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This is the first joint reference paper for the Ocean Energy Systems (OES) Task 10 Wave Energy Converter modeling verification and validation group. The group is established under the OES Energy Technology Network program under the International Energy Agency. OES was founded in 2001 and Task 10 was proposed by Bob Thresher (National Renewable Energy Laboratory) in 2015 and approved by the OES Executive Committee EXCO in 2016. The kickoff workshop took place in September 2016, wherein the initial baseline task was defined. Experience from similar offshore wind validation/verification projects (OC3-OC5 conducted within the International Energy Agency Wind Task 30) [1], [2] showed that a simple test case would help the initial cooperation to present results in a comparable way. A heaving sphere was chosen as the first test case. The team of project participants simulated different numerical experiments, such as heave decay tests and regular and irregular wave cases. The simulation results are presented and discussed in this paper.

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... In this study, numerical analysi performed using frequency-dependent coefficients with the two-body teraction. Figure 4 compares the results of the linear and weakly nonlinear analysis for the heave free-decay test with the reference literature when the initial position was 5 m above the water surface [37]. The results agree well. ...

... The time series of the linear and weakly nonlinear analysis have different magnitudes and phase angles because the difference between the nonlinear and linear hydrostatic force caused by the geometric nonlinearity of the sphere was large. Figure 4 compares the results of the linear and weakly nonlinear analysis for the heave free-decay test with the reference literature when the initial position was 5 m above the water surface [37]. The results agree well. ...

... A denotes the wave amplitude. The following PTO damping force was also applied to the external force vector of the float to evaluate the heave RAO with PTO damping [37]. ...

Interest in water wave power generation, a promising source of renewable energy, is increasing. Numerous types of wave energy converters (WECs) have been designed to transform wave energy into electricity. In this study, we focus on heaving point absorbers (HPAs) of the Wavestar type, which consist of multiple floats connected to a bottom-fixed ocean structure by structural arms and hinges. Each float moves up and down due to wave forces and produces electricity using the hydraulic power take-off (PTO) system connected directly to the float. A numerical procedure using the three-dimensional augmented formulation was developed to calculate the rotational motion of the float. The frequency-dependent coefficients were calculated using the hydrodynamic solver WAMIT. The nonlinear Froude–Krylov and hydrostatic forces were considered. For the environmental conditions, the wave data of four nearshore areas in Korea, obtained from the Korea Meteorological Administration (KMA), were used. Under the given environmental conditions, Buan was found to be the most suitable area among the locations selected for installing a Wavestar-type WEC without considering installation and maintenance costs.

... The validation cases presented in this section are based on a paper (see Wendt et al., 2017) published in the frame of the Ocean Energy Systems (OES) Task 10 on the simulation of a heaving sphere. Results from ECN simulations with a linear model using a state space representation are available for comparison. ...

... For the largest initial altitude (Figure 4.13b), the linear data and the non-linear simulation are not similar anymore, which is consistent as the initial altitude is large (equals to the radius of the sphere). The observed differences are consistent with those visible between linear and non-linear codes in the reference paper (Wendt et al., 2017). ...

... Simulations are performed for ten different wave periods, including the one corresponding to the analytically predicted resonance, and three wave steepness values. Note that the steepness definition used within the reference paper (Wendt et al., 2017) differs from that used in the preceding chapter: ...

Sailing yacht design has relied on steady state optimization for a long time, through the use of Velocity Prediction Programs (VPP). Nonetheless they have proved inadequate to handle accurately the stability trade-offs demanded by the state-of-the-art appendages as well as to assess their seakeeping abilities. The present thesis focuses on the study and development of a Dynamic Velocity Prediction Program (DVPP), a time-domain simulation tool that enables such studies. The program allows for 6 degrees-of-freedom calculation and implement a multibody algorithm. Different wind and wave models are available. The calculation of the loads relies on a weakly non-linear system-based approach. The implemented models use either load calculations at runtime on the body mesh, polynomial regressions on pre-computed dataset or semi-empirical formulas. Particular care has been drawn to the progressive validation of the numerical tool and several test cases of increasing complexity are presented. An experimental campaign has been conducted in a towing tank. The variations of the radiation coefficients with speed are studied. The experimental data is used for validation of the DVPP for two situations of interest: motions and loads in waves, and water entry-exit sequences. Simulations of existing offshore yachts, an Ultim trimaran and an IMOCA monohull, are presented. They consider different transient situations, from a maneuver to varying environmental conditions and point out the interest of dynamic studies, allowing to open a different field of optimization than VPPs.

