Load case analysis for a resonant. Wave Energy Converter

Transcription

1 KTH ROYAL INSTUTE OF TECHNOLOGY Lo Load case analysis for a resonant Master of Science Thesis Report Wave Energy Converter Harsha Cheemakurthy Student M.Sc. Naval Architecture HARSHA CHEEMAKURTHY Master of Science Degree Project in Naval Architecture i Stockholm, Sweden 2015

2 KUNGLIGA TEKNISKA HÖGSKOLAN MASTER THESIS Load Case Analysis for a Resonant Wave Energy Converter Student Harsha Cheemakurthy Supervisor Gunnar Steinn Ásgeirsson Pär Johannesson Examiner Anders Rosén A thesis submitted in fulfillment of the requirements for the degree of Master of Science in the Faculty of Naval Architecture

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4 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. i

5 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 nonconventional 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. ii

6 Table of Contents Abstract... 1i Acknowledgements... 2ii Table of Contents... 3iii Abbreviations... 6vi Symbols... vii Chapter Introduction Thesis Statement Motivation Objectives and Deliverables Thesis Project Overview Thesis Contributions to Project... 4 Chapter Background Introduction About Corpower Ocean (CPO) The Wave Energy Converter Forces acting on the WEC and its Equations of Motion WEC Scale Model Experiments Simulation Model in Simulink TM by CPO Chapter Theory Introduction Wave Energy Coordinate System Ocean Wave Theory Structure Failure Criteria iii

7 3.6 Fatigue Theory and Estimation of Design Life Modeling in Orcaflex TM Variation Mode and Effect Analysis (VMEA) Chapter Methodology Introduction Load Case Analysis Ultimate and Statistical Loads Fatigue Loads Automation Methodology Methodology of Extracting Results from Simulink TM Model Methodology for Operation in Orcaflex TM Variation Mode and Effect Analysis Chapter Results and Discussions Tools Developed for Analysis Experimental Data Results Discussion on Experimental Data Results Simulink Simulation Model Results Discussion on Simulation Model Results Discussion on Fatigue Results Results for irregular wave Survival Condition Waves Orcaflex TM Discussion on Results obtained from Orcaflex TM Variation Mode and Effect Analysis Chapter Secondary Objectives, Results and Evaluation Introduction A: Saved time series of positions/accelerations of parameters B: Scatter Plots of Buoy Motions in 6 DOF vs Rack Position iv

8 6.4 C: Peak acceleration summary in 6 DOF vs rack position D: Lateral and Vertical Force on tether vs rack position E: Wavespring Force vs Rack Position Scatter Plots for all sea states F: Wire Force vs Rack Position G: Transmission Force vs Rack Position Scatter Plots for all sea states H: Number of Wavespring Cut off events in each sea state F: Number of slack events in each sea state Discussion Chapter Conclusions, Limitations and Future Work List of Figures List of Tables References Appendix 1 WAFO Toolbox Appendix 2 Review of Structures that undergo extensive Fatigue Loading Appendix 3 Scaling of WEC from experimental model to life size model Appendix 4 Sea States and Notations investigated in Tank Tests and OrcaflexTM Appendix 5 Outputs generated from Experimental Tests in Wave Tank Appendix 6 Summary of Loads on Experimental Results Appendix 7 Simulation Model Peak and Load Statistics Appendix 8 Simulation Model Fatigue Loads Appendix 9 Additional Objectives Appendix 10 Peak Identification Matlab TM Code Appendix 11 Equivalent Load Estimation for Fatigue MatlabTM Code Appendix 12 Wave Interference and production of Irregular waves v

9 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 vi

10 Symbols : Acceleration in direction j : Acceleration Vector of an arbitrary point with respect to defined origin A D Ax b B B i C M d ds D : Projected Area of Bluff body normal to the flow direction : Added mass of component k in direction j : Wet Surface Area of Buoy : Fatigue strength exponent (material property) : Number of Blocks : Wave Drift Damping Coefficient : Inertial Coefficient : Damage experienced during the experimental signal duration : Infinitesimal area on buoy s body to be integrated : 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 d : Drag Force : Equivalent Load : Gas Spring Force : Hydrostatic Force : Slow Drift Loads : Inertial Force on cylinder : Weight of Buoy vii

11 F M Fn g H : Gravitational Force due to weight of Buoy : Lift Force : Morrison Force for cylinders : Froude Number : Sum of forces dues to Power Take Off Unit : Transmission Force : Radiation Force : Friction Force : gravitational acceleration : 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 viii

12 : 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 ix

13 ω 0 : 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 : Incoming wave frequency : Wave Encounter Frequency x

14 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. I. Certain governments are becoming aware of the problem and measures like the ( ) 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 I. 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. 1

15 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 TM. 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 1 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 1 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 2

16 iv. Estimation of Sea Loads for extreme cases in Orcaflex TM 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. 3

17 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 TM 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 XXVII 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 TM 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 TM is useful in predicting the fatigue life occurring in different combinations of sea states, thus extending the ability to predict for 4

18 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.. 5

19 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 2 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

20 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 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 7

21 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 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, a. Oscillating Module 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 8 Figure 2: Schematic of WEC

22 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 3 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 9

23 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 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. 10

24 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 III. 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 IV. 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 V VI, 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. 11

25 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.. XXXIV 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. VII 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 Te and H is substituted by. This has given encouraging results as published by Lopes et. al. VII where for irregular waves the results gave an increased capture width of a factor of 2,5 compared to a passive system. 12

26 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 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 PTO 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

27 The internal forces due to PTO can be further split into, (3) where is the gravitational force due to weight of oscillator and, and 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 radiation force, is the hydrostatic force and is the drag force. The total power absorbed by the buoy can be calculated by multiplying the external forces by the respective velocity component 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, 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. 14

28 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 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

29 For the case of WEC buoy, viscous drag will be most significant and can be expressed as, (6) where is the drag coefficient, is the wet surface area and is the relative velocity 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) 16

30 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 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 17

31 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 18

32 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. 19

33 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 Simulation Model in Simulink TM 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 TM, which is a special add-on package with MATLAB TM, developed by Mathworks TM. 20

34 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

35 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 TM modeling and finally ends with a section on variation mode and effect analysis (VMEA). 3.2 Wave Energy 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 22

36 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 23

37 Figure 9b: Identified Locations color coded according to energy potential. 1. (Source: wikimedia) VIII 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. IX 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 X. He divided them into three broad types. 1. Oscillating Water Column 2. Overtopping 3. Oscillating Bodies 24

38 There are then several sub categories under each of these categories. An entire list can be found at Wikipedia s wave energy page XI but a few devices worth mentioning are Pelamis, Wave Dragon, Wave Roller and PowerBuoy 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 Courtesyen.openei.org) XII The turbine is designed to turn in one direction despite bi-directional airflow. XIII XIV The device can be both floating type as well as fixed type and is usually more suitable for shallower waters 25

39 since it has to be tethered to the sea bed. There are over 1890 patented examples of OWC type of WEC devices. XXXV 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 Courtesyen.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. 26

40 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) 27

41 Figure 14: Heaving Buoy (Point Absorber) type of Oscillating Body WEC (Image Courtesyen.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 1 ) b. Y Sway (η 2 ) c. Z Heave (η 3 ) 28 Figure 15: The axis for the coordinate system

42 The three rotational degrees of freedom are, a. XX Roll (η 4 ) b. YY Pitch (η 5 ) c. ZZ Yaw (η 6 ) 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 XV 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) 29

43 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, 30

44 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 31

45 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, 2 a. The body s capability in generating waves (invisid waves) proportional to ζ a 3 b. Viscous Effects proportional to ζ a 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 32

46 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 nd 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 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. 33

47 In survival conditions, sum frequency effects can cause another phenomenon called ringing. It is a consequence of 3 rd and 4 th order sum frequency effects and is a transient resonant elastic motion 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 5 Subcritical Flow b. 2 x 10 5 < Rn <5 x 10 5 Critical Flow c. 5 x 10 5 < Rn < 3 x 10 6 Super Critical Flow d. Rn > 3 x 10 6 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. 34

48 Separation point is the point where the flow separates from the body and forms vortices (Figure 18). Figure 18: Flow past a cylinder 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 35

49 Velocity of the vortex in the wake of the cylinder is given by, (17) where, the same row. is the circulation of the vortex and l is the distance between two adjacent vortices in 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. 36

50 3.5 Structure Failure Criteria Ultimate Load for a structure from a structural point of view is the magnitude of load beyond which the structure will fail. By failure, it is meant that the structure will undergo a fatal fracture. In practice, we try to make sure that the maximum occurring forces on a structure fall well below the ultimate load capacity of the structure. For a structure to be safe it has to satisfy 3 conditions, 1. Ultimate Strength criteria 2. Stiffness Criteria 3. Fatigue Strength Criteria Fatigue Strength criteria will be discussed in detail in the next chapter Ultimate Strength Consider figure 20 which shows the stress strain relationship for structural steel which is a common construction material. In the figure, a. Point 1 refers to the Ultimate Strength. This is the maximum stress the material can take. Beyond this point if further force is added, the materials stress bearing capacity decreases. b. Point 3 refers to the point where the material finally breaks or fractures fatally. c. Point 2 refers to the yield strength. Until this point the ratio between stress and strain is constant and the material traces back to its original shape on releasing of load. d. Region 4 refers to Strain Hardening region. In this region, the material becomes very stiff and hardens but can no longer come back to its original shape on release of loading e. Region 5 refers to the necking region. In this region, the material starts to loose mass at the weakest link and the stress bearing capacity decreases until fracture. 37

51 Figure 20: Stress Strain Relationship for Structural Steel Yield Strength While designing a structure, we should keep the yield strength in mind instead of ultimate strength. For a material it is calculated using experiments. When a person ceases to come to its original shape after applying stress, the point is marked as Yield Strength point as shown in Figure 20. If a material s yield strength is known it can be tested for safety by computing the tensile stress in the cross section by using Equation (21) 3.6 Fatigue Theory and Estimation of Design Life Introduction Fatigue can be defined as the weakening of material as it is subjected to cyclic or repeated loading. It is a progressive sort of phenomenon and causes localized structural damage. The 38

52 nominal maximum stresses that cause fatigue can be a lot lower than the ultimate tensile stress or yield stress limit for the structure. Hence it is important to do a fatigue analysis and estimate the design life. Typically Fatigue is presented using S-N curves which are a correlation between the stress in a structure and the number of cycles of loading. Figure 21 shows a typical S-N Curve. Figure 21: Typical S-N (Stress vs Number of Loading Cycles) Curve As seen from Figure 21, each stress state S1 corresponds to Number of Cycles N1. In other words, if a structure was to be cyclically loaded such that the material develops a stress S1 then it will survive until N1 cycles and will fracture after that. The above graph represents an ideal situation where all loading cycles are of uniform magnitude. In reality, the WEC is subjected to loading cycles that are non-uniform in magnitude and occurrence. This is because waves in real life are irregular and they cause an irregular buoy response. Hence an S-N curve cannot directly be used for the present scenario. However, damage accumulation theory can be used in combination with the S-N Curve and the Rain Flow Counting Method. 39

53 3.6.2 Rain Flow Counting Method Rain Flow Counting Method is a tool for fatigue load analysis used to reduce a spectrum of varying stress into a set of simple stress reversals. The algorithm was developed by Tatsuo Endo and M. Matsuishi; 1968 XVIII and has been the most popular method lately for fatigue analysis Damage Accumulation and S-N Curve XIX Usually for a typical loading there will be cases where the structure undergoes irregular loading. In such cases, individual loads can be identified and clubbed into blocks (Figure22). Then the life span of the structure can be determined by using Palmgren-Miner Rule. The damage accumulation rule states that if there are k different stress amplitudes in a spectrum with amplitude contributing cycles and if is the number of cycles to failure, then, failure occurs when, ( ) (22) The S-N Curve in Figure 21 can be expressed using the Basquin relation XIX, ( ) (23) where, is the fatigue strength coefficient (material property) corresponding to the stress at failure for cycles, and is the fatigue strength exponent (material property). Here the reference number of cycles is chosen to 40

54 Figure 22: Clubbing of stresses according to Palmgren Miner Rule (Source: Wikipedia) Review of similar machine designs with Extensive Fatigue Loading Fatigue is a common and very important part of design analysis as the failure can be very sudden and can happen at loads much lower than the material s yield strength. In order to better prepare for fatigue, it is interesting to study similar existing machines that undergo extensive fatigue loading. Two such machines have been studied and the findings can be found in Appendix Fatigue and Equivalent Load Estimation When we talk of fatigue related failure, the critical question then becomes how much time is left until the structure fails due to fatigue damage. Based on the S-N curve and damage accumulation theory, one can predict the lifespan if we know exactly what loads have acted in the past and what loads are going to act in the future. But, this is not realistic in most real life cases. Alternatively, if we know how much time we want the structure to survive for how many cycles, we can deduce the one single load that would replace the entire spectrum of loading during the structure s life time. In other words, the damage will undergo the same damage due to this one 41

55 load as it would normally under a full spectrum of loads for the given time period. This load is called Equivalent Load. For a material, the S-N curve is standard and can be found in literature. For example, if the equivalent load was calculated for N cycles, then the corresponding stress amplitude can be found from the S-N curve. Using this stress amplitude and Equivalent Load with FOS, the cross section area of the concerned part can be deduced using Equation 21, Section In real life, we are interested in finding the equivalent load for a spectrum of sea states. If one knows the exact distribution of seastates in a target area across the design life span, one can assess the equivalent load for such a spectrum. This is done in two steps. Initially, the damage caused by the cyclic loads for each sea state are found with the assumption that only one sea state occurs in the spectrum for the design life time. Finally, once damages are found for each sea state, they are multiplied with the spectrum distribution of sea states normalized to one and then added to get total damage. This damage is then used to deduce the Equivalent Load using equation 25. The method for estimating this is further discussed along with Equivalent Load Results for Yue target site in Chapter 5, Section Definition of Equivalent Load XX We want to design the buoys tether such that it can survive for, 1. Design Life, = 25 years corresponding to, 2. an equivalent fatigue load with amplitude repeated, N 0 = 10 6 cycles In addition, we have determined the value of b as 4.8 from the corresponding Wöhler curve for steel and 5.5 for polyester. 42

