Load case analysis for a resonant Wave Energy Converter

KTH ROYAL INSTUTE OF TECHNOLOGY

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Lo

Master of Science Thesis Report

Harsha Cheemakurthy

Student | M.Sc. Naval Architecture

Load case analysis for a resonant Wave Energy Converter

HARSHA CHEEMAKURTHY

Master of Science Degree Project in Naval Architecture

Stockholm, Sweden 2015

KUNGLIGA TEKNISKA HÖGSKOLAN

MASTER THESIS

Load Case Analysis for a Resonant Wave Energy Converter

A thesis submitted in fulfillment of the requirements for the degree of Master of Science

in the

Faculty of Naval Architecture Student

Harsha Cheemakurthy

Supervisor

Gunnar Steinn Ásgeirsson Pär Johannesson

Examiner

Anders Rosén

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KUNGLIGA TEKNISKA HÖGSKOLAN

Abstract

Faculty Name Naval Architecture

Master of Science Thesis

Load Case Analysis for a Resonant Wave Energy Converter by Harsha Cheemakurthy

As we progress beyond the information age, there is a growing urgency towards sustainability. This word is synonymous with the way we produce energy and there is an awareness to gradually shift towards green energy production. Corpower Ocean aims at producing energy by utilizing the perpetual motion of

ocean waves through the motion of small floating buoys. Unlike previous designs, this buoy utilizes the phenomenon of Resonance thus greatly enhancing the energy output.

In the thesis, the simulation model developed by Corpower Ocean to virtually describe the buoy in operation was validated. This was done by comparing forces obtained from buoy scale model experiments, simulation model and ORCAFELX^TM software. After satisfactory validation was established,

the shortcomings in the simulation model were identified. Next the simulation model was used to generate data for all sea states for a target site with given annual sea state distribution. This information was then used to predict ultimate loads, statistical loads, motions and equivalent load for a given fatigue life and loading cycles. The results obtained are then treated with a statistical tool called Variation Mode and Effect Analysis to quantify the uncertainty in design life prediction and estimate the factor of safety.

The information will be used by the design team to develop the buoy design further. Finally the issue of survivability was addressed by checking buoy behavior in extreme waves in ORCAFLEX^TM. Different survivability strategies were tested and videos were captured for identifying slack events and studying

buoy behavior in Extreme conditions.

The work aims at validating a technology that is green from environmental and economic point of view.

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Acknowledgements

This master thesis is the culmination of all the knowledge that I gained during the past two years at KTH University, Stockholm. I want to express my gratitude to CorPower Ocean for giving me an opportunity to use my knowledge towards the development of a green energy solution. I feel there is a growing awareness towards non- conventional sources of energy and technology like the Corpower WEC will greatly boost the motivation for governments and companies to adopt green technology. I greatly enjoyed working and learning about wave energy. It was very interesting to learn about the technology behind the WEC and also got an insight of how development of new technology is managed. At the company, I really liked the atmosphere. There was a lot of free exchange of ideas, discussions and independence and different stages of thesis. Along with this, there were several mentors who were experts in their fields who guided me and gave valuable advice.

I would like to thank my supervisor at Corpower Ocean, Gunnar Steinn Ásgeirsson for constantly guiding me and supporting with all my queries. I am really grateful for all the help that I received from him in terms of meetings, supporting files and most importantly advise. His composed style of working was a great inspiration to me to look at producing results and perform better analyses.

Then, I would like to thank my supervisor at SP, Pär Johannesson for meeting several times and guiding me towards development of load case analysis and fatigue analysis. I learnt a lot about fatigue and statistical measures under his guidance and was really inspired by his diligence and systematic approach.

I would like to thank the CEO of Corpower Ocean, Patrik Möller, for giving me the opportunity to do my master thesis. His attitude is very encouraging and his ambition greatly inspiring me. Working under his leadership has greatly convinced me to work in the field of green technology.

I would like to thank other people at Corpower Ocean, especially Oscar Hellaeus for his guidance in fatigue analysis results extraction and Luiza Acioli for the collaborative work in slack event identification.

I would like to thank Matthieu Guérinel for running the simulation model in software and extracting the results.

I would like to thank for Dr. Jørgen Hals Todalshaug and Prof. Stefan Björklund for his inputs in Load Case Analysis and Fatigue Estimations for mechanical parts.

I would like to express immense gratitude to Prof. Anders Rosén for helping me choose the topic of my thesis work, guiding me in developing a project plan and keeping regular meetings to track my progress. I would like to thank him for teaching core subjects and being a mentor.

Finally, I would like to thank my family and friends, especially my parents for constantly supporting me right from day one. I feel immense gratitude for the love and support they have given me.

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Table of Contents

Abstract ...

i Acknowledgements ...

ii Table of Contents ...

iii Abbreviations ...

vi

Symbols... vii

Chapter 1 ... 1

Introduction ... 1

1.1 Thesis Statement ... 1

1.2 Motivation ... 1

1.3 Objectives and Deliverables ... 2

1.4 Thesis Project Overview ... 3

1.5 Thesis Contributions to Project ... 4

Chapter 2 ... 6

Background ... 6

2.1 Introduction ... 6

2.2 About Corpower Ocean (CPO) ... 6

2.3 The Wave Energy Converter ... 6

2.4 Forces acting on the WEC and its Equations of Motion ... 13

2.5 WEC Scale Model Experiments ... 17

2.6 Simulation Model in Simulink

by CPO ... 20

Chapter 3 ... 22

Theory ... 22

3.1 Introduction ... 22

3.2 Wave Energy ... 22

3.3 Coordinate System ... 28

3.4 Ocean Wave Theory ... 29

3.5 Structure Failure Criteria ... 37

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3.6 Fatigue Theory and Estimation of Design Life ... 38

