As a clean, abundant, and renewable source of energy with a strategic location in close proximity to global population regions, ocean wave energy shows major promise. Although much wave energy converter development has focused on large-scale power generation, there is also increasing interest in small-scale applications for powering the blue economy. In this thesis, the objective was to optimize the performance of small-sized, portable, oscillating-body wave energy converters (WECs). Two types of oscillating body WECs were studied: bottom hinged and two-body attenuator. For the bottom-hinged device, the goal was to show the feasibility of an oscillating surge WEC and desalination system using numerical modeling to estimate the system performance. For a 5-day test period, the model estimated 517 L of freshwater production with 711 ppm concentration and showed effective brine discharge, agreeing well with preliminary experimental results. The objective for the two-body attenuator was to develop a method of power maximization through resonance tuning and numerical simulation. Three different geometries of body cross sections were used for the study with four different drag coefficients for each geometry. Power generation was maximized by adjusting body dimensions to match the natural frequency with the wave frequency. Based on the time domain simulation results, there was not a significant difference in power between the geometries when variation in drag was not considered, but the elliptical geometry had the highest power when using approximate drag coefficients. Using the two degree-of-freedom (2DOF) model with approximate drag coefficients, the elliptical cross section had a max power of 27.1 W and 7.36% capture width ratio (CWR) for regular waves and a max power of 8.32 W and 2.26% CWR for irregular waves. Using the three degree-of-freedom (3DOF) model with approximate drag coefficients, the elliptical cross section had a max power of 22.5 W and 6.12% CWR for regular waves and 6.18 W and 1.68% CWR for irregular waves. A mooring stiffness study was performed with the 3DOF model, showing that mooring stiffness can be increased to increase relative motion and therefore increase power. / Master of Science / As a clean, abundant, and renewable source of energy with a strategic location in close proximity to global population centers, ocean wave energy shows major promise. Although much wave energy converter development has focused on large-scale power generation, there is also increasing interest in small-scale applications for powering the blue economy. There are many situations where large-scale wave energy converter (WEC) devices are not necessary or practical, but easily-portable, small-sized WECs are suitable, including navigation signs, illumination, sensors, survival kits, electronics charging, and portable desalination. In this thesis, the objective was to optimize the performance of small-sized, oscillating body wave energy converters. Oscillating body WECs function by converting a device's wave-driven oscillating motion into useful power. Two types of oscillating body WECs were studied: bottom hinged and two-body attenuator. For the bottom-hinged device, the goal was to show the feasibility of a WEC and desalination system using numerical modeling to estimate the system performance. Based on the model results, the system will produce desirable amounts of fresh water with suitably low concentration and be effective at discharging brine. The objective for the two-body attenuator was to develop a method of power maximization through resonance tuning and numerical simulation. Based on the two- and three-degree-of-freedom model results with approximate drag coefficients, the elliptical cross section had the largest power absorption out of three different geometries of body cross sections. A mooring stiffness study with the three-degree-of-freedom model showed that mooring stiffness can be increased to increase power absorption.