56 Using the above information we can formulate, (24) where, (25) = Life time Damage on the Buoy = damage experienced during the experimental signal duration (with amplitudes ) = time duration of experimental data = Equivalent Damage = Equivalent Load amplitude Equating the two equations, (26) we get the formula for the equivalent load as, ( ) (27) 43

57 3.7 Modeling in Orcaflex TM Introduction During the experimental tests, in École Centrale de Nantes, there were some wave tank limitations in terms of generation of higher sea states. Since higher sea states pertain to extreme waves, it is very important to study them to see how the buoy reacts and what forces it experiences in survival conditions. Results for survival cases can be generated using the SIMULINK model but there is a need to validate these results as higher sea states are very critical in determining survivability. For validation and studying the motion of buoy in extreme sea states, Orcaflex TM is used. As taken from the official website, OrcaFlex TM is the world's leading package for the dynamic analysis of offshore marine systems, renowned for its breadth of technical capability and user friendliness. OrcaFlex TM also has the unique capability in its class to be used as a library, allowing a host of automation possibilities and ready integration into 3rd party software. XXI Another advantage of using Orcaflex TM is the Graphic User Interface the software has (Figure 23). The graphics helps visualize the motion of the buoy under the influence of waves. The visualization helps identify key motions and snapping events in the tether. In addition, with Orcaflex TM one can test different survivability strategies and choose one that causes the least forces on the connecting parts. 44

58 TM XXII Figure 23: Graphic Use Interface for Orcaflex Theoretical Background for Orcaflex TM Simulation Setup Second Order Wave Excitation Force Orcaflex TM uses Newman s approximation to establish the off-diagonal elements in the Quadratic Transfer Function (QTF) matrix. Newman s approximation was originally written as, (28) where the subscripts j and k are row and column numbers in the QTF matrix. Then, jj and kk correspond to the diagonal elements and jk corresponds to an off diagonal element. Equation 28 is based on arithmetic mean of diagonal elements to estimate off-diagonal values in the QTF matrix. Instead of using the above formula, Orcaflex TM approximates by calculating the geometric mean value. Damping 45

59 Orcaflex TM estimates wave drift damping for the buoy using Aranha s XXXVI simplified method. It can be expressed as, (29) where B i is the wave drift damping coefficient, F i is the mean wave drift excitation, k 0 is wave number and ω 0 is the wave frequency. Damping coefficient is found by differentiation of the QTF matrix. the method can also include the effect of current by modifying the wave frequency into an encounter frequency given by, (30) where U is the current velocity and is the relative angle between wave and current. The new version of Orcaflex TM has made improvements in the computation by including developments in ocean wave theory done by Molin XXXII and Malenica XXXIII et al to make the computation reliable for all water depths and current wave interactions. For the mooring line, the slow drift damping is incorporated as part of the Morrison Equation which is given by, (31) where ρ is density of water, D is the diameter of circular body, C M is the mass coefficient and a is the undisturbed fluid acceleration at the strip s center. 46

60 3.8 Variation Mode and Effect Analysis (VMEA) Introduction The WEC by CPO is subjected to cyclic loads as mentioned earlier in the chapter 5 on Fatigue. Although the rain flow counting algorithm and fatigue theory give us specific equivalent loads for a given design life, the load estimation as well as the fatigue model suffers from uncertainty. XXIII This uncertainty of results is quantified with the Variation Mode and Effect Analysis (VMEA). The presentation here will follow the same lines as (Svensson & Sandström, 2014). XXIV This allows the designer to choose appropriate safety factors while designing the components that are sensitive from a fatigue point of view. VMEA is also helpful in identifying factors that are responsible in causing the most uncertainty. Such information helps the designer decrease contribution from such factors during the design stage to reduce the overall uncertainty and increase the overall efficiency to get an optimized product. At this stage, no experiments have been carried out to obtain fatigue results on the tether. Hence, the data is limited presently and is based on literature and data provided by CPO Reliability and VMEA Reliability can be defined as the probability that the structure is intact at the end of its predicted design life. In engineering, one aims for high reliability and this is usually done by comparing the external loads with the strength/stiffness of the structure at each time step. If the latter is greater than the external loads at all time steps until the design life, then structure s design life prediction can be called reliable. Engineering Design for reliability is subjected to a lot of uncertainties which include, 1. Material uncertainties, external loads and geometry 2. Modeling and Human Errors 3. Vaguely known sources of deviations from expected performance 47

61 Figure 24 shows how these above mentioned factors can skew the predicted results for design life. In the end we are interested in finding the safety factor ϒ which is directly influenced by the uncertainties. Figure 24: Illustration of the influence of uncertainty during the design process (Source: Svensson & Sandström, 2014 XXIV ) Safety Factors can be found using many methods but these in essence can be reduced to groups, 1. Combining safety factors on essential sources based on the worst case for all essential inputs. 2. Assign statistical distributions to all essential sources, perform a probabilistic evaluation and use a pre-determined low probability of failure to find a proper safety factor. In engineering practice, methodologies are usually based on the first group but the drawback with this group is the tendency to overdesign. A combination of worst cases often leads to highly improbable case. Another drawback with this group is the lack of knowledge of the actual probability of occurrence. The second group focuses more on obtaining quantified probabilities of failure for different sources of uncertainty by monitoring the entire process of uncertainty propagation through the model for load and strength. A drawback with this method is the lack of knowledge pertaining 48

62 to uncertainties and their assigned statistical distributions. This leads to application of advanced statistical methods based on inputs that can be very subjective. For point 2 and point 3 in the sources of uncertainties described above, we can only have rough estimates of their actual uncertainties. VMEA approach belongs to the second group of safety factor prediction. The inherent problem of weak knowledge on statistical uncertainties is solved by reducing the statistical complexity to second moment statistics. XXV This reduces the uncertainty to a scalar measure of the standard deviation of each source. Since we are working with fatigue life estimation, standard deviation is not a very good measure since it is variable for different lives. This is improved by converting the scale to a logarithmic one. Once the Logarithmic transformation of uncertainties is done, we are interested in calculating the overall standard deviation of the difference between load and strength. The individual standard deviations for each uncertainty source are calculated and combined using Gauss Approximation Formula to get the overall uncertainty Mathematical Principles of VMEA Here is a simple model for prediction of uncertainty based on the summation of individual contributions from different sources of uncertainty. The logarithmic fatigue life prediction can be formulated as, ( ) (32) where ( ) is the fatigue life model with damage parameter (subsea force, stress etc), the estimated parameter vector. The error in prediction can be written as, ( ) (33) 49

63 where is the actual relation for log life depending on damage driving parameter and the involved scatter in load and strength. Then we can approximate the prediction error by a simple summation, (34) where the quantities X i, represent different types of scatters or uncertainties respectively, and are assumed to have zero mean. In the analysis we only use the variances and co-variances of X i s, and not their exact distributions, which are often not known to the designer. It is more useful to convert the uncertainty into logarithmic form and then relate It to the overall life of the structure using a sensitivity coefficient. This is motivated by the Gauss Approximation Formula. For the transfer function from stress to design life, we have, (35) where is the stress corresponding to nominal values. For summing up individual contributions we make use of a statistical theorem of convergence called Central Limit Theorem. The theorem states that a Sum converges to a normal distribution with zero mean and finite variance when n tends to infinity, if X k s are independent and equally distributed with mean zero and finite variance. This theorem can be used to approximate log life as a normal distribution. Another important simplification we make is to reduce the life prediction model ( ) as a linear regression model. This can be motivated using Basquin Equation found in Chapter 3, Section (Equation 23) 50

64 Chapter 4 Methodology 4.1 Introduction On basis of the theory described in chapter 3, this chapter lists out the details of methodology adopted to perform the objectives. The chapter is divided into sections for General Load Case Analysis, Experimental Investigation, Simulation Results Extraction and Investigation, Fatigue Results Extraction, Simulation in Orcaflex TM followed by VMEA. 4.2 Load Case Analysis XXVI Introduction A load case can be defined as a set of forces acting on a buoy when subjected to a particular combination of wave height and wave period known as a sea state. In figure 25, each empty cell corresponds to a unique load case. The wave energy device has many parts and consequently subjected to many dynamic and static forces. The first step is to identify loads that are interesting to study. In this study, the aim is to find, 1. Ultimate Loads 2. Statistical Load Statistics like RMS, Mean, H1/3, H1/10 and H1/ Fatigue Loads 51

65 These forces will be calculated and recorded from different sources and compared so that we get the most accurate values for the subjected forces. The following sources will be used to record or compute forces, a. Experimental Results 4 b. Mathematical Model in SIMULINK 5 c. Finite Element Model in Orcaflex TM Based on the results obtained from above sources, 1. Mechanical Design Team will base the design of internal parts. 2. Material and thickness of tether will be chosen 3. Mathematical model will be validated 4. Buoy Design will be chosen from the two available alternatives 5. Design life for the buoy in the chosen area of operation will be estimated Methodology In the beginning we start with empty cells for sea states as shown in Figure 25 and we are interested in filling the cells with values for the loads mentioned earlier. The data needs to be filled for irregular seas, since in nature waves are always irregular. 4 Experiments were carried out it Centrale Nantes for 1:16 scale model of actual buoy design for different sea states including extreme conditions. 5 A mathematical model was developed in Simulink by Corpower Ocean, to simulate forces on a buoy when subjected to incoming waves. 52

66 Figure 25: Table of sea states that needs to be filled in to complete Load Analysis First, we start with Experimental Results. Experiments in a wave tank were carried out for certain sea states in École Centrale de Nantes for the sea states shown in Figure 26 In the figure, the experimental sea states have been marked with yellow boxes. Figure 26: Seastates that were tested in the wave tank (marked by yellow boxes) These experiments were carried out for regular seas as well as irregular seas for latching mechanism and Wavespring mechanism for both the buoy designs. In addition, numerous other tests like radiation and calibration were carried out. In total, there were 296 experiments that 53

67 were carried out. During the experiments, a gauge was placed on the tether of the buoy that measured the tensile loads on it. Once the results for peak and RMS loads on the tether are obtained for regular seas, they are used to validate 6 the results obtained from the SIMULINK TM mathematical model. For the purpose of validation irregular seas are not used since time of simulation for irregular seas in the wave tank was very small and hence not reliable in predicting a long term irregular sea state. After validation of mathematical model is achieved, we generate simulation data for irregular seas for all sea states of interest until the extreme sea states. Use of Orcaflex TM for higher sea states Since the higher sea states could not be validated in the experiments due to wave tank limitations, it is necessary to have a second source of results for higher sea states for validating the mathematical SIMULINK TM model. This is necessary since in higher sea states, the wave behavior and buoy interaction can be unpredictable. Higher sea states are modeled in Orcaflex TM for 6DOF single point moored buoy and the forces are recorded for the duration of the simulation. The resulting forces are then compared with the mathematical SIMULINK TM model for validation. Using the above described method we deduce Ultimate Loads, RMS Loads and Fatigue Loads. 4.3 Ultimate and Statistical Loads Peak Loads and Ultimate Strength During the experiments at the wave tank, the tension force on the tether was recorded in a time series. It is of interest to identify the peaks in the tensile forces. These peaks will give a 6 Validation is done by individually comparing the Peak and RMS values with the experimental results for different sea states. Due to tank limitations, experiments for higher sea states could not be performed. 54

68 design basis for choosing a suitable material and geometrical dimensions. The goal is to have a material that has yield strength higher than the strength calculated for peak tensile force on the tether after a suitable FOS (Factor of Safety) is applied Peak Identification Method for Ultimate Load Calculations In Dec-Jan 2013, work was done on peak identification methods developed by the US Navy XXXI and Mikael Razola XXX. A part of the code was used to write a new code designed to identify peaks in the data generated by the experimental tests carried out at École Centrale de Nantes for a given input of unfiltered time series (Figure 27). See Appendix 10 for the Matlab TM code on peak identification. Algorithm for identifying Peaks 1. Raw Data is loaded, and separate vectors for acceleration and time are created. (Figure 27) Figure 27: Unfiltered Data for Heave Acceleration 2. For the process of filtration, several thresholds are introduced. These thresholds represent time and acceleration values which are represented by the following variables. These variables are initialized. 55

69 a. mphdiff (threshold for force/acceleration in differential of force/acceleration) b. mpddiff (threshold for time in differential of force/acceleration) c. mphacc (threshold for force/acceleration) d. mpdacc (threshold for time) These parameters are the choice of the user. The parameters will later on be used to further filter beyond the general filter to identify peaks. 3. For initializing general filtration, Cutoff frequency is loaded. This is the choice of the user. Default is 10 hz but for the buoy forces a frequency of 5 Hz gave satisfactory filtration. Quality of filtration was determined by damage count. This is explained in the fatigue section. 4. Then the frequency of the data is calculated by finding the reciprocal of time difference between the first two readings. (36) where, fs represents the frequency of data recording while t1 and t2 represent the time values of consecutive time steps. 5. The cutoff frequency must be chosen such that the condition ( ) is satisfied. Then a Butterworth filter of order 9 is applied by default. The order can be changed by modifying the code. (Filtered values are shown in figure 28). The need and consequence of filtering is discussed in Section and

70 Figure 28: Comparison of filtered and unfiltered data (green is filtered data and blue is unfiltered data) 6. Now in the filtered data, the first differential of entire data is computed. In this data all positive points approaching infinity are made zero. See figure 29 after this step (the data is reversed in sign for purpose of representation). Figure 29: Differential of Heave Acceleration to filter out differentials lower than defined threshold 57