3.7 Modeling in Orcaflex

... 44

3.8 Variation Mode and Effect Analysis (VMEA) ... 47

Chapter 4 ... 51

Methodology ... 51

4.1 Introduction ... 51

4.2 Load Case Analysis... 51

4.3 Ultimate and Statistical Loads ... 54

4.4 Fatigue Loads ... 62

4.5 Automation Methodology ... 67

4.6 Methodology of Extracting Results from Simulink

Model ... 68

4.7 Methodology for Operation in Orcaflex

... 76

4.8 Variation Mode and Effect Analysis ... 79

Chapter 5 ... 83

Results and Discussions ... 83

5.1 Tools Developed for Analysis ... 83

5.2 Experimental Data Results ... 84

5.3 Discussion on Experimental Data Results ... 90

5.4

Simulation Model Results ... 92

5.5 Discussion on Simulation Model Results ... 100

5.6 Discussion on Fatigue Results ... 104

5.7 Results for irregular wave Survival Condition Waves Orcaflex

... 105

5.8 Discussion on Results obtained from Orcaflex

... 106

5.9 Variation Mode and Effect Analysis ... 108

Chapter 6 ... 111

Secondary Objectives, Results and Evaluation ... 111

6.1 Introduction ... 111

6.2 A: Saved time series of positions/accelerations of parameters ... 111

6.3 B: Scatter Plots of Buoy Motions in 6 DOF vs Rack Position ... 113

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6.4 C: Peak acceleration summary in 6 DOF vs rack position ... 120

6.5 D: Lateral and Vertical Force on tether vs rack position ... 123

6.6 E: Wavespring Force vs Rack Position Scatter Plots for all sea states ... 126

6.7 F: Wire Force vs Rack Position ... 127

6.8 G: Transmission Force vs Rack Position Scatter Plots for all sea states ... 129

6.9 H: Number of Wavespring Cut off events in each sea state ... 131

6.10 F: Number of slack events in each sea state ... 131

6.11 Discussion ... 133

Chapter 7 ... 135

Conclusions, Limitations and Future Work ... 135

List of Figures ... 140

List of Tables ... 145

References ... 147

Appendix 1 WAFO Toolbox ... 152

Appendix 2 Review of Structures that undergo extensive Fatigue Loading ... 153

Appendix 3 Scaling of WEC from experimental model to life size model ... 158

Appendix 4 Sea States and Notations investigated in Tank Tests and OrcaflexTM ... 160

Appendix 5 Outputs generated from Experimental Tests in Wave Tank ... 162

Appendix 6 Summary of Loads on Experimental Results ... 164

Appendix 7 Simulation Model – Peak and Load Statistics... 170

Appendix 8 Simulation Model – Fatigue Loads ... 174

Appendix 9 Additional Objectives ... 178

Appendix 10 Peak Identification Matlab

Code ... 181

Appendix 11 Equivalent Load Estimation for Fatigue MatlabTM Code ... 191

Appendix 12 Wave Interference and production of Irregular waves ... 196

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Abbreviations

DOF CPO

WEC QTF CAD

PTO RPM

FEM FOS KTH

IIT-M HSLA

Degree of Freedom Corpower Ocean

Wave Energy Converter Quadratic Transfer Function Computer Aided Design Power Take-Off

Rotations per minute Finite Element Method Factor of Safety

Kungliga Tekniska Högskolan

Indian Institute of Technology Madras

High Strength Low Alloy

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Symbols

⃗⃗ : Acceleration in direction j

⃗⃗ : Acceleration Vector of an arbitrary point with respect to defined origin A

: Projected Area of Bluff body normal to the flow direction

: Added mass of component k in direction j Ax : Wet Surface Area of Buoy

b : Fatigue strength exponent (material property) B : Number of Blocks

B

: Wave Drift Damping Coefficient C

: Inertial Coefficient

d : Damage experienced during the experimental signal duration dS : Infinitesimal area on buoy’s body to be integrated

D : Diameter of submerged body at water surface

: Equivalent Damage

: Life time Damage on the Buoy ̂ : Overall Error in estimation

: Mean Drag Force

: Excitation Force on Buoy

: Sum of External Forces : Frequency of vortex shedding , F

: Drag Force

: Equivalent Load

: Gas Spring Force

: Hydrostatic Force

: Slow Drift Loads

: Inertial Force on cylinder

: Weight of Buoy

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: Gravitational Force due to weight of Buoy : Lift Force

F

: Morrison Force for cylinders Fn : Froude Number

: Sum of forces dues to Power Take Off Unit

: Transmission Force

: Radiation Force : Friction Force

g : gravitational acceleration H : Wave Height

H1/10 : Statistical Mean of top 10 peaks in a data set H1/100: Statistical Mean of top 100 peaks in a data set H1/3 : Statistical Mean of top 3 peaks in a data set Hs : Significant Height

⃗⃗ : Direction vectors along x, y and z axis respectively

: Moment of Inertia of flywheel k : Wave Number

l

: Distance between two adjacent vortices in the same row behind a bluff body

: Mass of oscillator

: Direction vector for component k N : Number of Cycles of Loading

: Number of cycles of loading condition ‘k’

P : Total Pressure given as sum of static and dynamic pressure : Atmospheric pressure at sea level

Rn : Reynolds Number

: Radius of pin s : Scale

⃗ : Displacement Vector of an arbitrary point with respect to defined origin t : Time duration of experimental data

T : Time Period of Wave

: Second Order Transfer Functions for Slow Drift Loads

ix : Energy Period for irregular waves : Natural Period of Wave Energy Device

: Horizontal velocity component of water particle

: Flow velocity far away from body such that the body has no influence on the flow : Vertical velocity component of water particle

: Relative Velocity between Fluid and Body

̂ : Modeled Scatter Vector in VMEA model : water depth from water surface level

̂ : Modeled Uncertainty Vector in VMEA model : Phase angle of vortices shed

: Relative angle between wave and current : Circulation

: Displacement of body in water ϵ : Wave Phase

: Wave Elevation : Wave Height

: Threshold value where the buoy is unlatched : Heave Motion along z axis

: Sway Motion along y axis : Surge Motion along x axis : Roll Motion about x axis : Pitch Motion about y axis : Yaw Motion about z axis