... This project contributed to the International Energy Agency (IEA) Annex VI Ocean Energy Modelling Verification and Validation project. This was followed by work conducted under an IEA-OES task established in 2016, Task 10 -Wave Energy Conversion Modelling Verification and Validation [13]. ...

... In 2017, the first joint reference paper presenting initial results from IEA-OES Task 10 was presented at EWTEC in Cork [13]. An overview of the key finding presented in [13] is summarised below. ...

... In 2017, the first joint reference paper presenting initial results from IEA-OES Task 10 was presented at EWTEC in Cork [13]. An overview of the key finding presented in [13] is summarised below. ...

In WP3 of the RiaSoR 2 project, an approach to assess the reliability of the WEC loads estimated via numerical models was devised. The numerical assessment builds on work completed in RiaSoR 1 and applies the VMEA methodology to assess the effects of variations in key metrics and quantify the related uncertainty associated with the numerical load estimates [3]. Within the scope of RiaSoR 2, K2M developed in Task 3.1 [1] a baseline generic WEC model in a modified version of WEC-Sim (Wave Energy Converter SIMulator). This model was then used in Task 3.2 to estimate characteristic WEC loads, with the presentation of a numerical load uncertainty assessment in three working examples [2].
It was originally intended that Task 3.3 would present an initial validation exercise, comparing numerical results with available experimental data from the project partners. However, due to a lack of relevant physical data, a literature review on verification and validation studies for WEC models available in the public-domain was conducted.
This report is organised in four main sections. Following this introduction (Section 1), a brief review of current practices for WEC model verification and validation in the public-domain is given in Section 2. In Section 3, three examples of published numerical validation case studies for WEC devices are presented. Finally, a summary of potential next steps that could be integrated in follow-up projects to RiaSoR 2 are outlined in Section 4.
This report constitutes deliverable D3.3 of the RiaSoR 2 project, and is the third and final deliverable of WP3.

... Wave loading on fixed structures, like cylinders, was also studied by researchers like Alemi et al. (2017) and Mohapatra et al. (2019), using both linear and nonlinear models. Wendt et al. (2017) and Wendt et al. (2019) presented numerical results for a heaving sphere and a similar structure, and compared the prediction results from a large group of participants. While, in general, most papers in the field focus on the hydrodynamics of the wave-structure interaction, a few projects also concentrate on comparing different numerical models, like the Task 10 joint project coordinated by NREL (Wendt et al., 2017 andWendt et al., 2019), to ascertain which numerical methods might be better for such studies. ...

... Wendt et al. (2017) and Wendt et al. (2019) presented numerical results for a heaving sphere and a similar structure, and compared the prediction results from a large group of participants. While, in general, most papers in the field focus on the hydrodynamics of the wave-structure interaction, a few projects also concentrate on comparing different numerical models, like the Task 10 joint project coordinated by NREL (Wendt et al., 2017 andWendt et al., 2019), to ascertain which numerical methods might be better for such studies. ...

... Heaving sphere in waves is a classical case with analytical solutions based on linearized equations. The case was also used in the IEA-OES task 10 project that dealt with code to code comparison (Wendt et al., 2017). As such, a large number of numerical comparative data is available for the case. ...

The paper focuses on oscillating wave energy converters and studies the wave response of a spherical device adopted for a validation study. A validation study is performed for a sphere with heave free motion encountering waves of varying wave lengths and amplitudes. Initially heave decay simulations is performed by releasing the sphere into the water from two different heights. Next, wave simulations are performed for varying wave lengths and wave heights and compared with available experimental and numerical results. The effect of wave steepness has also been studied. The open source CFD toolkit, OpenFOAM, is used for the study and the results show good agreement with available data in the literature. The study concludes that the consideration of the sea conditions is essential while deciding the size of a wave energy converter for optimal energy extraction.

... Further, we will discuss the advantages, disadvantages and the range of validity of the different methods and tools studied. The first code-to-code comparison of a heaving sphere is described in a joint reference paper [23] and a follow-up paper that includes simulations on power performance and calculation of energy production [24]. The second part of this paper describes validation using existing experimental data presented for the first time. ...

... For decay cases with smaller initial displacements, the agreement between linear and nonlinear models tends to improve. More discussion on this topic is given in [23]. ...

