Design, Testing and Validation of a Scale Model Semisubmersible Offshore Wind Turbine under Regular...

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

http://www.researchgate.net/publication/265795516_Design_Testing_and_Validation_of_a_Scale_Model_Semisubmersible_Offshore_Wind_Turbine_under_Regular_Irregular_Waves_and_Wind_Loads?enrichId=rgreq-e5e281b3-3d52-4333-8f83-32f320db4549&enrichSource=Y292ZXJQYWdlOzI2NTc5NTUxNjtBUzoxNDM5OTg5MDc4NTA3NTJAMTQxMTM0MzQyMzU5NQ%3D%3D&el=1_x_2

http://www.researchgate.net/publication/265795516_Design_Testing_and_Validation_of_a_Scale_Model_Semisubmersible_Offshore_Wind_Turbine_under_Regular_Irregular_Waves_and_Wind_Loads?enrichId=rgreq-e5e281b3-3d52-4333-8f83-32f320db4549&enrichSource=Y292ZXJQYWdlOzI2NTc5NTUxNjtBUzoxNDM5OTg5MDc4NTA3NTJAMTQxMTM0MzQyMzU5NQ%3D%3D&el=1_x_3

http://www.researchgate.net/?enrichId=rgreq-e5e281b3-3d52-4333-8f83-32f320db4549&enrichSource=Y292ZXJQYWdlOzI2NTc5NTUxNjtBUzoxNDM5OTg5MDc4NTA3NTJAMTQxMTM0MzQyMzU5NQ%3D%3D&el=1_x_1

http://www.researchgate.net/profile/Laura_Rolo?enrichId=rgreq-e5e281b3-3d52-4333-8f83-32f320db4549&enrichSource=Y292ZXJQYWdlOzI2NTc5NTUxNjtBUzoxNDM5OTg5MDc4NTA3NTJAMTQxMTM0MzQyMzU5NQ%3D%3D&el=1_x_4


http://www.researchgate.net/institution/University_of_Strathclyde?enrichId=rgreq-e5e281b3-3d52-4333-8f83-32f320db4549&enrichSource=Y292ZXJQYWdlOzI2NTc5NTUxNjtBUzoxNDM5OTg5MDc4NTA3NTJAMTQxMTM0MzQyMzU5NQ%3D%3D&el=1_x_6


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

[email protected]

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

mailto:[email protected]

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


only case with Hs = 2.44 m and Tp = 8.1 sec ............................................................. 93


only case with Hs = 3.66 m and Tp = 9.7sec .............................................................. 93


only case with Hs = 5.49 m and Tp = 11.3 sec ........................................................... 94





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


- 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


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


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


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


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


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


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


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


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


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


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


- 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


- 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


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


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


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


∫ ( )

(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


- 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


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


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


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


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


- 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


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


( ) ∑[ ( ) (

) (

)]

(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


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


- 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


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


(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


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


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


√ (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

http://www.strath.ac.uk/naome/facilities/cmh/

http://www.ieawind.org/task_30/task30_Public.html

39


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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)


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)


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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)


0

0.25

0.5

0.75

1

1.25

1.5

1.75

5 15 25

Hea

ve

(m/m

)

Period (sec)


0

0.25

0.5

0.75

1

1.25

1.5

1.75

5 15 25

Su

rge

(m/m

)

Period (sec)


81


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


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


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


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


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


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


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


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


( ) ∑ ( ) ( )( )

(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


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


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


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


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



case with Hs = 2.44 m and Tp = 8.1 sec


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






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




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


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


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


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


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


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


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


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


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)


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)


106


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



Figure 5.10. Model in regular waves H = 6 m and Tp =11.3 sec

108



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


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


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


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


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


- 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

http://www.windspeed.co.uk/ws/index.php?option=displaypage&op=page&Itemid=100

http://www.windspeed.co.uk/ws/index.php?option=displaypage&op=page&Itemid=100


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)


125

Figure I.9. a) Vacuum, b) Laser distance meter, c) Reference balls panel

(a) (b) (c)


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:


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


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:


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


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


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:


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.


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


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


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


( ) ( ) ( ) ( )


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)


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)).


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


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


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


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)


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


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.


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.


149

Figure III.2. Platform dimensions in water plane

-

-

-

-

-

Calculation of the waver volume displaced:

20 m

6 m

14 m

V1 V2

V3


150

( )

∑

Calculation of the area moment of inertia of the water plane:

(

)

(

) (

)

∑ ∑


151

Figure III.3. Semisubmersible platform hydrostatic parameters

Design, Testing and Validation of a Scale Model Semisubmersible Offshore Wind Turbine under Regular...

Documents

Transcript of Design, Testing and Validation of a Scale Model Semisubmersible Offshore Wind Turbine under Regular...