̂ : Estimated Parameter Vector in VMEA model λ : Wave Length of wave

̈

: Acceleration of oscillator

: Density of liquid under investigation : Stress amplitude

: Fatigue strength coefficient (material property) : Mean stress

: Ultimate stress (material property)

: Diffraction Potential of water

x

: Damage Parameter for Fatigue in VMEA model : Velocity Potential of water

: Velocity Potential in Finite water depth : Velocity Potential in Infinite water depth : Wave Angular Frequency

ω0

: Incoming wave frequency

: Wave Encounter Frequency

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Chapter 1

Introduction

1.1 Thesis Statement

The thesis done in collaboration with Corpower Ocean (CPO) investigates the forces experienced by the wave energy converter (WEC) in different seastates and validates existing simulation models that describe the device.

1.2 Motivation

As we progress in to the next age, the world’s energy needs are growing at an alarming rate.

Over 80% of energy produced in the world comes from non-renewable sources like fossil fuels which has caused an alarming rate of deterioration of the environment.

. Certain governments are becoming aware of the problem and measures like the (20-20-20) are being set by the European Council with aims to decrease greenhouse gas emissions, increase energy efficiency and increase renewable sources of energy. Such similar policies and targets have brought about investments in renewable forms of energy and given rise to many new ideas. CPO has taken a step in this direction and is developing the WEC.

The device though proven successful in theory is still under nascent stages of development. It is

estimated that ocean waves can produce 4000 TWh of power if harnessed. If this device is

successful, potentially it could take care of 10-20% of world needs

. The work done in this

thesis would be a step in the development of this technology and one step closer to a greener

cleaner earth.

2 1.3 Objectives and Deliverables

As stated in the motivation, the concept of WEC developed by CPO is required to be practically validated. The objectives of this thesis focus on validating measured parameters in Tank Tests done in Ecole Centrale de Nantes in 2014 against results obtained from Simulation Models and Mooring Specific Software Orcaflex

. The primary objectives and CPO deliverables are as follows,

A. Theoretical Investigation i. Ocean Wave Theory

ii. Rainflow Counting and Damage Accumulation Theory

iii. Review of similar machine designs with extensive fatigue loading B. Development Tools

i. Graphical User Interface to compare two different Load Cases

ii. Matlab Code for automation of Data Filtering and Processing for Peak Identification and recording of Statistical

Parameters

iii. Matlab Code for Rain Flow Counting and Design Fatigue Life Estimation C. Load Case Analysis

i. Deduction of Peak Loads on mooring line obtained from experiments for Buoy 1 and Buoy 2 performed at École Centrale Nantes in 2014 and form basis for choice of buoy and mechanism

ii. Deduction of Peak Loads under Extreme wave conditions simulated in Wave Tank Experiments and using these loads as basis for deduction of minimum tether dimensions for the two materials under investigation by CPO

iii. Validation of Simulation Model by Comparison of Loads obtained from Experiments and Simulation Model Estimation of Statistical

loads from simulation model for given annual sea spectrum for selected European Atlantic coast site

1 Statistical Loads/Parameters refers to Peak Loads, RMS Loads, Mean Loads, A1/3 Loads, A1/10 Loads and A1/100 Loads

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iv. Estimation of Sea Loads for extreme cases in Orcaflex

and comparison with Simulation Model and form basis for selecting Buoy Survival Strategy

v. Estimation of Fatigue Related Damage and Estimation of Equivalent Load for individual seastates at target site. Estimation of Equivalent Load for an entire spectrum of Sea States with given seastate distribution data for the target site D. Statistical Analysis

i. Uncertainty and reliability analysis for estimation of Factor of Safety using VMEA – Variation Mode and Effect Analysis

1.4 Thesis Project Overview

The thesis addresses the objectives by dividing the contents into six chapters. Each chapter is written such that it forms the basis for the next chapter. The overview of the thesis is as follows,

In the beginning of the thesis a short one page abstract is written that highlights the motivation, importance and contributions of the thesis.

The first chapter introduces the topic of the thesis in a broad sense. Then the motivation behind the thesis work is established following which the objectives set by CPO and their utility are listed. Then the project overview and thesis outline as done in this section is presented.

Finally, this chapter ends with the contributions this thesis made.

The second chapter establishes the background information required to better understand and

perform the objectives. The WEC technology is introduced in this section along with its parts

and governing mechanics. Previous experiments performed and simulation tools developed for

the study are introduced here. Comments on the work done so far by CPO and the need for

further analysis are established.

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The third chapter establishes the theory required to fulfill the objectives. Wave Energy, Types of Converters, Ocean Wave Theory, Load Case Analysis, Fatigue Theory, Failure Criteria and VMEA are covered in this chapter.

The fourth chapter establishes the methodology adopted at different steps to fulfill the objectives. The chapter is arranged with different sections for treating experimental results, simulation model, Orcaflex

model and VMEA.

The fifth chapter lists out the results and discussions in a concise and effective manner. Since the results are numerous, the majority has been shifted to the appendices and this chapter contains only an overview and summaries of specific cases. The results are arranged in accordance with the objectives. Evaluations, weaknesses and observations are discussed after the results.

The sixth chapter introduces the additional objectives that were added to the scope at a later stage. Methodology is briefly discussed and then results and discussions are presented.

The seventh chapter is the conclusion

chapter and summarizes the conclusions for the objectives followed by establishing scope for future work.

1.5 Thesis Contributions to Project

The data generated in the thesis work was of use to the mechanical team at CPO. They are using it as design basis for designing parts of the WEC.