... This reduced resonance response yields a mean power prediction that is about 20% below the mean power predicted by the linear models. Additional details on the irregular wave analysis are covered in [23]. ...

The International Energy Agency Technology Collaboration Programme for Ocean Energy Systems (OES) initiated the OES Wave Energy Conversion Modelling Task, which focused on the verification and validation of numerical models for simulating wave energy converters (WECs). The long-term goal is to assess the accuracy of and establish confidence in the use of numerical models used in design as well as power performance assessment of WECs. To establish this confidence, the authors used different existing computational modelling tools to simulate given tasks to identify uncertainties related to simulation methodologies: (i) linear potential flow methods; (ii) weakly nonlinear Froude-Krylov methods; and (iii) fully nonlinear methods (fully nonlinear potential flow and Navier-Stokes models). This article summarizes the code-to-code task and code-to-experiment task that have been performed so far in this project, with a focus on investigating the impact of different levels of nonlinearities in the numerical models. Two different WECs were studied and simulated. The first was a heaving semi-submerged sphere, where free-decay tests and both regular and irregular wave cases were investigated in a code-to-code comparison. The second case was a heaving float corresponding to a physical model tested in a wave tank. We considered radiation, diffraction, and regular wave cases and compared quantities, such as the WEC motion, power output and hydrodynamic loading.

... A simulation result of 3600 s after a 100 s ramping period was used to remove the initial transient motions. Figure 4 compares the heave RAOs of the half-submerged sphere with the results of a previous study [41]. While [41] obtained RAOs in regular waves of respective frequencies, the present method calculated the RAOs at all frequencies from one time-domain simulation using cross-and auto-spectral densities. ...

... Figure 4 compares the heave RAOs of the half-submerged sphere with the results of a previous study [41]. While [41] obtained RAOs in regular waves of respective frequencies, the present method calculated the RAOs at all frequencies from one time-domain simulation using cross-and auto-spectral densities. The two independent results agreed well across all frequency ranges. ...

A Wavestar-type Wave Energy Converter (WEC) on an elastic foundation structure was investigated using an author-developed coupled dynamic analysis computer program. The program included an elastic foundation structure composed of beam elements, a multi-body dynamics model of the entire system, a hydrodynamics model of the dual-buoy, and fully coupled dynamics considering the interaction between the structure and WECs. The selected WEC models a heaving-point-absorber (HPA), one of the oscillating body systems which causes rotational motions of a connecting rod attached to the foundation structure. A rotational-damper-type hydraulic power take-off (PTO) system on the foundation structure produced electricity. The bottom-fixed foundation structure was modeled by three-dimensional beam elements, and the entire system, including HPA, was analyzed by multi-body dynamics. Random wave data at Buan, a nearshore region of Korea, collected by the Korea Meteorological Administration (KMA), was used as a demonstration study using the developed computer programs. Through the case study, the displacement and stress of the foundation structure were increased significantly by the dynamic coupling effects with the WECs, which underscores that the coupled dynamic analysis is essential for a reliable performance evaluation and the design of such a system.

... For this study, we selected the floating sphere used for the Ocean Energy Systems Task 10 Wave Energy Converter modeling and verification effort [23]. The floating sphere has a radius of 5.0 m, and its origin is located on the mean water surface at the center of the spherical body, with a summary of the model parameters provided in Table 1. ...

... General properties of the floating sphere[23] ...

This work revisits the theoretical limits of one-degree-of-freedom wave energy converters (WECs). This paper considers the floating sphere used in the OES Task 10 WEC modeling and verification effort for analysis. Analytical equations are derived to determine bounds on displacement amplitude, time-averaged power (TAP), and power-take-off (PTO) force. A unique result found shows that the TAP absorbed by a WEC can be defined solely by the inertial properties and radiation hydrodynamic coefficients. In addition, a unique expression for the PTO force was derived that provides upper and lower bounds when resistive control is used to maximize power generation. For complex conjugate control, this same expression only provides a lower bound, as there is theoretically no upper bound. These bounds assist in comparing the performance of the floating sphere if it were to extract energy using surge or heave motion. The analysis shows because of differences in hydrodynamic coefficients for each oscillating mode, there are different frequency ranges that provide better power capture efficiency. The influence of a motion constraint on TAP while utilizing a nonideal power take-off is examined and found to reduce the losses associated with bidirectional energy flow. The expression to calculate TAP with a nonideal PTO is modified by the mechanical-to-electrical efficiency and the ratio of the PTO spring and damping coefficients. The PTO spring and damping coefficients were separated in the expression, allowing for limits to be set on the PTO coefficients to ensure net power generation.

