator system to ensure a high quality wind field or appropriate
Doppler velocimeters to calibrate the wind.
An anemometer attached to a stick has been used to measure the instant wind speed
at the rotor position. The three fans have been placed on one of the tank’s carrier and
separated from the turbine position a sufficient distance to try to avoid turbulent wind
flow. The following table presents the mean wind speed values measured with the
anemometer.
Figure II.9. Anemometer attached to a carbon fiber stick to measure the instant wind speed in
the turbine testing position
Table II.11. Mean Wind Velocities Measurements (m/s) at 5, 5.5 and 6.5 meters from the
funs position
Fun Distance (m) Fun Velocity Program
1 2 3
5 0.9 1.4 2.3
5.5 0.9 1.4 2.1
6.5 0.8 1.4 2.1
With the formula for drag coefficient , the drag disk diameter can be calculated in
order to achieve the thrust force for survival conditions considering a drag coefficient
of 1.2 for flat disk (according to 3.4.4 Drag Disk Modelling (Rotor)).
ANNEX II Laboratory Diary
140
5th
Day - Friday, 25th June 2014
a) Irregular waves
Only irregular wave tests have been run today with the wave height and peak period
configurations cited in Table II.9. Each of the tests has run for 20 minutes.
Figure II.10. Floating system being tested in Irregular Waves
6th
day – Monday, 30th
June 2014
a) Regular Waves H = 2 m, H = 4 m
During the whole day the floating system has been tested in only regular waves for
wave height of 2 meters and 4 meters in full scale.
7th
day – Tuesday, 1st July 2014
a) Finish Regular Waves H = 4 m
b) Regular Waves H = 6 m
c) Rotate the model 60 degrees and test with Regular Waves H = 2 m
ANNEX II Laboratory Diary
141
a) Finish Regular Waves H = 4 m
We have finished testing and validating the tests in regular waves H = 4 m.
b) Regular Waves H = 6 m
Tests in regular waves H = 6 m have been run and validated. It has to be remarked
that testing with this wave height confirms the non-linearity effects we have
observed when previously testing with H = 2 m and H = 4 m.
c) Rotate the model 60 degrees and test with Regular Waves H = 2 m
In order to test the floating platform facing oblique waves the model has been rotated
60 degrees. In this manner, the model faces the waves with two of the offset columns
instead of one. Mooring lines have changed their position accordingly and just three
lines have been required instead of four.
8th
day – Wednesday, 2nd
July 2014
a) 60º Rotation. Regular Waves validation H = 2 m, complete H = 6 m
b) Assemble the wind turbine disk and new Inclining Test
a) 60º Rotation. Regular Waves validation H = 2 m, complete H = 6 m
Figure II.11. odel rotated and tested under H m regular waves
ANNEX II Laboratory Diary
142
b) Assembled of the disk and new Inclining Test
After finishing all only wave tests, the model is taken out of the tank. The disk is
assembled at the top of the model tower and the equivalent disk weight is removed
from the weight that had been attached to the tower. Then all the system is placed in
the Inclining Test small water tank. The inclining test is run twice. The first one tell
us how many millimeters we have to move the tower weight to achieve the same
center of gravity the model had before the disk was incorporated. The second
inclining test is just to confirm that after moving the weight the KG position is the
desired.
9th
day – Thursday, 3rd
July 2014
a) Place model in the tank at the testing position
b) Free Decay Tests: Pitch, Heave, Roll, Surge
c) Wind Speed Testing
d) Installation of the wind sentry set
e) Free Decay Tests with Wind: Pitch, Heave, Roll, Surge
a) Place model in the tank at the testing position
The model is launched in the testing tank and placed back in the testing position and
moored.
b) Free Decay Tests with Wind: Pitch, Heave, Roll, Surge
The natural frequency tests run again with the complete floating wind turbine system
assembled.
c) Wind Speed Testing
Another test with the anemometer attached to the stick shown in Figure II.9 is done.