The comparison with experimental data served as a tool for improving the simulation model in Simulink

which is now being extended to a 6 DOF model to cater for a more accurate representation of the WEC.

The Fatigue Equivalent Load results were useful for the mechanical design team who are using

at as design basis. The Fatigue model developed in Matlab

is useful in predicting the fatigue

life occurring in different combinations of sea states, thus extending the ability to predict for

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any given area in the world. This is of use for CPO in future analysis for predicting fatigue behavior at new test sites.

Variation Mode and Effect Analysis was developed and generalized to be extended for estimation of factor of safeties for future use for parts of the WEC device.

The results obtained from the thesis were featured in the company report and application for further funding which was successful.

Finally, I believe the thesis has brought the technology one step closer to realizing Earth’s Green Energy Requirement.

.

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Chapter 2

Background

2.1 Introduction

The WEC has already undergone several years of development from concept to scale model stage. In order to investigate to achieve the objectives, it is important to describe the work done so far that forms the basis for this thesis. This chapter introduces the Wave Energy Converter, its parts, mechanisms along with the tools that CPO has developed.

2.2 About Corpower Ocean (CPO)

CPO is a company founded in 2009 with a goal to harness Ocean Energy and is currently developing a WEC device. CPO uses the principle of resonance to increase the energy absorbed from point absorber

type WEC from incoming waves. CPO has been developing this technology with a focus on finding feasible solutions for robustness, low cost and power absorption from a broad spectrum of sea states.

2.3 The Wave Energy Converter

The wave energy converter by CPO is a light, low inertia device that is able to absorb energy from a wide spectrum of sea waves due to its geometric properties. Also due to its small size, it has good survivability in extreme waves and a low production cost.

2 More about types of wave energy converters can be found in Chapter 3, Section 3.2.2

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The small size has reciprocation that the natural period of the buoy becomes low. To compensate this, an active control method is installed in the form of Wavesprings that ensure the buoy is always in resonance with incoming waves. This combination of small size and active control gives the device a power absorption efficiency of two to five times higher than other similar WECs.

The WEC developed by CPO is a ‘Point Absorption’ type of Wave Energy Device. Its name derives from the fact that the buoy is very small in comparison with the countering wave. The heaving motion of the buoy is transferred to the Power Take-Off (PTO) where it is converted to electrical energy with the help of inbuilt generators. See Figure 1 for summary of advantages.

Figure 1: Summary of Advantages of Wave Energy Device by Corpower Ocean^II

2.3.1 The Mechanism

The WEC developed by CPO is a heaving point absorber, (Figure 2) which uses phase control by

use of pneumatic gas springs. The aim is to have a light buoy that is held at its equilibrium

position by a pre-tensioned gas spring. This gives the opportunity for the buoy to move fast,

upwards due to the hydrostatic forces and back down into the water due to the gas-spring, with

low inertia. Using the phase control by latching the aim is to make the buoy able to use a wide

range of waves for power absorption. The phase control enables management of the buoy in a

way that in every cycle it moves in phase with the wave. This gives the possibility for the buoy

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to move closer to a higher response frequency (closer to the natural period) resulting in larger heave amplification.

In simple words, the device converts oscillatory kinetic energy into electric energy by exploiting the concept of resonance to maximize range of motions.

2.3.2 Components of WEC

1. Power Take off Unit (PTO)

The PTO system is a custom designed unit that aims at combining the high load capabilities from hydraulics with the efficiency of a direct mechanical drive. The device is what converts the mechanical motion into useful electrical energy. Temporary energy storage is done in two steps which

help in smoothing out the power absorbed as compared to impulsive power input signals. The system has been designed for low overall inertia and high structural efficiency, aiming for a device that is effectively energized by a relatively broad range of waves using inherent phase control.

PTO has the following internal parts,

The PTO oscillator module consists of an oscillator that is connected to the tether, receiving the forces from the buoy through a wire that connects them. It consists of two cylinders which are interconnected through channels where a fluid interacts with two pistons. The compliance chambers and pistons form a gas spring that pulls the lightweight buoy downwards and balances it at its equilibrium position.

b. Transmission Module

The transmission module converts the linear motion of the oscillating rack into rotational motion. The oscillator has a double sided gear rack that is connected to two flywheels, which

Figure 2:

Schematic of WEC

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are accelerated as the rack moves. As the buoy and rack move upwards approximately half of the energy is stored in the gas spring and half of it accelerates one of the flywheels. When the buoy moves downwards the energy stored in the gas spring is released and the other flywheel is accelerated. The energy can be temporarily stored in each flywheel before the next wave cycle arises.

c. Electricity Generation Module

The generator module consists of two generators connected to each flywheel. They convert the energy stored in the flywheels into electrical power, gradually decreasing the rotational speed of the flywheels until they have come to a stop position before the next cycle starts. These steps give a smoother and stable power output from the peak.

2. Tether

The tether could be made of polyester or steel

and its main function is to fasten the buoy to the sea bed. It will be in tension during its entire life span to avoid snapping and associated impulse loads. Fatigue loads on the tether will be important to study as it is subjected to cyclic loading.

3. Connector at Sea floor

The tether will be connected to the sea floor by means of a latch and pinions driven in to the seabed.

4. Connector at Buoy

The tether will be connected to the PTO by means of a connector. This part will be subjected to cyclic loading and could be studied for fatigue loading.

3 Choice of material is still under investigation by CPO

10 5. Buoy

Currently there are two buoy designs under investigation as shown in Figure 3. Buoys are designed to be light weight and hydrodynamically smooth in the vertical direction to avoid energy losses due to friction or form resistance losses.

Figure 3: Buoys that are under investigation

2.3.3 What degrees of freedom are allowed

Based on the given geometry, only vertical motions are converted to electric energy in the PTO.

But in reality, the buoy will be subjected to all 6 degrees of freedom. The buoy should be designed in such a way that Heave motion dominates while other motions are suppressed.

