INVESTIGATION OF THE ROBUSTNESS OF AN OSCILLATING WATER COLUMN BREAKWATER UNDER EXTREME WAVE CONDITIONS BY INÉS BÁEZ RIVERO

Transcription

1 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero INVESTIGATION OF THE ROBUSTNESS OF AN OSCILLATING WATER COLUMN BREAKWATER UNDER EXTREME WAVE CONDITIONS BY INÉS BÁEZ RIVERO I

2 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero II

3 ERASMUS +: ERASMUS MUNDUS MOBILITY PROGRAMME Master of Science in COASTAL AND MARINE ENGINEERING AND MANAGEMENT CoMEM Investigation of the robustness of an Oscillating Water Column breakwater under extreme wave conditions Delft University of Technology 10 July 2018 Inés Báez Rivero

4 The Erasmus+: Erasmus Mundus MSc in Coastal and Marine Engineering and Management is an integrated programme including mobility organized by five European partner institutions, coordinated by Norwegian University of Science and Technology (NTNU). The joint study programme of 120 ECTS credits (two years full-time) has been obtained at two or three of the five CoMEM partner institutions: Norges Teknisk- Naturvitenskapelige Universitet (NTNU) Trondheim, Norway Technische Universiteit (TU) Delft, The Netherlands Universitat Politècnica de Catalunya (UPC). BarcelonaTech. Barcelona, Spain University of Southampton, Southampton, Great Britain City, University London, London, Great Britain During the first three semesters of the programme, students study at two or three different universities depending on their track of study. In the fourth and final semester an MSc project and thesis has to be completed. The two-year CoMEM programme leads to a multiple set of officially recognized MSc diploma certificates. These will be issued by the universities that have been attended by the student. The transcripts issued with the MSc Diploma Certificate of each university include grades/marks and credits for each subject. Information regarding the CoMEM programme can be obtained from the programme coordinator: Øivind A. Arntsen, Dr.ing. Associate professor in Marine Civil Engineering Department of Civil and Transport Engineering NTNU Norway Telephone: Cell: Fax: oivind.arntsen@ntnu.no CoMEM URL:

5 CoMEM Master Thesis This thesis was completed by: Inés Báez Rivero Under supervision of: Prof.dr.ir. Aarninkhof, S.G.J. Dr. ir. Bricker, J.D. ir. Jarquin Laguna, A. As a requirement to attend the degree of Erasmus+: Erasmus Mundus Master in Coastal and Marine Engineering and Management (CoMEM) Taught at the following educational institutions: Norges Teknisk- Naturvitenskapelige Universitet (NTNU) Trondheim, Norway Technische Universiteit (TU) Delft Delft, The Netherlands University of Southampton, Southampton, Great Britain At which the student has studied from August 2016 to July 2018.

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7 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero ACKNOWLEDGEMENT This thesis completes the Master of Science in Coastal & Maritime Engineering and Management (CoMEM) program carried out between the Norwegian University of Science and Technology (NTNU), Delft University of Technology (TUDelft), and the University of Southampton. My interest in renewable sources with low environmental impact evokes in me the attention to Wave Energy Converters (WEC). During my undergraduate studies in civil engineering I was able to develop a bachelor thesis in a related topic; Investigation of accumulator efficiency for application in WEC systems. Nowadays Oscillating Water Columns (OWCs) represent a promising source of renewable energy, using the action of waves. The efficiency of existing designs keeps improving and evolving to provide better and optimum results. I would like to thank the effort, considering the tight schedule of the WaterLab, to Sander Varder and the rest of the technicians and staff for their big support and help, specially managing time and helping me to do the experiments in such a short period of time. Thanks to all the members of my committee, for the good guidance during the meetings and along the process. Thanks to Jeremy Bricker, my daily supervisor, for being always available to meet with me and for his positive attitude and great support. Finally, thanks to friends and family. To my CoMEM family, thanks for making this adventure so special. I am really and truly grateful for each and one of you and the time shared. Thanks to Albert, Michelle, Tom, Chris and Charles for their support, the laughs and all the great moments shared during the thesis time. A special thanks to Nader Naderi, for all the long talks and the straggle moments figuring out the Cluster and ANSYS among others. To the rest of the CoMEMembers all over the world, thanks for all your love. To my closer friends, thanks for being there whenever I needed a kind word. A special thanks to Dácil, my favourite aerospace engineer, for your friendship along the years, I hope you enjoy reading this thesis. To my family, sister and parents, thanks for your love, generosity, energy, encouraging words, support and love. I feel really lucky to have such a great family. Gracias por ser mis remos, porque ningún mar en calma hizo experta a una marinera. Dedicated, with all my love in memory of Encar. Inés Báez Rivero Delft, July 2018 VII

8 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero SUMMARY The work presented will investigate the usage of Oscillating Water Columns (OWC) in Coastal Structures to understand the functionality requirements and the viability of installing these devices in caisson breakwaters. The main focus is put on the efficiency of the design, to achieve optimum results and to avoid possible failure of the structure. Comparison of different designs, J-OWC and U-OWC, and their behaviour under extreme conditions will be analysed to determine the most suitable design. The first phase of this work, is the validation of the model. Laboratory experiments of an OWC near design operating conditions are conducted in the WaterLab facilities at TUDelft. These laboratory results will validate the numerical models carried out using ANSYS Fluent. The second phase of this work will consist of a numerical modelling to investigate the response of the OWC to the extreme wave conditions experienced by the Mutriku, Spain OWC during the storm of Finally, the structural response of the OWC will be analysed, using MIDAS Civil. Since 1970s, the first prototypes of OWC were design and tested. This technology has improved considerably, however there are still issues in the field that can be improved. It is expected that with the reproduction of the numerical model, improvements for higher efficiency of the OWC can then be applied in the analysis for further incorporation on coastal structures, focusing in caisson breakwaters in this master thesis. KEYWORDS Wave Energy Converter (WEC) Oscillating Water Column (OWC) Structure robustness Caisson Breakwater VIII

9 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero TABLE OF CONTENTS ACKNOWLEDGEMENT...VII SUMMARY... VIII Keywords... VIII TABLE OF CONTENTS... IX LIST OF FIGURES... XI LIST OF TABLES... XIII INTRODUCTION... 1 Aim & Objectives...2 Motivation Renewable energy sources - WEC Environmental impacts Social impacts... 3 Research significance Current State of Research Economics and Capacity Knowledge Gaps... 5 Scope and Research Objectives Research Question Research Approach... 6 Thesis Outline...7 LITERATURE REVIEW... 8 General Background Marine Renewable Energy - Social, Environmental and Economic Effects... 9 OWC Evolution and Current State of Research Current Research on Analytical models Current Research on Force Loading Distribution Research on geometry optimization Classification of WEC concept Oscillating Water Column Principle of Operation Advantages and Disadvantages of shoreline water devices - OWC Resonance in an OWC Shoreline OWCs and their Application Breakwaters IX

10 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero Caisson Breakwater Integration of OWC into Caisson Breakwater Development and Case Studies Comparison of Designs J-OWC Design U-OWC Design Failure Mechanisms Case Study: Mutriku Turbines RESEARCH METHODOLOGY Introduction Methods of modelling Experimental se-up of the Laboratory tests Laboratory experiments characteristics CFD Modelling Set-up of the Numerical Model of the OWC ANSYS Boundary conditions RESULTS, OUTCOMES AND RELEVANCE OF THE VALIDATION Validation Results J-OWC shape Fully Open J-OWC shape Partially Open U-OWC shape Fully Open Conclusions of the chapter CASE STUDY: MUTRIKU OWC PLANT Case Study Results: Mutriku (Spain) Mutriku Results: L.W.L and 8 meters wave height Mutriku Results: L.W.L and 13.7 meters wave height Mutriku Results: MIDAS Civil Analysis Mutriku Results: Failure of the Structure Conclusions of the chapter CONCLUSIONS & RECOMMENDATIONS Conclusion Limitations Recommendations BIBLIOGRAPHY X

11 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero LIST OF FIGURES Figure 1 - Wave pressure distribution for a Caisson Breakwater structure (Mustapa et al., 2017) Figure 2 - OWC classification based on several aspects of WECs Figure 3 OWC PTO system Figure 4 - Percentage of wave energy development (Mustapa et al., 2017) Figure 5 Oscillating Water Column design Figure 6 - Example of resonance values for an OWC time-averaged power amplitude for constant turbine parameters (Kelkitli, 2018) Figure 7 - OWC - Estimation of the natural frequency Figure 8 -Fixed breakwater classification (Mustapa et al., 2017) Figure 9 - Conventional caisson breakwater with vertical front wall (Mustapa et al., 2017) Figure 10 - OWC plant integrated into a breakwater at Sakata harbour, Japan, Rated power 60 kw (Falcão and Henriques, 2016) Figure 11 OWC caisson breakwater shape with dimensions at Sakata harbour (Suzuki and Port, 2004) Figure 12 - PICO OWC plant (Portugal, 1999) (Falcão and Henriques, 2016) Figure 13 - Discretization of the plant and surrounding rocky bottom and coastline (Falcão, Henriques and Gato, 2016) Figure 14 - LIMPET OWC plant, at the island of Islay, Scotland, UK (Falcão and Henriques, 2016) Figure 15 -Comparison of J-OWC and U-OWC shape Figure 16 - Probability of annual exceedance of waves (y-axis showing the wave height and x-axis showing return period) Figure 17 - Picture of Mutriku OWC - highlight of failed sections (Memoria, 2009) Figure 18 - Detailed picture of failure at Mutriku OWC (Memoria, 2009) Figure 19 (a) Wells turbine, (b) Impulse turbine (Czech and Bauer, 2012) Figure 20 - OWC model in the Laboratory facilities at TUDelft (left front view, right back view) Figure 21 -Working principle of an OWC Figure 22 Cross-section of the J-OWC design with top part close Figure 23 - Cross-section of the J-OWC design with top part partially open Figure 24 - Cross-section of the J-OWC design with top part open Figure 25 - Cross-section of the U-OWC design with top part close Figure 26 - Cross-section of the U-OWC design with top part open Figure 27 Side view of the ANSYS-Fluent model XI

12 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero Figure 28 Validation of ANSYS-Fluent results for the front wall pressure sensor for a J- OWC when the top part of the OWC is open Figure 29 - Validation of ANSYS-Fluent results for the back-wall pressure sensor for a J- OWC when the top part of the OWC is open Figure 30 - Validation of ANSYS-Fluent results for the resonance oscillation inside of a J-OWC when the top part of the OWC is open Figure 31 - Comparison of the validation results for the resonance oscillation inside of a J-OWC when the top part of the OWC is partially open and when is fully open. 42 Figure 32 - Validation of ANSYS-Fluent results for the front wall pressure sensor for a U-OWC when the top part of the OWC is open Figure 33 - Validation of ANSYS-Fluent results for the back-wall pressure sensor for a U- OWC when the top part of the OWC is open Figure 34 - Validation of ANSYS-Fluent results for the resonance oscillation inside of a U-OWC when the top part of the OWC is open Figure 35 - Pressure points at Mutriku-OWC Figure 36 - Comparison of the five different geometries for 8 meters wave height when Low Water Level Figure 37 - Comparison of the five different geometries for 13.7 meters wave height when Low Water Level Figure 38 - Comparison of the OWC geometries front wall displacement for 8 meters wave conditions when LWL Figure 39 - Comparison of the OWC geometries front wall displacement for 13.7 meters wave conditions when LWL Figure 40 - Comparison of the OWC geometries back wall displacement for 8 meters wave conditions when LWL Figure 41 - Comparison of the OWC geometries back wall displacement for 13.7 meters waves conditions when LWL Figure 42 Comparison of the internal pressures in the front wall for the different geometries and wave conditions Figure 43 - Comparison of the internal pressures in the back wall for the different geometries and wave conditions Figure 44 - Change in the water level inside the OWC for the different storm conditions Figure 45 Comparison of the validation of ANSYS-Fluent results for the resonance oscillation inside of a U-OWC when the top part of the OWC is open, with different wall frictions situations Figure 46 -Detailed of the comparison of the validation of ANSYS-Fluent results for the resonance oscillation inside of a U-OWC when the top part of the OWC is open, with different wall frictions situations XII

13 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero LIST OF TABLES Table 1 Summary of the OWC (Falcão and Henriques, 2016) Table 2 - Wave conditions considered on the laboratory experiments Table 3 - Static pressures in the external part of the front wall Table 4 - Static pressures in the internal part of the front wall Table 5 - Static pressures in the internal part of the back wall XIII

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15 1. INTRODUCTION Chapter Summary Wave power is a pollution-free way to generate electricity, providing clean energy and protecting the environment in the process. In order to reduce the impact of human evolution and societal needs, renewable energies are a good option to consider in the long term. Solar and wind sources are the most visible leaders, but hydropower, produced from tidal and waves, has also been in the market for a long time, improving and evolving to better designs. Wave power energy devices capture the energy or power of the waves to transform it into electricity. The great potential of waves is unequivocal, although the development into a more competent market division is still developing, not being yet commercially capable of meet prospects (Howe and Nader, 2017). For a better understanding and predictability in the behaviour and interaction of the waves with WEC systems, this paper investigates the process of the waves arriving to the WEC. Further information is presented in Appendix A Ocean Wave Energy and Relation with Oscillating Water Columns. Numerical models are then used to examine the interaction of the waves with the structure and analyse its robustness under extreme wave conditions. 1

16 1. Introduction AIM & OBJECTIVES The paper deals with the development of OWC, a mechanical wave energy converter (WEC) near shore, that can be incorporated into breakwater structures. Different topics are addressed; theoretical background for a better understanding for the reader of why this renewable energy device is important nowadays. Some basic concepts on waves and energy conversion are addressed in this paper, with further detailed in appendix A. Likewise, presented advantages and disadvantages related to wave energy, information about nearshore OWC devices and the incorporation of these in sea defence structures, focusing for this master thesis in caisson breakwaters. With this development, I intend to reach a better understanding of which is the best way to combine sea defence structures with water power converters. The first objective of this paper will be to investigate and explore existing wave power converter knowledge and benefits or barriers when using them. Numerical and physical modelling will be used to represent different designs of OWC, J- OWC and U-OWC, and to analyse the response of its interaction with waves under extreme conditions. Designs will be based on different case studies, of existing and developing ideas. Focusing on a specific case study in Mutriku, Spain. Taking the failure of this device under a storm event in 2009 as an example, to investigate causes of failure and possible improvements, comparing the J-OWC structure build at the location, with other improved designs in the market, as it is the newer U-OWC design. MOTIVATION This study is motivated by the development of new alternatives and the improvement of existing ocean waves energy converter devices. WEC has a great potential on improving the conversion of energy and benefit human life, while reducing our footprint on earth and further damage to it. While solar energy depends on clear weather, and wind energy can be difficult to predict and needs a wide extension in area, land or offshore, wave energy is a continues source over day and night and it has the advantage to be integrated into other structures, saving space and being part of a necessary or already-build coastal protection structure RENEWABLE ENERGY SOURCES - WEC Development of renewable energy sources is a fundamental aspect to maintain the current demand of energy, providing an environmentally sustainable alternative. By developing renewable choices and controlling pollutants, it is possible to look far into a future where renewable energy technology provide considerable economic and environmental benefits. 2

17 1. Introduction During the development process of WEC a large variety of devices has been proposed for exploitation of waves. The current status is still limited, compared to other energy sources ENVIRONMENTAL IMPACTS Global warming and climate changes experienced, in the last decades with higher intensity, has an effect in the behaviour of natural forces, changing the predictions and leading to rising sea water level and storm activity (Vicinanza et al., 2012). Climate change, understood as natural cycles of changes of the distribution in the weather patterns in the long term, and global warming, considered as the direct effect of humans on the environment, results in changes in sea-level rising and more intense and frequent storm-surge. A big concern nowadays is to provide protection in the coasts, and also be environmentally friendly and respectful (Waterman, 2010). The combination of hard structure to protect against storms and high waves, with WECs, can highly benefit the coastal area providing a source of energy on a new or existing coastal protection construction, resulting in a double advantage (Howe and Nader, 2017). The high potential of waves for renewable energy resource, providing a substantial amount of new renewable energy to be exploited is the main reason why the development of WEC are of particular importance and is still developing for improvements. Furthermore, possible environmental impacts of OWCs do not present a significant disadvantage to be concern of, comparing them with other WEC installed in the ocean, or of course, compared to non-renewable resources. Lower emissions are expected, including construction, installation, operation and decommission. Another important point to highlight is the fact that OWC do not have movable part in the underwater system. The turbine is connected to the air chamber, which is located above the water level, and out of the reach of living organisms, reducing to minimum the risk of damaging marine life, unless other shoreline devices that can damage marine species (Buigues et al., 2006) SOCIAL IMPACTS Renewable energy diffusion and development is one of the main social concern and objectives of the 21 st century (Alberdi et al., 2011). Being this a clean and environmental friendly technology, with great potential in efficiency and improving on economical operation, from a social point of view, this is considered as a positive alternative. In some communities and depending on the design, WEC might have a negative repercussion concerning either visual impact, disrupting the region s harmony of the landscape and also possible concern of the noise. Not only during the construction process for nearby communities, but also the high level of noise the turbine or turbo 3

18 1. Introduction generator and the waves impacting against the structure can generate. In the case of several OWC being install in a plant, the level of noises can be a problem for nearby communities, but with the appropriate insulation or properly shielded, this problem can be reduced (Ortubia, Lo pez de Aguileta and Torre-Enciso, 2008). RESEARCH SIGNIFICANCE CURRENT STATE OF RESEARCH Nowadays a large variety of different WEC devices are available in the market. This development has a long history now, but even with the improvements till now, it is still not as affordable as necessary to consider it a compensable energy. Therefore, a big effort is still required to improve the development of these devices for a better future in their utilization, based on their effectiveness. Since the very beginning of design process, almost one thousand inventions has been patented, of which two hundreds have reached the stage of model testing and only a few have been constructed (Mustapa et al., 2017). This technology although still quite limited, it has reached the stage of development of full size prototypes, being one of the first examples the LIMPET experimental plant in Islay Island, UK. Other examples of OWC in caisson breakwater are found in the Sakata port in Japan or the Mutriku power plan in Spain (Simonetti et al., 2018). Further explanation on the evolution of this technology and the current state of research is presented in section 2.2 OWC Evolution and Current State of Research ECONOMICS AND CAPACITY The development of energy transformation from waves technology has always been behind when comparing it with other resources. The main issue for its development is in the economic performance, which still has not meet the future prospects required to make this technology a profitable investment (Contestabile et al., 2017). This is considered one of the greatest disadvantages of WECs, the high demands on capital spending for cost-effective commercialization. An appealing solution to reduce the high-cost, is to install WECs in existing coastal hard structures. Furthermore, the usage of nearshore structures facilitates access for construction, maintenance and grid connection, reducing problems and the total costs, when compared to offshore options (Contestabile et al., 2017). The integration of OWC into breakwaters is further analysed in section Caisson Breakwater. Also, the high payback period of these projects, expected in some cases, such as in a project developing at a Mediterranean Port, to be of 19 years, can be reduced when integrated into hard structures. At this port, the cost of the construction of an OWC integrated in a breakwater is 4% (Howe and Nader, 2017), which in the general picture 4