71 7. Next, the earlier loaded constant mphdiff is called. This constant creates a cutoff for the differential of heave acceleration. Any acceleration below the constant are filtered out. 7 Since the value chosen for mphdiff is a factor, it is made relevant by multiplying it with the standard deviation of the force differential vector before using as a cutoff threshold in the next step. (37) 8. Then locations of peaks are extracted using Matlab TM s inbuilt findpeaks function 9. Once the accelerations are filtered, it is necessary to filter on a time scale to remove peaks occurring very close in time. The constant mpddiff is called and made relevant like by multiplying it with mean peak location distance. This creates a horizontal threshold. 8 (38) 10. Next a loop is set up for finding the locations of acceleration peaks based on parameters defined in step 8 and 10. a. For one to number of peaks, b. To find the highest peak within the horizontal threshold mpddiff made in step 10. c. Then the corresponding location is recorded and stored as acclocs. 11. In this step we define a threshold based on acceleration directly. This acts as a vertical filter as it filters out accelerations lower than a certain threshold. This parameter is mphacc and is calculated as, (39) 7 The choice of this constant needs to be evaluated critically so that there is no loss of essential infromation especially for fatigue calculations. The procedure of choosing is explained in more detail in Section Like mphdiff, mpddiff is a function of itself. This step is done in order to make it relevant for the particular time series under investigation. For example, if mean peak distance is 4 seconds. Then mpddiff being 0.25, it would create a threshold for 1 second for filtration. 58

72 12. All acceleration peaks greater than this value are selected from the pool of acceleration locations that were recorded in step Now, we have a set of filtered acceleration values and their specific locations. 14. At this stage the result is pretty good but not complete yet. Now the final filter is applied. In the acceleration domain, a horizontal time threshold is created by multiplying the constant mpddiff with the mean distance between peak locations. (40) 15. The algorithm is set such that there can be only one peak in the horizontal time threshold. This justifies the fact that there is a time gap between two consecutive heave buoy motions. If there are two or more peaks within a time threshold, the program picks the largest of the two. 16. The final peaks and locations are recorded and plotted as shown in Figure 30. Figure 30: Final acceleration time series (Left figure shows only acceleration peaks while right figure shows steepness of successive peaks) The same algorithm is used to identify peak tensile forces. Figure 31 shows the identified peaks for a sample test arranged in order of decreasing magnitude. 59

73 Figure 31: Sorted Peaks in order of magnitude Apart from identifying the peaks, it is sometimes more important to note their occurrence. Hence, an FFT transformation was applied on the peaks and locations to plot the frequency of occurrence of different peaks. Figure 32 shows the spectrum of distribution for peaks Figure 32: Frequency of occurrence of peaks 60

74 4.3.2 Methodology of Extracting Results A total of 274 experiments were analyzed for peak forces. For each case, 1. Data was narrowed down to useful data based on start and stop time for each simulation. 2. Data was then filtered and peaks were identified 3. Useful Statistical parameters, a. H1/100 b. H1/10 c. H1/3 d. RMS e. Mean 4. For each case the peak was calculated as, (41) Here pretension force refers to the initial force the buoy is given at the start of the experiment. It is shown in Figures 33 and Figure 34. Pretension Force Figure 33: Pretension force at the start of the experiment 61

75 Pretension Force Figure 34: Zoomed in portion of the pretension force 4.4 Fatigue Loads Methodologies adopted for Rainflow counting and design life estimation are described in this section. The algorithms are based on understanding from Fatigue Theory in Chapter 3, Section Rain Flow Counting in Matlab TM A Matlab TM model was developed with the help of online resources and implemented based on the above algorithm that takes in an input array of stress values and gives out an output for 1. amplitude 2. mean 3. number of cycles (cycle or half cycle) 62 Figure 35: Rain Flow Counting output for 3 input stress value

76 4. begin time of extracted cycle or half cycle 5. period of a cycle A typical output is shown in Figure 35 and Figure 36. Figure 36: Output from a Rain Flow Counting Method Script Algorithm for counting cycles using Rain Flow method in Matlab TM 1. Reduce load-time data to a sequence of (tensile) peaks and (compressive) valleys. 2. Imagine that the time history is a template for a rigid sheet (pagoda roof). 3. Turn the plot clockwise by Imagine each peak as a source of water which drips down on to the next peak. 5. Count the number of half-cycles by identifying flow terminations. Flow terminates when, It reaches the end of the time history. It merges with a flow that started at an earlier peak. It flows and an opposite tensile peak has greater magnitude. 6. Repeat step 5 for valleys. 7. Assign a magnitude to each half-cycle equal to the stress difference between its start and termination. 8. Pair up half-cycles of identical magnitude to count the number of complete cycles. 63

77 4.4.2 Algorithm in Matlab TM for estimating fatigue damage and equivalent loads for different sea states Algorithm for computing equivalent loads in Matlab TM 1. Initialize data file. 2. Call subsea force time series from the file and then modify its time limits based on experiment start and stop time. (This information is available in an excel file runlist.xslx ) See Figure 37. Figure 37: Subsea Force after time series snipping based on start and end time 3. Initiate the WAFO 9 toolbox and use function dat2tp to compute all turning points. 4. Filter the turning points by removing insignificant turns. (Figure 38) 9 WAFO discussed in Appendix 1 64

78 Figure 38: Plot showing the rainflow cycles before (RED) and after (GREEN) filtration. 5. Estimate damage on the structure based on the turning points. 6. Compare damage before and after the turning point filtering. 7. Calculate the Rainflow Cycles using a function tp2rfc in WAFO, after satisfactory filtering of turning points is achieved. (Figure 39) 65

79 Figure 39: Rainflow Cycles with minima on X axis and maxima on Y axis for any given cycle 8. Plot graphs for Load Spectrum and Level Crossings (Figure 40). Figure 40: Load Spectrum with load cycle amplitudes and frequency of occurrence and Level Crossings distribution for estimating how many cycles cross which magnitude 9. Compute the Rainflow matrix by defining number of discretization levels. Plot the distribution of Rainflow cycles in a contour style plot. 66

80 10. Calculate the equivalent load using the formulae given in the mathematics section in Chapter 3, Section Scale the results to a full scale model by using appropriate scaling factors. 12. Estimate the RMS load from experimental/simulated data and compare it with the equivalent load. A total of 274 experiments and 146 simulation data files were analyzed for Equivalent Loads. For each case, 1. Data was narrowed down to useful data based on start and stop time for each simulation. 2. Data was then filtered and turning points were identified. 3. A threshold for data reduction was set up to reduce computational time. The choice of the threshold was computed using a for loop with the condition, that new damage after reduction should be at least 90% 10 of the original damage with full data. 4. The following output was extracted for each case, a. Lifetime Damage b. Max Load in lifetime c. Equivalent Load d. Data Reduction Threshold e. Wave Height f. Wave Period 4.5 Automation Methodology As there are numerous cases in simulation and experimental data that need to be analyzed for results, it was not practical to run the above algorithm for each case. Keeping this in time an automation algorithm was developed. Essentially, if all data files are kept in a folder, then the 10 The percentage 90% was after consultation with thesis supervisor Pär Johannesson from SP 67

81 automation code would pick up one file at a time, process it and store necessary data. The algorithm for automation is as follows, 1. Store all matlab data files for the seastates you want to analyze into one directory. 2. Initialize the directory. 3. Create a variable FilesNames for the directory using dir function. 4. Create a counter called NumFiles such that its length is two less than the number of files in the directory. 5. Create a for loop from one to NumFiles with a step size of Create variable A = FIlesNames(1 + 2*i).name 7. Then load the file using the load command as load([directory '\' A]) 8. Paste the code you want to execute for this loaded file. 9. Close the loop with end. This will cycle through all the files one after another in the loaded directory and process it for results. This can be further improved by adding a name recognition system. This was done for extracting results in a seastate matrix form. Its methodology is not discussed here. 4.6 Methodology of Extracting Results from Simulink TM 11 Model The GUI developed my Corpower in 2014 is designed to generate buoy motion and force data for any given seastate that can be fed (Figure 41). The options and process for extracting results are presented here. The constants are as mentioned in the figure. 11 Simulink, developed by MathWorks, is a graphical programming environment for modeling, simulating and analyzing multi-domain dynamic systems. Its primary interface is a graphical block diagramming tool and a customizable set of block libraries. as taken from Wikipedia. 68

82 Figure 41: GUI for running simulations of WEC for given set of input parameters Input Figure 41 shows the GUI for generating simulations for different wave parameters. As input, the mathematical model takes in the following, The chosen options are marked in bold for a comparative study. i. Wave Data a. Simulation Type Batch or Single Wave b. Wave Type Regular or Irregular c. Simulation Time 30 minutes d. Wave Period Variable in steps of 1 sec e. Wave Height Variable in steps of 0.5 m f. Peakness (gamma factor) Default value 3.3 g. Water Depth 50 m h. Location (9 preset locations E.g., West Islands, UK) 69

83 i. Alternatively an option to load wave data as time series N.A. 12 ii. Buoy Data a. Shape (6 buoy configurations available) HA1 b. Scale 1 (experiment results are scaled to full scale for comparison) c. Drag Coefficient in Surge and Heave direction 0. 9 in surge and 0.35 in heave 13 d. Buoy Mass kg e. Buoy Period 4.2 s f. Buoy Volume m 3 Point c to f are preloaded for each selected buoy but they can be changed manually iii. Controller Setting a. Mechanism (6 configurations available; Ex, Latching, Wavespring) b. Latch Control - NA c. Control Parameters Default iv. PTO settings (12 specific settings for mechanical variations) Default Operation After all the parameters are entered, the simulation is started by pressing the start simulation button. Once the simulation is over, the program prompts for a location to save the data. 12 Not applicable in this case. This option allows importing of wave data directly from the target site. 13 Drag Coefficients are available automatically when the buoy shape is chosen. These coefficients were calculated in a previous study. 70

84 4.6.3 Output The output after the simulation is completed is a.mat file. In addition a GUI with certain results gets generated as shown in Figure 42. The GUI gives results for, 1. Power Peak and mean Outputs for, a. Mechanical b. Transmission c. Generator d. Electrical e. Friction 2. Rack position, velocity and acceleration mean and peaks 3. Graph depicting different parameters The generated.mat file has information in the form of the following parameters, 1. Positions, Velocities and accelerations for a. Rack b. Buoy c. Flywheel 2. Force a. Radiation b. Drag c. Excitation or Diffraction d. Hydrostatic e. Wavespring f. PTO g. Friction h. Transmission i. Tether 3. Moments 4. Power 71

85 Figure 42: Output GUI during simulation process The simulation model is a 2 DOF model in Heave and Surge direction. 4.7 Methodology for Operation in Orcaflex TM Coordinate System The coordinate system of the buoy is chosen such that it coincides with the global coordinate system in Orcaflex TM. This avoids unwanted moments saves work later related to coordinate transformation for comparison with the mathematical SIMULINK TM model Elements and Geometry The mooring lines are modeled as pipe elements with zero inner diameter and zero bending stiffness since we are interested in analyzing for polyester and steel mooring lines with no bending stiffness. Since, the mooring line is not a pipe in reality, equivalent pipe dimensions are found to conserve the properties of weight and density. 76

86 The mooring line drag coefficient corresponding to nominal bar diameter was taken from DNV rules, 2010 as, C D = 2.4 for studless chain C D = 2.6 for studlink chain C D = 1.5 for fiber rope Orcaflex TM uses an iterative method based on Newton-Rhapson method to find the system equilibrium and uses an improved catenary equation to estimate the stiffness of mooring lines. The two buoy geometries are imported in Orcaflex TM and a 6 DOF single point mooring system is set up. The following two buoy geometries as shown in Figure 43 were input in the software. Figure 43: The two Buoy Geometries that are input into Orcaflex TM Load Definition Orcaflex TM allows the user to input conditions for waves, wind and current. 77

87 4.7.4 Sea States for Load Analysis The mooring system was subjected to the seastates OF2 to OF 9 as per Table in Appendix 4. All waves were given a heading of 180 degrees. This is not a significant setting as the buoy is symmetric around the z axis. Since there was no current or wind data present, they were not included in the load definition Import of time series to generate wave elevation It is possible to import the time series of wave elevation recorded during the model test in the wave basin, if direct comparisons have to be made for irregular cases. Orcaflex TM uses Fast Fourier Transform (FFT) to transform the input time series into a frequency distribution. Then each frequency component defines a unique wave. These waves are then combined by the principle of wave superposition to generate a wave form. This way one can generate the exact irregular wave that was used in the experimental wave tank test. It is interesting to note, the higher the number of components of wave, the higher is the simulation time in Orcaflex TM. This time dependence is primarily due to FFT. In general, the number of samples N that are used to represent a period must be a power of 2 such that N number of samples produces N/2 components. For the simulation only three wave components were used in one direction. Greater the number of components, greater is randomness in the incoming irregular wave chosen for simulation. See Appendix 12 for seeing how regular waves interact to produce irregular waves Import of second order drift coefficients from tank tests The mean drift coefficients are imported into the Orcaflex TM. These coefficients are taken from the diffraction tests done in the wave tank. This initiates the QTF matrix where terms for damping are input by Orcaflex TM. 78

88 4.7.7 Outputs Following outputs were extracted from the simulations for two degrees of freedom (surge and heave) 1. Buoy Positions 2. Buoy Velocities 3. Buoy Accelerations 4. Force on Tether 5. Force on Buoy 6. Moments on Buoy 7. Simulation Videos to identify critical snapping events 79