For example in the above buoy designs (Figure 3), Buoy 2 exhibits more resistance in heave

oscillatory direction. A Computational Fluid Dynamics (CFD) analysis is probably required before

one can quantify the performance of the buoy. In this thesis, choice of buoy is established by

studying individual forces based on experimental results performed on 1:16 scale models.

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2.3.4 Latching mechanism and its repercussions on impulse forces

Phase control by latching has been in development for many years and was originally proposed around 1980 by J.Falnes. and K.Budal

. Latching is an interesting approach of controlling the oscillation period of the system, bringing it closer to wave period of various sea states thus encouraging resonance. This way the body’s motions get amplified giving it a maximum velocity for that wave.

Latching is done by stopping the motion of the system at the extreme excursion when the velocity is zero and holding it there for a certain time. Subsequently, the device is released at the optimal moment. This is shown with curve c in figure 4. The main challenges when using latching control, as many other active control schemes, is that the system must be able to predict ahead of time the right moment to unlatch. For a heaving point absorber this

"anticipation" time is a quarter of the period of the natural frequency of the system before the maximum peak in excitation force

. It is therefore important to know the natural period of the WEC system, to be able to predict the time it should be released before the peak force. The more complicated challenge is to know when that peak will occur.

Latching has shown that it has the capability to significantly increase the absorbed power from

the wave. Studies have shown a gain of up to a factor of 4 compared to a device without

latching control. A. Babarit and A.H. Clement showed in their paper

, a gain by latching almost

up to a factor of 3, depending on the peak period. The increase was observed in experiments in

regular waves. There the system knows the height and period of the incoming wave. In nature,

the sea has different sea states with different combinations of wave height and periods, making

the prediction complex as that would optimally be based on a future value.

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Figure 4: Latching Mechanism where Curve (a) is the incident wave, Curve(b) is the resonant wave motion, Curve(c) is the actual movement of buoy subjected to latching..

Nevertheless, researchers are trying to overcome these difficulties by developing systems to cope with this challenge. There are predictive models that use local or distributed wave sensors to attempt to predict the incoming wave or models using non-predictive methods. A promising approach to provide a robust non-predictive method is to define an amplitude height for the water surface elevation and form the zero position as a threshold value to unlatch the buoy.

This is known as "threshold unlatch control". This means as the buoy is latched at its bottom position and the surface of the water reaches a given height (threshold) the buoy unlatches and vice versa for when it is latched at its top position. This is a close to optimal power absorption.

The equation for the threshold found by Lopes et. al.

is written as,

[ ( )] (1)

where, is the natural period of the device, H is the wave height and T is the period of the

wave, for regular waves. For irregular waves the threshold can be calculated in the same way,

where T is substituted by the energy period T

and H is substituted by . This has given

encouraging results as published by Lopes et. al.

where for irregular waves the results gave

an increased capture width of a factor of 2,5 compared to a passive system.

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Despite the advantages with latching, there is an inherent problem with effective power absorption. Latching involves sudden stopping and release of the buoy at critical positions to ensure resonance. These sudden mechanisms give rise to steep power surges which are difficult to capture in the short time they occur.

2.3.5 Wavespring and its improvement on impulse forces

To avoid the impulse problem with latching mechanism, pneumatic Wavesprings were developed that smoothen out the motion of the buoy in waves while ensuring resonance. This way the power absorbed does not come from steep surges in forces but instead comes from a continuous buoy response.

The working of the Wavesprings is classified as per the requirements of CorPower Ocean and will not be discussed here.

2.4 Forces acting on the WEC and its Equations of Motion

The forces on the point absorbing buoy can be represented according to Newton’s second law of motion as,

Sum of all forces = mass x acceleration

(2)

where, m represents the mass of the system, the acceleration,

as external forces due to

waves and F

as internal forces on buoy due to the PTO. The PTO is made up of several

components, the details of which can be found in Section 2.3.2.

14 The internal forces due to PTO can be further split into,

(3)

where

,

are transmission force, gas spring force and friction force respectively which are transmitted to the buoy through the wire.

The external forces due to waves are pressure based forces due to different wave body interactions. It can be further broken down into,

(4)

where, is the excitation force,

is the hydrostatic force and

the drag force. The total power absorbed by the buoy can be calculated by multiplying the external forces by the respective velocity component.

2.4.1 Excitation Force or Diffraction Force

The diffraction force is the result of integrating the pressure distribution over the wet surface area of a fixed buoy for an incident wave. In other words, when the buoy is fixed and restricted in its motion, the force experienced by it when an incoming wave passes is known as the excitation or diffraction force. More about this force will be discussed in Chapter 3, 3.4.

2.4.2 Radiation Force

The radiation force is the force experienced by the body when it is forced to oscillate in the

absence of waves. It is found by integrating the pressure distribution over the body’s surface.

15 2.4.3 Hydrostatic Force

The hydrostatic force is the force experienced by a stationary buoy in calm water. It is simply the difference between the buoyancy force and the gravitational force. It can be expressed as Newton’s second law as,

(5)

where is the submerged volume of the body,

is the weight of the buoy and

is the hydrostatic force.

2.4.4 Drag Force

Drag is the resisting force a body experiences when there is a relative motion between the body and the surrounding fluid. Drag is a complex phenomenon and broadly it can be split into two components,

1. Viscous Drag 2. Form Drag

There are numerous other sources of drag such that wave making drag, spray drag etc but they are insignificant in this case.

Viscous Drag is due to skin friction while form drag is due to the body’s shape. More discussion

on this is presented in Chapter 3, Section 3.4.

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For the case of WEC buoy, viscous drag will be most significant and can be expressed as,

(6)

where is the drag coefficient,

2.4.5 Equations of Motion

During experiments and simulating modeling, data was also extracted that described the motion of the buoy in 6 DOF. The governing equations for this motion are as follows.