19 1. Introduction and for the economic magnitude of such a construction, represents a very low increment of the total capital cost. Therefore, although in the economic aspect this technology does not reach desirable standards yet, the attraction of the OWC concept is based on; its simplicity, with few moving parts, its adaptability to different location, its integration to existing or new structures, its reliability, relatively easy to maintain and its space efficiency (Hydro, 2012) KNOWLEDGE GAPS The previous mentioned economical aspect is not the only issue in relation to WEC devices. The integration of this technology with coastal structures to reduce the costs brings other design problems with it (Mustapa et al., 2017). The cost of any WECs is determined according to the efficiency of the device. The first aspect to be covered is the location of the construction. For each specific case, a number of variables have to be consider; the design and type of WECs to be installed, the type of waves approaching at the coast, the tidal range and the bathymetry. Operation under extreme conditions seems to be one of the main problems WECs would face. The strength of the structure suffers under these rare occasional conditions, which can lead to a total failure of the coastal structure to which the WEC is attached to. Also, and in the case of using existing coastal structures, different design challenges has to be considered when integrating a WEC, this can be a very complex work to do (Mustapa et al., 2017). Focusing on OWC, several issues can be taken into account, such as the type of turbine to be used depending on the designs. The most common type of air turbine is the Wells turbine, but the symmetric shape of its blades, can reduce the efficiency (Khchifati, Terkaoui and Alterkaoui, 2015), section 2.11 Turbine develops this topic. Another problem is related to the resonance condition in ocean waves and its intermittency (Henriques et al., 2016), also the pressure in the air chamber of an OWC can cause problems, the general maintenance, the diffraction of waves before reaching the OWC, are some examples of the main problems. SCOPE AND RESEARCH OBJECTIVES The primary scope and research objectives of this thesis are presented in the following section RESEARCH QUESTION The design of an OWC is a complex matter, which presents various uncertainties. During years of implementation and development of new designs, still presents several trouble spots. 5

20 1. Introduction A general design is not feasible, as it depends on different characteristics depending on the location and wave characteristics. Based on case studies, different problems can be identified and improved. Specially under extreme wave events, when the structure suffers the most, and for which waves form with little time and therefore are extremely difficult to predict with accuracy. Based on the effectiveness and improvement of the design, this thesis focuses on the following key research question: Main Question: - To investigate the robustness of OWCs designs for structural optimisation under extreme wave conditions Sub-Questions: - To define different OWC shape designs based on case studies and literature review - To compare the structural response of J-shape and U-shape OWC designs under extreme wave conditions based on the conditions experienced at Mutriku (Spain) during the storm of To investigate wave pressures produced on the OWC structures - To determine the best structural option under extreme wave conditions RESEARCH APPROACH In order to understand these questions, the key research objectives have been set as: Comparing different OWC-designs: 1. To validate numerical model with physical model. 2. To develop numerical model to reproduce realistic situation. 3. To analyse wave forces acting on the structure under extreme wave conditions using ANSYS-Fluent. 4. To analyse the behaviour of the structure under extreme wave conditions. 5. To define the most appropriate OWC design option for the case study at Mutriku (Spain) under the storm conditions of New ideas and contribution of the project To contribute in the design and development of OWC breakwater, focusing in the robustness of the device under extreme wave conditions. 6

21 1. Introduction THESIS OUTLINE I. Chapter 1: INTRODUCTION; outline the general approach for this study, the motivation, the aim and objectives. II. Chapter 2: LITERATURE REVIEW; provides a summary of the important concept and the necessary background information relevant for the reader. III. Chapter 3: RESEARCH METHODOLOGY; reviews the methodology used to define the design and necessary information to model an OWC breakwater. IV. Chapter 4: RESULTS, OUTCOMES AND RELEVANCE OF THE VALIDATION; presents the result of the validation from comparing the CFD modelling with ANSYS and the laboratory work carried out at TUDelft WaterLab facilities. V. Chapter 5: CASE STUDY: MUTRIKU OWC PLANT; provides further discussion of the findings. VI. Chapter 6: CONCLUSIONS & RECOMMENDATIONS; presents a summary and closure of the findings, providing recommendations learnt through the investigation and analysis, with possible recommendations for future studies in the topic. Appendices include details about: A. Ocean Wave Energy and relation with OWC B. ANSYS Fluent General Theory and Fundamentals C. Model Set Up and Boundary Conditions on ANSYS Fluent D. Experimental Model Set Up in the WaterLab at TUDelft E. Model Calibration F. Results Comparison G. Midas Civil 7

22 2. LITERATURE REVIEW Chapter Summary This chapter provides an overview of the background information necessary to understand the principle of an OWC and the evolution of the designs until current situation. It presents an overview of literature relating the wave power extracting breakwater design. To begin with, section 2.1 starts with a brief introduction of energy production and its characteristics and consequences. Following details on ocean wave energy and how this is transported towards the coast are presented in Appendix A. Section 2.2 starts with the evolution and current state of research, focusing in the evolution of research on analytical models, force loading distribution on OWC and the evolution on geometry optimization. Section 2.3 presents a detailed classification of OWC, followed by section 2.4 principle of operation of OWC. Section 2.5 shows advantages and disadvantages of OWC, focusing on resonance disadvantages in the following section 2.6. Finally, section 2.7 presents an overview of the integration of OWC in caisson breakwaters, with different case studies in Section 2.8. Section 2.9 shows a more detailed analysis of a specific case study. Finally, section 2.10 focuses on the operation of the turbine in relation to an OWC. 8

23 2. Literature Review GENERAL BACKGROUND Global energy consumption has increased considerable over the past decades and it is estimated to continue increasing exponentially, with new designs and devices being developed and researched (Vyzikas et al., 2017). Traditional methods of energy production are contributing to serious environmental problems, in occasion worsen by human activities, putting the oceans under risk. Leading to pollution by acidification of the oceans, unsustainable resources extraction and coastal development (Hammar et al., 2017). A pollution-free power generation is pointing the way to the future, which includes the renewable energy industry and within existing possibilities, marine power is a source of quality energy, with a wide range of benefits to human welfare and prosperity. New energy resources are increasingly everyday attempting to harness the enormous natural energy offered to come to build a society that uses ocean resources wisely and make it less vulnerable to the risks associated with them. Some other aspects of this new source are not particular benefit, such as the economic aspect, which is currently not economically competitive compared with others. But on the bright side, the interest on developing this technology is still very alive and keeps increasing (Hammar et al., 2017) MARINE RENEWABLE ENERGY - SOCIAL, ENVIRONMENTAL AND ECONOMIC EFFECTS Energy demand increased has become a challenging problem of the global economy. During the last decades, environmental issues has been treated and faced internationally, to meet minimum requirements and decrease pollution levels to counteract worrying levels affecting the environment (Henriques et al., 2016). Climate Change Policy Rio Earth Summit (1992), an important achievement of the summit was an agreement on the Climate Change Convention which in turn led to the Kyoto Protocol (1997), the Doha amendment (2012) and the Paris Agreement (2016). The United Nations Framework Convention on Climate Change (UNFCCC) main objective is to stabilize greenhouse gas concentrations. The Kyoto Protocol was adopted in Kyoto, Japan, on 11 December 1997 and entered into force on 16 February This protocol is an international agreement linked to the UNFCCC, which commits its parties by setting internationally binding emission reduction targets. Recognizing that developed countries are principally responsible for the current high levels of GHG emissions in the atmosphere as a result of more than 150 years of industrial activity, the Protocol places a heavier burden on developed nations under the principle of "common but differentiated responsibilities." (Henriques et al., 2016). 9

24 2. Literature Review With organizations and government pushing to a change, including more renewable options, the development of clean energy sources is nowadays a big concern, actively being addressed. Key Environmental Issues Like with other human activities, in the marine environmental, the exploitation phase, involving construction, can have an effect in the surrounding area. Not only, the construction of coastal structures can cause changes in sediment transport and flow dynamics, also the construction might produce changes in the living organisms. Social As stated before in the introduction, visual and noise effects of OWC can be a concern in the public eye, that might restrict the development of this technology. The noise of the turbine, generally being this Wells turbine, can be reduced using a noise attenuation chamber. This has been used in the case of the LIMPET shoreline plant design (Vyzikas et al., 2017). Economic Although wave energy is one of the most promising renewables, there are still problematic points to keep developing and improving. The cost efficiency compared with other type of renewable alternatives is behind and still does not meet requirements (Contestabile et al., 2017). WEC economic efficiency depends on the following considerations (McCormick and Michael, 2013): - The magnitude and dependability of the wave resource - The cost of construction and maintenance of the WEC - The energy transmission from the site to the user In addition, current existing models to estimate the costs of a wave energy project are often oversimplified, being not fully attractive in the market (Astariz and Iglesias, 2015). The cost of wave energy is estimated to be about p/kwh, this improves with any new generation of devices that are developed, and eventually transforms into a more cost-effective technology. Investing in new technologies to continue improving and evolving this technology is a key point for future generations (Minns, 2012). OWC EVOLUTION AND CURRENT STATE OF RESEARCH Although the concept was already known in the 1940s, when the first floating OWC was designed and installed in 1947, it was not until 1965 in Japan, where the commercialization of OWC started to get interest, and further in 1980s when promotion 10

25 2. Literature Review of its construction actually woke up a real interest in this technology (Falcão and Henriques, 2016). Since the 80s, numerous inventors have been inspired to convert wave energy, with the first patent in 1799 by Girard father and son in France (Falcão, 2014). Since the very beginning of design process, almost one thousand inventions has been patented, of which two hundreds have reached the stage of model testing and only a few have been constructed (Contestabile et al., 2017). The situation in Europe changed dramatically once in 1991 the European Commission included wave energy in their R&D program, funding the renewable wave energy program, involving a large number of teams active in Europe. One of the first prototypes examples can be found in Toftestallen, Norway, where in kW were produced by this prototype. Another successful example is the OWC in the Island of Islay, Scotland, a shoreline prototype able to produce 75kW, another successful example is the Sakata OWC built in Under extreme circumstances, some of the existed OWC prototypes designs were not able to resist the severe weather conditions. This is the case of the Osprey in the UK and the greenwave in Australia (Falcão and Henriques, 2016). Also, in the case of Mutriku in Spain, different storms damaged the structure of OWC cells, resulting in severe consequences for the WEC (Contestabile et al., 2017). Further information on specific case studies can be found in the section 2.8 Development and Case Studies CURRENT RESEARCH ON ANALYTICAL MODELS Wave energy plants have been under research and development since 1982, when with a simplified analytical model and assuming a simplified rigid piston approach, modelling of the free surface water level inside the OWC and the interface below the OWC lip was carried out by Evans. Later analysis by Evans and Porter in 1995 and Ma in 1995 also investigated this issue (Horko, 2007). Sarmento and Falcao in 1985 continue with the investigation, developing numerical models in 2-Dimensions for simplified geometries and using first order assumptions, were able to model the spatial variation of the free surface shape within the OWC chamber (Horko, 2007). Ravindran and Swaminanthan in 1989, also developed mathematical modelling to investigate the turbine and the geometry of OWC, which were later experimentally tested, verified and optimised. This study allowed to design and built full-scale prototype plants (Horko, 2007). Clément in 1996 analysed the non-linear radiation response of an OWC according to geometric parameters using a numerical wave tank. Finally, 3-Dimensional numerical studies were developed in 1996 and 1999 by Lee et al. and Brito-Melo et al., focusing in 11

26 2. Literature Review commercial improvement and implementation, analysing the hydrodynamics behaviour of the OWC and studying the radiation-diffraction of floating bodies (Horko, 2007). Current investigation on CFD studies the non-linear interaction between waves and the OWC, focusing on the viscous flow separation, turbulence and wave breaking. The thermodynamic and hydrodynamic processes involved in the interaction between the waves entering the OWC and the air chamber (Simonetti et al., 2018) CURRENT RESEARCH ON FORCE LOADING DISTRIBUTION At the end of the 19 th century, observational studies were conducted on wave forces on breakwaters (Cuomo et al., 2010). The research focusing on OWC started in 1978 with Evan analysing the extraction efficiency of wave energy, considering the size of the system, wave condition and direction. Later in 1982, also Evans, investigated the relationship between the efficiency in extraction and the pressure distribution along an OWC (Lopes et al., 2009). From then, the research evolution on OWC has followed a long process of investigation and development. Further development was provided by Sarmento and Falcao in 1985, defining the effect of air pressure inside the chamber under radiation flow condition. Brendmo et al. in 1996, described the effect of two OWC and provided their application criteria. Clement studied the optimisation of the geometry for the front wall of the OWC in 1997, using a two-dimensional simulation model. Later in 2000, Tseng et al. focused in analysing the extraction efficiency of energy, using a self-design OWC. In 2005, Hong et al. studied the pressure, water level, spring and damping coefficient influenced in an OWC. Finally, the last research investigation relevant to mention is the one conducted in 2010 by Yin et al. using numerical modelling with ANSYS-FLUENT, to simulate the pressure variation in the air chamber of an OWC (Kuo et al., 2015). In direct relation to breakwater influenced, the research investigation started in 1988 by Takahashi et al., who investigated the wave absorption capability of a modified OWC with caisson breakwater. In 1992, the port construction in Sakata started, where a fully OWC breakwater was placed for power generation. The results were verified with Goda s formula, developed in 1973, which provides a good estimation of the wave forces acting on the OWC caisson breakwater. In 1994, the conclusion the Jayakumar reached after investigation was that the forces acting on OWC caisson breakwater are smaller than those acting on a conventional vertical wall breakwater. Further investigation by Müller and Whittaker in 1995, revealed that the wave pressure acting on the back wall of the chamber are more important that on the front wall, this is due to the flow field turbulence and the reflectivity (Boake et al., 2002). In 2005, Thiruvenkatasamy et al. studied the influence of the configuration of the system on the final force distribution acting on the OWC, according to the structure size, density of the caisson and the size of the vent. Liu et al. in 2010, analysed the possibility of using 12

27 2. Literature Review the weight of the structure itself to resist the wave force and help in the stability. Also, in this year, Huang et al. calculated horizontal wave force, applying linear potential flow theory, see Figure 1. Figure 1 - Wave pressure distribution for a Caisson Breakwater structure (Mustapa et al., 2017) Finally, mention that in 2009 Torre-Encis et al., developed the design for the construction of a OWC at the Basque country in Spain (Mutriku), which has been operating since 2011 for a total capacity of 300kW (Kuo et al., 2015). The global analysis of the pressure distribution on a caisson breakwater can be used to define local stability, which can be extrapolated to the stability of a OWC caisson breakwater in cases of sliding, overturning or exceedance bearing capacity (Cuomo et al., 2010) RESEARCH ON GEOMETRY OPTIMIZATION The effect of the different geometries to the response of the OWC under different wave conditions is a very important factor that has been study and analyse throughout the history of evolution of this device. Evans and Porter in 1995 estimate the importance of the front wall submergence depth in a theoretical analysis, but in practice, the thickness and front lip shape should also be considered (Wang and Kim, 2013). Another problem when modelling this device is the flow in and out of the air chamber. Kamari et al. modelled the oscillation of the water surface inside the OWC by a thin rigid plate. Asid Zullah et al., modelled flow simulation using ANSYS. Contribution to the geometry for maximum power was investigated for constant waves using ANSYS (Bouali and Larbi, 2013). In 2007, Morris-Thomas et al carried experiments related to the repercution of the design of the front wall in the effectiveness of the OWC, considering different shape, draught 13

28 2. Literature Review and wall thickness. The conclusion of this investigation is that the shape in the form of the front wall do not highly affect the resonance of the OWC. The main difference was found in the immersion depth of this mentioned front wall, giving, for depeer immersion narrower values in the resonance efficiency curve. Also the increase of the thickness of the front wall has a narrower effect in the resonance efficiency curve, although less influential. The shape, roundeness or sharpness of the end of this front wall also changes the behaviour in the resonance curve, producing a higher resonance effectiveness for those shapes with smoother curvature (Kamath, 2015). CLASSIFICATION OF WEC CONCEPT WEC devices can be categorised based on several aspects including the location of operation, wave condition and working principle (Czech and Bauer, 2012). Figure 2 presents the classification of WECs, with highlights in blue for the relevant OWC classification. 14

29 2. Literature Review Classification of WEC Operation Principle Oscillating Water Column Overtopping Device Wave-Activated Bodies (WABs) Point Absorber Location Off-shore (> 40 m) Near-Shore (>10-25 m) On-shore Wells Power Take-off System Air turbines Impulsive Linear generators Hydraulic systems Directional Characteristics Point Absorber Terminator Attenuator Figure 2 - OWC classification based on several aspects of WECs 15

30 2. Literature Review For the purpose of this thesis, an OWC is included in the classification of a shoreline device, integrated in breakwater structure. Due to its location, do not require mooring or underwater long lengths sea cables to connect the WEC to the grid. The main disadvantage of this location, is that waves carry less energy since some is lost in the transport to the shore. Further information on this can be found in Appendix A. To add to this, because of the dynamic nature of the shore, this can cause problems in the OWC (Czech and Bauer, 2012). According to the Power Take Off system shown in Figure 3, for an OWC, consist of a selfrectifying axial-flow air turbine. The turbine can be found connecting the air chamber with the WECs. The reason to use airflow is because, compared to the velocity of waves, the air flow is higher, and also easier to couple to a generator (Czech and Bauer, 2012). Primary Conversion Pneumatic Extraction Secondary Conversion Tertiary Conversion Figure 3 OWC PTO system This air turbine has the capability to operate with a bidirectional airflow and always rotate in the same direction. The efficiency of the OWC is directly related to the performance of the turbine, therefore the design and election of this element is crucial for the system. The two most commonly used type of turbines are the Wells turbine and the impulse turbine (Czech and Bauer, 2012). More details on the turbines operation and usage can be found in upcoming section 2.11 Turbine. OSCILLATING WATER COLUMN PRINCIPLE OF OPERATION In general, the oscillating wave principle is the most popular and famous WEC system. Figure 4 presents the percentage information of WEC according to the development is presented. The OWC is a partially submerged structure shoreline device, with a bottom opening to allow wave energy to enter and then transform that energy into electricity. For further information on wave energy transport, extraction and transformation related to OWC see Appendix A on Ocean Wave Energy and relation with OWC. Figure 4 - Percentage of wave energy development (Mustapa et al., 2017) 16

31 2. Literature Review This mentioned opening at the bottom of the column, see Figure 5, is located right below the minimal water level, allowing waves to enter. The water level inside the column fluctuates with the incoming waves, and thanks to the resonance produced in the OWC, the water level difference inside the OWC is enhanced. Further information on resonance in OWC is provided in section 2.6 Resonance in an OWC. At the top part of the OWC there is an air chamber, which compresses air as the water level rises and decompresses the air as the water level falls down. The difference in pressure in the air drives a turbine, which is responsible to transform the movement of the turbine into electricity (Mustapa et al., 2017). Front wall of concrete chamber Turbine and Generator Air flow Air column MHWS Motion of water column Incoming wave Figure 5 Oscillating Water Column design ADVANTAGES AND DISADVANTAGES OF SHORELINE WATER DEVICES - OWC Ocean wave power is a source of energy which does not involve large CO2 emissions, and it has become the conspicuous form of ocean energy. Apart from the ocean thermal energy, which uses the sun s heat as a constant source of energy, it is possible to use the ocean mechanical energy, produced by tides and waves. As explained in the introduction, this paper will focus on nearshore OWC devices, being this, a type of ocean mechanical energy device. The energy produced is unfortunately an intermittent source of energy difficult to predict, a forecast estimation several days in advance can be predicted, but is difficult to be accurate enough in these predictions and obtain maximum efficiency (Falcão, 2010). The need in this case is a device able to handle a wide range of incident wave power levels, from extreme storm conditions to near flat seas (Czech and Bauer, 2012). In spite of this, because it depends on the wind and tides, this derivate a pollution free type of technology, since waves generates little or no pollution to the environment compared to other sources and it reduces fossil fuel consumption, which is one of the worst problems trying to be avoided nowadays (Czech and Bauer, 2012). 17