89 4.7.8 Survival Strategies Two survival strategies are tested in Orcaflex TM, 1. Strategy 1: The buoy is pulled down underwater where it is held until the wave passes 2. Strategy 2: The buoy is let loose and allowed to move with the incoming waves such that it is detuned with the incoming waves. Such strategies are tested and corresponding forces recorded. Figure 44 shows a slack event for OF7. SLACK Figure 44: Slender Buoy undergoing a slack event under the influence of an extreme sea state OF7 4.8 Variation Mode and Effect Analysis Some Definitions Fatigue Strength: The stress range corresponding to fatigue life of one million cycles Fatigue Load: The structure s stress range scaled by a factor equal to beta root of the target life in cycles over one million, where beta is the fatigue exponent for the material. Fatigue Beta Norm: The beta root of the average of stress ranges raised to the power of beta. 5

90 4.8.2 The Corpower WEC Buoy As described in the chapter on Fatigue, there are several connections, the buoy body and the tether that are sensitive to fatigue failure. As part of thesis work, VMEA estimations were done for these several sensitive areas but in this report only the tether will be presented. The tether is estimated for two materials polyester and steel. In this report, results for only the steel wire will be presented to preserve conciseness. The tether is subjected to tensile loads as the buoy undergoes motions in the vertical plane due to the influence of waves. As part of load data, we have inputs from a mathematical model as well as experimental results. Hence all loading information was obtained from these sources. The strength data for the steel wire is obtained from literature Uncertainties Values obtained for strength and load will be subjected to certain uncertainties. These are assessed by means of their standard deviations and by the difference between their logarithmic values. For uncertainties that are termed as scatter, their sources are not very well understood or random and they could be due to lack of knowledge. They may be improved later by further study in the field Design Life The material will be designed for a life time of 25 years strong enough to withstand at least 1 million cycles 14 of Equivalent Load. VMEA will then predict the uncertainty of the predicted life for the tether. Based on this information a fatigue strength representing 95% survival probability will be estimated to give the steel tether dimensions. 14 Life Span of 25 years and 1 million cycles were given by CPO as inputs according to their design requirements. 80

91 4.8.5 Inputs for VMEA Equivalent Fatigue Load Values for Equivalent Fatigue Loads are taken from the fatigue analysis done in Chapter 5. Fatigue Exponent Next we need to estimate the fatigue exponents or beta factor for steel wire. For this we use DNV rules for the estimation of fatigue component (42 ) The given DNV design equivalent strength needs to be transformed to the nominal equivalent strength by increasing it with two standard deviations. We then have the fatigue component as and nominal equivalent strength for steel rope as MPa Calculated from S-N Curve for steel with 81

92 4.8.6 Sources of Uncertainty Nominal Equivalent Load The Nominal Equivalent Load is based on scaled experiments which are extrapolated to real environments by scaling, modeling and summation over sea states. This process can have the following sources of uncertainty. 1. Scaling and Experimental Equivalence 2. Friction 3. Extrapolation Model 4. Relevance of Rain Flow count 5. Sampling Error in experiments 6. Sampling of service environment Strength For the assessment of material strength, the following sources of uncertainty are present. 1. Scatter in fatigue strength from experiments 2. Parameter Uncertainty 3. Model Error, Linearity 4. Model Error, Palmgren Miner 5. Model Error, Mean value influences 6. Laboratory Uncertainty 82

93 Chapter 5 Results and Discussions 5.1 Tools Developed for Analysis Data Comparison Tool For the purpose of comparison, a mathematical tool was developed in Matlab TM that takes in two different experimental data files and then compares them for different parameters like, 1. Minimum and Maximum Values 2. Sorted Peaks 3. Frequency Distribution 4. Statistical Measures With the help of the tool, one can compare, 1. Two different Buoys for the same seastate 2. Different control mechanisms like latching or Wavesprings 3. A buoy in different seastates Figure 45 shows the starting interphase and Figure 46 shows an example of sorted peaks for a buoy in different sea states. 83

94 Figure 45: GUI for loading data files for comparison Figure 46: Result GUI with options to compare two different data files Other Tools In addition to the Comparison Tool, specific codes were written for general future use at CPO. These have been described in Chapter 4 and some of the codes can be found in appendices. These tools are, 1. Rainflow Count Estimator 2. Equivalent Load for Fatigue Life Calculator 3. Data Filtration and Peak Identification 4. Factor of Safety estimator using VMEA 5.2 Experimental Data Results Peak Loads for all experimental cases All the experimental data was processed according to the methodology described in Chapter 4. Peak Loads and Fatigue Equivalent Loads were estimated for all experimental cases, 84

95 which have been summarized in Appendix 6. The cases are sorted in accordance with their ID numbers which were assigned during experiments Peak Loads in Survival Seastates From all the cases, the peak loads experienced by the buoy in survival conditions are interesting as they can form the basis for designing the dimensions and selecting the material for the tether. Table 2 and Table 3 summarize tension force peaks recorded for Buoy 1 and Buoy 2 under survival seastate simulations in wave tank. All forces in the table have been scaled to a full scale model by selecting an appropriate scaling factor according to Appendix 3. The negative sign indicates tension in the tether. BUOY 1 ID No. Peak Load (MN) Hs (m) Tp (s) Type Wavespring Wavespring Wavespring ID No. 16 Peak Load (MN) Hs (m) Tp (s) Type Wavespring Wavespring Wavespring Wavespring Linear Damper Latching Latching 16 For more details on the ID number and type of experiment, please consult Runlist.xslx which can be procured on request from CPO. 85

96 Table 2: Summary of Peak Forces acting on the tether for Buoy 1 for Survival Sea States for a full scale buoy (The negative sign is an indication of tensile loads) BUOY 2 ID No. Peak Load (MN) Hs (m) 17 Tp (s) Type Wavespring Wavespring Wavespring Wavespring Wavespring Latching Latching ID No. Peak Load (MN) Hs (m) 18 Tp (s) Type Latching Table 3: Summary of Peak Forces acting on the tether for Buoy 2 for Survival Sea States for a full scale buoy (The negative sign is an indication of tensile loads) Deduction of Cross-sectional area of tether based on Peak Experimental Loads At the time, there are two primary materials that are under investigation, Steel and Polyester. In addition HSLA steel has been added to the list for added reference. For both Buoys, The tensile stress in the tether can be calculated Equation 21 in Chapter 3 Section Since the dimensions of the tether are not decided at this point, the present information will be used to deduce minimum cross-sectional area for the tether. This has been deduced in Table Wave Height and Time Period in Table 2 and Table 3 have been scaled to full scale by using an appropriate scaling factor taken from Appendix Wave Height and Time Period in Table 2 and Table 3 have been scaled to full scale by using an appropriate scaling factor taken from Appendix 3. 86

97 Buoy Material Peak Tensile Load (MN) Factor of Safety 19 Yield Stress (MPa) Cross Section Area (cm 2 ) Steel HSLA Steel Polyester Steel HSLA Polyester Table 4: Assessment of Minimum cross-section area of tether based on yield strength and Maximum Experimental Loads in Wave Tank Test at Nantes, Fatigue and assessment of Equivalent Load for irregular seastate wave tank experiments Fatigue is caused by cyclic loading on a structure. It is interesting to assess equivalent loads for irregular seastate experiments since an irregular seastate will have a larger variation and frequency of cyclic loads as compared to a regular wave,. Table 5 summarizes Equivalent Loads for a design life of 25 years and 1 million cycles for Buoy Similar results can be found for Buoy 2 in Table 6. ID No. Equivalent Load (MN) BUOY 1 Wave Height (m) Wave Period (s) Ultimate Load/ Equivalent Load Factor of Safeties are as deduced in section 5.9 using VMEA 20 Time span of 25 years and 1 million cycles were stated as requirements by CPO 87

98 Table 5: Equivalent Loads for Fatigue Design Life of 25 years and 1 million cycles in irregular seas for Buoy 1 ID No. Equivalent Load (MN) BUOY 2 Wave Height (m) Wave Period (s) Ultimate Load/ Equivalent Load Table 6: Equivalent Loads for Fatigue Design Life of 25 years and 1 million cycles in irregular seas for Buoy Fatigue Equivalent Loads and comparison with RMS Loads for Survival Cases Table 7 and Table 8 summarize the Equivalent loads for survival cases for a 1:16 scale model and its comparison with RMS loads. 88

99 BUOY 1 ID No. Equivalent Load (kn) RMS Load on Buoy (kn) Hs (m) Tp (s) Mechanism Eq. Load/ RMS Wavespring Wavespring Wavespring Wavespring 1.84 ID No. Equivalent Load (kn) RMS Load on Buoy (N) Hs (m) Tp (s) Mechanism Eq. Load/ RMS Wavespring Wavespring Wavespring Latching Latching Latching 1.29 Table 7: Fatigue Loads, Design Life and Equivalent Load for Buoy 1 for 1:16 scale model in irregular waves BUOY 2 ID No. Equivalent Load (kn) RMS Load on Buoy (N) Hs (m) Tp (s) Mechanism Eq. Load/ RMS Wavespring Wavespring Wavespring Wavespring Latching

100 Latching Latching 1.42 Table 8: Fatigue Loads, Design Life and Equivalent Load for Buoy 2 for 1:16 scale model in irregular waves The aim of comparing Equivalent Loads with the RMS loads was to see if there is an observable range. With a few exceptions, it can be said that the ratio lies between 1 and 1.4 usually. 5.3 Discussion on Experimental Data Results Need for pretension When the buoy was setup in the testing facility (Figure 6), the wire at the bottom of the buoy went through the tensile force sensor. Since the buoy s motion under the influence of waves can be impulsive, a pretension was necessary to accurately record the change in tension in the connecting wire. So in the initial position, the buoy is pulled down a little to give the wire a pretension value. As the buoy oscillates in water, the forces are measured with the pretension as the reference value Wavespring/Linear Damper as compared to latching As seen from the results for survival cases in Table 2 and Table 3, the maximum tension recorded for A Wavespring system was lower than Latching system. This happens because the Wavespring smoothens out the motions, thus the acceleration curves are continuous and differentiable and the impulsive forces get minimized or negated Buoy Performance It was generally observed from the results for all regular, irregular and survival cases that Buoy one recorded lesser forces on tether in comparison with Buoy 2 for most of the cases, especially the higher sea states. Another factor for choosing the buoy was the power 90

101 generated by the buoy in which Buoy one performed better overall. The overall lower force and higher generated power can be explained by the principal of conservation of energy. Here energy brought from waves is converted into power generated, kinetic energy, strain energy and energy losses. Since the force on the tether is less, it will take lower strain energy which in turn means more energy is available for conversion into useful power. So, it can be concluded that Buoy 1 has better survivability and performance as compared to Buoy Sources of Noise in Experimental Data and the need for filtration During the tank testing, there are several factors that can create noise. Most prominent are the reflection of waves from the side walls of the wave tank. Hence an experiment can be performed only for a limited time until wave reflection from walls is insignificant. Other sources of noise are micro vibrations due to generators that can cause the sensors to over record. Noise is usually treated by using a suitable low pass frequency filter Choice of Filter and Corresponding Performance The choice of filter and its characteristics can play a big role in the output of useful data. For the purpose of filtering, 3 different filters were tried, 1. Butterworth Filter This filter was the most suitable one gave fairly good filtration results for 9 th order function with a filtration frequency of 2.5 Hz. 2. Kaiser Filter This filter relied on inputs for lower band and upper band frequencies and had room for oscillations and ripples within the filtration process. This filter tended to over filter the 91

102 results either on the lower band or upper band. Narrowing down the exact frequency range proved to be challenging as each raw_data case behaved differently. 3. Ideal Filter This is a common digital filter that takes frequency as input. The filtration results were not very good as it tended to shift the raw data vertically in force scale and gave spurious results for some cases while it behaved well for other cases. Of the three filters, the Butterworth filter seemed the most reliable. 5.4 Simulink Simulation Model Results The Simulation model s data was used to perform the following tasks, 1. Run Simulations for those sea-states which were tested in the wave tank as shown in Figure 26 in Section Perform validation by comparing the results obtained from Experiments and Simulation Model for same sea states. 3. Run Simulations for all missing sea states as shown in Figure 25 in Section Analyze data and generate outputs as per deliverables in Chapter 1. Here comparison of results between Experimental and Simulation Results are presented. Detailed results of Fatigue Loads can be found in Appendix 8 and results for Ultimate and Statistical Loads can be found in Appendix 7. F_Subsea in the experimental data file and F_wire in the Simulation data file were compared for Mean, RMS and peak values. There was good agreement and the ratio of Simulation is to Experiment was reasonable around 1.1. Figure 47, shows different ratios of RMS values that were compared for the two sources. 92

103 Figure 47: Ratio of RMS Loads between Simulink simulation loads and experimental loads for force on the buoy tether in irregular waves. Top half of table represents Buoy 1 for Wavespring and Bottom Half of table represents Buoy 2 for Wavespring Since Peak Loads can be rogue despite adequate filtration, a more dependable measure for validating would be RMS Loads. Thought the ratio was not exactly 1 the range was satisfactory with limits between 1.03 and Table 9 shows the ratio of Peak Loads between simulation and experimental model results. As it can be seen, the ratio is around The difference can be explained by the fact that the simulation model is 2 DOF and by conservation of energy, overestimate in surge and heave direction. Buoy 1 Buoy 2 93

104 Wave Height (m) Wave Period (s) Simulation Peak/ Experimental Peak Table 9: Ratio of Peak Forces in tether obtained from experimental and simulation model for Buoy 1 and Buoy Statistical Loads Maximum Loads Max Loads_Peaks Tp Hs Table 10: Peak Loads in N for a full scale buoy recorded on the tether based on simulation data As seen from Table 10, the peak loads become quite significant and similar in magnitude for sea states with time periods greater than 10 seconds and wave height greater than 2.5 m. The highest peaks were observed for the highest waves with Hs = 7.5 m and Tp = 13 94