The equations of motion for the buoy can be split into two cases, 1. Engaged to flywheel

2. Disengaged with flywheel

Engaged Condition

(7)

17 Disengaged Condition

(8)

2.5 WEC Scale Model Experiments

In July 2014, the wave tank at École Centrale de Nantes was booked to carry out experiments on two 1:16 scale buoy designs. The goal was to obtain data and observe the behavior of the buoys under the influence of waves. Data in the form of forces, power and buoy motions were recorded with the help of sensors installed on the buoy.

2.5.1 Experimental Setup

The wave tank at the University is located at LHEEA Lab for Hydrodynamics, Energetics and Atmospheric Environment Department. It is a very robust tank capable of simulating waves, wind and currents. Figure 5 shows an experiment at the facility. Its specifications are in Table 1.

Parameter Dimension (m)

Length 50

Breadth 30

Depth 5

Table 1: Specification of Wave Tank Testing Facility

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Figure 5: Wave Tank Testing Facility at École Centrale de Nantes in 2014

For the experiment, the buoy was attached to a tether which was driven through a simple pulley placed at the bottom of the tank. The other end of the tether was then connected to another device that provided a pre-tension and measured the tension in the device. The set-up is as shown in Figure 6.

Figure 6: CAD representation of Buoy in Wave Tank with device to measure tension in tether

19

For the testing of the Buoy the following equipment was used, a. A strain gauge to measure the tension in the tether

b. Motion sensors on top of buoy shown by bright white lights (Figure 7) c. CPU to actively control the buoy motions

d. Cameras

Figure 7: Picture showing bright white lights installed on buoy to record the 6 DOF motion of buoy

Due to limitations in Tank Dimensions and available time, all seastates could not be experimented. Hence, only selected seastates were tested. In Figure 8, the yellow boxes represent the sea states for which experiments were carried out. The blue box represents the tank limitation. Any seastates lying outside the blue box could not be tested.

These experiments were carried out for regular seas as well as irregular seas for latching (linear

damper) mechanism and Wavespring mechanism for both the buoy designs. In addition,

numerous other tests like radiation tests and calibration were carried out. In total, there were

296 experiments that were carried out.

20

Figure 8: Seastates that were tested in the wave tank (marked by yellow boxes)

The entire list of data obtained from an experiment can be found in Appendix 5. Since the output signal was raw, it requires certain processing before useful results can be extracted. The methodology for this can be found in Chapter 4.

2.6 Simulation Model in Simulink

by CPO

In the previous section we saw that experimental tests were performed to test the validity of the technology. But since, it is very expensive and time consuming to book a wave tank, an alternative way of testing the buoys was required.

Keeping these factors in mind, a simulated platform that would replicate the results from a tank

tests on a computer was devised. Such a model could be used at the user’s convenience to test

the buoy in all kinds of sea states for different buoy configurations. Thus, a mathematical model

based on Ocean Wave Theory, Buoy Motions and Forces described in Section 2.4 was

developed in SIMULINK

, which is a special add-on package with MATLAB

, developed by

Mathworks

.

21

The model presents itself in the form of a GUI in which various parameters are entered and the

program outputs results. More details about this simulation model can be found in Chapter 4,

Section 4.6.

22

Chapter 3

Theory

3.1 Introduction

This chapter describes all the necessary theoretical background required to understand the thesis and develop algorithms to establish the analyses performed in this thesis work. Beginning with description of Wave Energy, the chapter progresses with sections on Ocean wave theory, Fatigue theory with emphasis on rain flow counting method, review of other machines with extensive fatigue loading, stress strain relationships, Orcaflex

modeling and finally ends with a section on variation mode and effect analysis (VMEA).

3.2 Wave Energy

3.2.1 Wave Energy and its Potential

Over 71% of the earth’s surface is covered with water and a natural consequence of the large

surface area in a dynamic atmosphere is the existence of waves. Ocean Waves can be visualized

as oscillating columns of water. These waves are not only perpetual but also propagate energy

across the globe. Wave Energy Converters are devices that are designed to harness the energy

stored in water waves by means of an electro-mechanical contraption. CorPower Ocean is a

company that is working on developing Wave Energy Convertors. The idea is to harness the

kinetic energy stored in sea and ocean waves and convert it into useful electricity by means of

electro-mechanical contraptions. There has been previous interest in the field of wave energy

but due to certain complications the devices have been expensive and unsustainable. But unlike

other previously patented designs, the design developed by CorPower Ocean exploits the

23

phenomenon of resonance thus greatly increasing the power output as compared to conventional wave energy convertors. The current design has been tested over the last year using a scale model in a wave flume in École Centrale de Nantes, France. Results have been promising and it was observed, the energy density was over 5 times higher than previous designs. The tests showed an energy/ton ratio comparable to wind energy. Full Scale models are scheduled for testing in the coming year.

There is immense potential for wave energy along coast lines of major cities. Certain spots have been identified as shown in Figure 9a and Figure 9b. It can provide green sustainable energy and meet the present electric demand. In addition, the technology can be used to power remote islands. The effect of the devices on marine life is yet to be studied but owing to no exposed moving parts and no emissions, it can be guessed that marine life will not be impacted greatly. But the presence of wave energy buoys might hinder the passage of sea traffic.

Figure 9a: Identified Locations where Wave Energy Device can be potentially used 1. (Source:

UserfulWaves) ^VIII

24

Figure 9b: Identified Locations color coded according to energy potential. 1. (Source: wikimedia)^VIII

3.2.2 Wave Energy Converters and its types

Wave Energy is present in sea waves as kinetic and potential energy stored in the oscillating water particles. Wave Energy Converters essentially convert this kinetic energy into useful electrical energy or mechanical power.

The process of extraction of energy from waves has inspired many novel techniques working on different principles in the past. Though most of the technologies are still in an experimental stage, the interest in the field has led to a growing community and allowed archiving the progress.