32 2. Literature Review Some other characteristics of OWCs is that they are usually combined with other structures such as breakwaters, so it is a fantastic way of protection of the shoreline combined with energy production, having little impact on aquatic life and as they are nearshore or in ports have easy access and maintenance (Hydro, 2012). Also, the negligible demand on land use is an important aspect, which this combination solves in the best possible way by shearing civil costs. On the other hand, as the waves propagate into the shore, they are modified by seabed, causing refraction, diffraction, bottom friction and wave breaking which can cause loss of energy, or it can damage the device, which it can be expensive (Falcão, 2010), (Clément et al., 2002). Another point to take into account is the relative easy access for installation and maintenance this devices provide, since because of their location on the shore is not necessary specialised machinery, or deep-water mooring nor long sub-sea electrical cables (Khan et al., 2017). In contraposition, the main disadvantage of wave power, is the randomness behaviour and variability in several time-scales from wave to wave. The characterization of the wave climate can be complicated, but necessary for the design of any hard structure. (Falcão, 2014) The absorption of wave energy can be a complex hydrodynamic process, in which radiation and diffraction of waves need to be considered, see Appendix A for further information. This is why, the majority of the work done at the beginning of the development and for a long time in the 70s and 80s, was mainly theoretical work on hydrodynamics. Being the development of the design of WEC also of high complexity, with theoretical and numerical analysis and physical and numerical testing involved. Due to bed friction and other process during transportation of energy, less energetic reaches the shoreline, which could be compensated with energy concentration due to diffraction or refraction depending on the bathymetry. Reducing the losses in the process of extraction and conversion of energy can be also a limitation in the process design, increasing the difficulties. Model scaling can also lead to problems, real (viscous) fluid effects (large eddy, turbulence). Another limitation that OWC can experience is related to the frequency. The frequency in the OWC should match of the incoming wave for it to operate correctly. Real waves are not single-frequency, so phase-control to achieve resonance, can cause problems, several phase-control strategies have been proposed (Falcão, 2014). RESONANCE IN AN OWC Related to the efficiency of an OWC is the resonance. The maximum peak of resonance in an OWC will determine the most effective condition when the device generates more energy, which will depend on the type of incoming wave and the geometry of the OWC. 18

33 2. Literature Review The maximum peak of resonance is found for a specific wave frequency, as shown in Figure 6. For very high frequencies, the column of water at the OWC will not have time to react to the oscillation. High frequencies acting in a big mass, will not generate almost any motion in the body, giving a low resonance value. Also, for low wave frequencies, the body of water will behave almost as a quasi-steady, following the motion of the incoming waves, and giving low resonance in the OWC. Only a specific narrow range of wave frequencies will give high levels of resonance and the most profitable wave energy conversion. Figure 6 shows a typical example of a resonance curve. Figure 6 - Example of resonance values for an OWC time-averaged power amplitude for constant turbine parameters (Kelkitli, 2018) The difference of oscillation inside of the water column with respect to the incoming wave can cause problems. The amplitude of oscillation inside the column will depend among other parameters, primarily on the frequency of the incoming wave (Kelkitli, 2018). The natural frequency of oscillation is related to the submerged depth and the mass of water moving in the column. The shape and size of the air chamber is directly related to the incoming wave characteristics. Nearshore, the energy is concentrated in a horizontal motion. The calculation of the device resonant frequency can be calculated knowing the geometrical size of the opening, the forces, damping and stiffness. The damping on the OWC is relevant to know to get a more accurate approximation of the available power that will be transferred to the PTO (Webb, Seaman and Jackson, 2005). In an ideal scenario, the resonance will follow the working principles, but due to the action of different incident waves, super-posing each other can create a non-uniform motion, affecting the action of the incident waves. The motion of the water column under normal regular conditions will behave under a range spectrum, generating a studied resonance, but superposition of different waves or other external factors affecting the approaching waves can change this behaviour. 19

34 2. Literature Review The calculated value for the resonance can change compared to the real scenario. Based on a series of experiments, lower efficiency is to be expected, never reaching 100% of efficiency. Is expected that for the free surface oscillation values in the air chamber when comparing the experimental data with numerical modelling, to obtain good results. On the other hand, the chamber pressure values obtained, especially around the resonance peak did not match those obtained from the numerical model estimation (Kamath, 2015). A rough estimation for the natural frequency in an OWC is proposed as: Where: w T 2 = w T is the resonant frequency g is the acceleration due to gravity (9.81 m/s 2 ) g 9.81 = = 4.69 m 1.1 H T + S H T is the depth of submergence of front lip (0.32 m) S 1 is the stream line that runs between the internal OWC water surface and a point between the OWC lip and the sea-bed. The streamline is a quarter of an ellipse ( m for an OWC diameter of 0.16 m) Figure 7 - OWC - Estimation of the natural frequency 20

35 2. Literature Review SHORELINE OWCS AND THEIR APPLICATION BREAKWATERS CAISSON BREAKWATER The integration of an OWC in a caisson breakwater is the most popular option, due to its simplicity, cost effectiveness and durability (Mustapa et al., 2017). A breakwater is a manmade structure constructed to resist wave action (Mustapa et al., 2017). Focusing on fixed breakwater, other than floating design, the classification can be found in Figure 8. Fixed Breakwater Block-work Vertical Composite Caisson Caisson Horizontal Composite Caisson Piled Conventional Caisson Figure 8 -Fixed breakwater classification (Mustapa et al., 2017) An example of a conventional caisson breakwater can be found in the following Figure 9. This structure counts with a square flat 90º concrete block, laying on top of bedding layer and covered by a thin stone layer to act as scour protection. The direction of the breakwater is perpendicular to the incoming waves, causing partial reflection when wave break at the flat wall surface or big splashes (Mustapa et al., 2017). In the case of extreme conditions and changes in wave acceleration amplitudes, large impact forces act in the breakwater, which in the long term reduces the lifespan of the structure (Mustapa et al., 2017). The main advantages of this type of breakwater is the economic use of material at locations with large water depth, more than 15 m, with high resistance to large wave heights. Another benefit is the constant cross-section along the structure with large tidal range. This structure is able to accommodate and combine other functions, such as quay-wall or WEC. On the other hand, some of the most noticeable problems are the seabed preparation and foundation requirements, such as levelling to resist large foundation loads. Risk of scour could also be a problem, difficult to repair and maintain (Verhagen, 2017). Figure 9 - Conventional caisson breakwater with vertical front wall (Mustapa et al., 2017) 21

36 2. Literature Review INTEGRATION OF OWC INTO CAISSON BREAKWATER The integration of the OWC structure into breakwaters has several advantages: the constructional costs are shared, and the access for construction, operation and maintenance of the wave energy plant become much easier. The design of the Sakata breakwater in Japan in 1990, was the first successful design ever completed. The design consists of a caissons breakwater with a design able to accommodate the OWC and the equipment behind. The second successful construction was adopted at the port of Mutriku, Spain, with 16 air chambers, each with a Wells turbine rated at 18.5 kw (Falcão, 2014). This is further developed in section 2.8 Development and Case Studies. With the development of effective technology and new devices, OWC breakwaters are still not as commercialized, because is still not cost effective. In general; projects are small, so do not reach a cost effective status, also the equipment needed are too expensive for the dimensions of the construction, and the grid connection available at coastal sites are still too expensive (Hydro, 2012). The future challenge of the industry is to reach an equilibrium between cost and efficiency, so that the technology is further commercialised. Some governments, being aware of this situation, actively support the wave-generated electricity development (Hydro, 2012). The high-level Cost of Energy (LCOE) of ocean waves need improvement to obtain better conversion efficiency results and produce more electricity. Two approaches are considered to meet cost-efficiency requirements for OWC devices (Howe and Nader, 2017); 1. Implementation of the structure grid performance, to synchronise the wave extraction, for better conversion of energy. This way, the efficiency is improved 2. Implementation of installation of OWC into pre-existing structures and new structures. This way, the installation, construction and maintenance are shared with the structure, reducing the final cost. DEVELOPMENT AND CASE STUDIES Yoshio Masuda, considered as the father of modern wave energy technology, studied this field since 1940s, developing the first commercialised floating OWC in Japan in This was equipped with a conventional unidirectional air turbine, and its corresponding system of rectifying valves. Also, Masuda developed the first large-scale OWC plant in the sea, the Kaimei in Japan in This consisted of a large barge, with thirteen OWC openbottom chambers underwater, including unidirectional air turbines (Falcão and Henriques, 2016). Continuing with this country, in Japan in 1983, a shore-fixed OWC with 40 kw Wells turbines was installed at Sanze. The good results obtained from this project leaded to the 22

37 2. Literature Review development in 1990 to two larger OWC. In Sakata, a 60 kw fixed-owc breakwater was installed with the development of a new port, integrating five chambers in front of the caisson (Howe and Nader, 2017). Dimensions of the construction of the Sakata OWC are shown in Figure 11. The construction consisted of a row of concrete caissons on a rubble mound foundation, with a bottom opening which forms the capture chamber. The planned length of the construction is 1900 m, with an average water depth of 18 m. This project is officially the first case of WEC integration into a breakwater with Wells turbines. The sharing of the structure construction, allowed the reduction in total costs (Falcão and Henriques, 2016). Figure 10 - OWC plant integrated into a breakwater at Sakata harbour, Japan, Rated power 60 kw (Falcão and Henriques, 2016). Figure 11 OWC caisson breakwater shape with dimensions at Sakata harbour (Suzuki and Port, 2004) Later in that same year, at Trivandrum, southern India, a 125 kw bottom-standing OWC plant was installed, testing different types of air turbines, Wells and impulse turbines. The development in Europe was leaded by the United Kingdom. In 1975, the National Engineering Laboratory (NEL) developed the design of a bottom-standing structures, with the same principle that OWC breakwater, using Wells turbine. This was never built, and the program and development in the country stop without major results and without any full-sized prototype construction (Falcão and Henriques, 2016). In 1995, Norway integrated an OWC into a cliff at Toftestallen. Not much information of the performance of this plant was shared, but it is unofficially known that the results were rather lower, compared to expectation, rated at 500 kw. In 1988, the plant was 23

38 2. Literature Review destroyed during a storm event, with the detachment of the OWC to the concrete foundation (Falcão and Henriques, 2016). After this event, the development remains unchanged, focusing on the academic research, until late 1990s when further development thanks to the European Commission in 1991, which included wave energy in their research and development program. Continuing with the progress achieved in Sakata, two fully-sized fixed-structure were built in Europe (Falcão and Henriques, 2016). The completion of an OWC at Pico, in the Azores island in Portugal, also equipped with Wells turbines was completed in 1999, see Figure 12. This plant rated 400 kw, it was built into a vertical cliff, and its location was selected based on the natural wave energy concentration and easy access (Falcão, Henriques and Gato, 2016) Figure 12 - PICO OWC plant (Portugal, 1999) (Falcão and Henriques, 2016). Figure 13 - Discretization of the plant and surrounding rocky bottom and coastline (Falcão, Henriques and Gato, 2016) Completed in 2000, the LIMPET OWC plant built in Islay, Scotland (Figure 14), consists of an OWC shoreline WEC carved into a rocky cliff. Originally rated at 500 kw, counts with Wells turbines. The original turbine system had to be replaced, and nowadays the plant is used to test turbines. Over turbines has been tested for commercial projects (Hydro, 2012). Figure 14 - LIMPET OWC plant, at the island of Islay, Scotland, UK (Falcão and Henriques, 2016). In 2001 in China at the province of Guangdong, another OWC plant, rated 100 kw was built, near-shore OWC. In 2005, oceanlinx OWC constructed a bottom-standing 24

39 2. Literature Review nearshore prototype to test the performance at port Kembla in Australia. Later in 2008, and following the Sakata design and development, a multi-chamber OWC plant was constructed on shore breakwater at Mutriku harbour in Spain (Falcão and Henriques, 2016). The design counts with 16 Wells turbine, fitted to turbo-generation units, giving a nominal rating of 4MW (Torre-Enciso et al., 2009). This is the first construction of a OWCbreakwater working as a power station, and not built as an addition to an already existing planned breakwater (Hydro, 2012). In 2014, in Australia at port Adelaide, the greenwave, which is a large bottom-standing OWC, rated 1 MW was constructed, rated 1 MW. The latest design constructed, in 2015, are the Yongsoo plant at Jeju Island, South Korea, rated 500 kw, is a Bottom-standing OWC. Also, in 2015, REWEC3, at the port of Rome, a U-shape OWC breakwater was constructed at the harbour of Civitavecchia. This construction counts with 17 caissons of 136 OWCs (Falcão and Henriques, 2016). A summary of the OWC is presented in Table 1: Table 1 Summary of the OWC (Falcão and Henriques, 2016). DEVICE RATED COUNTRY YEAR DESCRIPTION TURBINE JAPAN (FLOATING) OWC - Japan 1965 Floating Unidirectional air turbine NEL PROGRAM - Scotland, UK 1975 Bottomstanding structures self-rectifying Wells turbine KAIMEI Lower than expected Kaimei, Japan 1978 Floating Unidirectional air turbines JAPAN SHORE- FIXED 40 kw Japan 1983 Shore-Fixed Wells turbine OWC AT TOFTESTALLEN 500 kw Toftestallen, Norway 1985 Shore-Fixed Vertical-axis Wells turbine BREAKWATER AT SAKATA HARBOUR 60 kw Sakata 1990 Shore-Fixed breakwater Wells turbine BOTTOM- STANDING OWC 125 kw Trivandrum, India 1990 Bottomstanding Wells turbine OWC ON THE ISLAND OF ISLAY 75 kw island of Islay, Scotland 1991 Shore-Fixed Wells turbine OSPREY 1 MW Scotland 1995 Large nearshore bottomstanding OWC Wells turbine PICO 400 kw Island of Pico, Azores, Portugal 1999 Near-shore-cliff OWC Wells turbine 25

40 2. Literature Review LIMPET ISLAY PLANT 500 kw Islay, Scotland, UK 2000 Near-shore-cliff OWC Wells turbine SHORELINE OWC PLANT IN CHINA 100 kw Guangdong, China 2001 Shoreline OWC plant Unidirectional turbine OCEANLINX OWC 20 kw Port Kembla, Australia 2005 Bottomstanding nearshore prototype - MUTRIKU 18.5 kw/turbine 296 kw in total Mutriku harbour, Basque Country, Spain Multi-chamber OWC plant breakwater 16 Wells turbines OCEANLINX GREENWAVE 1 MW Port Adelaide, Australia 2014 Large bottomstanding OWC - YONGSOO PLANT 500 kw Jeju Island, South Korea 2015 Bottomstanding OWC - REWEC3 - port of Rome, harbor of Civitavecchia, Italy 2015 U-shape OWC breakwater 17 caissons of 136 OWCs The selection highlighted in grey in Table 1, represents those devices installed in breakwaters, as explained in section Integration of OWC into Caisson Breakwater. COMPARISON OF DESIGNS The different designs to be compared under this master thesis are the J-OWC shape and the U-OWC shape, see Figure 15. [a] J-OWC [b] U-OWC Figure 15 -Comparison of J-OWC and U-OWC shape 26

41 2. Literature Review J-OWC DESIGN The called J-OWC (Figure 15 [a]) is the general and first design of this type of device. Implemented in different locations and in different forms, it seems to be a design that generally works, although, reaching high success level has not been improved to desired levels in the last decades. The increment in the total cost has been considered as a negative side and has slow down improvements. In the case of an OWC being constructed in a breakwater structure, the extra cost, considering the results in energy conversion has not been attractive enough yet (Falcão and Henriques, 2016). The principal of operation for the J-OWC as explain in section 2.4. Principle of operation, consisting of a submerged opening below minimum water surface, which allows the water level inside the column to fluctuate with the incoming wave. In general, the resonance inside the J-OWC column is smaller than the incoming wave. To improve the situation, complex phase control devices were proposed to reach the specific and best resonance conditions. Because of the difficulty of reaching the necessary resonance, a new design has been implemented and develop, with promising future and better results (Laface and Carillo, 2013) U-OWC DESIGN A new kind of OWC caisson breakwater, known as U-OWC has been developed based on the J-OWC design (Figure 15 [b]). The main advantage of this device is the production of natural resonance without the necessity of any further device for phase control, allowing better results in the percentage of energy conversion. It also provides extra protection to the device, reducing the direct impacts against the structure. Based on Boccotti experiments, the designer of this new device, the new design gives better performance for a wider range of waves, including high waves. These experiments consist of two scaled flied experiments carried out in the Sicily Channel (Italy). From this experiments and learning process, the U-OWC, also called REWEC3, has been installed in two locations in Italy; the port of Civitavecchia (Tyrrhenian sea), the port of Pantelleria (Sicily Channel). The number of U-OWC along the coast of the Mediterranean Sea is expected to increase rapidly in the next years (Laface and Carillo, 2013). The principle of operation of the U-OWC is slightly different from the J-OWC explained. Including now a wall in front of the OWC, creating a front vertical duct, with an opening in the upper part making the connection to the sea. On the bottom part, this is connected to the OWC column, which is likewise connected to the air chamber in the top part of the column. According to the inventor and designer of the U-OWC Boccotti, although the only difference with the traditional design is the vertical duct, this new configuration improves the hydrodynamics inside the column. Since the waves do not propagate directly into the OWC structure but provide a piston water motion in front of the OWC, improving the 27

42 2. Literature Review wave energy conversion for all scenarios, heavy and light sea states. This is meanly because for the new design, the amplitude of the water level fluctuation is greater, giving better result of resonance with smaller wind waves. Another improvement is that the eigenperiod is greater, which implies better performance with swell and large wind waves (Laface and Carillo, 2013). In conclusion, the new designs offer different advantages, according to Boccotti, resonance conditions are improved, reaching optimal conditions without phase control devices. This induces higher amplitude in the resonance inside of the column, which leads to higher change in pressure in the air chamber, allowing the turbine a better performance. Finally, the structure is less likely to get damage, providing a better resistance, since the front wall works as extra protection to the OWC column (Laface and Carillo, 2013). FAILURE MECHANISMS CASE STUDY: MUTRIKU Mutriku in the Basque country (Spain) is a project started in 2005 to implement the coast and promote clean energy by building a Wave Energy Conversion plant. The location and orientation in the north of Spain, makes it suitable for the purpose (Memoria, 2009). For the pre-design of the plant, a detailed study of the maritime climate at the site was necessary (Ortubia, Lo pez de Aguileta and Torre-Enciso, 2008). The series of data considered is from the Bilbao-Vizcaya outer buoy, for the years 1990 to 2005, with a maximum wave height of 10 meters, see Figure 16, point indicated in blue. With that series of data, the design height determined for the project was 7.7 meters (Torre-Enciso, Marqués and Aguileta, 2010). In the upcoming years, from 2007 to 2009 five temporals happened in the area, all exceeding any of the previous experienced from 1990 to 2005 (Torre-Enciso, Marqués and Aguileta, 2010), with a maximum wave of 13.7 meters, see Figure 16 indicated in red. If the series of data considered include this last years, so from 1990 to 2009, the design height for the project would have been of 9.2 meters. However, indicated in Figure 16 in red, during 2007 to 2009, there have been up to five other storms. This difference in the number of storms, increasing after 2007, were not considered in the Mutriku OWC design, which had a damaging impact in the structure once it was constructed. 28

43 2. Literature Review Figure 16 - Probability of annual exceedance of waves (y-axis showing the wave height and x-axis showing return period) That 1.5 meters difference in the design estimation for the J-OWC shape at Mutriku, could be said to be the cause of damage of parts of the construction. After the storms, the first damage estimation, recognised damage in four of the sections, indicated in Figure 17, as point 1, 2, 3 and 4. Figure 17 - Picture of Mutriku OWC - highlight of failed sections (Memoria, 2009) In the external wall of the OWC, the bottom part of the external wall failed, first causing cracking in the concrete structure, and in some occasion failure of the entire front wall. This cracking can be found, especially in the areas of connection between the front wall and the continuation of that vertical structure to form the top part where the turbine can be found, see Figure