105 seconds. It is interesting to note that the worst loading is not observed for longer wave periods. This is a consequence of constructive interference and resonance phenomenon at certain wave periods. Table 11, 12 and Table 13 show the results for the Mean, RMS and average of top 10 forces. The maximum recorded Peak Load was 4.18 MN at Hs = 7.5 m and Tp = 13 s. In addition, a factor of safety as determined by VMEA will need to be applied depending on the material used. The FOS s can be found in Table 21. Mean Loads Hs Max Loads_Mean Tp Table 11: Mean Loads in N for a full scale buoy recorded on the tether based on simulation data The maximum recorded Mean Load was 3.46 MN at Hs = 7 m and Tp = 13 s. In addition, a factor of safety as determined by VMEA will need to be applied depending on the material used. The FOS s can be found in Table 21. RMS Loads 95

106 Hs Max_Loads_RMS Tp Table 12: RMS Loads in N for a full scale buoy recorded on the tether based on simulation data The maximum recorded RMS Load was 3.05 MN at Hs = 7.5 m and Tp = 12 s. In addition, a factor of safety as determined by VMEA will need to be applied depending on the material used. The FOS s can be found in Table 22. H 1/10 Peak Loads (Average of Top 10 highest loads) A10_Max Loads Tp NaN Hs Table 13: A 1/10 Loads in N for a full scale buoy recorded on the tether based on simulation data The maximum recorded H 1/10 Load was 3.85 MN at Hs = 7.5 m and Tp = 15 s. In addition, a factor of safety as determined by VMEA will need to be applied depending on the material used. The FOS s can be found in Table

107 5.4.2 Deduction of Cross-sectional area of tether based on Peak Simulation Loads In line with Section 5.2.3, there are two primary materials that are under investigation by CPO, Mild Steel and Polyester. In addition HSLA steel has been added to the list for added reference. In Section it was deduced that Buoy 1 has better performance and hence the following analysis has been done only for it. The tensile stress in the tether can be calculated Equation 21 in Chapter 3 Section Since the dimensions of the tether are not decided at this point, the present information will be used to deduce minimum cross-sectional area for the tether. This has been deduced in Table 14. Material Peak Tensile Load (MN) Factor of Safety 21 Yield Stress (MPa) Cross Section Area (cm 2 ) Steel Buoy 1 HSLA Steel Polyester Table 14: Assessment of Minimum cross-section area of tether based on yield strength and Maximum Simulation Loads in Wave Tank Test at Nantes, Factor of Safeties are as deduced in section 5.9 using VMEA 97

108 5.4.3 Fatigue Loads Equivalent Load Hs Fatigue_Equivalent Load Tp Table 15: Equivalent Loads in N for a full scale buoy for fatigue predicted for the tether based on simulation data If one observes Table 15 for Equivalent Load for different sea states, the equivalent load keeps increasing as the significant wave height increases but it is really interesting to note that the equivalent load for any wave height increases up to a time period of 11 seconds and then decreases thereafter. A wave period of 11 seconds might coincide with the periodic of the buoy s natural period which causes constructive interference resulting in resonance. Life time Damage Hs Fatigue_Lifetime Damage Tp E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+37 Table 16: Life time damage for full scale buoy due to fatigue predicted for the tether based on simulation data at Yue 98

109 The life time damage as shown in Table 16 is a measure that in itself does not give any information but can be translated into predicting the equivalent load for a desired life time. This means that the above data can be used to compute the equivalent lifetime damage for a target site with given sea state scatter information. Further this value can be used to compute one equivalent load for an entire area Equivalent Load Estimation for Yue target site For estimating the equivalent load, first the equivalent damage is to be estimated for a target site. It is done by multiplying the normalized sea state distribution factors (Table 17) for a target site with lifetime damages as shown in Table 18. Results here are presented for a target site named Yue. Yue time Table 17: Normalized Scatter distribution of different sea states for target site Yue After Table 16 and Table 17 are multiplied we get the target life time damage distributions as shown in Table 18. Here each cell in the table corresponds to damage contribution due to that sea state at Yue over a life time of 25 years. 99

110 Yue Life Time Damage per sea state for 25 years time E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Table 18: Life Time Damage distribution of different sea states for target site Yue The summation of Table 18 gives the life time damage for the entire sea state for 25 years. This corresponds to x This information is used to compute the equivalent life using Equation 27. For yue scatter site the equivalent load is estimated as 2682 KN. The same principle is extended to compute equivalent loads at other target sites around the world. 5.5 Discussion on Simulation Model Results RMS values vs peaks to validate When we compare the results of experimental data and simulation data, it is more useful to compare the RMS values instead of the peaks. Since, peaks can originate from sources of noise and may not give an accurate representation of the actual phenomenon if its occurrence is very rear. Hence for the purpose of validation, both peaks and RMS values were used Lack of 6 DOF model The simulation model is designed for two degrees of freedom in the direction of heave and surge. Hence rotations are not captured in the model. This accounts for the difference in 100

111 ratios for different sea states. By conservation of energy, due to lack of rotations, the motions in surge and heave get exaggerated as compared to a realistic case. The model is currently being developed to include all 6 degrees of freedom. On completion, the model will be able to give a much clearer representation of the actual phenomenon Variation of Peak Loads with wave period and wave height Equivalent Loads for Fatigue As can be seen from figure 48, the calculated equivalent loads, for a life span of 25 years, increase in magnitude as the wave height increases. The slope of the curve is steep for wave heights up to 2.5 m and gradually flatten beyond 5.5 m wave height. This interesting observation indicates to the fact that, if the significant wave height increases beyond 5.5 m, it does not affect the material choice and dimensions of the concerned part. A possible reason behind this observation is the relative size of the buoy with respect to the incoming wave. Beyond 5.5 m large part of the buoy remains submerged and this could cause the normalization of Equivalent Load. This observation needs further study to validate the reason. N Variation Variation of of L Eq F Eq with with Hs Hs Tp = 13 Tp = 15 Tp = 14 m Figure 48: Variation of Fatigue Equivalent Load for 25 years with Wave Height The variation of equivalent loads with time period is not monotonous and there are certain peaks and troughs that are observed at different time periods. These peaks are not same for 101

112 all wave heights and can occur at different time periods. A likely cause of this is the interference of incoming waves with the natural period of the buoy. Constructive interference results in peaks while destructive interference results in troughs. This can be observed in Figure 49. N Variation of of L F Eq Eq with Tp Tp Hs = 7.5 Hs = 7 Hs = 6.5 s Figure 49: Variation of Fatigue Equivalent Load for 25 years with Time Period Peak Loads As seen from Figure 50, the peak loads variation with wave height shows a general trend that is flat from 1.5 m onwards but looking closely it is observed that the peaks undulate along this flat line. It is interesting to see that the peak loads don t vary so steeply after a wave height of 1.5 m. This is a good thing in terms of material selection and dimensions of the concerned part when designing for different offshore sites. 102

113 N Variation of Peak Loads with Hs Tp = 13 Tp = 12 Tp = 14 m Figure 50: Variation of Peak Loads for 25 years with Wave Height A possible reason for the shallow rise and undulation between 1.5 m and 6 m could be related to resonance. At certain wave heights, constructive interference might be causing the humps while destructive interference causing the troughs. Further study is required to ascertain the exact reason behind the shallow rise. A possible reason could be the influence of the shape of the buoy. N Variation of Peak Loads with Tp Hs = 7.5 Hs = 7 Hs = 6.5 s Figure 51: Variation of Peak Loads for 25 years with Time Period It can be seen in Figure 51 that the variation of Peak Loads with wave height is similar in nature with that for equivalent loads. There are crests and troughs observed and it is likely that this is caused due to constructive and destructive interference between the incoming wave and the buoy motions. 103

114 5.6 Discussion on Fatigue Results RMS vs Equivalent Load As can be seen from Table 12 and Table 15, the RMS value of Loads acting on the buoy are always lower than the equivalent load. This is a good indication since the analysis is based on the predilection that the buoy survives one million cycles of loading equal to the equivalent load. A similar trend was observed for all experimental cases. Also a comparison between peak forces and equivalent load was made. The respective ratios can be found in Appendix Estimation of Equivalent Load for a target site using damage factor for individual sea states During the estimation of equivalent load for each sea state for a given life time, one of the steps is to estimate the damage undergone by the tether during the said period. If the damage for all the sea states are known for the target life, then these values can be normalized to one and multiplied with sea state occurrence frequency to compute the overall damage in the target site. This overall damage can then be used to estimate the Life time Equivalent Load for the target site Uncertainty in Fatigue Life Prediction When a fatigue experiment is carried out for the same material in the exact same physical conditions, the results can still vary. This is due to certain internal and external factors that result in the overall variance of results from mean value. This is usually addressed by including a factor of safety that is estimated using past experience or derived after treating the results with statistical tools. This is addressed in VMEA in Chapter 4, Section Fatigue Sensitive Parts in Buoy In addition to the tether, the internal mechanism of the buoy also undergo extensive cyclic loading. Some of these forces are available through the simulation model designed in 104

115 Simulink TM, but other mechanical parts like frames and connectors need an FEM model to be studied for fatigue damage. This was not part of the scope but currently work is ongoing in modeling the buoy in Solidworks TM by the Mechanical Engineer for Corpower Ocean Fatigue Equivalent Load Estimation for a Target site The life time damage estimated for each sea state can be extended to calculate the life time damage for a target site with sea state scatter distribution. This is done by multiplying distribution of each sea state with the life time damage for that sea state. Then the summation of damages for each sea state gives the overall damage for 25 years. This can then be translated to calculate the Equivalent Load for the target site. Calculations are based on the results obtained from the Simulink TM mathematical model. Results of this can be found in section Results for irregular wave Survival Condition Waves Orcaflex TM Peak Accelerations of the buoy in surge and heave direction have been presented in Table 19. As can be seen from the table, the accelerations are extremely large and this could possibly be a modeling error. Since the software was unavailable in Corpower and Remote Access time was limited, the case could not be further investigated. Sea State Hs (m) Tp (s) Max Acceleration (Surge (m/s 2 )) Min Acceleration (Surge (m/s 2 )) Max Acceleration (Heave (m/s 2 ) Min Acceleration (Heave (m/s 2 ) 105

116 OF OF OF OF OF OF OF OF Table 19: Summary of accelerations (surge and heave) on Buoy 1 under survival conditions - Survival Strategy Discussion on Results obtained from Orcaflex TM Which survival case is better Based on the simulation results, it was concluded that the case when the buoy is pulled under water and stored performed much better in terms of forces on buoy and tether as compared to the case when the buoy was left to move with the waves. Figure 44 shows a case when the buoy is left to move with the waves and in this case, there were slack events that were observed. From a strength point of view, one wants to avoid slack events as they impulsive forces that may lead to failure Identification of Slack Events and Buoy Survival Behavior With the help of simulations, it was visually possible to see the buoy in motion under the influence of incoming waves. The two survival strategies could be visually checked and critical events like snapping were identified. Even though the software overestimated the 22 The Sea State IDs are according to Appendix

117 forces, the motions were able to give the engineers at CPO good insight. More information on number of slack events can be found in Chapter Why Orcaflex TM results overestimate all accelerations When the Orcaflex TM model was done, the buoy was done as one single unit that is connected to the tether. This means the relative motion between the buoy and the rack was not modeled in Orcaflex TM due to design limitations. Due to this the buoy behaves like a rigid system that results in over estimation of buoy accelerations. It would be interesting to see if this design limitation can be overcome to get more realistic results Lack of Orcaflex TM at Corpower Ocean Orcaflex TM software was not available at Corpower Ocean Stockholm Office and only access to the software was through a consultant engineer in Portugal. All design inputs were provided to him and he executed the modeling and extraction of results for the study. In parallel, it was possible to get remote access to Orcaflex TM server at Indian Institute of Technology Madras (IIT-M) to carry out some simulation studies. But as the access time was limited, a complete independent study could not be performed Comparison with Simulation Model Results Since the accelerations estimated by the software were very high it was deduced that there has been a modeling error. Since the results were erroneous, they were not compared. It was envisaged to do a further study and rectify the problem but lack of software, Limited support from CPO Consultant Engineer for Orcaflex TM in Portugal and limited Remote Access at IIT-M were impeding. 107

118 5.9 Variation Mode and Effect Analysis Uncertainty Evaluation The presented table is from experimental data and scatter/error estimations provided by (Svensson). XXIV Factor of Safety Assessment for Steel Input Result Uncertainty Components Scatter Uncertainty Sensitivity Coefficient ( c ) t-correction factor ( t ) standard deviation ( s ) Scatter Uncertainty Total Strength Strength Scatter x Statistical Uncertainty in Strength x Adjustment Uncerainty CA/VA x Reference Data Relevance x Mean Value Influence x Laboratory Uncertainty x Total Strength Uncertainty Load Pool Measurements, Scatter x Scaling x Distribution of Hf x Model Uncertainty x Friction x Total Load Uncertainty Wohler Experiment x Total Exponent Uncertainty Total Uncertainty Table 20: VMEA results for steel tether based on experimental data The factors of uncertainty listed in the list in Table 20 are for Strength, Load and Wohler Exponent which are added together quadratically to give the overall uncertainty of This number is the uncertainty in the difference between logarithms of strength and load. In other words, it can be said that the uncertainty is at 21% between strength and load. Assuming a normal distribution for the difference between logarithms of strength and load, we calculate the 95% quantiles in the distribution corresponding to 1.64 times the overall uncertainty. Thus we have our new overall uncertainty as 0.21 x 1.64 = This is denoted as the variation distance and this value is the value required to ensure 95% probability of survival during the design life. A variation distance of 0.34 corresponds to a safety factor of 1.41 obtained by taking the anti-logarithm. (e 0.34 = 1.41) 108