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: As a renewable energy source, wave energy has the potential to contribute to the increasing global demand for power. In South Africa specifically, the country’s energy needs may easily be satisfied by the abundance of wave energy at the South-West coast of the country. Commercially developing and utilizing wave energy devices is not without its challenges, however. The ability of these devices to survive extreme weather conditions and the need to achieve cost-efficacy while achieving high capacity factors are but some of the concerns. Constant changes in wave heights, lengths and directions as well as high energy levels and large forces during storm conditions often lead to difficulties in keeping the complexity of the device down, avoiding over-dimensioning and reaching high capacity factors. The point absorber device developed as part of this research is based on an innovation addressing the abovementioned issues. An approach is followed whereby standard "offthe- shelf" components of a proven hydraulics technology are used. The size of the device is furthermore adaptable to different wave climates, and the need for a control system is not necessary if the design parameters are chosen correctly. These characteristics enable low complexity of the device, excellent survivability and an exceptionally high capacity factor. This may lead to low capital as well as low operationand maintenance costs. In this paper the working principle of this concept is presented to illustrate how it utilises the available wave energy in oceans. The results obtained from theoretical tests correlate well with the experimental results, and it is proven that the device has the ability to achieve high capacity factors. As the device makes use of existing, "off-the-shelf" components, cost-efficient energy conversion is therefore made feasible through this research. / AFRIKAANSE OPSOMMING: As ’n hernubare/ herwinbare energiebron bied golfenergie die potensiaal om by te dra tot die bevrediging van die stygende globale energie-navraag. In spesifiek Suid-Afrika kan die oorvloed van beskikbare golfenergie aan die Suid-Weskus van die land gebruik word om aan die land se energiebehoeftes te voldoen. Betroubaarheid en oorlewing in erge weerstoestande, koste-effektiwiteit en die behaal van hoë kapasiteitsfaktore is beduidende struikelblokke wat oorkom moet word in die poging om ’n golfenergie-omsetter wat kommersieël vervaardig kan word, te ontwikkel. Daarby dra voortdurende veranderings in golfhoogtes, -lengtes en -rigtings sowel as hoë energievlakke en groot kragte tydens storms by to die feit dat dit moeilik is om die kompleksiteit van die stelsel laag te hou. Dit terwyl daar voorkom moet word dat die toestel oorontwerp en verhoed word dat hoë kapsiteitsfaktore bereik word. Die puntabsorbeerder-toestel wat in hierdie navorsing ontwikkel is, bestaan uit ’n ontwerp wat spesifiek ontwikkel is om die bogenoemde probleme aanspreek. ’n Unieke benadering is gevolg waardeur standaard, maklik-bekombare komponente gebruik is en die komponent-groottes ook aangepas kan word volgens golfgroottes. Indien die ontwerpsdimensies akkuraat gekies word, is die moontlikheid verder goed dat ’n beheerstelsel nie geïmplementeer hoef te word nie. Hierdie eienskappe verseker lae stelselkompleksiteit, uitstekende oorlewingsvermoë en ’n uitstaande kapasiteitsfaktor. Lae kapitaal- sowel as onderhoudskostes is dus moontlik. Die doel van hierdie dokument is om die werking van die konsep voor te stel en teoreties sowel as prakties te evalueer. Die resultate van teoretiese toetse stem goed ooreen met eksperimentele resultate, en dit is duidelik dat die toestel hoë kapasiteitsfaktore kan behaal. Aangesien die toestel verder gebruik maak van bestaande komponente wat alledaags beskikbaar is, word die koste-effektiewe omsetting van golfenergie dus moontlik gemaak deur hierdie navorsing.

Wave Energy Converters (WEC) are used to transform energy stored in ocean waves into electrical energy. One type of WECs consists of buoyant bodies. To extract energy from their motion, hydraulic cylinders can be used to generate hydraulic power. For conversion into electric power various systems have been analysed in literature. However, the focus was put on efficiency and rigorous analyses of the system behaviour are still missing. In this paper an exemplary system consisting of two hydraulic cylinders, switchable check valves, accumulators and three motor-generator sets is analysed with help of simulation and measurement. This exemplary system is called WavePOD and was installed at the Institute for Fluid Power Drives and Controls (IFAS) of RWTH Aachen University together with Aquamarine Power and Bosch Rexroth for testing. In this paper the data collected during various test phases is used for system analysis and for validating the simulation. The simulation model is presented. The system’s response to various switching operations is investigated. Comparing the simulation with measurements validates the system`s dynamic model.