44 2. Literature Review Figure 18 - Detailed picture of failure at Mutriku OWC (Memoria, 2009) For the purposes of the energy resource, according to the location and the bathymetry, the average energy flow in the winter is to be 18,5 kw/m, in the summer 4,8 kw/m and in the months of transition 8,8 kw/m, reaching a total power of 296 kw(ortubia, Lo pez de Aguileta and Torre-Enciso, 2008). The implementation after the big storm in 2009, consisted in a protection of the front wall, to avoid further damage in case of other extreme wave conditions, avoiding direct impact against the structure. This will be considered for all the modules, not only those affected in the storm, to reduce the probability of damaging in a similar climate situation, therefore all 16 modules will be reinforced. The solution, to repair the affected chambers consisted of including in front of the existing front wall a portico piece in order to re-direct the wave energy to the bottom and avoid direct impact in the structure. In front of the existing wall a limestone block wall is built, to reach to the 10 meters needed for future protection against future storms conditions. This raises the question as to whether the original J-OWC design of the OWC was the most appropriate, and if other possible designs would have avoided or reduced the damage. TURBINES As mention in previous section on the 2.3 Classification of WEC concept, according to the Power Take-off System, for an OWC, the most commonly used type of turbine are the Wells turbine and impulse turbine (Czech and Bauer, 2012). Wells turbine The Wells turbine is a low-pressure turbine capable to rectifies the air stream, see Figure 19 (a). The main advantage of this turbine is the bidirectional allowance, which means that even the airflow passing in and out, this still rotates in the same way. The blades of the turbine which are symmetric, can lead to an efficiency drop during conversion. Because of the shape of the blades, aerofoil-shaped bodies produce aerodynamic forces, 30

45 2. Literature Review for which, and due to the symmetric of the body, the drag coefficients are higher than for other asymmetric cases, also it can produce flow separation, this can produce, in rare occasions, that the driving torque becomes negative. This type of turbine requires a large size motor or generator to start-up. Impulse turbine In the case of the usage of impulse turbines, see Figure 19 (b), which are self-pitched, controlled turbines with guided vanes. Guide vanes are pivoted and can freely rotate. When airflow changes direction, these guide vanes change their orientation to meet the right position according to the airflow, acting as a nozzle or diffuser for each situation. This type of turbine has a more complex design and operation than Wells turbines, and so if the guide vanes fail in their function the whole system fails. In general, comparing both types of turbines, the impulse turbine presents a better efficiency in operation than the Wells turbine, but since the Wells turbine has a wider range of operation, this is consider to have an overall higher efficiency (Czech and Bauer, 2012). Figure 19 (a) Wells turbine, (b) Impulse turbine (Czech and Bauer, 2012) The type of turbines chosen for the Mutriku OWC are Wells turbines fixed pitch, which gives them great robustness and simplicity. The symmetrical design of the blades, which allows that independently of the direction of the air, it always turns in the same direction, generating constant energy, with no need for any rectifier device for air flow. They have two rotors of five blades that spin separated by the generator, which is cool down by air (Ortubia, Lo pez de Aguileta and Torre-Enciso, 2008). 31

46 3. RESEARCH METHODOLOGY Chapter Summary This chapter explains the methods used to design the models to generate a realistic scenario of breakwater devices with OWC. Laboratory experiments under normal conditions are design and manufacture to evaluate hydrodynamic conversion efficiency of a single chamber of the OWC breakwater. This laboratory experiments will help to validate a numerical model to these conditions. A further step will consist of a numerical modelling using ANSYS of different designs of a real cased based for comparison in their performance under normal and extreme wave conditions, to improve the design and robustness of the structure under pressure loads. Finally, to investigate the structural response during extreme wave conditions. 32

47 3. Research Methodology INTRODUCTION METHODS OF MODELLING The purpose of this thesis is to analyse the performance of different OWC geometries under extreme wave conditions, studying the structural response under wave loads of different magnitude and study the robustness of the structure. In order to do so, physical and numerical modelling are required. The Mutriku design (see section 2.8 Development and Case Studies) is taken as a reference design for the develop of the different experiments and comparison of designs. Also taking as a reference, the 2009 storm that caused damage in this specific OWC, for the study of pressures in the structure leading to failure. Physical modelling, although time consuming, is necessary for a better understanding in the model configuration and the characteristics of an OWC, and to confirm theoretical results and validate numerical modelling. ANSYS Fluent is used for numerical modelling. This method presents a number of advantages, being less time consuming than laboratory experiments and allowing to do more and different simulations in a shorter period of time. For further details on ANSYS Fluent software see appendix B ANSYS Fluent General Theory and Fundamentals. EXPERIMENTAL SE-UP OF THE LABORATORY TESTS For validation purposes, laboratory tests are required for this master thesis, allowing a better understanding of the interaction of the waves and the OWC structure. The scale ratio used, is based on the real case study at Mutriku (Spain), being the most well documented project. According to the facilities available at the TUDelft Water Lab, the scale is 1:25. Further details on the scale of the model are presented in Appendix D, section 1.3. A disadvantage to mention when working in laboratory experiments, is that the scaling factor, which although is taken into consideration, can present difficulties to accomplish for air compressibility effects. Considering this, air compressibility is not taken into consideration in these tests. Instead, pressures in different locations of the structure are considered, as well as water levels at different points of the wave tank. A bigger model, will result in more accurate results, but this will involve other problems, as increase in the price, time-consumption in the construction process and sometimes, complexity for a more accurate representation (Simonetti et al., 2018) LABORATORY EXPERIMENTS CHARACTERISTICS Oscillating Water Column Characteristics A simple geometry of an OWC system is tested in the laboratory facilities at TUDelft for validation of the CFD numerical modelling. Based on the Mutriku OWC case study (see 33

48 3. Research Methodology previous section 2.10 Failure Mechanisms Case Study: Mutriku), a 1:25 model is design in wood according to the dimensions of the wave tank (see Figure 20). Figure 20 - OWC model in the Laboratory facilities at TUDelft (left front view, right back view) Pressure sensors are located in three different positions. One in the front wall, as it can be seen in Figure 20 - left, to register the pressure of the incoming wave. A second pressure sensor is located in the back wall of the model (Figure 20 right). This back pressure sensor will allow a better understanding of the incoming wave energy reaching the inside of the air chamber. The last pressure sensor is located at the top of the model (Figure 20 right), which will give information of the air compression happening in the chamber, which related to the second pressure sensor at the back, will facilitate a better understanding of the relation between the incoming wave and the wave energy transformation related to the air compression in the air chamber. Oscillating Water Column Resonance The resonance of an OWC relates directly to the efficiency of this. Figure 21 shows the difference in pressure in the air chamber that drives the turbine. Based on the first set of experiments, showed in Table 2, are used in the laboratory experiments. Figure 21 -Working principle of an OWC 34

49 Table 2 - Wave conditions considered on the laboratory experiments 3. Research Methodology Case Water level (m) OWC model type H S (m) T P (S) 1 0,47 J-shape 0, ,47 J-shape 0, ,47 J-shape 0, ,47 J-shape 0, ,47 J-shape 0, ,47 J-shape 0, ,47 J-shape 0, ,47 J-shape 0, ,47 J-shape 0, This set of waves are carried out for different designs. First a J-shape OWC, as describe in section 2.9 Comparison of Designs, carried out for; first an open top part (see Figure 22), this will allow to record the water elevation inside of the OWC, and based on that, calculate the resonance curvature. A second set of experiment for the J-shape is carried out with a partially close top part (see Figure 23). This allows a more realistic scenario and a closer behaviour to having a turbine installed with the OWC, allowing only part of the air to exchange with the outer part. Finally, the third set of experiments for J-shape is carried for a total closure of the top part of the OWC (see Figure 24). At this top cover, a pressure sensor is installed, allowing to record the change in pressure produced by the difference in resonance according to each type of wave, allowing a better understating of the real air pressures obtained by the air-turbine, in a hypothetical realistic scenario. Note that both, the front pressure sensor and the back pressure sensors showed in Figure 22, Figure 23, Figure 24, Figure 25 and Figure 26 measure the pressures from the left side of each wall, where the wave is coming from. The set of experiments according to the top part differences are: Figure 22 Cross-section of the J-OWC design with top part close 35

50 3. Research Methodology Figure 23 - Cross-section of the J-OWC design with top part partially open Figure 24 - Cross-section of the J-OWC design with top part open The same set of experiments, with the same wave characteristics, as seen in Table 2 is also carried out for a U-shape OWC design. Figure 25 - Cross-section of the U-OWC design with top part close Figure 26 - Cross-section of the U-OWC design with top part open For further reference of the model calibration of the mention pressure sensors and wave gauges used to measure the water level at different points of the wave tank, refer to appendix E Model Calibration 36

51 3. Research Methodology CFD MODELLING Since the early developments of OWC in 1970s there have been advances using Computational Fluid Dynamic (CFD) techniques and software. In this way is possible to analyse and simulate non-linear interaction between the waves and the WEC device, the air in the chamber, the hydrodynamics and the aerodynamics effect with simulation of the air phase (Simonetti et al., 2018). Facilitating also comparison of variations on the geometry and other specification affecting the system, that in the lab facilities will take too much time and effort to consider them all (Horko, 2007). From the beginning of the century, CFD development has commercialised, expanding to new software such as ANSYS-CFX, Star-CD or ANSYS-FLUENT. Application of these software to ocean engineering problems is still limited and results are generally used in a qualitative manner rather than quantitatively. In relation with OWC, commercial CFD has mostly been used only in relation to the airflow through the upper structure, so there is still a lengthy path ahead on investigation (Horko, 2007). (For further information in the operation of ANSYS-FLUENT, see Appendix B ANSYS Fluent) SET-UP OF THE NUMERICAL MODEL OF THE OWC ANSYS Numerical model of the OWC design, wave generation and their interaction are simulated using Fluent of ANSYS. The aim is to validate the Fluent results with the laboratory work in order to understand the differences of fluent with respect to the real case at the laboratory and be aware of ANSYS Fluent limitations. The same wave tank characteristics, geometries and wave conditions are represented with Fluent. Supplementary information of the model set up and boundary conditions for ANSYS Fluent can be found in appendix C Model Set Up and Boundary Conditions and ANSYS Fluent BOUNDARY CONDITIONS Characteristics of the model set up are defined as following; K-epsilon turbulence model is used for these tests, which is the most common model used in CFD. In order to give a general description of turbulence this model uses a twotransport equation model, where the first transported variable is the turbulence kinetic energy (k) and the second variable is the rate of dissipation of turbulence energy (ε). Open channel Wave Boundary Conditions is used, allowing to generate waves with defined characteristics as shown on previous Table 2. For each of these waves, an averaged flow velocity magnitude (m/s) is calculated, allowing to maintain constant average water depth along the wave tank. As waves come in, there is a flow proportional and in the opposite direction. Detailed information on these values are presented in table 3 in Appendix C Model Set Up and Boundary Conditions and ANSYS Fluent. 37

52 3. Research Methodology The Inlet is defined as the left wall of the box representing the wave tank, this will be the area where wave will start propagating. Outlet is defined as the top part of the box, also a small are on the right wall above where the model is located. The model is located at the right part, 35 meters from the inlet wall. Representing the same conditions as in the laboratory experiments. Further information in wave theory can be found in Appendix A - Ocean Wave Energy in Relation with Oscillating Water Column. Outlet Inlet OWC model Figure 27 Side view of the ANSYS-Fluent model Note that waves in ANSYS Fluent are reflected at the inlet (Figure 27), in contrast to the laboratory experiments execution, for which, the wave tank is capable to absorb the reflected wave. Considering this situation, and knowing the distance of the wave tank, and the period it takes for the wave to propagate, the period of 19 to 57 seconds, approximately, this will vary depending on the wave period, are used. The comparison of the laboratory results and numerical modelling can be found in Appendix F Results Comparison. 38

53 4. RESULTS, OUTCOMES AND RELEVANCE OF THE VALIDATION Chapter Summary The most relevant results obtained from the validation of the different geometries are presented in this section. Physical and numerical experiments are analyzed and compared. First, a J-OWC shape results, with the top part of the OWC open and partially open. This last one to represent a more realistic scenario with a turbine. Pressure sensors are located in the front and back wall of the OWC laboratory prototype, so they can be compare with the ANSYS-Fluent results. The water level inside of the OWC, to check the resonance behavior for different wave scenarios is also compared for validation purposes. 39

54 4. Results, Outcomes and Relevance of the Validation VALIDATION RESULTS Validation of the results obtained with fluent ANSYS is necessary to confirm that the performance and outcomes match with a physical modelling, confirming also, that the boundary conditions defined in ANSYS-Fluent matches with reality, see Appendix C Model Set Up and Boundary Conditions on ANSYS Fluent. This will also allow to generate other scenarios, with certainty on the accuracy of ANSYS-Fluent results. A certain of validations are presented in this section, focusing in the pressure sensor in the front and back wall and the resonance inside of the OWC J-OWC SHAPE FULLY OPEN The validation of the results shows a correlation between the results obtained for J-OWC when comparing the physical and numerical modelling. This is shown in Figure 28, which shows the laboratory experiment results and ANSYS-Fluent for the front wall pressure sensor, as seen in previous Figure 22. In general, the curvature coincides very precisely in Figure 28. Notice that the laboratory experiment range is shorter, covering from period 1,7 sec to 2,5 sec. This is due to limitations at the WaterLab, which is not an issue when using ANSYS-Fluent. Figure 28 Validation of ANSYS-Fluent results for the front wall pressure sensor for a J-OWC when the top part of the OWC is open. Figure 29, shows the validation for the back-wall pressure sensor, see Figure 23. Notice that the back-wall pressures present higher values. Therefore, inside of the OWC, pressures are generally higher for the J-OWC shape. This confirms, as stated by Müller and Whittaker in 1995, that the wave pressure acting at the back wall are higher than those acting in the front wall, due to the flow field and the reflectivity (Boake et al., 2002). 40

55 4. Results, Outcomes and Relevance of the Validation Figure 29 - Validation of ANSYS-Fluent results for the back-wall pressure sensor for a J-OWC when the top part of the OWC is open. In the case of the resonance inside of the OWC for the J-OWC, for the same wave height, with the increase of the wave period, the resonance increases linearly, until it reaches a point of maximum resonance. In this case, and for a wave height of 0.05 m, this is at a period of 1,7 sec. After which, the resonance amplitude reduces, see Figure 30. Figure 30 - Validation of ANSYS-Fluent results for the resonance oscillation inside of a J-OWC when the top part of the OWC is open J-OWC SHAPE PARTIALLY OPEN In the case of a J-OWC when the top part of this is only partially open, the level of resonance inside reduces in comparison when this is fully open. By having a partially open scenario, a more realistic representation is achieved, considering a situation for a turbine. Considering the turbine connected to the air chamber, this allows part of the air to pass through, influencing the resonance inside. When the air compressibility reaches a limit, the water at the bottom of the OWC, encounters a resistance, which decreases its 41

56 4. Results, Outcomes and Relevance of the Validation maximum. Figure 31, shows the influence of a turbine, in comparison with a top open OWC. Figure 31 - Comparison of the validation results for the resonance oscillation inside of a J-OWC when the top part of the OWC is partially open and when is fully open. To mention here as well, ANSYS Fluent assumes the air to be incompressible. Therefore, the validation when the top part cover is fully closed, is not considered for this master thesis. This fact, will affect to the partially close scenario on Figure 34, which explains the higher values for the ANSYS Fluent experiments U-OWC SHAPE FULLY OPEN This sub-section presents the results obtained from the comparison of the results for the physical and numerical model for a U-OWC. The front pressure sensor comparison for U- OWC (geometry showed in Figure 25), showed in Figure 32, present a similar curvature. Figure 33, showing the comparison of the back-pressure sensor, where lower periods, presents a correlation in values. However, higher period values, show a disaggregation in the values. As the period values increases, ANSYS-Fluent back pressure values increase faster than the physical modelling. 42

57 4. Results, Outcomes and Relevance of the Validation Figure 32 - Validation of ANSYS-Fluent results for the front wall pressure sensor for a U-OWC when the top part of the OWC is open. Figure 33 - Validation of ANSYS-Fluent results for the back-wall pressure sensor for a U-OWC when the top part of the OWC is open. The resonance of the U-OWC for lower periods of 1,7 sec matches the physical and numerical model. As the period increases, both curves diverge. Figure 34 shows these curves, for which the ANSYS-Fluent results are higher than the laboratory experiments 43

58 4. Results, Outcomes and Relevance of the Validation Figure 34 - Validation of ANSYS-Fluent results for the resonance oscillation inside of a U-OWC when the top part of the OWC is open. CONCLUSIONS OF THE CHAPTER In this section, the conclusions of the results of the validation are presented. The concluding remarks can be stated as: o The validation of the J-OWC, showed in sections and presents a good correlation of the physical and numerical modelling o The validation of the U-OWC in section presents: A good correlation for the front pressure sensor (Figure 32). The back-pressure sensor comparison shows a deviation of the ANSYS- Fluent curve (Figure 33). This could be explained due to the friction of the walls, which was not taken into account for the numerical simulation with ANSYS Fluent. This has influence the results, since due to the geometry of the OWC, the front vertical duct for the U-shape, is narrow, considering the dimensions. The fluid has to pass through that narrow space. Therefore, the back and inside validations are influenced by this fact after a certain period of time, explaining why, for lower periods, the match is more certain with the laboratory results, than for higher periods. 44

59 5. CASE STUDY: MUTRIKU OWC PLANT Chapter Summary This section presents the results of the structural analysis for the Mutriku OWC. Numerical model with ANSYS-Fluent for different OWC geometries are considered under extreme wave conditions. Different water levels and wave heights are compared, obtaining the static pressures values in the structure. This information is then used in MIDAS Civil software, for further structural analysis of the front and back walls. 45

60 5. Case Study: Mutriku OWC Plant CASE STUDY RESULTS: MUTRIKU (SPAIN) The storm conditions and the geometry of the J-OWC are based on the Mutriku OWC. The storm conditions are presented in previous section 2.10 Failure Mechanisms Case Study: Mutriku, and the geometries for J-OWC and U-OWC can be found in sections J-OWC Design and U-OWC Design. Two waves for high-water level and low-water level are compared. This are also based in the Mutriku situation storm in Further information in the dimensions of Mutriku OWC and storm conditions can be found in appendix D, 1.1 Case Studies OWC - Dimensions. The results of the structural analysis, carried out with ANSYS-Fluent, are presented here. Further information on this software can be found in Appendix B ANSYS Fluent General Theory, Fundamentals and Model Execution. In total there have been compared four different wave scenarios, two wave heights, of 8 meters and 13.7 meters for low water level and high-water level (+4.5m). Here there are presented two of the wave scenarios considered, further information about this scenarios and others can be found in Appendix G Case Study: Mutriku Results with ANSYS Fluent. In order to obtain a more accurate comparison of the pressures in the structure for the different situations, the static pressures are taken for the same storm moment, considering where most of the peak pressure points happened. Finally, a structural analysis is completed with MIDAS Civil, additional information on this software can be found in Appendix H Case Study: Mutriku Results with MIDAS Civil. ANSYS-Fluent Pressure Points To study the pressures in the walls, sixteen points are selected, these are showed in Figure 35 in burgundy circles and tagged with the corresponding point number. Figure 35 also shows the geometry of the J-OWC with the front and back wall. Five of these points are located in the external part of the front wall (Point 1 to Point 5), another five points in the internal part of the front wall (Point 6 to Point 10), and the final six points in the back wall (Point 11 to Point 16). 46