119 Extending the above analysis for Polyester tether, see (Svensson) XXIV, we have in Table 21, Factor of Safety Assessment for Polyester Input Result Uncertainty Components Scatter Uncertainty Sensitivity Coefficient ( c ) t-correction factor ( t ) standard deviation ( s ) Scatter Uncertainty Total Strength Strength Scatter x Statistical Uncertainty in Strength x Palmgren Minor Error x Mean Value Influence x Laboratory Uncertainty x Total Strength Uncertainty Load Pool Measurements, Scatter x Relevance of Rainflow count x Model Uncertainty x Friction x Scaling x Total Load Uncertainty Wohler Experiment x Total Exponent Uncertainty Total Uncertainty Table 21: VMEA for polyester tether based on experimental data Reliability Evaluation Steel Tether Total Uncertainty Variation Distance Factor of Safety 1.41 (correction for 95% probability of survival) Polyester Tether Total Uncertainty Normal Distribution Correction 0.56 Factor of Safety 1.75 (correction for 95% probability of survival) Table 22: Reliability and factor of safety for Steel and Polyester tethers for experimental data 109

120 110

121 Chapter 6 Secondary Objectives, Results and Evaluation 6.1 Introduction In early May 2015, additional objectives were added to the scope of thesis. The entire list of objectives can be found in Appendix 9. Some results will be presented discussed here. These results are of importance to the mechanical design team who are working with the internal dimensions of PTO and mechanical drive system. In this chapter, only specific results have been presented. Full results can be found in the supporting data folder on request from CPO. 6.2 A: Saved time series of positions/accelerations of parameters This was a very interesting requirement and poised a challenge addressing the difference between theory and practice. The FEM Software Solidworks TM was to be used in assessing the internal fatigue stresses in a half scale buoy. Though very robust, the software had the limitation that it could not take more than 50,000 points for each time series input. Since the data generated by the Simulink TM model had over 78,000 points for each sea state, there was a need to condense the data. Another limitation with the software was that of time. Setting up of one time series took approximately 7 minutes of the designer s time. For 170 sea states, the time was very large and the work tedious. A solution of using a Macro was suggested but since each time series had certain different parameters, setting up a Macro was not helpful. Given these two limitations, the following solution was thought of and implemented, 111

122 1. The time series was run through different filters and reduced to a combination of peak and trough points. So, any point in between a crest and a trough in a wave was discarded. 2. This reduced data was then analyzed for the life time damage it caused in a matlab program. Now the data was filtered against vertical peak thresholds and horizontal time thresholds and life time damage was checked after filtration. A 90% of original damage was considered as the limiting factor. Based on these techniques, the data points in each time series was greatly reduced. (Table 23) Table 23: Final count of data points after reduction based on above algorithm But there still remained the problem of manually entering each sea state that took 7 minutes per sea state. This was solved by combining sea states into one long sea state upto 50,000 points. 1. For a given target site, the scatter of occurrence was noted in a matrix. (See Table 24). 2. For each se astate, the ratio of current sea state occurrence and minimum sea state occurrence was calculated. For example, if sea state for Hs=3 and Tp=4 the occurrence was 1800 hours and the minimum sea state occurrence was for Hs= 4 and Tp=5 at 18 hours, then the ratio for the former sea state is Based on these ratios, the time series for sea states were multiplied by the ratio factor and added at the end of the first sea state s data. The addition was continued while the total number of points was less than 50,000 points. Since addition and scaling large ratios was consuming lot of data points, the data sets were separated for ratios up to 4. In other words, for any given data combination group the highest ratio between maximum and minimum occurrence within the group would be 4. Such data segregation 112

123 was possible since Solidworks TM has the ability to multiply a given time series input by a factor. This greatly reduced the number of input files. Finally there were only 12 inputs that had to be input into the FEM software. time Table 24: Scatter Distribution of each Sea State at offshore site name Yue 6.3 B: Scatter Plots of Buoy Motions in 6 DOF vs Rack Position In this report results only for one particular case for experimental results have been presented. An exhaustive list of figures for Experimental data have been compiled in a separate file. The following graphs pertain to ID 115 in experimental results given in Table 25. Hs 1:16 Hs 1:1 Tp 1:16 Tp 1: Table 25: Wave Parameters for ID115 The recorded accelerations in the following groups represent the buoy motion in a short time interval. 113

124 b. Heave The buoy acceleration in heave direction is usually fluctuates between -0.1 m/s 2 and 0.1 m/s 2 except for one instance where there is a steep rise in acceleration that is observed at mean position. In the case, the acceleration rises up till 0.4 m/s 2. This is most likely due to a coding error and can be ignored. See Figure 52 and Figure 53 for details. Figure 52: Buoy acceleration (m/s 2 ) in heave direction vs rack position (m) Figure 53: Buoy acceleration (m/s 2 ) in heave direction vs rack position (m) and their occurrences c. Surge 114

125 The surge of the buoy in this particular case is more fluctuating as compared to heave. This could be resonance induced. As seen in figure 54 and figure 55, there is sharp impulsive acceleration observed at mean position and the peak goes from -0.2m/s 2 to 0.2 m/s 2. This is again due to a coding error during mathematical model formulation. Figure 54: Buoy acceleration (m/s 2 ) in surge direction vs rack position (m) Figure 55: Buoy acceleration (m/s 2 ) in surge direction vs rack position (m) and their occurrences d. Sway 115

126 As seen from figure 56 and 57, the acceleration patters in similar to that in surge direction. This is expected since the buoy is symmetric in all directions. The peak at mean position is observed in surge and heave as well due to the error. The undulations in sway accelerations with respect to rack positions could be interesting in the internal parts fatigue behavior. Figure 56: Buoy acceleration (m/s 2 ) in sway direction vs rack position (m) Figure 57: Buoy acceleration (m/s 2 ) in sway direction vs rack position (m) and their occurrences e. Pitch The pitching is quite undulating over one buoy cycle as seen from Figure 58 and Figure

127 Figure 58: Buoy acceleration (degree/s 2 ) in pitch direction vs rack position (m) Figure 59: Buoy acceleration (degree/s 2 ) in pitch direction vs rack position (m) and their occurrences f. Roll As expected due to symmetry, the acceleration pattern is very similar to that in pitching. The peak roll acceleration is observed at 0.01m rack position as seen in Figure 60 and Figure

128 Figure 60: Buoy acceleration (degree/s 2 ) in Roll direction vs rack position (m) Figure 61: Buoy acceleration (degree/s 2 ) in Roll direction vs rack position (m) and their occurrences g. Yaw The observed yaw accelerations in Figure 62 and Figure 63 are usually small except during one instance where there is a sharp acceleration observed at mean position which could be due to a modeling error. The present yaw values indicate that torsion should be kept in mind during design. 118

129 Figure 62: Buoy acceleration (degree/s 2 ) in yaw direction vs rack position (m) Figure 63: Buoy acceleration (degree/s 2 ) in yaw direction vs rack position (m) and their occurrences h. Resultant Acceleration in XY plane By combining accelerations in Surge and Sway direction, the resultant XY plane acceleration was calculated. As seen in Figure 64 and Figure 65, the peak acceleration was observed nearmean position and the peak is at 0.21 m/s

130 Figure 64: Buoy acceleration (m/s 2 ) in XY plane vs rack position (m) Figure 65: Buoy acceleration (m/s 2 ) in XY plane vs rack position (m) and their occurrences 6.4 C: Peak acceleration summary in 6 DOF vs rack position a. Maximum Acceleration Summary (Table 26) 120

131 Max Accelerations m/s^2 m m/s^2 m m/s^2 m deg/s^2 m deg/s^2 m deg/s^2 m m/s^2 m Buoy Full Scale Full Scale ID No. Surge a Rack Posn Sway a Rack Posn Heave a Rack Posn Roll accn Rack Posn Pitch a Rack Posn Yaw accn Rack PosnResultant XYRack Posn Number Wave H Wave T B E E E-02 B B B E E-03 B B B B B E E E E-02 B B B B B B B B B Table 26: Maximum accelerations in 6 respective rack b. Minimum DOF vs positions Acceleratio n Summary (Table 27) 121

132 m/s^2 m m/s^2 m m/s^2 m deg/s^2 m deg/s^2 m deg/s^2 m m/s^2 m Buoy Full Scale Full Scale ID No. Surge a Rack Posn Sway a Rack Posn Heave a Rack Posn Roll accn Rack Posn Pitch a Rack Posn Yaw accn Rack PosnResultant XYRack Posn Number Wave H Wave T B E E E-04 B B B E E B E B B B B E B B B B B B B B B Table 27: Minimum accelerations in 6 DOF respective rack vs positions 122

133 If one observes Table 26 and Table 27, In general the sea state corresponding to Hs = 4 m and Tp = 10 s was the worst in terms of accelerations for Buoy 1 and Buoy 2. Buoy 1 recorded higher accelerations in surge and heave as compared to Buoy 2. The values presented here are for a 1:16 scale model. On the negative side of the cycle, the maximum accelerations were observed for the same seastate corresponding to Hs = 4 m and Tp = 10 s for both Buoys. 6.5 D: Lateral and Vertical Force on tether vs rack position During the experiments, simulation modeling and Orcaflex TM modeling, the forces for vertical and lateral component on the tether were not separated. There was only tension force that was recorded. In order to resolve this in vertical and horizontal components, the buoy position data was used. From the known buoy position at each time step, the angles with respect to vertical were deduced. These angles are then used to resolve the tensile force on tether in the two respective vertical and horizontal components. For ID 115, the scatter plots of resolved forces vs rack positions are as follows in Figure 66, 67, 68 and Figure 69. Horizontal Force 123

134 Figure 66: Horizontal Wire Force and its distribution with respect to rack position Figure 67: Horizontal Wire Force and its distribution with respect to rack position and number of occurrences Vertical Force 124

135 Figure 68: Vertical Wire Force and its distribution with respect to rack position Figure 69: Vertical Wire Force and its distribution with respect to rack position and its occurrences A table of bins and occurrences was also created that can be easily extended to represent the scenario in a test site with given sea state distributions. 125

136 6.6 E: Wavespring Force vs Rack Position Scatter Plots for all sea states Wavespring force during the experimental stage was simulated to be executed through the motor. Since this is digital, it is expected to have a smooth behavior. This can be seen in Figure 70 and Figure 71 for ID 115. Also plotted is the number of occurrences for different rack positions. 70 Figure 70: Wavespring Force and its distribution with respect to Rack Position 126

137 Figure 71: Wavespring Force and its distribution with respect to Rack Position and number of occurrences 6.7 F: Wire Force vs Rack Position ID 004 Regular wave with parameters given as, Hs 1:16 Hs 1:1 Tp 1:16 Tp 1: Table 28: Wave parameters for ID 004 in simulation model Figure 72 shows the distribution for wire force for a regular wave with parameters listed in Table 28. It is interesting to note how predictable the distribution pattern is. This raises the important point of unreliability of regular wave experiments for studying real life scenarios. 127

138 Figure 72: Wavespring Force vs Rack Position for Regular Wave ID 004 ID 108 Irregular wave with parameters Hs 1:16 Hs 1:1 Tp 1:16 Tp 1: Table 29: Wave parameters for ID 108 in simulation model 128

139 Figure 73: Wavespring Force vs Rack Position for irregular Wave ID 108 As can be seen from the Figure 72 and Figure 73, the wire force is a less predictable for an irregular wave, with parameters in Table 29. In a previous section this force was resolved into two respective components. A bin table was also created to estimate the number of occurrences. 6.8 G: Transmission Force vs Rack Position Scatter Plots for all sea states For ID 115 with parameters in Table 25 we have the following distribution as shown in figure 74 and figure 75, 129

140 Figure 74: Transmission Force and its distribution with respect to rack position Figure 75: Transmission Force and its distribution with respect to rack position and number of occurrences 130

141 6.9 H: Number of Wavespring Cut off events in each sea state The number of Wavespring cut off events corresponds to the number of brakes the mechanism experiences in 30 minutes. These values can be extrapolated to represent values for a period of 20 years. Braking was identified by looking at turning points and checking the number of occurrences when the turning point is higher than 2.5 m. Table 30 shows the number of brake occurrences in 30 min. This information can then be used to dimension the valves. Adjusting the valves might decrease the number of brakes. Braking per 30 min time Table 30: Number of Wavespring Cut off events for a 30 min cycle F: Number of slack events in each sea state For each sea state, it was identified the number of occurrences when the tension in the tether became zero. This indicated a slack in the tether since it cannot take any compressive loads. The number of occurrences were identified for each sea state from the experimental data and tabulated as in Table 31. The number of slack events was identified based on the 23 Analysis done by Corpower Ocean Engineer Gunnar Stein Ásgeirsson 131

142 pretension in the buoy tether. This pretension is measured in the sensor by submerging the buoy in water until a specified marker on the buoy as a starting condition. It was observed that there were no slack events for irregular non survival sea states. For some cases, the tension in the tether came close to zero but did not reach zero. The experiments corresponded to about minutes of runtime. Since the number of slacking occurrences need to be scaled for a 20 year period, the observed slacks can be very large over the lifetime of the buoy. ID No. Number of Slack Events Buoy No. Experiment Type Hs (m) B1 Survival B1 Survival B1 Survival B1 Survival B1 Survival B2 Survival B2 Survival B2 Survival B1 Focus 32 - Table 31: Number of Slack Events for each Case Tp (s) Figure 76 shows a slack event for ID 296 which is a focus wave with a wave height of 32 m. 132

143 Slack Event Figure 76: Slack Event marked at t = 62 seconds with measure subsea force falling below zero 6.11 Discussion Torsion Stress It was observed from yaw angular velocity and acceleration results, that the buoy is yawing considerably. This motion can cause torsion in the attached tether. To overcome this situation, a swivel is placed at the interface that will take care of any twisting motions of the buoy. Due to this addition, there will be negligible torsional stress developed in the tether Number of Break Occurrences As can be seen from Table 30, the number of brake occurrences corresponds to around 2 million brake cycles per year. This is a very big number as the number of oscillations per year corresponds to 5 million. In other words, there is a brake event roughly every 2.5 oscillations. This high number of brake occurrences can be greatly reduced with a proper combination of breaking algorithm and generator control. 24 Another study indicates that the 24 Comment made by Corpower Ocean Scientist - Jørgen Hals Todalshaug 133