3.2.3 Types of Wave Energy Converters

Because of the immense number of designs, it was important to characterize them. Such a distinction was made by Antnonio F. and O. Falcao

. He divided them into three broad types.

1. Oscillating Water Column 2. Overtopping

3. Oscillating Bodies

25

There are then several sub categories under each of these categories. An entire list can be found at Wikipedia’s wave energy page

but a few devices worth mentioning are Pelamis, Wave Dragon, Wave Roller and PowerBuoy.

3.2.3.1 Oscillating Water Column

An Oscillating Water Column (OWC) is a wave energy device that uses the flow of air to turn a turbine. A typical device has a large cavity of air in a sloping cavity such that it gets narrower as we move up. The device has an opening on top and in this opening a turbine is placed. This entire device is then put in water with waves. The schematic is shown in figure 10.

As the wave crest passes the structure, the water moves up in the cavity. The constriction in space compresses the air and pushes it through opening on top while turning the turbine.

Similarly as the wave trough passes the structure, the water level in the cavity falls, thus reducing the internal pressure. This sucks the air from outside thus turning the turbine as this happens.

Figure 10: Schematic of how an Oscillating Water Column works. (Image Courtesy- en.openei.org)^XII

The turbine is designed to turn in one direction despite bi-directional airflow.

The device

can be both floating type as well as fixed type and is usually more suitable for shallower waters

26

since it has to be tethered to the sea bed. There are over 1890 patented examples of OWC type of WEC devices.

3.2.3.2 Overtopping

An overtopping type of wave energy device (Figure 11) is unique in its way of capturing energy from waves since it uses conversion of potential energy into useful mechanical energy to turn turbines. This device is a partially submerged device and there can be found shore based and floating models.

Figure 11: Schematic of an Overtopping type of wave energy converter (Image Courtesy- en.openei.org)

When a wave crest passes the device, the water overflows into the device. The overflowing

water is then collected in a funnel where it is stored for a while. When the wave trough falls

directly under the device, the water in the funnel is released through a turbine situated at the

bottom of the funnel. This flow turns the turbine. An existing example of this type of device is

the sea dragon.

27 3.2.3.3 Oscillating Bodies

This is a very wide group and includes diverse technologies based on oscillatory motion of device. The devices can be attenuator type (Figure 12) or heaving buoys (Figure 14) or of pitching type (Figure 13). In general, these devices consist of a moving body that is influenced by motion of waves. This motion is converted into useful electrical or mechanical energy.

Figure 12: An Attenuator type of Oscillating Body WEC (Image Courtesy-en.openei.org)

Figure 13: A Pitching type of Oscillating Body WEC (Image Courtesy-en.openei.org)

28

Figure 14: Heaving Buoy (Point Absorber) type of Oscillating Body WEC (Image Courtesy- en.openei.org)

These devices are usually found in relatively deeper seas where wave heights are higher than in shallow waters. This also means that they have to be relatively higher survivability in comparison with other types of WEC devices.

Under this category, if the oscillating device is small compared to the incident waves, then the WEC device is called a Point Absorber type Wave Energy Device. The WEC by CPO is a point absorber type of device which will be discussed in detail in the subsequent chapters.

3.3 Coordinate System

For the purpose of the study, an earth fixed coordinate system has been chosen as shown in figure 15. Typically, a body in water has 6 degrees of freedom. Three of them are translational while three are rotational. The three translational degrees of freedom are,

a. X – Surge (η

) b. Y – Sway (η

) c. Z –Heave (η

)

Figure 15: The axis for the coordinate system

29 The three rotational degrees of freedom are,

a. XX – Roll (η

) b. YY – Pitch (η

) c. ZZ – Yaw (η

)

Based on the principal motions described above, the motion for an arbitrary point located at (x,y,z) on the buoy can be calculated as,

⃗ (9)

For all calculations the reference frame used is an inertial frame of reference. This means the coordinate system is not accelerated.

3.4 Ocean Wave Theory

There are different types of waves that can be studied under ocean wave theory. They are, a. Linear Waves – Steepness H/λ is small. Hence there is no breaking.

b. Non Linear Waves – Higher Order Wave theory used to account for wave breaking.

c. Long Crested Waves – 2D waves d. Short Crested Waves – 3D waves

e. Regular Waves – Waves have a single ω (circular frequency) and λ (wave length) f. Irregular Waves – Waves have several ω and λ.

g. Short-term sea state – Statistical measure of frequencies and directions for short periods

h. Long-term sea state – Statistical measure of frequencies and directions for long periods For a regular wave, its shape can be described as,

(10)

30

If we have several regular waves, we can add them to produce an irregular wave. So, in other words an irregular wave can be described as a sum of sine or/and cosine functions.

Particle velocities in a wave are given by its velocity potential and can be written as,

(11)

for shallow and deep water respectively, where, g is the gravitational constant, is the wave amplitude, is the wave frequency, k is the wave number, h is the water depth and z is the depth at under investigation. Then the velocities are given as,

and

(12)

We are intereseted in the excitatition forces caused by a regular wave on a small volume structure. Since the buoy can be considered as a small volume structure, the excitation forces on it are,

∫ ∑

(13)

where P the total pressure and is given by,

(14)

which is the sum of dynamic and hydrostatic pressure, where is the water density, z is the water depth, is the wave amplitude, is the wave frequency and k is the wave number.

Ocean waves often interact with each other to produce complex phenomenon that produce

different types of forces for different structures. For a Buoy, the following effects are relevant,

31

a. Wave Frequency Effect – Buoy is linearly excited by frequencies within the wave frequency range.

b. Sum-Frequency Effect – This effect can excite resonant oscillations in heave, pitch and roll. This phenomenon is known as ‘springing’ and can contribute to fatigue of tethers.

Since the buoy is restrained by vertical forces, its motion is dominated by natural periods in heave, pitch and roll. In addition to these forces, it is also important to see which type of forces dominate for the buoy.