The hydrodynamic properties of a horizontal cylinder which is free to pitch about an off-centred axis are studied and used to derive the equations of motion of a wave energy converter which extracts energy from incoming sea waves with a linear power-take-off mechanism. The present work follows from a recent study which compared the performance of an off-centred cylinder with those of the Edinburgh Duck wave energy converter. The small decrease in performance found is offset by a reduction in the likely costs associated with the manufacturing of the cylindrical cam compared with those of the asymmetric profile. As part of the survivability strategy in very energetic seas-states it had been planned to completely submerge the device so as to reduce the mooring forces. However, experiments with scale models show that a good absorption capacity is retained even when fully-submerged. The hydrodynamic properties of a horizontal cylinder that pierces the free-surface and of one that is fully submerged are therefore of central concern in this study. These properties are well known for the case of very long cylinders but they are now found for cylinders with different widths, drafts, submergence levels and water-depths. The hydrodynamic forces and moments at the off-centred axis are, furthermore, derived through the application of transformation formulae. The equation of motion of the off-centred cylinder is derived for one degree of freedom and its performance as a wave energy converter is analysed. A relationship which relates the resonance of the device with the location of the off-centred axis and its mass distribution is derived and used to optimize the design for average sea conditions attained at a real location. Design cases associated with three diameters of the cylinder are looked into detail for both a fully-submerged and free-surface piercing cylinder. The one degree of freedom model is extended to include a multi-body which has three degrees of freedom in order to describe the dynamics of a proposed wave powered desalination system based on a cylindrical Duck device. This mathematical model is derived through linearised Lagrangian equations of motion in which the hydrodynamic forces are included as generalised external forces. The advantage of such approach is to reduce the number of equations associated with multi-body systems by removing the reaction forces of holomonic constraints from the system of equations to solve. This model is validated through experiments with a scale model performed in the curved tank of the University of Edinburgh with both regular waves and mixed seas.

This thesis is titled The influence of a nonlinear Power Take Off on a Wave Energy Converter. It looks at the effect that having a nonlinear Power Take Off (PTO) has on an inertial referenced, slack moored, point absorber, Wave Energy Converter (WEC). The generic device studied utilizes relative heave motion between an axi-symmetric cylinder and an internal mass, for the PTO to operate between. The PTO is the part of the WEC that transforms the relative motion into electricity. In this work, three different types of nonlinear PTO and a linear PTO are presented, tested, analysed and compared. The three nonlinear PTO types are: • A PTO that extracts energy in only one direction, either in relative compression or expansion. • A linear PTO and an additional endstop or peripheral PTO, that can only extract energy when the relative position of the internal mass has reached a pre-determined position. • A PTO that has damping forces that are quadratically proportional to the relative velocity. A numerical simulation has been built based upon a Runge-Kutta time series progression. The model uses the summation of the excitation force from the waves, the radiation force from the movement of the cylinder, the buoyancy force and the PTO forces. These combine to cause acceleration of the mass of the external cylinder, with an equal and opposite PTO force acting on the internal mass. The excitation force and added mass values are obtained from the boundary element method software, WAMIT. Prony’s method is used to obtain an approximate radiation force, based upon the radiation time force history. This numerical model operates on both a 1:40 scale and a full sized model. The numerical model finds the optimal PTO parameters, for different PTO setups, in irregular sea states. This optimum is based on the power extracted as well as indications of the reliability and lifetime of the system. The numerical simulation presents results showing how the nonlinearity of the PTO influences the motions of the WEC, resulting in dissimilarities between the Response Amplitude Operator (RAO) results, obtained from regular seas, and the Linear Transfer Function (LTF), found from irregular sea testing. The experimental model has been tested in the Curved Wave Tank facility at the University of Edinburgh, with a 1:40 scaled model. It used a central rod both as a support structure and to limit the movement of the cylinder and internal mass to heave. Between the cylinder and internal mass a spring and pneumatic damper operate in parallel, in various setups. It was tested in regular and irregular sea states and the position of the internal mass and cylinder was monitored. The experimental model was tested to ascertain the time series motions, RAO, LTF, the relative phase between the bodies and the power extracted for different wave climates. The numerical and experimental work were compared to allow confidence in both models. They showed relatively good agreement for the RAOs, LTFs and predictions of the relative phase but there was discrepancies in the predicted power for both regular and irregular seas. This difference is due to the difficulties in obtaining the relative velocities in the experimental model, resulting in a significant error in power prediction, since the power is proportional to the square of the relative velocities. The conclusions show that having a mono-directional PTO as opposed to a bi-directional PTO results in an approximately equal or greater power extraction in a variety of different sea states. An additional endstop or peripheral damper can increase the total power that a WEC extracts, in some situations, and may be advantageous depending upon the other potential benefits it brings to the WEC.