61 5. Case Study: Mutriku OWC Plant Front wall Back wall Figure 35 - Pressure points at Mutriku-OWC MUTRIKU RESULTS: L.W.L AND 8 METERS WAVE HEIGHT Figure 36 presents the composition of images for the different OWC geometries considered for Low Water Level with waves of 8 meters. Figure 36 [a] presents a J-shape, for which the internal pressures, in burgundy colour in the figure, are higher than for the rest of the geometries. Figure 36 [b] [c] [d] [e] present U-shape OWC. The main difference with Figure 36 [a], is the decrease of the internal pressures. High pressures in the back wall of the J-OWC, relates to the work developed by Müller and Whittaker in 1995, as mentioned in section Current Research on Force Loading Distribution, explaining that the wave pressures action on the back wall are more important and higher than those acting in the front wall, due to the flow field turbulence and the reflectivity (Boake et al., 2002). This is true in the case of the J-OWC Figure 36 [a], reducing the back-wall pressures for all situations of U-OWC. It is also noticeable the increase of the external pressures in the front wall of the OWC, with the presence of a U-wall, this can be seen in burgundy colour in Figure 36. In the case of the J-OWC in Figure 36 [a], waves approaching the structure can easily be dissipated in other directions. However, in the case of the U-OWC in Figure 36 [b] [c] [d] [e], as the waves enter in the OWC and passes over the U-wall, due to the path of the fluid, the pressures affect the front wall in a specific location. According to the height of the U-wall, the pressures in the front wall will be maximum at the edge level of the U- wall. As the U-wall increases from 4 meters to 7 meters, the front wall pressures also increase affecting a longer section of the front wall. This can be explained considering the area of impact. 47

62 5. Case Study: Mutriku OWC Plant [a] Front wall Back wall [b] U-wall [c] [d] [e] Figure 36 - Comparison of the five different geometries for 8 meters wave height when Low Water Level Related to the pressure points in Figure 35, Table 3 presents the pressures for the different geometries. According to these values, the increase of the pressure sensor for the U shape is most noticeable in the front wall at the level of the U-wall edge, these values are marked in bold in Table 3. For the U-shape when the U-wall is 4 meters, the highest-pressure value in point 5, matching with the edge of the U wall and representing an increase in the static pressure of that point of the wall of 76% compared to the J- shape. The U-shape for a U-wall of 5 meters, shows the higher pressure at point 5, with an increase of the 63.4% of the pressure compared to the J-OWC. For a U-wall of 6 meters, the increased compared to the J-OWC is found in point 5, with an increase of 94.1% of the pressure and when the U-wall is 7 meters, the higher pressure is found in point 3, with an increase of 234.7% of the pressure. 48

63 5. Case Study: Mutriku OWC Plant Table 3 - Static pressures in the external part of the front wall OWC Point 1 pressure (Pa) Point 2 pressure (Pa) Point 3 pressure (Pa) Point 4 pressure (Pa) Point 5 pressure (Pa) J 37957, , , , ,6 U4 7268, , , , ,9 U , , , , ,2 U , , , , ,7 U , , , , ,7 Presented in Table 4 and Table 5, are the static pressure values for all the five geometries here considered, for each pressure point. It is noticeable a reduction of the pressures inside of the OWC for the U-shape. This reduction is in the order of 90% compared to the J-shape. In consequence, a visible characteristic of the U-shape is the reduction of the internal pressures in the column, compared with the J-shape. Table 4 - Static pressures in the internal part of the front wall OWC Point 6 pressure (Pa) Point 7 pressure (Pa) Point 8 pressure (Pa) Point 9 pressure (Pa) Point 10 pressure (Pa) J , , , , ,3 U4 2307, , , , ,7 U5 814, , , , ,4 U6 1257,8 1421, , , ,7 U7 1004,0 1133, , , ,0 Table 5 - Static pressures in the internal part of the back wall OWC Point 11 pressure (Pa) Point 12 pressure (Pa) Point 13 pressure (Pa) Point 14 pressure (Pa) Point 15 pressure (Pa) Point 16 pressure (Pa) J , , , , , ,3 U4 2785, , , , , ,7 U5 812, , , , , ,0 U6 1255,3 1507, , , , ,1 U7 1002,1 1135, , , , ,4 49

64 5. Case Study: Mutriku OWC Plant MUTRIKU RESULTS: L.W.L AND 13.7 METERS WAVE HEIGHT Figure 37 presents the compositions of the five geometries considered for a different wave scenario. This scenario is low water level with 13.7 meters waves. Figure 37 [a] presents a J-OWC geometry, the simplest designs. Figure 37 [b] [c] [d] [e] shows U-OWC with front walls of 4, 5, 6 and 7 meters. The results of this wave scenario show similar outcomes as previous scenario for eight meters waves, as showed in Figure 36. The J-OWC in Figure 37 [a] presents higher internal pressures in the column, showed in burgundy colour. The U-shape, Figure 37 [b] [c] [d] [e], with a U-wall in front of the OWC, shows a reduction in the internal pressures of the column. This is true for all the U-OWC, compared to J-OWC design. In relation to the static pressures in the front wall of the OWC, this wave scenario presents a more irregular behaviour, compared to previous wave consideration, Mutriku Results: L.W.L and 8 meters wave height. Although in any case, the static pressures in the front wall increase for the U-shape compared to the J-shape, the increase of the values is not consistent and in accordance to the increment in the U-wall shape. Figure 37 [b] present the results for a U-OWC with U-wall of four meters. It can be seen that there is an increment in the front wall pressures, although these seems to happen for a longer area than expected. The increment in the pressures do not only happened at the level of the end edge of the U-wall, corresponding to point 5, but it happens also at point 4 and point 3. Figure 37 [c], present similar pressures in the front wall as the J- shape. There is an increment in the pressures at point 4, corresponding to the edge of the U-wall for 5 meters. But in general, the pressures seem to be consistent and similar to the J-shape situation. Figure 37 [d], for a U-OWC with U-wall of 6 meters shows an increased in the pressures at point three, corresponding to the edge of the U-wall for this case, as expected. To finish with, Figure 37 [e] shows the geometry considering a U-wall of seven meters, for which the pressures in the front wall seems to be similar to the J- OWC case. 50

65 5. Case Study: Mutriku OWC Plant [a] Front wall [b] U-wall [c] [d] [e] Figure 37 - Comparison of the five different geometries for 13.7 meters wave height when Low Water Level MUTRIKU RESULTS: MIDAS CIVIL ANALYSIS With the static pressures results from ANSYS Fluent, structural analysis is performance with MIDAS Civil, see appendix H Case Study: Mutriku Results with MIDAS Civil for further information about the software and additional results. The front and back wall of the OWCs are further analysed with MIDAS Civil for a better understanding of the structural behaviour. The beam stresses and the resultant displacement according to the pressures can be calculated MUTRIKU RESULTS: FAILURE OF THE STRUCTURE Under uniaxial stress conditions, brittle materials failure is produced when the material begins to fracture. Brittle materials such as gray cast iron, concrete or ceramics tends to 51

66 5. Case Study: Mutriku OWC Plant fail suddenly by fracture with no apparently yielding. The fracture occurs when normal stress reaches the ultimate tensile stress, σult. Failure would occur when the maximum principle stress σ1 in the material reaches a limiting value that is equal to the ultimate normal stress the material can sustain when it is subjected to simple tension. The design and construction of the Mutriku OWC, was originally not made to accommodate the OWC plant. Certain changes in the design were made posteriori. Precast concrete parts for the construction of the OWC were attach to the main body of the breakwater. According to the analysis of Torre-Enciso (2010), it is appreciated that the concrete of the prefabricated parts and the concrete filling between the cells was not the most accurate union. Therefore, the front wall did not work as a single wall of 1.65 cm think, but as three joined layers of 40, 85 and 40 cm (Torre-Enciso, Marqués and Aguileta, 2010). In addition, works in open sea, cause other problems. During the erection of the columns, and due to the wave conditions, the works had to be interrupted several times, so the filling concrete does not present continuity throughout the column (Torre-Enciso, Marqués and Aguileta, 2010). In conclusion to this, the failure of the Mutriku OWC structure is due to the failure of the joints between the precast concrete parts and the in-situ construction, and partially to possible fracture of the concrete by shear stresses, causing cracklings in specific locations. This was already explained in section 2.10 Failure Mechanisms Case Study: Mutriku. The true shear strength of concrete is difficult to determine because is normally affected by other stresses to the structure (Lindeburg, 2015). Based on this, the displacement of the beam is presented, which, with further information on the stresses in the joints could conclude in the failure limit for the front and back walls. MIDAS Civil Results Figure 38 presents the results of the MIDAS Civil displacement analysis for the five types of OWC geometries compared in this thesis for 8 meters wave height when Low Water Level. Figure 38 [a] shows the displacement result for the J-OWC shape. This shape is the most affected by the incoming waves, and therefore the front wall will suffer higher displacement (0,016 m). Figure 38 [b] [c] [d] [e] shows the results for U-OWC with U-walls of 4, 5, 6 and 7 meters. The displacement for these geometries are reduced to m in the case of 4 meters U-wall, m for a 5 meters U-wall, m for a 6 meters U- wall and m for a 7 meters U-wall. Showing a considerable reduction for any of the U-OWC compared to the original J-OWC at Mutriku. 52

67 5. Case Study: Mutriku OWC Plant Figure 38 - Comparison of the OWC geometries front wall displacement for 8 meters wave conditions when LWL Figure 39 shows the MIDAS Civil results for Low Water Level with 13.7 m waves. The results, as with the previous scenario, also shows a reduction in the displacement for the front wall when having a U-OWC shape compared to J-OWC. The J-OWC presents a displacement of m (Figure 39 [a]), which reduces to m for a 4 (Figure 39 [b]) 53

68 5. Case Study: Mutriku OWC Plant and a 5 meters (Figure 39 [c]) U-wall and meters in the case of a 6 meters U-wall (Figure 39 [d]). In the case of having a 7 meters U-wall (Figure 39 [e]), the displacement of the front wall increases in comparison with the J-OWC, being this meters. Figure 39 - Comparison of the OWC geometries front wall displacement for 13.7 meters wave conditions when LWL 54

69 5. Case Study: Mutriku OWC Plant The internal back wall is also analysed using MIDAS Civil, considering the J-OWC and U- OWC designs under different wave circumstances. Figure 40 shows the analysis of the back wall for Low Water Levels for 8 meters wave heights, and Figure 41 for 13.7 meters wave heights. The results of the analysis for the lower wave, for the J-OWC shown in Figure 40 [a] presents the highest displacement, being at point 14 of meters. The U-OWC geometries present smaller displacements being these; m for the U-wall of 4 meters (Figure 40 [b]), m for the U-wall of 5 meters (Figure 40 [c]), m for the U-wall of 6 meters (Figure 40 [d]) and m for the U-wall of 7 meters (Figure 40 [e]). Figure 41 shows the comparison of displacements of the back wall for Low Water Levels for 13.7 meters wave height. The maximum displacement is found for the J-OWC design, having a displacement of m showed in Figure 41 [a]. The reduction for the U-OWC designs is considerable for this scenario of 13.7 meters waves, similar as for waves of 8 meters. The displacements generated when considering the U-OWC shapes are; m for the U-wall of 4 meters (Figure 41 [b]), m for the U-wall of 5 meters (Figure 41 [c]), m for the U-wall of 6 meters Figure 41 [d]) and m for the U-wall of 7 meters (Figure 41 [e]). Therefore, the reduction of the displacement for both wave cases are considerable and similar, improving the reaction of the structure under extreme wave conditions for the U-OWC shapes. Additional results on MIDAS Civil and analysis can be found in Appendix H Case Study: Mutriku Results with MIDAS Civil. 55

70 5. Case Study: Mutriku OWC Plant Figure 40 - Comparison of the OWC geometries back wall displacement for 8 meters wave conditions when LWL 56

71 5. Case Study: Mutriku OWC Plant Figure 41 - Comparison of the OWC geometries back wall displacement for 13.7 meters waves conditions when LWL 57

72 5. Case Study: Mutriku OWC Plant CONCLUSIONS OF THE CHAPTER In this section, the conclusions of the results of the Mutriku OWC analysis are presented. The concluding remarks can be stated as: o Focusing in the Low Water Level results for 8 meters and 13.7 meters wave height; Compared to the J-OWC, there is a reduction on the pressures in the column for the U-OWC shape. The pressures affecting the external face of the front wall increases in area as the front wall height increases. o According to the MIDAS Civil analysis and the beam displacement; The front wall for the J-OWC presents higher displacement, of at least meters, reducing more than 75% for U-OWC. The back wall, present smaller displacement than the front wall, in the order of meters for the J-OWC, and reducing in 80% for the U-OWC 58

73 6. CONCLUSIONS & RECOMMENDATIONS Conclusions: 1. Validation Accurate validation results for the J-OWC shape Validation of the U-OWC shape o Acceptable validation for the pressures at the front wall o Diverges for higher period values for the pressure at the back wall and the resonance inside of the OWC J-OWC partially open presents reduced values than J-OWC fully open validation results for peak resonance periods 2. Case Study: Mutriku General analysis of the geometries, conclude in lower static pressures and less beam stresses and displacement for the geometry with a vertical duct in front, U-OWC o Internal pressures in the OWC reduces for all U-OWC o External pressures in the front wall, compared to J-OWC, reduce in area for U-OWC with lower U-wall, and increase for higher U-wall Final analysis, o Based on the displacement and the water level difference inside the OWC: U-OWC with a vertical front duct of 4 meters is the option with fewer risks of structural damage. 59

74 6. Conclusions and Recommendations CONCLUSION This master thesis attempts to investigate in detail the robustness of an OWC breakwater under extreme wave conditions. A real case study has been taken as example, this is the OWC plant at Mutriku, Spain. In order to proceed with numerical investigation of this design, validation is required (See Section 4.1). With validation purposes, a series of physical and numerical models are compared, ensuring that the results are compatible and equivalent. From here, numerical models of the case study at Mutriku, comparing different wave conditions can be carried out. KEY FINDINGS Based on the research questions posed and considering the outcomes of this study, the key findings are presented as: Validation 1. How accurate is the validation performance for this study? It is concerning, that the validation of the J-OWC is very accurate (section J-OWC shape Fully Open), and the validation of the U-OWC (section U-OWC shape Fully Open) is not as precise. This has been conducted in the same laboratory conditions and following the same numerical approach and boundary conditions. This could be explained due to the friction of the walls. The J-OWC with an opening at the bottom, reduces to the minimum the interaction of the fluid with the OWC walls. On the other hand, the U-OWC shape, which presents a vertical narrow duct in front of the OWC, forces the fluid to pass through it. The constant movement of the fluid through the narrow duct, produces a friction between the fluid and the walls. This wall friction was not taken into account in the numerical model with ANSYS-Fluent, which can explain why the results for the J-OWC are accurate, while the U-OWC validation is acceptable for the front wall but diverges for the back wall and the resonance inside the OWC, which are affected by the duct. 2. Comparison of a partially closed top cover versus an open top cover of a J-OWC The aim of this comparison is to represent via a partially open top part of the structure a more realistic scenario. The presence of a turbine connected to the air chamber, will allow to release part of the compressed air inside of the air chamber, the movement of the turbine will then transfer to a generator to complete the wave energy conversion system. The presence of a turbine and the top cover part, reduces the resonance inside of the OWC, compared to a fully open version. Section J-OWC shape Partially Open shows this reduction, especially in the resonance peak for period of 1,7 sec, for which the values of the resonance for partially open OWC reduces in comparison of those for a fully open OWC. 60

75 6. Conclusions and Recommendations Case study: Mutriku 3. Comparison of the geometries The results of this study show that the pressures affecting the internal structure of the OWC, reduces when using a U-OWC. Improving the total displacement and beam stresses of the front and back wall, therefore reducing the risk of failure of the structure under extreme wave conditions, exposed to high wave pressures. 4. Pressures in the OWCs The pressures inside of the OWC reduce for the U-OWC shape, as the external pressures in the front wall increases, see Figure 42 for the internal pressures in the front wall and Figure 43 for the internal pressures in the back wall. The reduction of the internal forces when using a U-OWC design, compared to J-OWC reduces and remains almost constant for the different height of the vertical duct in front of the OWC. However, the pressures of the front wall experience an increase of the pressures as the vertical duct in front of the OWC increases to 7 meters height, especially for the higher water levels (explained in Section 5.3). The conclusion of the structural analysis, considering the front and back pressures is that the optimum alternative design is a U-OWC with a lower vertical front duct. A higher vertical duct, could be counterproductive, with an increase of the internal pressures in the OWC. Figure 42 Comparison of the internal pressures in the front wall for the different geometries and wave conditions 61

76 6. Conclusions and Recommendations Figure 43 - Comparison of the internal pressures in the back wall for the different geometries and wave conditions 5. Appropriate design of the OWC to reduce displacement According to the previous point, and according to the displacement results of the beams with MIDAS Civil (Figure 38, Figure 39, Figure 40 and Figure 41), the U-OWC show better structural results, with smaller displacement of the front and the back wall. With a reduction of at least 75% for the front wall and more than 80% for the back wall, the U- shape is a more appropriate option to minimise structural damaging. 6. Water Level in the column Figure 44 shows the water level changes inside the OWC for the different storm conditions here considered. It is seen that there is a reduction on the average water level change in the column from the J-OWC to the U-OWC and also as the U-wall increases to U-wall of seven meters. Having a higher water level difference under storm conditions, it is concluded that the J- OWC is the optimal alternative for power generation, followed by the U-shape with a U- wall of four meters. 62

77 6. Conclusions and Recommendations Figure 44 - Change in the water level inside the OWC for the different storm conditions Final conclusions on Mutriku OWC Based on the structural analysis with MIDAS Civil, the best option to reduce damages for the internal pressures under storm conditions would be a U-OWC of U-wall of four, five or sex meters (Figure 42 and Figure 43). The front wall external pressures, present lower pressures for the J-OWC and U-OWC with lower U-walls. If the water level difference in the column is also considered, and accounting for the structural analysis, the design that presents less risk for the structure, and allows a high energy production, based on the water level difference, is the U-OWC shape with the vertical front wall of 4 meters LIMITATIONS o The laboratory experiments carried out are limited in the range of wave conditions that can be used. Avoiding any over plashing of the water over the wave tank, leading to limitations in the wave periods to be used. Panels on the side of the wave tank can be a simple solution, which will allow to increase the range of wave conditions. o Ansys Fluent restriction in the number of cells, limits the analysis to a 2D version. o Midas Civil structural analysis is considered for a 2D structure. Consequently, the front wall which is attached to the OWC from the top and side edges, in the structural analysis is considered as a cantilever concrete beam, only attached from the top. A similar limitation happens with the back wall, which is attach to the rest of the structure on the four edges, but Midas civil analysis is carried out in 2D, and therefore, only top and bottom attachment are considered. 63

78 6. Conclusions and Recommendations RECOMMENDATIONS 1. Wider range of laboratory data for validation The range of wave conditions to be used in the laboratory facilities for the scaled model is limited. Although the validation is accurate and proved, a higher range of data will verify the total resonance curvature. 2. More pressure sensors in the structure for the laboratory experiment The laboratory experiment model counts with 3 pressure sensors, one in the front wall, one in the back wall, and one in the top cover of the OWC when this is fully close. The analysis of the validation could be improved by having the pressure sensors located lower in the structure, otherwise, the water level is limited, to ensure that the pressure sensors are always submerged. Another alternative could be to have more pressure sensors in the model, so more pressure data is available to compare with numerical model. 3. Improvements on the validation analysis of the U-OWC To improve the U-OWC validation, further analysis of the numerical modelling comparing different wall frictions can be implemented. The following image, shows the original results, compared to implemented numerical models accounting with the wall duct friction. It can be seen an improvement in the validation when friction is taken into account. This could be further investigated in the numerical model and improved. Figure 45 Comparison of the validation of ANSYS-Fluent results for the resonance oscillation inside of a U-OWC when the top part of the OWC is open, with different wall frictions situations 64