144 mechanism of wave to wave generator control strongly reduces the number of braking events Number of Slack Events It was observed that there are negligible slack events that were observed for irregular cases. This implies that during the service condition of the buoy, it will rarely experience slack events or impulsive forces. Although for the survival cases, a number of slack events were observed and this needs further development of survival strategies and further studies in a simulated environment for higher sea states. This is particularly important since these numbers only correspond to 15 minutes of simulated data. If scaled to a lifetime of 20 years, number of slack events can be very large. 25 Result from Master thesis by Tianzhi Zhou which is still in process of completion 134

145 Chapter 7 Conclusions, Limitations and Future WorkXXVII The study was set out to validate the simulation model by comparison with experimental data and generate new data, in the form of Forces, Motions, Equivalent Loads for Fatigue Loading, Uncertainty and tether dimensions, useful for the design team at CPO to develop the WEC. The study also sought in developing tools for analyses and generation of new data for future use. During the process, certain trends in Statistical and Equivalent Fatigue Loads were noticed which have been given possible explanations. The study also delved into investigating WEC interactions in extreme conditions in Orcaflex TM but due certain limitations the results suffered from unreliability. Following this, the study dealt with an uncertainty study using Variation Mode and Effect Analysis for the prediction of the Factor of Safety. Finally, the study culminated with answering secondary objectives added to the scope on a later date. The subject of the thesis was wide and its goals were accomplished by achieving intermediate goals like understanding what Wave Energy was, how it is connected to principles of marine design and mechanics, how the WEC worked, to be able to develop algorithms and finding solutions to objectives. The following list compiles the findings with respect to the major objectives achieved during the study with reference to Section Development Tools A Graphical User Interface with options to compare two different load cases enabled comparison of buoy shapes, mechanisms, sea states and wave type for forces. Two different algorithms in Matlab TM were developed for filtration of raw data, using four alternate filter options, and identifying peaks and recording load statistics like RMS, Mean, H1/10, H1/3 and H1/

146 An algorithm in Matlab TM was developed to estimate equivalent load for a given design life and number of cycles based on Rain Flow Counting and Damage Accumulation Theory. - Load Case Analysis Peak Loads on mooring line were deduced for all the experiments carried out at wave tank test in École Centrale Nantes in They can be found in Appendix 6.On Basis of results, Buoy 1 was chosen as it registered lower forces in comparison with Buoy 2 which results in a less loaded tether and provides greater survivability in extreme conditions. Another observation was that the Wavespring system registered lower forces than the latching system. Some extreme wave conditions were simulated in the wave tank and the forces encountered by the buoy can be found in Table 2 and Table 3 for Buoy 1 and Buoy 2 respectively. On basis of most extreme load for each buoy, cross section of tether was deduced for three materials; regular steel, HSLA steel and Polyester. Of the materials, HSLA steel required the least cross section area for the tether at 85 cm 2 and 86 cm 2 for buoy 1 and buoy 2 while Polyester required the highest cross section area at 508 cm 2 and 516 cm 2 respectively. The simulation model was validated by comparing load cases for irregular waves and Wavespring configuration for both buoys with load cases from experimental tests. For validation, RMS loads were used as a basis for comparison. The ratio of Simulated RMS loads to Experimental RMS loads was found to lie between 1.03 and The Simulation model was deemed reasonable and formed basis for data generation for other objectives. The higher prediction by the simulation model was attributed to it being a 2 DOF model instead of a realistic 6 DOF model which caused amplification in heave and surge responses following the principle of conservation of energy. A similar ratio between Peak loads of simulated data and experimental data varied between 1.19 and From the validated simulated model, data for all missing sea states in Figure 8 were generated for target site Yue, the results for which have been compiled in Appendix 7. The most extreme peak load was identified as 4.18 MN for wave height 7.5 m and time period 13 s. The cross section of the tether was determined on basis of this load 136

147 for three materials of steel, HSLA steel and Polyester. HSLA steel gave the lowest cross section as cm2. Survival sea states that could not be tested during wave tank experiments were simulated in Orcaflex TM and buoy accelerations in heave and surge were extracted. But the results suffered from unreliability as the model over predicted parameters. Additionally, videos were generated to show the motion of the buoy under the influence of waves which were used to identify critical snap events and test two buoy survival strategies of latching and free moving. It was found that latching the buoy proved a better strategy. Equivalent Load and fatigue damage for all sea states were generated for Yue for a design life of 25 years and one million cycles in Table 16 and Table 18. The cumulative damage for 25 years at Yue was found to be x and equivalent load as 2682 kn. - Statistical Analysis The uncertainties in theory, modeling and literature based on experimental findings were treated and quantified to assess the overall uncertainty in predicting design loads. The overall uncertainty was transformed into a factor of safety which was calculated for steel as 1.41 and for polyester as Secondary Objectives On basis of simulation model generated data, interesting trends of buoy internal forces in relation with rack position were recorded and can be found in Chapter 6 Slack events were investigated numerically and it was observed that for irregular non survival sea states, no slack events were observed. This has a great positive repercussion on the survivability of the buoy in normal operational conditions. There was a braking event roundabout every 3 cycles and this inspires the need to optimize the generator wave control to reduce the number of braking events that causes a loss of efficiency. The work in the thesis was very extensive and multifaceted and hence it was not possible to make one specific conclusion or answer a specific question but provide several answers and data for development of WEC. The work done was very interesting and rewarding from a knowledge point of view but there were a few limitations, which are, 137

148 Lack of 6 DOF simulation model. Its repercussions were, o The simulation model always over predicted the forces on the buoy in surge and heave. o The rotational motions of the buoy could not be studied or compared with experimental results. Absence of Orcaflex TM software access at CPO. Its repercussions were, o Higher Survival sea state results from Simulation Model could not be validated with software generated results. o Buoy motions could not be generated for the missing 4 DOF in simulation model Lack of previous Hydrodynamic study on Buoy response in waves. o Certain trends like flattening of equivalent load at sea states beyond 2 m, was explained on logic instead of theoretical backing The study has offered an evaluative perspective on wave energy technology and the following work for the future can be envisaged. There have been several design changes since the previous experiments were carried out. It would be particularly interesting to test a scaled buoy with PTO and check its performance. Since data could not be obtained for higher survival sea states it would be interesting to perform the tests in a larger wave tank to get data corresponding to extreme cases. The Orcaflex TM model tended to overestimate the buoy accelerations and forces on the components. It would be interesting to further study the modeling and incorporate a more exhaustive buoy design with internal moving parts. Fatigue analysis for the internal frames and connectors could be studied for stresses in an FEM atmosphere. These parts were not simulated in the simulation model and it would be great to study these parts in depth. In spite of development several wave energy technologies in the past, we are yet to see a fully commercial unit. The WEC by CPO has made a great effort in its innovative approach to envisage the wave energy converter. The data produced so far looks sturdy and I feel confident that this technology could one day provide power for us in a green way. 138

149 139

150 List of Figures Figure 1: Summary of Advantages of Wave Energy Device by Corpower Ocean... 7 Figure 2: Schematic of WEC... 8 Figure 3: Buoys that are under investigation 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..12 Figure 5: Wave Tank Testing Facility at École Centrale de Nantes in Figure 6: CAD representation of Buoy in Wave Tank with device to measure tension in tether 18 Figure 7: Picture showing bright white lights installed on buoy to record the 6 DOF motion of buoy Figure 8: Seastates that were tested in the wave tank (marked by yellow boxes) Figure 9a: Identified Locations where Wave Energy Device can be potentially used 1. (source Wikimedia) VIII Figure 9b: Identified Locations color coded according to energy potential. 1. (Source: wikimedia) Figure 10: Schematic of how an Oscillating Water Column works. (Image Courtesyen.openei.org) Figure 11: Schematic of an Overtopping type of wave energy converter (Image Courtesyen.openei.org) 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) Figure 14: Heaving Buoy (Point Absorber) type of Oscillating Body WEC (Image Courtesyen.openei.org) Figure 15: The axis for the coordinate system

151 Figure 16: Classification of wave forces for different geomtry ranges against incoming wave lenghts (Source: Marilena Greco Lecture Notes TMR4215: Sea Loads, NTNU) Figure 17: Slow Drift motions in opposite direction of wave due to viscous effects Figure 18: Flow past a cylinder Figure 19: Flow separation for different flow regimes Figure 20: Stress Strain Relationship for Structural Steel Figure 21: Typical S-N (Stress vs Number of Loading Cycles) Curve Figure 22: Clubbing of stresses according to Palmgren Miner Rule (Source: Wikipedia) Figure 23: Graphic Use Interface for Orcaflex TM Figure 24: Illustration of the influence of uncertainty during the design process (Source: Svensson & Sandström, 2014 XXIV ) Figure 25: Table of sea states that needs to be filled in to complete Load Analysis Figure 26: Seastates that were tested in the wave tank (marked by yellow boxes) Figure 27: Unfiltered Data for Heave Acceleration Figure 28: Comparison of filtered and unfiltered data (green is filtered data and blue is unfiltered data) Figure 29: Differential of Heave Acceleration to filter out differentials lower than defined threshold Figure 30: Final acceleration time series (Left figure shows only acceleration peaks while right figure shows steepness of successive peaks) Figure 31: Sorted Peaks in order of magnitude Figure 32: Frequency of occurrence of peaks Figure 33: Pretension force at the start of the experiment Figure 34: Zoomed in portion of the pretension force Figure 35: Rain Flow Counting output for 3 input stress value Figure 36: Output from a Rain Flow Countine Method Script

152 Figure 37: Subsea Force after time series snipping based on start and end time Figure 38: Plot showing the rainflow cycles before (RED) and after (GREEN) filtration Figure 39: Rainflow Cycles with minima on X axis and maxima on Y axis for any given cycle Figure 40: Load Spectrum with load cycle amplitudes and frequency of occurrence and Level Crossings distribution for estimating how many cycles cross which magnitude Figure 41: GUI for running simulations of WEC for given set of input parameters Figure 42: Output GUI after simulation is completed Figure 43: The two Buoy Geometries that are input into Orcaflex TM Figure 45: GUI for loading data files for comparison Figure 46: Result GUI with options to compare two different data files Figure 47: Ratio of RMS Loads between simulation loads and experimental loads for force on the buoy tether in irregular waves. Top half of table represents Buoy 1 for Wavespring and Bottom Half of table represents Buoy 2 for Wavespring Figure 48: Variation of Fatigue Equivalent Load for 25 years with Wave Height Figure 49: Variation of Fatigue Equivalent Load for 25 years with Time Period Figure 50: Variation of Peak Loads for 25 years with Wave Height Figure 51: Variation of Peak Loads for 25 years with Time Period Figure 52: Buoy acceleration (m/s 2 ) in heave direction vs rack position (m) Figure 53: Buoy acceleration (m/s 2 ) in heave direction vs rack position (m) and their occurrences Figure 54: Buoy acceleration (m/s 2 ) in surge direction vs rack position (m) Figure 55: Buoy acceleration (m/s 2 ) in surge direction vs rack position (m) and their occurrences Figure 56: Buoy acceleration (m/s 2 ) in sway direction vs rack position (m) Figure 57: Buoy acceleration (m/s 2 ) in sway direction vs rack position (m) and their occurrences Figure 58: Buoy acceleration (degree/s 2 ) in pitch direction vs rack position (m)

153 Figure 59: Buoy acceleration (degree/s 2 ) in pitch direction vs rack position (m) and their occurrences Figure 60: Buoy acceleration (degree/s 2 ) in Roll direction vs rack position (m) Figure 61: Buoy acceleration (degree/s 2 ) in Roll direction vs rack position (m) and their occurrences Figure 62: Buoy acceleration (degree/s 2 ) in yaw direction vs rack position (m) Figure 63: Buoy acceleration (degree/s 2 ) in yaw direction vs rack position (m) and their occurrences Figure 64: Buoy acceleration (m/s 2 ) in XY plane vs rack position (m) Figure 65: Buoy acceleration (m/s 2 ) in XY plane vs rack position (m) and their occurrences Figure 66: Horizontal Wire Force and its distribution with respect to rack position Figure 67: Horizontal Wire Force and its distribution with respect to rack position and number of occurrences Figure 68: Vertical Wire Force and its distribution with respect to rack position Figure 69: Vertical Wire Force and its distribution with respect to rack position and its occurrences Figure 70: Wavespring Force and its distribution with respect to Rack Position Figure 71: Wavespring Force and its distribution with respect to Rack Position and number of occurrences Figure 72: Wavespring Force vs Rack Position for Regular Wave ID Figure 73: Wavespring Force vs Rack Position for irregular Wave ID Figure 74: Transmission Force and its distribution with respect to rack position Figure 75: Transmission Force and its distribution with respect to rack position and number of occurrences Figure 76: Slack Event marked at t = 62 seconds with measure subsea force falling below zero Figure 77: Components of a Gas Turbine Jet Engine XVIII

154 Figure 78: Gas Turbine Blade and varying strain and temperature distributions during operation XVIII Figure 79: Scatter of Strain measured on a turbine blade after different cycles of loading XVIII. 154 Figure 80: Crack initiation in notches and its propagation trajectory as seen through FEM Analysis XIX Figure 81: Design improvements to improve the fatigue strength in mechanical parts XIX