... Table 4.4 shows that the computational time of the algebraic nonlinear model is similar to the linear model, while the remeshing routine is several times slower. It is important to highlight that the remeshing approach is coded in Fortran, while the linear and algebraic models are implemented in Matlab, which is between one and two orders of magnitude slower than lower-level coding languages, such as C or, indeed, Fortran [164]. Despite being written in a slower language, the fact that the algebraic approach still computes much faster than the remeshing approach further supports its merit as a computationally efficient method. ...

... Therefore, such a method has the potential to run roughly in real time, or a little slower, depending on the particular implementation. However, these considerations are for computations performed in Matlab, which is between one and two orders of magnitude slower than lower level coding languages, such as C or Fortran [164]. With C or Fortran implementation, therefore, real time execution is easily achievable. ...

One of the major challenges facing modern industrialized countries is the provision of energy: traditional sources, mainly based on fossil fuels, are not only growing scarcer and more expensive, but are also irremediably damaging the environment. Renewable and sustainable energy sources are attractive alternatives that can substantially diversify the energy mix, cut down pollution, and reduce the human footprint on the environment. Ocean energy, including energy generated from the motion of wave, is a tremendous untapped energy resource that could make a decisive contribution to the future supply of clean energy. However, numerous obstacles must be overcome for ocean energy to reach economic viability and compete with other energy sources. Energy can be generated from ocean waves by wave energy converters (WECs). The amount of energy extracted from ocean waves, and therefore the profitability of the extraction, can be increased by optimizing the geometry and the control strategy of the wave energy converter, both of which require mathematical hydrodynamic models that are able to correctly describe the WEC-fluid interaction. On the one hand, the accuracy and representativeness of such models have a major influence on the effectiveness of the WEC design. On the other hand, the computational time required by a model limits its applicability, since many iterations or real-time calculations may be required. Critically, computational time and accuracy are often mutually contrasting features of a mathematical model, so an appropriate compromise should be defined in accordance with the purpose of the model, the device type, and the operational conditions. Linear models, often chosen due to their computational convenience, are likely to be imprecise when a control strategy is implemented in a WEC: under controlled conditions, the motion of the device is exaggerated in order to maximize power absorption, which invalidates the assumption of linearity. The inclusion of nonlinearities in a model is likely to improve the model's accuracy, but increases the computational burden. Therefore, the objective is to define a parsimonious model, in which only relevant nonlinearities are modelled in order to obtain an appropriate compromise between accuracy and computational time. In addition to presenting a wider discussion of nonlinear hydrodynamic modelling for WECs, this thesis contributes the development of a computationally efficient nonlinear hydrodynamic model for axisymmetric WEC devices, from one to six degrees of freedom, based on a novel approach to the nonlinear computation of static and dynamic Froude-Krylov forces.

... The time history of heave displacement is shown in Figure 4. The obtained results are compared with those from two reference studies by Wendt et al. [20] and Cerik and Choung [17], and the decoupled analysis in OrcaFlex. A good agreement can be observed, despite a subtle difference in the periods of heave displacement. ...

Ship collisions with floating bridges in the navigation area are complex processes involving highly nonlinear dynamics, large structural deformations, and fluid-structure interactions (FSI). In the traditional approach for collision analyses, the external dynamics and internal mechanics of the ship-bridge system are treated independently. Limitations have been reported for this decoupled method in predicting the structural responses during oblique collisions. This study introduces an algorithm to integrate the external dynamics and internal mechanics in ship-floating bridge collision studies, addressing the complexities of a multibody system. The external dynamics of a traveling ship colliding with a floating bridge is modeled using OrcaFlex, while the internal mechanics is simulated in LS-DYNA. Through the developed algorithm, two analyses are conducted interactively. The algorithm incorporates the considerations of hydrodynamic forces acting on the floating bodies, their six degrees of freedom (6DOF) motions, and the structural internal forces within the multibody system. The simulation results reveal that the collision forces, effective stress, plastic strain of the striking ship and the struck pontoon, as well as the energy dissipation, are sensitive to the boundary conditions applied to the pontoon.

... We examine the 1 degree-of-freedom (1DoF) problem of a heaving sphere. This is a case that has been used repeatedly within the Ocean Energy System wave energy modelling task (OES-WEMT) [20]- [22]. The heaving sphere was initially numerically modelled in full-scale (with a sphere diameter of D=10 m) [21], [23], but later experimental test was performed in modelscale (D=0.3 m) by Kramer et al. [22]. ...