79 6. Conclusions and Recommendations SST Figure 46 -Detailed of the comparison of the validation of ANSYS-Fluent results for the resonance oscillation inside of a U-OWC when the top part of the OWC is open, with different wall frictions situations See appendix B ANSYS-Fluent General theory and fundamentals, section Turbulence models, for detailed explanation in the turbulence models k-epsilon and k- omega used. 4. Further investigation on the influence of a turbine in the resonance of an OWC The incorporation of a partially open top cover of an OWC (figure 22), aims to represent the OWC behaviour with a turbine integrated in the system. The opening chosen for the cover is just a representative example, and not an accurate calculation of the dimensions of the opening for a similar behaviour of a wells turbine, or any other turbine to be used depending on the design. Taking this into account, it can be calculated for a specific type of turbine, the amount of air exchange per period of resonance and from there, calculated the opening necessary in the top cover to represent the behaviour of a specific turbine. 5. Numerical analysis of more extreme wave conditions and water levels. A wider variety of wave conditions, with different wave heights and different water levels for each geometry, could give a better understanding on the behaviour of the fluid with the front vertical duct and a better final analysis on the best design alternative. 6. Analysis of wave pressures for U-OWC with lower front duct Since in the bigger picture, considering the reduction of walls displacement and the water level in this situation, the best option is to have a U-OWC with a vertical front duct of 4 meters. It would also be interesting to investigate the response of the structure with lower levels of this front duct. 7. Midas Civil analysis 3D consideration 65

80 6. Conclusions and Recommendations The structural analysis carried out with Midas Civil is a simple 2D analysis, which could be improve to a 3Danalysis 8. Structural analysis with distributed pressures The pressure information from the front and back walls, is applied in Midas Civil as point loads and not as distributed loads. This should be considered, and further analysis of the structure with distributed pressures can be implemented. 66

81 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero BIBLIOGRAPHY Alberdi, M. et al. (2011) Complementary control of oscillating water column-based wave energy conversion plants to improve the instantaneous power output, IEEE Transactions on Energy Conversion, 26(4), pp doi: /TEC Astariz, S. and Iglesias, G. (2015) The economics of wave energy: A review, Renewable and Sustainable Energy Reviews, 45, pp doi: /j.rser Boake, C. B. et al. (2002) Overview and Initial Operational Experience of the LIMPET Wave Energy Plant, Proceedings of The 12th International Offshore and Polar Engineering Conference, (January), pp Bouali, B. and Larbi, S. (2013) Contribution to the Geometry Optimization of an Oscillating Water Column Wave Energy Converter, TerraGreen 13 International Conference Advancements in Renewable Energy and Clean Environment. Elsevier B.V. doi: /j.egypro Buigues, G. et al. (2006) Sea energy conversion: problems and possibilities, International Conference on Renewable Energies and Power Quality (ICREPQ 06), p. 8. doi: /repqj Clément, A. et al. (2002) Wave energy in Europe: Current status and perspectives, Renewable and Sustainable Energy Reviews, 6(5), pp doi: /S (02) Contestabile, P. et al. (2017) Wave loadings acting on innovative rubble mound breakwater for overtopping wave energy conversion, Coastal Engineering. Elsevier, 122(January), pp doi: /j.coastaleng Cuomo, G. et al. (2010) Breaking wave loads at vertical seawalls and breakwaters, Coastal Engineering, 57(4), pp doi: /j.coastaleng Czech, B. and Bauer, P. (2012) Wave Energy Converter Concepts. Falcão, A. (2014) Modelling of Wave Energy Conversion, pp Falcão, A. F. d. O. (2010) Wave energy utilization: A review of the technologies, Renewable and Sustainable Energy Reviews, 14(3), pp doi: /j.rser Falcão, A. F. O. and Henriques, J. C. C. (2016) Oscillating-water-column wave energy converters and air turbines: A review, Renewable Energy, 85(November 2017), pp doi: /j.renene Falcão, A. F. O., Henriques, J. C. C. and Gato, L. M. C. (2016) Air turbine optimization for a bottom-standing oscillating-water-column wave energy converter, Journal of Ocean Engineering and Marine Energy. Springer International Publishing, 2(4), pp doi: /s Hammar, L. et al. (2017) Introducing ocean energy industries to a busy marine environment, Renewable and Sustainable Energy Reviews. Elsevier Ltd, 74(January 2016), pp doi: /j.rser

82 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero Henriques, J. C. C. et al. (2016) Design of oscillating-water-column wave energy converters with an application to self-powered sensor buoys, Energy, 112, pp doi: /j.energy Horko, M. (2007) CFD Optimisation of an Oscillating Water Column Wave Energy Converter, M.Sc Thesis. Howe, D. and Nader, J. R. (2017) OWC WEC integrated within a breakwater versus isolated: Experimental and numerical theoretical study, International Journal of Marine Energy. Elsevier Ltd, 20, pp doi: /j.ijome Hydro, V. (2012) A review of oscillating water columns, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 370(1959), pp doi: /rsta Kamath, A. (2015) CFD based Investigation of Wave-Structure Interaction and Hydrodynamics of an Oscillating Water Column Device. Kelkitli, M. I. (2018) Analysis of the Ocean Falls Wave Energy Converter in Regular Waves. Delft. Khan, N. et al. (2017) Review of ocean tidal, wave and thermal energy technologies, Renewable and Sustainable Energy Reviews. Elsevier Ltd, 72(October 2015), pp doi: /j.rser Khchifati, M. I. E., Terkaoui, A. and Alterkaoui, A. (2015) Wave Power Generator (W.P.G). Kuo, Y. S. et al. (2015) Wave loading distribution of oscillating water column caisson breakwaters under non-breaking wave forces, Journal of Marine Science and Technology (Taiwan), 23(1), pp doi: /JMST Laface, V. and Carillo, A. (2013) Installing U-Owc Devices Along Italian Coasts, Proceedings of the ASME nd International Conference on Ocean, Offshore and Arctic Engineering, (June), pp doi: /OMAE Lindeburg, M. R. (2015) Civil engineering reference manual for the PE exam. Fifteenth. Belmont, CA. Lopes, M. F. P. et al. (2009) Experimental and numerical investigation of non-predictive phase-control strategies for a point-absorbing wave energy converter, Ocean Engineering, 36(5), pp doi: /j.oceaneng McCormick and Michael, E. (2013) Ocean wave energy conversion. Courier Corporation. Memoria, D. (2009) PROYECTO BÁSICO DE REPARACIÓN DE LA CENTRAL UNDIMOTRIZ DEL PUERTO DE MUTRIKU - Documento 1. MEMORIA, Eusko Jaurlaritza - Gobierno Vasco. Minns, J. E. S. (2012) Comparative performance of a novel oscillating water column wave energy converter. Mustapa, M. A. et al. (2017) Wave energy device and breakwater integration : A review, Renewable and Sustainable Energy Reviews. Elsevier Ltd, 77(March), pp doi: /j.rser Ortubia, I., Lo pez de Aguileta, L. I. and Torre-Enciso, Y. (2008) Implantación de una central undimotriz en el nuevo dique de abrigo al puerto de mutriku. 68

83 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero Simonetti, I. et al. (2018) Evaluation of air compressibility effects on the performance of fixed OWC wave energy converters using CFD modelling, Renewable Energy. Elsevier Ltd, 119, pp doi: /j.renene Suzuki, M. and Port, S. (2004) Performance of Wave Power Generating System Installed in Breakwater at Sakata Port in Japan., 14th International Offshore and Polar Engineering Conference, ISOPE, 1, pp Torre-Enciso, Y. et al. (2009) Mutriku Wave Power Plant: from the thinking out to the reality, 8th European Wave and Tidal Energy Conference (EWTEC 2009), pp Available at: Enciso_et_al_2009.pdf. Torre-Enciso, Y., Marqués, J. and Aguileta, L. I. L. de (2010) Mutriku. Lessons learnt. Bilbao: ICOE. Verhagen, H. J. (2017) Breakwater design, (January). Vicinanza, D. et al. (2012) Innovative Breakwaters Design for Wave Energy Conversion, Coastal Engineering Proceedings, 1(33), p. 1. doi: /icce.v33.structures.1. Vyzikas, T. et al. (2017) Experimental investigation of different geometries of fixed oscillating water column devices, Renewable Energy, 104, pp doi: /j.renene Wang, H. A. O. and Kim, M. (2013) Wave Energy Extraction From an Oscillating Water Column in a Truncated Circular Cylinder, M.Sc Thesis, (August). Waterman, R. E. (2010) Integrated Coastal Policy via Building with Nature, TU Delft, p. 69. Webb, I., Seaman, C. and Jackson, G. (2005) Oscillating water column wave energy converter evaluation report, the Carbon Trust. Available at: 69

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85 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero APPENDICES List of Figures... III List of Tables... V Appendix A Ocean Wave Energy in Relation with Oscillating Water Column... 1 Ocean Wave Energy Hydrodynamics... 1 Ocean Wave Transport Energy transport & Power extraction from waves... 4 Nonlinear wave theory Stokes Wave Power extraction... 6 OWC Hydrodynamic Capture Efficiency...7 Appendix B ANSYS Fluent General Theory, Fundamentals and Model Execution Theoretical background...8 Introduction Navier-Stokes Equations The RANS Equations Turbulence Models User-Defined Scalar (UDS) Transport Equations Single Phase Flow MultiPhase Flow Two Phase Flow Modeling Model Execution: High Performance Computing or Cluster General Procedure Appendix C Model Set Up and Boundary Conditions on ANSYS Fluent General Validation Set Up Mesh Sizing for Validation Boundary conditions for Validation Information on Outflow for Validation Case Study: Mutriku Mesh Sizing for Mutriku I

86 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero Boundary conditions for Mutriku Information on the Outflow for the Mutriku case study Pressure sensors Appendix D Experimental model set up in the Water Lab at TuDelft Experimental Method and General Information Case Studies OWC - Dimensions General Laboratory Information Scale Model Appendix E Model Calibration...29 Appendix F Laboratory and ANSYS Fluent Result Comparison for Validation...33 Appendix G Case Study: Mutriku Results with ANSYS Fluent Mutriku Results: H.W.L and 8 meters wave height Mutriku Results: H.W.L and 13.7 meters wave height Appendix H Case Study: Mutriku Results with MIDAS Civil Theoretical background Results from Midas Civil on the Beam Stress and Displacement Anslysis Discussion of Results References...57 II

87 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero LIST OF FIGURES Figure 1 - Properties of waves under various depth conditions (Holthuijsen, 2007) Figure 2 -Estimated annual mean power distribution in Europe (Gleizon et al., 2017)... 4 Figure 3 - Sketch a nonlinear wave profile (McCormick and Michael, 2013)... 5 Figure 4 - Fraction function for blue phase in VOF method Figure 5 Section of the mesh on ANSYS Fluent Figure 6 Mesh image of the cross-section of the ANSYS-Fluent representation of Mutriku in Spain Figure 7 - Detailed section of the pressure points location defined in ANSYS-Fluent for Mutriku. Showing the 16 pressure points defined and the line for the water level measurement Figure 8 - Cross-section of the J-OWC at Mutriku (Spain) (Memoria, 2009) Figure 9 - Cross-section of the OWC REWEC3 in the Civitavecchia harbour (Arena et al., 2013) Figure 10 Geometries of the J-OWC and U-OWC and location of the pressure sensors in the different walls Figure 11 - Detail of laboratory model dimensions Figure 12 - Detailed cross-section of J-OWC showing the pressure sensors locations Figure 13 - Detailed cross-section of J-OWC showing the wave gauges locations Figure 14 - Front Wall Pressure Sensor Validation Figure 15 - Back Wall Pressure Sensor Validation Figure 16 Wave gauge validation inside of the OWC Figure 17 - Wave gauge validation 3 meters from the OWC Figure 18 - Wave gauge validation 7 meters from the OWC Figure 19 - Wave gauge validation 11 meters from the OWC Figure 20 -Comparison of the front wall pressure sensor ANSYS-Fluent and the Laboratory experiments for T=2,3 sec Figure 21 - Comparison of the back-wall pressure sensor ANSYS-Fluent and the Laboratory experiments for T=2,3 sec Figure 22 - Comparison of the wave gauge inside of the OWC ANSYS-Fluent and the Laboratory experiments for T=2,3 sec III

88 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero Figure 23 - Comparison of the wave gauge 7 meters from the OWC ANSYS-Fluent and the Laboratory experiments for T=2,3 sec Figure 24 - Comparison of the wave gauge 11 meters from the OWC ANSYS-Fluent and the Laboratory experiments for T=2,3 sec Figure 25 - Comparison of the five different geometries for 8 meters wave height when High Water Level Figure 26 - Comparison of the five different geometries for 13.7 meters wave height when High Water Level Figure 27 - Sign convention for ECS and element forces (or stresses) of a beam element (MIDAS GEN, no date) Figure 28 - Comparison of the OWC geometries front wall displacement for 8 meters wave conditions when HWL Figure 29 - Comparison of the OWC geometries front wall displacement for 13.7 meters wave conditions when HWL Figure 30 - Comparison of the OWC geometries front wall beam stress for 8 meters wave conditions when LWL Figure 31 - Comparison of the OWC geometries front wall beam stress for 13.7 meters wave conditions when LWL Figure 32 - Comparison of the OWC geometries front wall beam stress for 8 meters wave conditions when HWL Figure 33 - Comparison of the OWC geometries front wall beam stress for 13.7 meters wave conditions when HWL Figure 34 - Comparison of the OWC geometries front wall displacement for 8 meters wave conditions when HWL Figure 35 - Comparison of the OWC geometries front wall displacement for 13.7 meters wave conditions when HWL Figure 36 - Comparison of the OWC geometries front wall beam stress for 8 meters wave conditions when LWL Figure 37 - Comparison of the OWC geometries front wall beam stress for 13.7 meters wave conditions when LWL Figure 38 - Comparison of the OWC geometries front wall beam stress for 8 meters wave conditions when HWL Figure 39 - Comparison of the OWC geometries front wall beam stress for 13.7 meters wave conditions when HWL IV

89 Investigation of the Robustness of an OWC Breakwater Under Extreme Wave Conditions Inés Báez Rivero LIST OF TABLES Table 1 - Characteristics of the model for ANSYS Fluent for validation Table 2 - Characteristics of the mesh sizing for ANSYS-Fluent for validation Table 3 - Outflow information for ANSYS-Fluent, depending on wave conditions for validation Table 4 - Characteristics of the geometry for ANSYS Fluent for Mutriku case study Table 5 - Characteristics of the mesh sizing for ANSYS-Fluent for Mutriku case study Table 6 - Outflow information for ANSYS-Fluent, depending on wave conditions for Mutriku Table 7 - Classification of laboratory experiments according to the top part of the OWC Table 8 - Dimensions of wave tank at TUDelft Water Lab Table 9 model experiment scaled from Mutriku prototype Table 10 - Static pressures in the external part of the front wall Table 11 - Static pressures in the internal part of the front wall Table 12 - Static pressures in the internal part of the back wall Table 13 - Static pressures in the external part of the front wall Table 14 - Static pressures in the internal part of the front wall Table 15 - Static pressures in the internal part of the back wall V

90 APPENDIX A OCEAN WAVE ENERGY IN RELATION WITH OSCILLATING WATER COLUMN OCEAN WAVE ENERGY An oscillating water column obtains energy from ocean waves to convert it into useful electricity for society. An important feature of ocean waves is their high energy density, which is the highest among renewable energy sources. Law of conservation of energy states that energy can be neither be created nor be destroyed, but it transforms from one to another. This is the principle Wave Energy Converter Systems uses, converting the ocean energy carried by waves; a mechanical motion that can be transform into electricity (Clément et al., 2002). Wave energy is transported thousands of kilometres with little energy loss, which can change depending on different external factors. Water particles move position, the work required to make this movement possible, represents potential energy, and the wave particle move, represents kinetic energy (Holthuijsen, 2007) HYDRODYNAMICS In hydrodynamics, basic equations to explain mass and momentum conservation are the continuity (eq. 1.1) and Navier-Stokes equation (eq 1.2) (Holthuijsen, 2007). Basic assumptions: Constant density, no viscosity Rigid, impermeable bed Only external force: gravitation δρ δt + (ρν ) = 0 cos 1.1 Dν Dt = 1 ρ ρ tot + ν 2 ν + 1 ρ f 1.2 Where ρ: density [Kg/m 3 ] ν : velocity [m/s] t: time [sec] 1

91 ρ tot : total pressure [Pa] ν: kinetic viscosity coefficient [Pa s] f : external forces [N ] The free surface is the interface between water and air, which position is defined as: z = η(x, y, t) Considering only gravitational forces f = ρg, and atmospheric pressure ρ tot = ρ atm as pressure on the surface of the fluid. From previous equations, the mathematical expression for the free-surface displacement is shown in eq 1.3 (McCormick and Michael, 2013): Where: H: wave height [m] T: wave period [s] λ: wave length [m] η = H 2 cos (2πx λ According to linear wave theory, wave period is defined as: 2πt T ) 1.3 T = 2π [ 2πg λ 1/2 tanh (2πh λ )] = 1 f = 2π ω 1.4 The wave length is defined as: Individual waves travel at a phase velocity c, described as: Where k is the wave number defined by: λ = gt2 tanh (2πh 2π λ ) 1.5 c = λ T = gt 2π tanh(kh) 1.6 k = 2π λ 1.7 The water particles within the wave travel with horizontal and vertical components for shallow water, where h < 1, the approximate expression is: λ 20 u = H 2 g h cos(kx ωt) 1.8 2

92 and w = πh T (z + h) sin(kx ωt) 1.9 h Figure 1 - Properties of waves under various depth conditions (Holthuijsen, 2007). OCEAN WAVE TRANSPORT The total instantaneous wave-induced potential energy in a column, is the potential energy in the presence of waves minus the potential energy in the absence of waves, for potential energy being defined as a slice of water with thickness z and surface area x y, is given as ρgz Δx Δy Δz. (Twidell and Weir, 2015). E potential = 1 4 ρga Where a is the wave amplitude [m] The corresponding time-averaged total instantaneous kinetic energy in that same defined slice of water is E kinetic = 1 4 ρga The total time-averaged, wave induced energy per unit horizontal area is: E total = E potential + E kinetic = 1 2 ρga2 (J/m 2 ) 1.12 E total = ρgh The energy per unit wavelength in the direction of the wave, per unit width of wave front, is: 3

93 E λ = Eλ = 1 2 ρga2 λ 1.14 Where: λ = πρg2 a 2 ω ENERGY TRANSPORT & POWER EXTRACTION FROM WAVES Wave power being measured in KW/m is the power contained in each meter per wave crest. This power moves in circular particle motions, with both potential and kinetic energy as defined previously (eq and 1.11). The movement of the particles is defined by the Airy wave equations, which describes linear waves (Minns, 2012). Stokes wave equations describes non-linear waves, with a higher order of the equation. The order of the equation determines the correlation between the result and reality, the higher the correlation, the better this is defined (Minns, 2012). The transport of energy or power across vertical section of the water can be calculated considering the pressures in the water and the resulting displacements (Twidell and Weir, 2015). Figure 2 -Estimated annual mean power distribution in Europe (Gleizon et al., 2017) The transfer of wave energy from point to point in the direction of the wave is characterised by the wave power or energy flux, which is commonly represented as: P = 1 8 ρgh2 c g b 1.16 Where c g is the group velocity, and is given as: c g = c 2 {1 + 2kh } = nc 1.17 sinh (2kh) In shallow water (where h < λ ), however, the waves remain stationary with respect to 20 the group boundaries; thus c g = c (Shallow water) When waves are traveling towards the coast, they are influenced by a range of factors: 4