The high sensitivity of the anemometer and the big dispersion of the wind speed
values give us serious doubts about the performance of the anemometer or/and the
ANNEX II Laboratory Diary
143
relative steady wind flow. Therefore, it has been decide to install a wind sentry set to
have better measurements of the mean wind speed.
d) Installation of the wind sentry set
The wind sentry set is made up of a 3-cup anemometer and a wind vane mounted on
a small crossarm. The set is assembled on an aluminum profile which has been
carefully attached to the ceiling by the lab technicians. The wind sentry set is placed
0.914 m behind the center of the model and closer to the side of the tank to avoid the
wind flow disturbances right behind the model.
e) Free Decay Tests with Wind: Pitch, Heave, Roll, Surge
The natural frequency tests are carried out under the wind force. The carrier with the
three funs is placed 4m ahead the model.
…
Figure II.12. Free decay tests: a) Pitch and b) Surge
10th
day – Friday, 4th
July 2014
a) Test with Wind and Regular Waves H = 2 m and H = 6 m
b) Test wind Wind and Regular Waves Hs = 2.44, Hs =5.49 & Hs =10.5
a) b)
ANNEX II Laboratory Diary
144
c) Wind Sentry Set Test
a) Test with Wind and Regular Waves H = 2 m and H = 6 m
Tests and validation tests in regular waves and wind with H = 2 m and H = 6 m (H =
1 m and H = 4 m could not been run due to time constraints issues). The procedure
for each of these tests was:
1. 10 seconds of no wind and no waves in order to record the zero value
2. Switch on the fans and run the test with just wind load during 30 seconds
3. Switch on the waves maker and stop after waves are stabilized for at least 1
minute
Figure II.13. Image of the model from the Qualisys Cameras Software
b) Test wind Wind and Irregular Waves Hs = 2.44, Hs =5.40 & Hs =10.5
The test procedure has been similar to the regular waves one:
1. 10 seconds of no wind and no waves in order to record the zero value
2. Switch on the fans and run the test with just wind during 30 seconds
3. Switch on the waves maker and run the test for 20 more minutes
ANNEX II Laboratory Diary
145
c) Wind Sentry Set Test
After finishing all the floating system tests in regular and irregular waves and with
and without wind, the model has been taken out from the tank and the aluminum
structure which supports the wind sentry set has been moved till the model testing
position. Four tests have been run for at least 3 minutes to know what the real wind
velocity in the model rotor position was.
ANNEX II Laboratory Diary
146
147
ANNEX III
III. - Calculation of OFWT
Hydrostatic Properties
Due to the lack of reference of the OC4-DeepCwind semisubmersible wind turbine
whole system centre of gravity ( or ), this annex include the
calculations done in order to achieve it, from the dimensions and mass properties of
the individual elements of the system. In addition, the rest of hydrostatic properties
as water volume displacement is calculated.
III.1 OFWT Centre of gravity
(from SWL)
(from SWL)
( ) ( ) ( )
ANNEX III Hydrostatic Properties
148
III.2 Platform Hydrostatic Properties
Hydrostatic properties of the OC4-DeepCwind semisubmersible wind turbine system
are calculated because some of them are needed as an input for the inclining tests.
Equations from 2.4 Hydrostatic Properties & Stability are used for the calculations.
IV. - Figure III.1. DeepCWind Offset Column Stability Diagram
(2.34)
Where is the distance from the keel (K) to the center of buoyancy, is the
metacentric radius and is the distance from the keel to the center of gravity of the
float.
The metacentric radius is calculated by Equation (2.35).
(2.35)
where is the area moment of inertia of the water plane and is the displaced
volume.
ANNEX III Hydrostatic Properties
149
Figure III.2. Platform dimensions in water plane
-
-
-
-
-
Calculation of the waver volume displaced:
20 m
6 m
14 m
V1 V2
V3
ANNEX III Hydrostatic Properties
150
( )
∑
Calculation of the area moment of inertia of the water plane:
(
)
(
) (
)
∑ ∑
ANNEX III Hydrostatic Properties
151
Figure III.3. Semisubmersible platform hydrostatic parameters