Numerical models based on the linear potential flow equations are of paramount importance in the design of wave energy converters (WECs). Over the years methods such as wave stretching, nonlinear Froude-Krylov and Morrison drag have been developed to overcome the short-comings of the underlying assumptions of small amplitude wave, small motion and inviscous flow. In this work we present a different approach to enhance the performance of the linear method: a hybrid linear potential flow – machine learning (LPF-ML) model. A hierarchy of high-fidelity models – Reynolds-Averaged Navier-Stokes, Euler and fully nonlinear potential flow – is used to create training data for correction factors targeting nonlinear hydrodynamics, pressure drag and skin friction, respectively. Long short-term memory (LSTM) networks are then trained and added to the LPF model. LSTM networks are heavy to train but fast to evaluate so the computational efficiency of the LPF model is kept high. Simple decay tests of generic bodies (sphere, box, etc) are used to validate the LPF-ML model. Finally, the LPF-ML is applied to a model-scale point-absorber WEC to assess the power production.

... The heaving sphere was initially investigated in full-scale (with a sphere diameter of D=10 m) as the first test case of the OES-WEMT [12]. Decay, regular waves and irregular wave cases, with different power take-off (PTO) damping coefficients, were investigated in [12], [37]. The decay test was later re-visited in model-scale (D=0.3m) in Kramer et al. [13]. ...

High-fidelity models become more and more used in the wave energy sector. They offer a fully nonlinear simulation tool that in theory should encompass all linear and nonlinear forces acting on a wave energy converter (WEC). Studies using high-fidelity models are usually focusing on validation of the model. However, a validated model does not necessarily give reliable solutions. Solution verification is the methodology to estimate the numerical uncertainties related to a simulation. In this work we test four different approaches: the classical grid convergence index (GCI); a least-square version (LS-GCI); a simplified version of the least-square method (SLS-GCI); and the ITTC recommended practice. The LS-GCI requires four or more solutions whereas the other three methods only need three solutions. We apply these methods to four different high-fidelity models for the case of a heaving sphere. We evaluate the numerical uncertainties for two parameters in the time-domain and two parameters in the frequency domain. It was found that the GCI and ITTC were hard to use on the frequency domain parameters as they require monotonic convergence which sometimes does not happen due to the differences in the solutions being very small. The SLS-GCI performed almost as well as the SL-GCI method and will be further investigated.

... Heave motions of a sphere with 5.0 m initial displacement from literatureWendt et al. (2017). ...

... To gain confidence in using numerical models and assessing the accuracy of these codes, the International Energy Agency Ocean Energy Systems (IEA OES) Task 10 project [830] compared a large number of linear, weakly nonlinear, and highly nonlinear codes on a simple WEC system of a heaving buoy. The main outcome of this project demonstrated that, in steep waves, the weakly nonlinear codes are able to capture higher-order peaks in the WEC response because of the consideration of nonlinear hydrostatics and Froude-Krylov forcing, and therefore they predict a reduced mean power output of the WEC that is closer to the reality. ...

... To gain confidence in using numerical models and assessing the accuracy of these codes, the International Energy Agency Ocean Energy Systems (IEA OES) Task 10 project [830] compared a large number of linear, weakly nonlinear, and highly nonlinear codes on a simple WEC system of a heaving buoy. The main outcome of this project demonstrated that, in steep waves, the weakly nonlinear codes are able to capture higher-order peaks in the WEC response because of the consideration of nonlinear hydrostatics and Froude-Krylov forcing, and therefore they predict a reduced mean power output of the WEC that is closer to the reality. ...

... To gain confidence in using numerical models and assessing the accuracy of these codes, the International Energy Agency Ocean Energy Systems (IEA OES) Task 10 project [830] compared a large number of linear, weakly nonlinear, and highly nonlinear codes on a simple WEC system of a heaving buoy. The main outcome of this project demonstrated that, in steep waves, the weakly nonlinear codes are able to capture higher-order peaks in the WEC response because of the consideration of nonlinear hydrostatics and Froude-Krylov forcing, and therefore they predict a reduced mean power output of the WEC that is closer to the reality. ...