This thesis presents an assessment of a modular flap-type wave energy converter. Comparisons are made to an equivalent width rigid device. All quoted relative difference results here use the rigid device as the reference point. The variables that are evaluated are the power capture and surge and yaw foundation loads. The power capture is evaluated at both module and device level, while the foundation loads are assessed just at the device level. The investigation is carried out through testing of a 30th scale physical model in a wave tank. A key output from the work is the development of the physical model. The model consists of six flap modules, mounted on a common base structure. Each module contains a highly controllable and compact power take off system. The devices are tested in a range of conditions, primarily consisting of regular waves of different period and direction. The damping strategy employed is the simplest approach available, setting the achievable damping level on each module to be the same. For the modular device in head-on regular waves, the results show that the power capture increases significantly moving from the outer to the central modules. On average, the central pair of modules produce 68 % of the total mean power, the inner modules 25 % and the outer modules only 7 %. Between the devices, it is shown that the power captures in head-on waves are similar, with a mean relative difference of -3 %, with +/-5 % uncertainty. Thus, no statistically significant change in power capture is shown. In off-angle waves, the mean relative difference is –1 %, with +/-4 % uncertainty. However, for the highest wave direction that was tested in, 27.5 degrees, the modular device outperforms the rigid flap, by 10 %, with uncertainty of +/-1 %. The surge foundation loads are shown to be very similar for the two devices - in head-on waves, the mean relative difference is +2 %. Depending on the level of applied damping, however, significant differences in the yaw foundation loads are shown. Using damping where the power capture is maximised, the yaw loads increase by a mean of 10 %; using damping where the power to load ratio is instead maximised, the modular yaw loads are 26 % lower. Finally, the economics of the power production is estimated through division of the power capture with a cost metric, the foundation loads. While this does not provide a full techno-economic assessment, it effectively captures the interdependency of the power capture and foundation loads for the devices. The mean relative differences in the power per load ratios of the devices are found to be similar across the wave conditions. In the head-on waves, the differences are between –8 and –0.4 %, depending on damping strategy; in the off-angle waves, the differences are between –6 and +10 %. For both sets of wave conditions, the modular flap performs better when the damping is set to maximise the ratio of power capture to foundation loads. The work concludes that the modular and rigid devices produce power and experience foundation loads at similar levels in head-on waves. Given the high power capture efficiency, nearshore location, simple mode of operation and high survivability of the flap-type WEC, this suggests that the modular device is a viable stand-alone concept. The work also finds that in off-angle waves, some benefits can be achieved with an appropriately damped modular system, notably in improved power capture and reduced yaw foundation loads. These could reduce the sensitivity that flap-type devices have in off-angle waves and allow expansion of the width and hence capacity of machines. Further work should extend the wave conditions tested in, by using more irregular and directional waves, and investigate more damping strategies and geometries. Economic assessment should also be carried out.