155 List of Tables Table 1: Specification of Wave Tank Testing Facility Table 2: Summary of Peak Forces acting on the tether for Buoy 1 for Survival Sea States for a full scale buoy (The negative sign is an indication of tensile loads) Table 3: Summary of Peak Forces acting on the tether for Buoy 2 for Survival Sea States for a full scale buoy (The negative sign is an indication of tensile loads) Table 4: Assessment of Minimum cross-section area of tether based on yield strength and Maximum Experimental Loads in Wave Tank Test at Nantes, Table 5: Equivalent Loads for Fatigue Design Life of 25 years and 1 million cycles in irregular seas for Buoy Table 6: Equivalent Loads for Fatigue Design Life of 25 years and 1 million cycles in irregular seas for Buoy Table 7: Fatigue Loads, Design Life and Equivalent Load for Buoy 1 for 1:16 scale model in irregular waves Table 8: Fatigue Loads, Design Life and Equivalent Load for Buoy 2 for 1:16 scale model in irregular waves Table 9: Ratio of Peak Forces in tether obtained from experimental and simulation model for Buoy 1 and Buoy Table 10: Peak Loads in N for a full scale buoy recorded on the tether based on simulation data Table 11: Mean Loads in N for a full scale buoy recorded on the tether based on simulation data Table 12: RMS Loads in N for a full scale buoy recorded on the tether based on simulation data Table 13: A 1/10 Loads in N for a full scale buoy recorded on the tether based on simulation data

156 Table 14: Assessment of Minimum cross-section area of tether based on yield strength and Maximum Simulation Loads in Wave Tank Test at Nantes, Table 15: Equivalent Loads in N for a full scale buoy for fatigue predicted for the tether based on simulation data Table 16: Life time damage for full scale buoy due to fatigue predicted for the tether based on simulation data at Yue Table 17: Normalized Scatter distribution of different sea states for target site Yue Table 18: Life Time Damage distribution of different sea states for target site Yue Table 19: Summary of accelerations (surge and heave) on Buoy 1 under survival conditions - Survival Strategy Table 20: VMEA results for steel tether based on experimental data Table 21: VMEA for polyester tether based on experimental data Table 22: Reliability and factor of safety for Steel and Polyester tethers for experimental data Table 23: Final count of data points after reduction based on above algorithm Table 24: Scatter Distribution of each Sea State at offshore site name Yue Table 25: Wave Parameters for ID Table 26: Maximum accelerations in 6 DOF vs respective rack positions Table 27: Minimum accelerations in 6 DOF vs respective rack positions Table 28: Wave parameters for ID 004 in simulation model Table 29: Wave parameters for ID 108 in simulation model Table 30: Number of Wavespring Cut off events for a 30 min cycle Table 31: Number of Slack Events for each Case Table 31: Table of scaling factors for different parameters related to buoy water interaction 159 Sea states and their notations analyzed in experiments and software (Grayed sea states were analyzed in ORCAFLEX TM and white sea states were tested in a wave tank) Cases tested in Orcaflex TM with Wave Spectrum Type used for analysis

157 References [I] Key World Energy Statistics. International Energy Agency URL /publications/freepublications/publication/keyworld2014.pdf [II] The CorPower Wave Energy Converter. Official Website. URL corpower-technology/corpower-wave-energy-converter/ [III] J. Falnes and P.M. Lillebekken. Budal's latching-controlled-buoy type wave-power plant. 5th European Wave Energy Conference 2003, paper H1, submitted , revised URL [IV] J. Falnes. Principles for capture of energy from ocean waves. phase control and optimum oscillation. URL [V] A. Babarit and A.H. Cl ement. Optimal latching control of a wave energy device in regular and irregular waves. Applied Ocean Research (2): DOI: /j.apor URL _Wave_Energy_Device_in_Regular_and_Irregular_Waves [VI] A. Babarit, G. Duclos, and A.H. Clem ent. Benefit of latching control for a heaving wave energy device in random sea th Int Offshore and Polar Engineering Conference, volume 1, pages , URL _of_latching _control_for_heaving_wave_energy_device_in_random_sea [VII] M.F.P. Lopes, J. Hals, R.P.F.Gomes, T. Moan, L.M.C. Gato, and A.F.deO. Falc ao. Experimental and numerical investigation of non-predictive phase-control strategies for a point-absorbing wave energy converter URL

158 [VIII] Santoña and Mutriku. Usefulwaves. URL 02/17/santona-and-mutriku/ [IX] Andrew M. Cornett. A global wave energy resource assessment.2008 Conference: International Offshore and Polar Engineering Conference, At Vancouver, Canada, Volume: ISOPE-2008-TPC-57 URL _assessment [X] Antonio F. de O. Falcao. Wave energy utilization: A review of the technologies Renewable and Sustainable Energy Reviews 14 (2010), page , URL net/publication/ _wave_energy_utilization_a_review_of_the_technologies [XI] Wave Power Wikipedia Page. URL [XII] Wave Energy Converters. URL [XIII] Nicole Johnson and Eric Olson. What is an oscillating water column? University of Wisconsin Madison, URL /presentationnovideos.pptx. [XIV] Energy and the Environment-A Coastal Perspective. Oscillating water column, URL [XV] O.M.Faltinsen: Sea Loads on Ships and Offshore Structures, Cambridge University Press, URL [XVI] Richard Fitzpatrick. Boundary Layer Separation in Fluid Mechanics. URL as.edu/teaching/336l/fluidhtml/node90.html 148

159 [XVII] SMS-491: Physical solutions of everyday problems in aquatic sciences. URL [XVIII] Tatsuo Endo and M. Matsuishi; 1968; The Rainflow Method in Fatigue URL [XIX] Stress Life Diagram (S-N Diagram) URL N%20diagram.pdf [XX] Thomas Svensson and Pär Johannesson; 2013; Reliable fatigue design, by rigid rules, by magic or by enlightened engineering. Fatigue Design 2013, International Conference Proceedings. URL [XXI] Orcaflex Software Official Website. URL [XXII] Orcaflex Software Official Website URL OrcaFlex/ [XXIII] Dawn An, Joo-Ho Choi, Nam H. Kim and Sriram Pattabhiraman Fatigue life prediction based on Bayesian approach to incorporate field data into probability model. Structural Engineering and Mechanics, Vol. 37, No. 4 (2011) URL Papers/paper50.pdf [XXIV] T. Svensson, J. Sandström.2014.Load/Strength analysis of wave energy components. SP Rapport 2014:80. URL [XXV] Johansson, P., Chakhunashvili, A., Barone, S., Bergman, B., 2006, Variation Mode and Effect Analysis: a Practical Tool for Quality Improvement, Quality and Reliability Engineering International, Vol. 22, pp URL qre.773/abstract [XXVI] Johannesson, P., and Speckert, M. (editors) (2014): Guide to Load Analysis for Durability in Vehicle Engineering. ISBN Wiley: Chichester. URL WileyCDA/WileyTitle/productCd html 149

160 [XXVII] Elements for writing a good Conclusion Chapter URL downloads/4be165997d2ae_writing_the_conclusion_chapter,_the_good,_the_bad_and_the _Missing,_Joe_Assan%5B1%5D.pdf [XXVIII] B. A. Cowles High cycle fatigue in aircraft gas turbines an industry perspective, 1996, International Journal of Fracture April 1996, Volume 80, Issue 2-3, pp [XXIX] Dragi Stamenković, Katarina Maksimović, Vera Nikolić-Stanojević, Stevan Maksimović, Slobodan Stupar, Ivana Vasović, 2010, Fatigue Life Estimation of Notched Structural Components. Strojniški vestnik - Journal of Mechanical Engineering 56(2010)12, , UDC 629.7: URL _2010_046_Stamenkovic_3k.pdf. [XXX] Mikael Razola, 2014, Peak Identification Methods, URL System/DownloadDocumentFile.ashx?DocumentFileKey=a5d4fb9a ef-963f- 5017f03d78f1 [XXXI] John Zseleczky, 2012, Behind the Scenes of Peak Acceleration Measurements, The Third Chesapeake Power Boat Symposium Annapolis, Maryland, June 2012 URL org/higherlogic/system/downloaddocumentfile.ashx?documentfilekey= ff a9b5e [XXXII] Molin B, Second-order hydrodynamics applied to moored structures. A state-of-the-art survey. Ship Technology Research. 41, URL [XXXIII] Malenica S et al, Wave and current forces on a vertical cylinder free to surge and sway. Applied Ocean Research, 17, URL publication/ _wave_and_current_forces_on_a_vertical_cylinder_free_to_surge_an d_sway 150

161 [XXXIV] Johannes. Falnes. Cambridge University Press, Ocean Waves and Oscillating Systems. URL /CBO [XXXV] Wave Energy Converters URL energy_converters [XXXVI] Aranha J A P, A formula for wave drift damping in the drift of a floating body. J. Fluid Mech. 275, URL /displayabstract?frompage=online&aid=

162 Appendix 1 WAFO Toolbox WAFO is a toolbox of Matlab TM routines for statistical analysis and simulation of random waves and random loads. 26 The toolbox has tools for the following calculations. Fatigue Analysis Fatigue life prediction for random loads Theoretical density of rainflow cycles Sea modelling Simulation of linear and non-linear Gaussian waves Estimation of seamodels (spectrums) Joint wave height, wave steepness, wave period distributions Statistics Extreme value analysis Kernel density estimation Hidden Markov models

163 Appendix 2 Review of Structures that undergo extensive Fatigue Loading Two cases have been presented and discussed here. Gas Turbine Components in Jet Engines A typical gas turbine is composed of components as shown in Figure 77. In particular, the turbine is subjected to high cycle fatigue loads. This is the single largest cause of component failure in modern military gas turbine engines. XXVIII. Figure 77: Components of a Gas Turbine Jet Engine XVIII The gas turbine is essentially a propeller with multiple blades coming out of a pod as shown in figure 78. The blade of the turbine is subjected to repeating negative and positive pressure distributions. This results in high frequency cyclic loads on the blade. The problem is further accentuated by the presence of temperature fluctuations. This high frequency of cyclic loading abbreviated as HCF is what causes the turbine blades to fail during operation at loads much lower than yield strength of blade material. 153

164 Figure 78: Gas Turbine Blade and varying strain and temperature distributions during operation XVIII Figure 79, shows the distribution of strain on the blade against the number of load cycles. It can be observed, as the number of cycles increase, the allowable strain range keeps decreasing which indicates failing resistance against cracking. We can follow the minimum curve (dotted line) to design a part but this often leads to over dimensioning. Several statistical methods like Bayesian Approach and VMEA have been developed to calculate more realistic outputs. VMEA (Variation Mode and Effect Analysis) will be used in this report to assess the fatigue in the WEC. Figure 79: Scatter of Strain measured on a turbine blade after different cycles of loading XVIII 154

165 Notched Structural Components Surface and through-thickness cracks are a common occurrence in holes and at notches in structural components. It is interesting to note that, such cracks are present during a large percentage of the useful life of these components. XXIX These cracks originate as micro cracks which slowly propagate until they become critical enough to cause failure. Figure 80 shows the typical places where cracks due to fatigue originate and propagate. These areas represent areas where stress concentrations are present and over repeated loading cycles, these areas are much more susceptible to failure than other parts. Figure 80: Crack initiation in notches and its propagation trajectory as seen through FEM Analysis XIX For notches and holes, as concluded by the paper Fatigue Life Estimation of Notched Structural Components 19, fatigue analysis can be done with fair accuracy using an FEM environment. They had good correlation between experimental and computational results. Based on analysis, fatigue strength can be increased in notches and holes by making design changes as shown in Figure

166 156

167 Figure 81: Design improvements to improve the fatigue strength in mechanical parts XIX 157

168 Appendix 3 Scaling of WEC from experimental model to life size model Based on Ocean Wave Theory, scaling from experimental model to real life model is done best using Froude Scaling. Froude number is the ratio between inertia and gravitational force. It is hence useful in ensuring dynamic scaling between model and full scale is maintained. Froude scaling ensures gravity forces are correctly scaled. Since waves in the ocean are gravity waves, Froude scaling ensures that wave resistance and wave forces are correctly scaled. (43) Then dynamics similarity can be achieved by equating the Froude numbers for model and full scale as follows, (44) where U is the relative velocity between body and fluid and L is the length of body along the direction of flow. By using Froude scaling we compromise on the viscous scaling and surface tension effects due to water s viscosity. Since this is of minor importance, it can be ignored. Given below in Table 31 are Froude scaled factors for different parameters that are used as part of the analysis. 158

169 Table 31: Table of scaling factors for different parameters related to buoy water interaction 159

170 Appendix 4 Sea States and Notations investigated in Tank Tests and OrcaflexTM The following table lists all sea state parameters and associated symbols, Seastate Notation Wave (s) Period Wave (m) Height Seastate Notation Wave (s) Period Wave (m) Height I OF I OF I OF I OF I OF I S I S I S I S OF S OF S Sea states and their notations analyzed in experiments and software (Grayed sea states were analyzed in ORCAFLEX TM and white sea states were tested in a wave tank) 160

171 Cases tested in Orcaflex TM with Wave Spectrum Type used for analysis. Water depth H s T p γ Wave spec. State no. [m] [m] [s] type OF1 25,00 3,00 4,2 5,0 JONSWAP OF2 25,00 1,50 5,7 1,5 JONSWAP OF3 25,00 3,00 5,7 5,0 JONSWAP OF4 25,00 4,50 5,7 5,0 JONSWAP OF5 25,00 5,50 7,1 5,0 JONSWAP OF6 25,00 6,50 8,5 5,0 JONSWAP OF7 25,00 7,50 9,9 4,9 JONSWAP OF8 25,00 8,50 11,3 3,6 JONSWAP OF9 25,00 8,50 12,7 2,1 JONSWAP OF10 40,00 8,50 12,0 2,8 JONSWAP OF11 40,00 10,50 14,0 2,2 JONSWAP OF12 40,00 11,00 16,0 1,2 JONSWAP OF13 40,00 11,00 18,0 1,0 JONSWAP OF14 40,00 11,00 20,0 1,0 JONSWAP 161

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

173 163