94 o Change of depth, shallow enough to affect the wave o Irregular coast line (e.g. islands) o Currents As ocean waves reach the coast they begin to shoal, decreasing the speed when they start feeling the seafloor and increasing in wave heights. The wave profile changes to a narrower crest and broader trough, these breaking waves are highly non-linear (Gleizon et al., 2017). Sea water level (SWL) and mean water level (MWL) coincide for linear waves, but in the case of non-linear wave, SWL will be below MWL. MWL is half the distance from trough to crest, on the other hand, SWL is defined by the water depth (McCormick and Michael, 2013). Figure 3 - Sketch a nonlinear wave profile (McCormick and Michael, 2013) NONLINEAR WAVE THEORY STOKES WAVE The behaviour of waves in shallow waters can be explained by the Stokes second order theory. This introduces an irrotational water wave theory, that utilises series representations of wave properties. The accuracy will depend on the number of terms contained in the series. For example, Stokes first order theory is just like the linear theory. For the Stokes second order theory, the accuracy of determining the wave profile, the mass being transported and the breaking condition improves (McCormick and Michael, 2013), therefore, the shallow water wave profile obtained is: H 2 η = H 2 cox(kx ωt) k 2 h 3 cos[2(kx ωt)] 1.18 Where the first term of the equation is the linear profile, and the second term is the correction to the first order linear theory. At the crest it can be assumed that: 5

95 cos(kx ωt) = cos[2(kx ωt)] = For shallow water, the breaking condition according to Stokes second order theory is: ωh b 2kh [1 + 3 H b 8 k 2 h 3] = gh 1.20 And the breaking height is: H b = 16π2 h 2 3gT 2 [ gT2 4π 2 h ] 1.21 For shallow water, using the Stokes second order theory, the total wave energy is (McCormick and Michael, 2013): And the wave power is: E = ρgh2 λb 8 P = ρgh2 c g b 8 H 2 [ k 2 h6] 1.22 H 2 [ k 4 h6] POWER EXTRACTION From the incoming power flux of waves and knowing the width of the device, the power available at the device can easily be calculated. From previous equation 1.23 and for a capture width given as: C w = ρgae kz sin ωt 1.24 In addition to this complexity, sea waves normally propagate in many different directions, and therefore WEC have to be able to convert the energy coming from many directions. Otherwise, part of the power would be lost in the process. Also, waves randomness adds complexity to the prediction on their behaviour (Minns, 2012). In practice, and in the case of nearshore WEC location, waves approach from an arc, rather than from all points. Also, in practice, predicting waves can be possible since they will have a similar approach to the coast, but in the case of extreme events, waves form with little time and hence they are extremely very difficult to predict. For this reason, survivability of the structure under extreme conditions must be a primary design parameter (Minns, 2012). 6

96 OWC HYDRODYNAMIC CAPTURE EFFICIENCY Considering Stokes second order waves, the conversion capability of the device can be expressed as (Simonetti et al., 2015): P w = 1 ω 16 ρgh2 k (1 + 2kh sinh(2kh) ) ( k 4 h 6) 1.25 H 2 Where ω is the wave frequency K is the wave number H is the water depth Considering the air chamber as incompressible, the average hydrodynamic power can be expressed as: P hydro = 1 T OWC t=t OWC dη t P t dt A OWC dt OWC t= The OWC capture efficiency can be expressed as: ε = P hydro P w

97 APPENDIX B ANSYS FLUENT GENERAL THEORY, FUNDAMENTALS AND MODEL EXECUTION ANSYS develops, commercialize and supports engineers as a simulation software. In order to predict how a determined fluid, reacts under a realistic representation of an environment, ANSYS-Fluent extension may be used (Calisto, 2016). This software is designed to use finite element method (FEM) and finite volume method (FVM), to evaluate partial differential equations in the form of algebraic equations (ANSYS, 2009). 1. THEORETICAL BACKGROUND This appendix describes the theoretical background for the basic physical models that ANSYS FLUENT uses for fluid flow. INTRODUCTION ANSYS fluent provides modelling capabilities for a wide range of fluid flow problems, being able to distinguish from; incompressible and compressible, laminar and turbulent fluids, steady-state or transient analyses, free-surface and multiphase flow models, relation of gas-liquid flows (ANSYS, 2009) NAVIER-STOKES EQUATIONS ANSYS solves equations for momentum and mass. In global term the motion of fluid can be described by Navier-Stokes equations. For a compressible Newtonian fluid, conservation of mass and momentum are described as shown respectively in the following equations (ANSYS, 2009): ρ t +. (ρu) = ρ ( u t + u. u) = P + μ 2. u + F 2.2 For incompressible fluid the equations can be rewritten as follows (ANSYS, 2009): 8

98 U x + V y + W z = U t V t W t U U U + U + V + W x y z = 1 ρ V V V + U + V + W x y z = 1 ρ + U W x + V W y + W W z = 1 ρ P x + v U ( 2 x U y U z 2 ) + F X P y + v V ( 2 x V y V z 2 ) + F Y P z + v Z ( 2 x Z y Z z 2) + F Z Where P is pressure U, V and W are velocity in x,y and z direction respectively FX, FY and Fz are external forces in x,y and z direction respectively ν is kinematic viscosity t is time ρ is fluid density μ is dynamic viscosity The first four terms in the left-hand side of the equation represent inertia forces. The first term in the RHS represents pressure forces. The second term in RHS represents viscous forces and the last term correspond to the external forces. So far, there have been described four equations (1 continuity and 3 conservation of momentum) and also 4 unknowns (3 velocities and 1 pressure). It suggests that by having the magnitude of velocities and pressures at boundaries, the problem can be solved. However due to non-linearity, analytical solutions can only be found for simple cases when viscosity dominates the whole system (ANSYS, 2009) THE RANS EQUATIONS Reynolds-averaged Navier-Stokes (RANS) is the most common method used to solve flows. Reynolds decomposition is used to derive RANS equation from Navier-Stokes equations. Velocity and pressure are decomposed into an ensemble average and a fluctuating part (ANSYS, 2009). u i = u + u 2.7 P = p + p 2.8 Inserting Reynolds decomposition for velocity and pressure into NS equation, and after averaging of the equations, the RANS equation is derived as (ANSYS, 2009): 9

99 ρ( t (u i) + (u iu j)) = p + μ 2 u i + F x j x i x j x i (ρu ) i x iu j 2.9 j This equation has an extra term in comparison with Navier-Stokes equation. The last term in the right-hand side of the equation has been produced by the nonlinear advection term and is related to Reynolds stresses (ANSYS, 2009): q ij = ρu i u j 2.10 i = j q 11, q 22, q 33 i j s ij Normal Stresses Shear Stresses The RANS equation can be simplified by assuming that in case of turbulent flow, the pressure gradient is the dominant term, being this much bigger than the gradient in the normal stresses. Also, for cases assuming that the Reynolds number turbulent shear stresses are of higher importance than the viscous shear stresses. Near the wall, the second assumption mentioned does not hold anymore, since the viscous stresses are dominant (ANSYS, 2009). Considering the above-mentioned assumptions, simplified RANS equation can be written as: ρ( t (u i) + (u iu j)) = p + F x j x i (s i x ij ) 2.11 j The presence of Reynolds stresses terms adds 3 unknowns, which left us with a nonclosed set of equations. Turbulence models are required to close this set of equations. Each model has its own advantages and disadvantages and provides some estimation of Reynolds stresses (ANSYS, 2009) TURBULENCE MODELS One of the most well-known turbulence models is the semi-empirical K-ε model. Although it has a simple framework in comparison with other turbulence models, due to its robustness and reasonable accuracy, it has been used for a wide range of turbulent flow simulations. Turbulence length and time scales in K-ε method are determined by solving two different sets of equations. One should note that the primary assumptions behind k-ε model are the fact that flow is completely turbulent, and also that the molecular viscosity is really small (ANSYS, 2009). In ANSYS-Fluent there are also two modified version of K-ε; the realizable k-ε and the RNG k-ε. The following equation is hold for the turbulent kinetic energy k, turbulent dissipation rate ε, and turbulent viscousity μt (ANSYS, 2009): 10

100 μ t = ρ C μ k 2 ε 2.12 Where Cμ is a constant. One of the other well-known turbulence models is K-ω model. The shear stress transport (SST) K-ω models includes also transport of the turbulence shear stress by turbulent viscosity. This advantage makes K-ω SST mode more reliable in predicting the magnitude and location of flow separation (ANSYS, 2009). These two models will be considered in the calibration simulations with ANSYS-Fluent, to compare the results and analyse them, see Figure 46 in section 6.2 Recommendations. USER-DEFINED SCALAR (UDS) TRANSPORT EQUATIONS SINGLE PHASE FLOW For an arbitrary scalar φ k, ANSYS-Fluent solves the equation: δρφ k δt + δ δx i (ρu i φ k Γ k δφ k δx i ) = S φk k = 1,, N 2.13 Where the volume fraction is defined by α l, physical density by ρ l and velocity of phasel by u i. Γ k and S φk are the diffusion coefficient and source term you supplied for each of the N scalar equations. The diffusion term is (Γ k φ k ) The mass flux for phase-l is defined as F l = α l ρ l u i ds S 2.14 If the transport variable described by φ l k represents the physical field that is shared between phases, or is considered the same for each phase, then the scalar is associated with a mixture of phases φ k. The generic transport equation for the scalar is (ANSYS, 2009): δρ m φ k δt + (ρ m u m φ k Γ k m φ k ) = S k m k = 1,, N 2.15 Conservation equations for laminar flow in an inertial (non-accelerating) reference frame are presented. The equations that are applicable to moving references frames are presented in flows with Moving References Frames (ANSYS, 2009). 11

101 MULTIPHASE FLOW TWO PHASE FLOW MODELING Volume of fluid model (VOF) is used to capture the free surface. This method contains three main part: a method to locate the interface, a method to track the surface through grid mesh, and special boundary condition for interface (ANSYS, 2009). For multiphase flows, ANSYS-Fluent solves transport equations for two types of scalars; per phase and mixture. For each fluid in the domain, a variable called fraction function (α) is defined per cell. Fraction function for each phase, basically describes what percentage of cell is occupied by that phase. Sum of fraction functions in each cell should be one. As an example, the fraction function for fluid phase (blue phase) is shown in Figure 4. Figure 4 - Fraction function for blue phase in VOF method Based on the α factor, appropriate properties of the fluid are given to each cell. As an example, density follows this equation (Raja, 2012): ρ = γρ i + (1 γ) ρ j 2.16 Conservation of mass equation for fraction function of each phase should be achieved to be able to track the free surface. For the i th phase, the volume fraction equation takes the form of (ANSYS, 2009): 1 [ ρ i t (α iρ i ) + (α i ρ i u i ) = s αi + (m ij m ji) ] 2.17 Where m ij is the mass transfer from phase i to phase j and m ji is the mass transfer from n j=1 phase j to phase i. s αi is source term which is by default cero. In locations where a cell has only one phase, the standard interpolation method is used as it is the case for one phase flow. In the interface region the Geometric Reconstruction Scheme which is based on the linear method is used. This linear form of interface is used for calculation of advection of fluid through the cell (ANSYS, 2009). 12

102 For flows involving species mixing or reactions, a species conservation equation is solved. For turbulent flows, additional transport equations are solved. 2. MODEL EXECUTION: HIGH PERFORMANCE COMPUTING OR CLUSTER Due to the quality of the mesh and the amount of time steps needed for this project, it was necessary to use a High-Performance Computer (HPC), also usually referred to as cluster. This part of the appendix aims to explain the general process that needs to be taken in order to run Fluent on the cluster. GENERAL PROCEDURE For running any software or code in the cluster, it is necessary to have a software able to display remote applications in windows computers. In this case, MobaXterm is the one chosen, but there are other free softwares that could be used. Using this, it is now possible to get access to the computer cluster of your department. There is no Graphical User Interface (GUI) at the cluster, therefore, all the Fluent commands need to be written in script and journal files, using TUI language (Auweraert, 2015). In total there is necessary to have four files; case, data, journal and the script file. 1. Case file; after setting up the model in the fluent interface, this file contains the different characteristics and boundary conditions necessary for the cluster to run. File; write; case 2. Data file; once the case is set up, this is initialised in Fluent and saved. File; write; data. 3. Script or sh file; is the file to be submitted and send to the cluster. This contains essential information, such as to tell the cluster to open and run Ansys-Fluent and which version, 18.1 in this case. The available versions in the cluster can to be checked prior. This also contains other information such as the number of cores to be used, usually all users use 20 cores for cluster034, the time this will take and the journal file to run. 4. The journal file contains information for Fluent. Although all of the required information is saved in the case file, some of the data, mostly related to time steps and the frequency to save data, are re-defined in the journal file. When the script and journal files finish, the case and data are uploaded to the cluster, where they run. 13

103 Examples of script and journal file are presented for a hypothetical fluent case called test1 : (Note that line starting with semicolon ; are just information and comments for the user) Cluster script or.sh file ;Define number of required nodes and cores #PBS -l nodes=1:ppn=20 ;Define approximate required time of your simulation #PBS -l walltime=40:00:00 ;Define a specific name for each of your jobs #PBS -N Cluster034 ;Load your preferable ansys version; define if your model is 2d or 3d Journal file ;Read your journal file by rcd command and then your case file name rcd test1.cas y ;Define the place for fluent to start with, for instance compute defaults from a velocityinlet called inlet /solve/initialize/compute-defaults/velocity-inlet inlet /solve/initialize/open-channel-auto-init ; Initialize the solution /solve/initialize/initialize-flow ; Set up auto-save intervals, for instance 1000 /file/auto-save data-frequency 1000 Once the above-mentioned files are prepared, the job can be submitted to the cluster. Since the cluster is run on the Linux platform, is useful to know some basic commands on Linux. Here are some of the most common commands: Submit your job: qsub yourjob.sh Move to a folder: cd foldername Go back to previous folder: cd.. 14

104 View active jobs and available cores on cluster: show q View active jobs for a specific netid: qstat -u yournetid To find which folder are you at: pwd To delete a submitted job: qdel jobid Other useful information: When submitting the files (data, case, journal and script) to the cluster, make sure they are all in the same folder in the cluster. You can easily create sub-folders in MobaXterm. It is not necessary to be connected to the internet during the whole process of running in the cluster. Once the Fluent case is send to the cluster it will continue running without internet. The geometry for Ansys Fluent can be imported from AutoCad (saved as.igs) The cluster will consider the information saved in your journal file related to time step, number of iteration, output intervals, UDF files, etc. and not the one defined in the case file. When defining approximate required time of your simulation in the script file, is always better to have extra time. Otherwise the cluster will stop the simulation before this one finishes. 15

105 APPENDIX C MODEL SET UP AND BOUNDARY CONDITIONS ON ANSYS FLUENT 1. GENERAL Ansys Fluent works as a process of different steps. The first step is to create the geometry. This can be done in ANSYS-Fluent Design Modeler, which is the corresponding extension, or it can also be imported from other programs, such as AutoCAD, as a.igs file. The next step is to create the mesh. Here the user can define the size of the mesh, this will impact on the quality of the work. In this case, since the waves are propagating in a specific area of the geometry, the quality of the mesh in that area is more accurate, see Area 1 in Figure 5. The third step in ANSYS-Fluent is the setup, where the user can define the boundary conditions. Followed by Solutions and Results, where the user can check for the most convenient way of representing the results. 2. VALIDATION SET UP MESH SIZING FOR VALIDATION Based on the laboratory model dimensions (see Appendix D section 1.3 Scale Model), the same conditions are reproduced with ANSYS Fluent. Figure 5 present a section of the ANSYS-Fluent wave tank for a J-OWC Fully-open scenario. Notice that the same mesh size has been used for the other scenarios. Area 1 Area 2 Figure 5 Section of the mesh on ANSYS Fluent 16

106 Table 1 - Characteristics of the model for ANSYS Fluent for validation CHARACTERISTICS OF THE MODEL LENGTH X LENGTH Y LENGTH Z BOUNDING BOX 35 m 0,8 m 0 m SURFACE AREA m 2 NODES ELEMENTS Table 2 - Characteristics of the mesh sizing for ANSYS-Fluent for validation CHARACTERISTICS ON THE MESH SIZE MAX FACE SIZE AREA 1 (LEFT CENTER) AREA 2 (RIGHT CENTER AND BOTTOM) BOUNDING BOX 0.15 m m m For a higher accuracy in the results, the mesh is finer is certain areas around the OWC and also in the centre part along the x-axis, which is the area where the wave propagates. Ansys-Fluent, for the generation of waves needs a minimum in the size of the mesh along propagation. BOUNDARY CONDITIONS FOR VALIDATION This section presents the steps followed for setting up the boundary conditions using Ansys-Fluent After creating the geometry, generating the mesh and defining the Inlet, outlet and other areas/walls of interest, depending on the case, the next step in the work bench procedure is the set-up. General, Solver Type Velocity formulation Time 2D Space Pressure-based Absolute Transient Planar Gravity Y: (m/s 2 ) Models 17

107 Multiphase Volume of fluid Viscous model Materials Open channel wave BC K-epsilon model Fluid Air. Primary phase Water-liquid (from fluent databased). Secondary phase Boundary Conditions Inlet Outlet Wave conditions Wave theory Initialization method type: velocity - inlet type: pressure - outlet Short Gravity Waves Second Order Stokes Standard Initialization Compute from Inlet Open channel initialization method Flat INFORMATION ON OUTFLOW FOR VALIDATION For each series of runs, for the J-OWC and U-OWC, when fully open, partially open and close, a compensatory outflow is required. Otherwise the defined wave tank in Ansys, will fill up with time. The wave tank in ANSYS-Fluent is represented as a close box, with an inlet at one end and the OWC at the other end. The inlet has to allow the waves in and also an equivalent outflow to keep a constant water level. In order to maintain a constant water level of 0.47 along the tank in Ansys, the following outflows are used: Table 3 - Outflow information for ANSYS-Fluent, depending on wave conditions for validation T (SEC) L (M) OUTFLOW (M/S) 0.9 1,2430-0, ,5014-0,0145 1,1 1,7615-0, ,2 2,0193-0,0135 1,3 2,2732-0, ,4 2,5230-0,0125 1,5 2,7688-0, ,6 3,0111-0,

108 1,7 3,2506-0, ,8 3,4874-0,0105 1,9 3,7219-0, ,9546-0,0095 2,1 4,1855-0, ,2 4,4150-0,0085 2,3 4,6432-0, ,4 4,8703-0,0075 2,5 5,0964-0, ,6 5,3216-0,0065 2,7 5,5460-0, CASE STUDY: MUTRIKU In this master thesis, a real case scenario will be carried out. Focusing on an OWC in Mutriku (Spain). The characteristics of the geometry and the wave conditions for this case are well documented. In order to represent this case, the following characteristics are used in the numerical simulation in ANSYS-Fluent. MESH SIZING FOR MUTRIKU The geometry and dimensions of the Mutriku OWC are represented in ANSYS-Fluent as shown in Figure 6. Area 2 Area 1 Area 2 Area 3 Figure 6 Mesh image of the cross-section of the ANSYS-Fluent representation of Mutriku in Spain 19