We have from the figure 16, it can be seen that,

Figure 16: Classification of wave forces for different geomtry ranges against incoming wave lenghts (Source: Marilena Greco Lecture Notes TMR4215: Sea Loads, NTNU)

a. For λ/D < 5 – Diffraction Forces Dominate

b. For λ/D > 5 and H/D < 10 – Mass forces Dominate c. For H/D > 10 – Viscous Forces Dominate

Non linear effects become important as H/D = λ/7D is surpassed.

Depending on which area the buoy is operated, the dominating forces will vary.

In the case of a diffraction problem, the body is fixed and interacts with the incident waves. The

forces arising can be split into two forces arising from two separate potentials. One is the

incident wave velocity potential and the other is the diffraction velocity potential such that the

32

total excitation force can be given as the integral of these velocity potentials over the area of the wet surface area given as,

∫

∫

(15)

In the case when viscous forces dominate, mean drift loads are caused which are connected with the wave amplitude as follows,

a. The body’s capability in generating waves (invisid waves) – proportional to ζ

b. Viscous Effects – proportional to ζ

When the wave amplitude and wave length of a waves is sufficently large relative to the cross sectional dimensions of the buoy, viscous effects can cause important wave drift forces. In such a case, third order forces dominate over second order forces.

Viscous effects can create a mean drift force that causes the body to move against the waves.

This is because at the wave crest, the fluid velocity is parallel with the wave velocity whereas in the trough fluid velocity is parallel with the wave velocity but in the opposite direction. Hence there are opposite forces acting on the buoy at the same time due to viscous effects. If the phase of the heave motion is such that the largest part of the buoy is at the wave trough, then there will be a mean drag force in the opposite direction of the wave. See Figure 17 for reference,

Viscous Drag force in opposite direction

Figure 17: Slow Drift motions in opposite direction of wave due to viscous effects

33

Slow Drift motions are caused by resonance oscillations that are excited at frequencies lower than the incoming wave frequencies. These motions are cause by nonlinear interactions in steady state conditions. Since these motions are caused by low frequencies one needs at least two incoming waves with different frequencies and amplitudes to cause these motions. When these two waves interact destructively a new wave with lower frequency is formed which causes these resonant oscillations. These type of oscillations are common in irregular waves.

For a moored structure with a small water plane area, the slow drift motions can occur in both the horizontal as well as the vertical plane. Mathematically slow drift loads can be expressed as,

( )

( ) (16)

where

refer to transfer functions of the slow drift loads (2

order transfer functions),

is the wave amplitude, is the wave frequency and is the wave phase. There transfer functions depend only on first order solutions for regular waves.

3.4.1 Sum Frequency Effects

In an irregular sea, two waves with frequencies ω1 and ω2 may interact constructively to give sum frequencies of the type,

a. 2 x ω1 b. 2 x ω2 c. ω1 + ω2

These effects are caused when an incident wave interacts with a reflected wave. An interesting

phenomenon associated with sum frequency effects is the phenomenon of springing. It is a

steady state elastic resonant motion in the vertical plane which results in the fatigue of tethers.

34

In survival conditions, sum frequency effects can cause another phenomenon called ringing. It is a consequence of 3

and 4

order sum frequency effects and is a transient resonant elastic motion.

3.4.2 Viscous Wave Loads

In order to understand viscous wave loads, it is important to learn a bit about fluid mechanics and specifically, the flow past a cylinder and the generation of vortices.

When considering flow past a cylinder, the behavior depends on the type of flow. The type of flow is decided by the Reynolds Number (Rn). Different flow regimes for a circular cylinder are as listed below,

a. Rn < 2 x 10

– Subcritical Flow b. 2 x 10

< Rn <5 x 10

– Critical Flow

c. 5 x 10

< Rn < 3 x 10

– Super Critical Flow d. Rn > 3 x 10

– Trans – Critical Flow

In the subcritical regime the boundary layer is always laminar, whereas in super critical and trans-critical regimes the boundary layer becomes increasingly turbulent upstream of the separation point.

Boundary layer can be defined as the area around the surface of the body where the fluid velocity is lower than the ambient flow velocity. Its thickness can be defined as the distance between the body’s surface and the point where the tangential velocity component is 99% of the ambient flow velocity.

Laminar flow is a flow where there is no intermixing of fluid streams. It is a well-organized flow.

Turbulent flow is characterized by disorder and intermixing of fluid streams. It is defined by a

mean component and a fluctuating component about the mean.

35

Separation point is the point where the flow separates from the body and forms vortices (Figure 18).

XVI

The vorticity in the boundary layer is not zero because of the differential in the tangential velocity as one moves away from the cylinder. This causes a net rotation which gives rise to vorticity. As the flow separates, this vorticity gives rise to vortices which are shed in the wake region of the cylinder. Based on the flow regime, the vortices are shed in a different manner as shown in figure 19.

Figure 19: Flow separation for different flow regimes^XVII Figure 18: Flow past a cylinder

36

Velocity of the vortex in the wake of the cylinder is given by,

(17)

where, is the circulation of the vortex and l is the distance between two adjacent vortices in the same row.

The importance of vortex shedding is that it induces force components in parallel and normal directions. In the normal direction alternate vortex shedding causes a force known as life force.

| | (18)

The vortex shedding also causes an oscillatory drag force which is given by,

(19)

Thus the lift force and drag force have different time periods. The lift force oscillates with a period of while the drag force oscillates with a period of /2.

Viscous Wave Loads become important for oscillatory ambient flow which is the case with sea waves. For cylinders, wave loads when viscous forces matter are calculated using the Morrison’s Equation given as,

| |

(20)

where ~ 1.8 and ~ 0.7 which have been found experimentally.

The equation assumes λ/D > 5. The equation is not valid at free surfaces as the velocity

distribution cannot be described by a linear wave, because at free surface, nonlinear effects

matter.