The original aim of the research project was to investigate the mechanism of power capture from sea waves and to optimise the performance of a vee-shaped floating Wave Energy Converter, the Floating Clam, patented by Francis Farley. His patent was based on the use of a pressurised bag (or ‘reservoir’) to hold the hinged Clam sides apart, so that, as they moved under the action of sea waves, air would be pumped into and out of a further air reservoir via a turbine/generator set, in order to extract power from the system. Such “Clam Action” would result in the lengthening of the resonant period in heave. The flexibility of the air bag supporting the Clam sides was an important design parameter. This was expected to lead to a reduction in the mass (and hence cost) of the Clam as compared with a rigid body. However, the present research has led to the conclusion that the Clam is most effective when constrained in heave and an alternative power take-off is proposed. The theoretical investigations made use of WAMIT, an industry-standard software tool that provides an analysis based on potential flow theory where fluid viscosity is ignored. The WAMIT option of Generalised Modes has been used to model the Clam action. The hydrodynamic coefficients, calculated by WAMIT, have been curve-fitted so that the correct values are available for any chosen wave period. Two bespoke mathematical models have been developed in this work: a frequency domain model, that uses the hydrodynamic coefficients calculated by WAMIT, and a time domain model, linked to the frequency domain model in such a way as to automatically use the same hydrodynamic and hydrostatic data. In addition to modelling regular waves, the time domain model contains an approximate, but most effective method to simulate the behaviour of the Clam in irregular waves, which could be of use in future control system studies. A comprehensive series of wave tank trials has been completed, and vital to their success has been the modification of the wave tank model to achieve very low values of power take-off stiffness through the use of constant force springs, with negligible mechanical friction in the hinge mechanism. Furthermore, the wave tank model has demonstrated its robustness and thus its suitability for use in further test programmes. The thesis concludes with design suggestions for a full-scale device that employs a pulley/counterbalance arrangement to provide a direct connection to turbine/generator sets, giving an efficient drive with low stiffness and inherently very low friction losses. At the current stage of research, the mean annual power capture is estimated as 157.5 kW, wave to wire in a far from energetic 18 kw/m mean annual wave climate, but with scope for improvement, including through control system development.

This thesis discusses the development of a Numerical Wave Tank (NWT) capable of describing the coupled behaviour of Wave Energy Converters (WECs) and their moorings under extreme wave loading. The NWT utilises the open-source Computational Fluid Dynamics (CFD) software OpenFOAM(R) to solve the fully nonlinear, incompressible, Reynolds-Averaged Navier-Stokes (RANS) equations for air and water using the Finite Volume Method (FVM) and a Volume of Fluid (VOF) treatment of the interface. A method for numerically generating extreme waves is devised, based on the dispersively-focused NewWave theory and using the additional toolbox waves2Foam. A parametric study of the required mesh resolution shows that steeper waves require finer grids for mesh independence. Surface elevation results for wave-only cases closely match those from experiments, although an improved definition of the flow properties is required to generate very steep focused waves. Predictions of extreme wave run-up and pressure on the front of a fixed truncated cylinder compare well with physical measurements; the numerical solution successfully predicts the secondary loading cycle associated with the nonlinear ringing effect and shows a nonlinear relationship between incident crest height and horizontal load. With near perfect agreement during an extreme wave event, the reproduction of the six degree of freedom (6DOF) motion and load in the linearly-elastic mooring of a hemispherical-bottomed buoy significantly improves on similar studies from the literature. Uniquely, this study compares simulations of two existing WEC designs with scale-model tank tests. For the Wavestar machine, a point-absorber constrained to pitch motion only, results show good agreement with physical measurements of pressure, force and float motion in regular waves, although the solution in the wake region requires improvement. Adding bespoke functionality, a point-absorber designed by Seabased AB, consisting of a moored float and Power Take-Off (PTO) with limited stroke length, translator and endstop, is modelled in large regular waves. This represents a level of complexity not previously attempted in CFD and the 6DOF float motion and load in the mooring compare well with experiments. In conclusion, the computational tool developed here is capable of reliably predicting the behaviour of WEC systems during extreme wave events and, with some additional parameterisation, could be used to assess the survivability of WEC systems at full-scale before going to the expense of deployment at sea.