109 The characteristics of the geometry used in ANSYS-Fluent for the Mutriku case study are presented in Table 4. Table 4 - Characteristics of the geometry for ANSYS Fluent for Mutriku case study CHARACTERISTICS OF THE MODEL LENGTH X LENGTH Y LENGTH Z BOUNDING BOX m 93.7 m 0 m SURFACE AREA 7103 m 2 NODES ELEMENTS The characteristics of the mesh size used in ANSYS-Fluent for the Mutriku case study are presented in Table 5. For a higher accuracy of the results, and considering the area of wave propagation, the mesh is finer in the central area, see Figure 6. Table 5 - Characteristics of the mesh sizing for ANSYS-Fluent for Mutriku case study CHARACTERISTICS ON THE MESH SIZE MAX FACE SIZE (AREA 3) AREA 1 (CENTER) AREA 2 (TOP AND BOTTOM AROUND AREA 1) BOUNDING BOX 2.0 m m 0.7 m BOUNDARY CONDITIONS FOR MUTRIKU For Ansys-Fluent General, Solver Type Velocity formulation Time 2D Space Pressure-based Absolute Transient Planar Gravity Y: (m/s 2 ) Models Multiphase Volume of fluid Open channel wave BC 20

110 Viscous model K-epsilon model Materials Fluid Air. Primary phase Water-liquid (from fluent databased). Secondary phase Boundary Conditions Inlet Outlet Wave conditions Wave theory Initialization method Compute from Open channel initialization method type: velocity - inlet type: pressure - outlet Short Gravity Waves Second Order Stokes Standard Initialization Inlet Flat INFORMATION ON THE OUTFLOW FOR THE MUTRIKU CASE STUDY For each series of runs, for the J-OWC and U-OWC, when fully open, partially open and close, a compensatory outflow is required, otherwise the defined wave tank in Ansys, will fill up with time. In order to maintain a constant water level of 0.47 along the tank in Ansys, the following outflows are used: Table 6 - Outflow information for ANSYS-Fluent, depending on wave conditions for Mutriku SCENARIO TYPE T (sec) L (m) WATER LEVEL (m) H (m) OUTFLOW (m/s) 1 12,8 229,7 3,4 8-0, ,8 233,96 7,9 8-0,04 J-OWC 3 14,5 275,4 3,4 13,7-0, , ,9 13,7-0, ,8 229,7 3,4 8-0,02 6 U-OWC 12,8 233,96 7,9 8-0,04 7 Front wall 4m 14,5 275,4 3,4 13,7-0, , ,9 13,7-0, ,8 229,7 3,4 8-0,02 10 U-OWC 12,8 233,96 7,9 8-0,04 11 Front wall 5m 14,5 275,4 3,4 13,7-0, , ,9 13,7-0,16 21

111 13 12,8 229,7 3,4 8-0,02 14 U-OWC 12,8 233,96 7,9 8-0,04 15 Front wall 6m 14,5 275,4 3,4 13,7-0, , ,9 13,7-0, ,8 229,7 3,4 8-0,02 18 U-OWC 12,8 233,96 7,9 8-0,04 19 Front wall 7m 14,5 275,4 3,4 13,7-0, , ,9 13,7-0,16 PRESSURE SENSORS In ANSYS-Fluent is possible to obtain the desire pressure information for specific points. This could be done in the after processing. After running the models, is possible to upload the results in the CFD-Post and define the process post-running the models. This method is more time consuming in general. A more convenient way to obtain pressure values from ANSYS-Fluent is to define them in the set-up step. After initializing, is possible to define under Solutions > Monitors > Report Definitions, a new surface report. Point 1 Point 2 Point 3 Point 4 P 6 P 7 P 8 P 9 Point 11 Point 12 Point 13 Point 14 Point 5 P 10 Point 15 Point 16 Figure 7 - Detailed section of the pressure points location defined in ANSYS-Fluent for Mutriku. Showing the 16 pressure points defined and the line for the water level measurement In this case, 16 pressure points are defined. The first step is to define these points as new surfaces in the x, y coordinates. The next step now is to define the characteristics of the 22

112 monitor. Under Report Definitions > Area-Weighted Average is possible to define the characteristics and report type. Also, the water level inside of the OWC and in front of it is of interest. This will also be monitored previous to running the model. In this case, the lines where the water level are of interest are defined. It can be seen in Figure 7 the defined line inside of the OWC in black. To define the monitor, this are the steps followed: Report Definitions > New > Surface report > Integral. Field variable: phases, water. 23

113 APPENDIX D EXPERIMENTAL MODEL SET UP IN THE WATER LAB AT TUDELFT 1. EXPERIMENTAL METHOD AND GENERAL INFORMATION The experimental laboratory model is based on the Mutriku OWC (Spain). This needs to be scaled down according to the wave tank dimensions. This Appendix presents the dimensions of the real case in Mutriku, the dimensions of the wave tank at the WaterLab in TUDelft and the final scaling dimensions to be used for the model experiment. CASE STUDIES OWC - DIMENSIONS The geometry used at the laboratory experiment is based on the Oscillating Water Column at Mutriku, Spain. Considering the WaterLab facilities and the wave tank to be used, the prototype is scaled down to 1:25. The Mutriku OWC is a J shape type of OWC. Note that the top area, where the generator is placed, presented in Figure 8 with a blue shadow is not considered for the model experiment shape. This is the are reserved for the turbine, the generator and other transformation systems, not of interest here. For the model, only the OWC is considered. However, and being aware of this area on top, different top covers are considered. Fully open, to analyse the resonance inside of the OWC; partially open, to represent a more realistic scenario with the presence of a turbine; and close, to analyse the pressure of the compressed air in the top wall area. Another type of OWC is also considered, this is called a U-OWC shape. This design incorporates a wall in front of the OWC, creating a vertical duct, normally located below the water level. A design developed from Italy is taken into account for the shape of the U-OWC, see Figure 9. 24

114 Figure 8 - Cross-section of the J-OWC at Mutriku (Spain) (Memoria, 2009) Figure 9 - Cross-section of the OWC REWEC3 in the Civitavecchia harbour (Arena et al., 2013) 25

115 The validation of the physical and numerical model is based on comparing these two designs, J and U OWC, and their behaviour in a physical scenario, paying special attention to the resonance produced inside of the OWC for different wave situations. GENERAL LABORATORY INFORMATION For validation purposes, a series of laboratory experiments were carried out at the WaterLab in the facilities of TUDelft. The following combinations were considered for executing the lab experiments. Table 7 - Classification of laboratory experiments according to the top part of the OWC OWC Top part Open J - SHAPE Partially Open Close Open U-SHAPE Partially Open Close Wave tank size Table 8 - Dimensions of wave tank at TUDelft Water Lab EFFECTIVE LENGTH WIDTH MAXIMUM DEPTH 39 m 0.8 m 0.85 m The wave generator at the wave tank is a hydraulic driven piston, which allows automatic reflection compensation, and flow and waves combination mode. Three pressure sensors are located in the different walls of the OWC, see Figure 10, and also four wave gauges to measure the resonance inside of the OWC and the incoming waves at three different locations along the wave tank. 26

116 Figure 10 Geometries of the J-OWC and U-OWC and location of the pressure sensors in the different walls. SCALE MODEL The dimensions of the real case model are scaled down according to the limitations of the laboratory wave tank dimensions. Geometry similarities are easily achieved by the scaling factor for lengths. Length scales: L model L prototype = 1 λ 4.1 Table 9 model experiment scaled from Mutriku prototype PROTOTYPE MODEL EXPERIMENT h opening 3.5 m 0.14 m h wall m 0.46 m h wall2 9 m 0.36 m b in 4 m 0.16 m b exterior 2 m 0.08 m b 2 6 m 0.24 m b 1 4 m 0.16 m 27

117 Figure 11 - Detail of laboratory model dimensions Different wave periods and the pressures inside of the air chamber are also considered when scaling the real scenario with the following factor: Period scales: T model T prototype = 1 λ 4.2 Pressure scales: P model P prototype = 1 λ

118 APPENDIX E MODEL CALIBRATION The laboratory work at TUDelft WaterLab consisted of a series of different geometries for Oscillating Water Column with the J shape and the U shape. Three pressure sensors and four wave gauges were used to estimate the pressures in the structure, the incoming wave and the resonance inside of the water column. The pressure sensors are located in the front wall of the column, the back wall of the column and the top part wall for those scenarios when is close, see Figure 10 and Figure 11. Figure 12 - Detailed cross-section of J-OWC showing the pressure sensors locations The Wave gauges are located, at 11 meters, 7 meters and 3 meters from the front wall of the OWC. For the fully open and partially open cases also a wave gauge inside of the column is place, allowing to measure the resonance inside of the column. Figure 13 - Detailed cross-section of J-OWC showing the wave gauges locations The calibration of the model is presented in the following images, where for five different water levels scenarios readings are taken. This will allow to determine the relationship of the voltage as a result. In the case of the pressure sensors to obtain the relation to pressure and in the case of the wave gauges to meters height. 29

119 Pressure (V) Pressure (V) Pressure (V) Pressure Sensor at the Front Wall y = x Depth (m) Figure 14 - Front Wall Pressure Sensor Validation Pressure Sensor at the Back Wall y = x Depth (m) Figure 15 - Back Wall Pressure Sensor Validation Wave Gauge inside the OWC y = x Depth (m) Figure 16 Wave gauge validation inside of the OWC 30

120 Pressure (V) Pressure (V) Pressure (V) Wave Gauge 3m from the OWC y = x Depth (m) Figure 17 - Wave gauge validation 3 meters from the OWC Wave Gauge 7m from the OWC y = x Depth (m) Figure 18 - Wave gauge validation 7 meters from the OWC Wave Gauge 11m from the OWC y = x Depth (m) Figure 19 - Wave gauge validation 11 meters from the OWC 31

121 Note that the pressure sensor at the top wall inside of the OWC is not validated. Due to scale factor issues with air compressibility, this information will not be used in this report. The data, however has been useful to double check the laboratory results, and the changes in the air compression inside of the air chamber in the laboratory OWC and compare it with expected values, based on theoretical information. 32

122 APPENDIX F LABORATORY AND ANSYS FLUENT RESULT COMPARISON FOR VALIDATION Example of the comparison of the results for the physical and numerical modelling for wave period of 2,3 seconds are presented in this section, see Figure 20, Figure 21, Figure 22, Figure 23 and Figure 24. To avoid reflected waves during the experiments and considering the distance of the model at the wave tank from the wave maker, the data has been limited to the first 50 seconds. Figure 20 -Comparison of the front wall pressure sensor ANSYS-Fluent and the Laboratory experiments for T=2,3 sec 33

123 Figure 21 - Comparison of the back-wall pressure sensor ANSYS-Fluent and the Laboratory experiments for T=2,3 sec Figure 22 - Comparison of the wave gauge inside of the OWC ANSYS-Fluent and the Laboratory experiments for T=2,3 sec 34

124 Figure 23 - Comparison of the wave gauge 7 meters from the OWC ANSYS-Fluent and the Laboratory experiments for T=2,3 sec Figure 24 - Comparison of the wave gauge 11 meters from the OWC ANSYS-Fluent and the Laboratory experiments for T=2,3 sec 35

125 APPENDIX G CASE STUDY: MUTRIKU RESULTS WITH ANSYS FLUENT The Mutriku numerical results with ANSYS-Fluent for High Water Levels are presented in this section. For 16 defined points, the static pressure sensors are obtained and represented in Figure 25 and Figure MUTRIKU RESULTS: H.W.L AND 8 METERS WAVE HEIGHT The results for High Water Levels for 8 meters wave heights (Figure 25) show a constant and low internal pressure in the OWC. And also, a constant and low static pressure level for the front wall, except when for the U-wall is seven meters, for which the pressures on the front wall increase unequivocally (Figure 25 [e]). [a] [b] [c] [d] [e] Figure 25 - Comparison of the five different geometries for 8 meters wave height when High Water Level 36

126 Table 10, Table 11 and Table 12 present the results from the numerical analysis with ANSYS-Fluent for the external part of the front wall, the internal part of the front wall and the back wall. This are the original values from which the composition of Figure 25 has been realised. Table 10 - Static pressures in the external part of the front wall OWC POINT 1 PRESSURE (PA) POINT 2 PRESSURE (PA) POINT 3 PRESSURE (PA) POINT 4 PRESSURE (PA) POINT 5 PRESSURE (PA) J 44293, , , , ,2 U , , , , ,3 U , , , , ,0 U , , , , ,4 U , , , , ,1 Table 11 - Static pressures in the internal part of the front wall OWC POINT 6 PRESSURE (PA) POINT 7 PRESSURE (PA) POINT 8 PRESSURE (PA) POINT 9 PRESSURE (PA) POINT 10 PRESSURE (PA) J , , , , ,0 U , , , , ,2 U , , , , ,4 U , , , , ,3 U , , , , ,8 Table 12 - Static pressures in the internal part of the back wall OWC POINT 11 PRESSURE (PA) POINT 12 PRESSURE (PA) POINT 13 PRESSURE (PA) POINT 14 PRESSURE (PA) POINT 15 PRESSURE (PA) POINT 16 PRESSURE (PA) J , , , , , ,9 37

127 U , , , , , ,3 U , , , , , ,6 U , , , , , ,4 U , , , , , ,4 2. MUTRIKU RESULTS: H.W.L AND 13.7 METERS WAVE HEIGHT The results for High Water Levels for waves of 13.7m are shown in Figure 26. From these results, it is noticeable the strong decrease in the internal pressures with the presence of a U-wall design. Figure 26 - Comparison of the five different geometries for 13.7 meters wave height when High Water Level Table 13, Table 14 and Table 15 show the results from the numerical analysis with ANSYS- Fluent for the external part of the front wall, the internal part of the front wall and the 38

128 back wall. This are the original values from which the composition of Figure 26 has been realised. Table 13 - Static pressures in the external part of the front wall OWC POINT 1 PRESSURE (PA) POINT 2 PRESSURE (PA) POINT 3 PRESSURE (PA) POINT 4 PRESSURE (PA) POINT 5 PRESSURE (PA) J , , , , ,9 U , , , , ,1 U , , , , ,1 U , , , , ,9 U , , , , ,4 Table 14 - Static pressures in the internal part of the front wall OWC POINT 6 PRESSURE (PA) POINT 7 PRESSURE (PA) POINT 8 PRESSURE (PA) POINT 9 PRESSURE (PA) POINT 10 PRESSURE (PA) J , , , , ,9 U , , , , ,1 U , , , , ,5 U , , , , ,6 U , , , , ,9 Table 15 - Static pressures in the internal part of the back wall OWC POINT 11 PRESSURE (PA) POINT 12 PRESSURE (PA) POINT 13 PRESSURE (PA) POINT 14 PRESSURE (PA) POINT 15 PRESSURE (PA) POINT 16 PRESSURE (PA) J , , , , , ,4 U , , , , , ,9 39

129 U , , , , , ,0 U , , , , , ,9 U , , , , , ,3 40

130 APPENDIX H CASE STUDY: MUTRIKU RESULTS WITH MIDAS CIVIL 1. THEORETICAL BACKGROUND In order to solve the structural aspect of this master thesis, Midas Civil is used. Midas is a finite element solution software to model, design and the analysis of civil engineering generic problems. Midas Civil is an integrated solution system for bridge and civil engineering. This software is recognized for its user-friendly system, with a remarkable and fast designed GUI (Graphic User Interface). The software has been verified with numerous examples (MIDAS IT Co. Ltd, no date). Midas Civil solves, for beam elements, displacement and maximum stress at the intermediate points or end nodes. Midas Civil for 2D elements is based on the Timoshenko Beam theory. This theory considers the stiffness effects of tension/compression, shear, bending and torsional deformations (MIDAS GEN, no date). Functions related to the elements Midas Civil allows to define some characteristics, such as the material properties, the cross-sectional properties, the boundary conditions at any ends, as a hinged, fixed or endrelease support. Figure 27 - Sign convention for ECS and element forces (or stresses) of a beam element (MIDAS GEN, no date) 41

131 For the purposes of this case, a solid rectangular bar of concrete is considered Effective Shear Area (A sy, A sz ) The effective shear area is used to formulate the shear stiffness in y and z direction of the cross-section. If this is not considered, the shear deformations are also omitted. For a solid rectangular bar, the effective shear area is: A sy = 5 6 BH 8.1 A sz = 5 6 BH 8.2 Torsional Resistance (I xx) The stiffness resisting torsional moments is expressed as: I xx = T θ 8.3 Where; Ixx is the torsional resistance T is the torsional moment or torque θ is the angle of twist Each section type will have a different way of solving the torsional resistance eq. This will vary depending on the thickness of the section and on whether they are open or close shapes. For solid rectangular bars, the torsional resistance is: Area Moment of Inertia (I yy, I zz ) I xx = ab 3 [ a b b4 (I 12a4)] 8.4 The area moment of inertia is used to compute the flexural stiffness resisting bending moment. This is calculated relative to a centroid point. Area moment of inertia about the ECS y-axis I yy = z 2 da 8.5 Area moment of inertia about the ECS z-axis I zz = y 2 da

132 First Moment of Area (Q y, Q z ) The first moment of area is used to compute the shear stress at a particular point on a section Q y = zda 8.7 Q z = yda 8.8 For symmetrical sections, the shear stresses at a particular point are: τ y = V y Q z I zz b z 8.9 τ z = V z Q y I yy b y 8.10 Where; V y is the shear force acting in the ECS y-axis direction V z is the shear force acting in the ECS z-axis direction I yy is the area moment of the inertia about the ECS y-axis I zz is the area moment of the inertia about the ECS z-axis b y is the thickness of the section at the point of shear stress calculation in the ECS y-axis direction b z is the thickness of the section at the point of shear stress calculation in the ECS z-axis direction 2. RESULTS FROM MIDAS CIVIL ON THE BEAM STRESS AND DISPLACEMENT ANSLYSIS This section presents the results of the MIDAS Civil structural analysis, showing the displacement and the beam stresses in the beams. The displacement of the front and back wall for Low Water Levels are showed in the main report in Figures 38, 39, 40 and 41. Here there are shown the displacement result for High Water Levels for the front wall showed in Figure 28 and Figure 29. The beam stresses in the front wall are shown in Figure 30, Figure 31, Figure 32 and Figure 33. Back wall displacement when High Water Levels are presented in Figure 34 and Figure 35. The corresponding beam stresses for the back wall are presented in Figure 36, Figure 37, Figure 38 and Figure

133 DISCUSSION OF RESULTS Figure 28 shows the displacement of the front wall for HWL and 8 m waves, a high displacement is produced for the J-OWC shape (Figure 28 [a]), reducing for all the U-OWC designs except for the U-shape with a U-wall of seven meters (Figure 28 [e]). Although the reduction is not quantitatively considerable, but only a few millimetres. Maximum displacement happens for the U-OWC with seven meters front wall, that considering the high pressures in the front wall (see also Figure 25), these results are expected. A similar behaviour is presented for the front wall for HWL and 13.7 m waves, Figure 29. The maximum displacement is shown for the U-shape with seven m front wall (Figure 29 [e]). Figure 26 shows the static pressures for the different geometries. Also, J-OWC (Figure 29 [a]) shows high displacement of the front wall, leaving the U-shape for four, five and six meters U-wall with lower displacement values. Figure 30, Figure 31, Figure 32 and Figure 33 show the beam stresses in N/m 2, in general the higher shear stresses are presented of the J-OWC and the U-OWC with wall of seven meters, being this the designs more like to fail due to shear stresses causing a cracking in the structure. However, and as mention, the focus of the failure is primarily due to the joint of the different parts, pre-cast and in-situ. Figure 34 and Figure 35 show the displacement of the back wall, which principally present similar values for all the extreme wave conditions, showing little difference. Figure 36, Figure 37, Figure 38 and Figure 39 show the beam stresses of the back wall in N/m 2, which in general, and according to the static pressures in the back wall of the structure present a big difference in values for the High Water Level scenarios, increasing the shear stress than for Low Water Level. 44

134 Figure 28 - Comparison of the OWC geometries front wall displacement for 8 meters wave conditions when HWL 45

135 Figure 29 - Comparison of the OWC geometries front wall displacement for 13.7 meters wave conditions when HWL 46

136 Figure 30 - Comparison of the OWC geometries front wall beam stress for 8 meters wave conditions when LWL 47