Commercial viability of Wave Energy Converters (WEC) depends on addressing not only the energetic effciency, but also in solving the practical issues related to manufacturing methods, access to technology, handling, transportation and installation, operation and maintenance, impact on marine life and most importantly the cost per kW-h. The UFCAP WEC is one concept which has the potential to facilitate handling, manufacturing, and installation activities as well as to be able to lower the current wave energy cost per kW-h, however its feasibility had not been properly assessed nor proved. It consists of multiple interconnected Oscillating Water Columns (OWC) chambers, it is modular, and simple, with no-moving parts in contact with the water and can use a simpler one-direction turbine which is more economic, and more effcient than self-rectifying turbines used in most of the OWCs devices. Testing of the device to fully assess its feasibility required a low pressure check-valve, and a customized turbine which were developed during the present work. Check-valves are widely used in the industry for medium or high-pressures, but were not available at all for large-flows with low-pressure-differences. A novel check-valve was devised for this application, along with the scaled UFCAP prototypes developed to be tested in a wave-flume and in the ocean to validate UFCAPs concept feasibility, and identify critical design parameters and features such as the conduit/air-chamber ratio. Ocean tests allowed to observe performance at component and assembly levels, learning new failure-modes and stablishing best-practices for future deployments. Testing confirmed the UFCAP WEC is not only an idea, but a concept which works and can generateing electricity at a competitive cost. / Graduate

Empirical models based on linear and nonlinear potential theory that determine the forces on Wave Energy Converters (WECs) are essential as they can be used for structural, mechanical and control system design as well as performance prediction. In contrast to empirical modelling, Computational Fluid Dynamics (CFD) solves the mass and momentum balance equations for fluid domains. CFD and linear potential theory models represent two extreme in terms of capturing the full range of hydrodynamic effects. These are classified as white box models and the structure of these models is completely derived from first principles understanding of the system. In contrast black box models like a Artificial Neural Networks and Auto-Regressive with, Exogenous Input (ARX), map input and output behaviour of a system without any specific physics based structure. Grey box models do not strictly follow a first principles approach but are based on some observations of relationships between the hydrodynamic effects (e.g. buoyancy force) and system state (e.g. free surface height). The objective of this thesis is to propose a data driven grey box modelling approach, which is computationally efficient compared to high fidelity white box mod- els and still sufficiently accurate for the purpose of determining hydrodynamic forces on heaving WECs. In this thesis, a unique data driven approach that combines features from existing works in modelling of WEC and application of nonlinear hysteretic systems is developed. To that end a CFD based Numerical Wave Tank that could provide the data needed to populate the new modelling framework is used. A hull which hydrodynamically represents a Self Reacting Point Absorbers (SRPAs) with heave plate is subjected to pan-chromatic wave fields and is forced to oscillate concomitantly. The results provide evidence that a SRPA with heave plate exhibits nonlinear relationships with motion parameters including relative position, velocity and acceleration. These parameters show causal relationships with the hydrodynamic force. A simulation methodology to establish confidence in the components of a model framework is developed and the hydrodynamic forces on SRPAs with heave plate and bulbous tank have been analyzed and compared. Two sets of numerical simulation were conducted. Firstly, the WECs were restricted to all degrees of freedom and subjected to monochromatic waves and later the WECs were oscillated at various frequency in a quiescent numerical tank. These results were validated against existing experimental data. Earlier attempts by other authors to develop a data-driven model were limited to simple hulls and did not include rate dependent nonlinearities that develop for heave plates. These studies laid the foundation to current work. The model framework developed in this thesis accounts for the nonlinear relationship between force and parameters like velocity and acceleration along with hysteretic relationship between force and velocity. This modelling framework has a nonlinear static, a hysteresis (Bouc-Wen model) and a dynamic (ARX model) block. In this work the Bouc-Wen model is employed to model the hysteresis effect. Five different models developed from this modelling framework are analyzed; two are state dependent models, while the other three required training to identify dynamic order of model equations. These latter models (Hammerstein, rate dependent Hammerstein and rate dependent KGP models) have been trained and validated for various cases of fixed and oscillating HP cylinder. The results demonstrate significant improvement (max 39%) in prediction accuracy of hydrodynamic forces on a WEC with heave plate, for the model in which a rate dependent hysteresis block is coupled with Hammerstein or KGP models. / Graduate