... A more detailed comparison of the key differences between the WS, linear potential flow and CFD models with regards to WEC applications can also be found in Ding et al. (2019b). Validation of the ECN WS code used in this study against other available hydrodynamic models and experimental data has also been performed in Wendt et al. (2017) and Wendt et al. (2019), respectively. ...

Multi-mode Wave Energy Converters (WECs) are designed to harvest energy simultaneously from multiple hydrodynamic modes, thereby maximising power absorption. The behaviour of each mode must be carefully considered, given that hydrodynamic and geometric coupling between modes can lead to severe reductions in power if improperly designed. This study aims to investigate how the design of a planar three-tethered WEC can be used to tune the surge, heave and pitch hydrodynamic modes to achieve maximum power absorption. The effect of various tether arrangement and mass distribution design parameters on the performance of a WEC subjected to both geometric and hydrodynamic nonlinearities was investigated. Results indicated that, to absorb the most power in regular waves, the tether configuration should be adjusted such that the surge and heave dominant rigid body modes are resonant with the incident wave. Geometric nonlinearities associated with the tether arrangement were found to cause sub-harmonic excitations which severely compromised device performance, with further reductions in power when nonlinear hydrodynamics were considered. In irregular waves, the optimal design became more strongly driven by performance in surge. Overall, maximum power was achieved when all three tethers were attached close to one another on the bottom of the buoy.

... Non-streamlined bodies such as conical and cylindrical shapes result in some nonlinear effects that arise from changing the water plane and wetted surface areas during the heaving motion of the floating body [52] . The most important effects of these nonlinearities are evident during the first, large oscillations [56] . For heaving point absorbers, nonlinear Froude-Krylov effects are crucial to reproduce the WEC behavior under large relative motions. ...

In this paper, two smoothed particle hydrodynamics (SPH) models, namely SPH-W and SPH-C were used to evaluate the motion response of a point absorber wave energy converter (WEC). In the SPH-W model, a long wave flume was constructed and a long simulation was performed to obtain the motion response of the WEC. In the SPH-C model, the SPH method is only used to find the hydrodynamic coefficients of the device by analysing a few seconds of free-decaying motion of WEC in calm water in a much smaller numerical flume. Then, these coefficients were inserted in the equation of motion of a heaving WEC that was solved using a 4th order Runge-Kutta (ODE45) solver in MATLAB. First, the energy conservation property of the WCSPH model was examined through a standing wave benchmark test. Then, the wave-point absorber interaction was simulated. While the simulation time for SPH-C model is much smaller than that of SPH-W, it gave almost similar results for the motion response of WEC. Then, these two models were used to evaluate the effects of the control force and the draft of a cone-cylinder point absorber on its hydrodynamic responses. The results showed that compared to the effect of the supplementary inertia, changes in the draft of the WEC have a small influence on its hydrodynamic responses. The buoy draft has an inverse relationship with both added mass and damping coefficients. However, increasing the supplementary mass increases the added mass and decreases the hydrodynamic damping coefficients.

... In particular, offshore wind energy is an area of great focus worldwide because of its contribution to sustainable socioeconomic and environmental development (Li and Yu, 2018). The cumulative global installed offshore wind capacity is expected to grow from 14 GW in 2016 to 41 GW in 2022 (Wendt et al., 2017). In addition, it is estimated that Europe will invest approximately 20 billion euros in the wind energy market by 2030, 60 % of which will be spent on the establishment of offshore wind farms (Wu et al., 2019). ...

The increasing demand for offshore wind turbines with larger capacity brings challenges concerning their original foundation design. This study introduces a new type of monopile foundation with internal restriction plates that aim to enhance the bearing capacity of the entire structure. Two types of improved monopiles are proposed through the addition of one-hole and four-hole restriction plates. A series of centrifuge tests are performed to study the response of the improved piles under lateral loading conditions in saturated sand. The pile-soil interactions are characterized using finite element analysis. A sensitivity study and a parametric study are performed using numerical tests. In offshore applications, the improved pile can provide larger lateral resistances than the open-ended pile foundation. This improvement is proportional to the pile diameter. The four-hole restriction plate is more effective than the one-hole plate for larger diameter piles. The rotational axis is located at 80 % of the embedment depth, and the distribution of earth pressure is determined. A theoretical method is proposed to calculate the ultimate lateral capacity of the novel monopile containing restriction plates.

... Here, multiple research institutions and R&D companies from 12 countries collaborate with the focus on the development of numerical models for simulating wave energy converters (WECs) [5]. A floating sphere was chosen as a practical representation of a simple wave energy convertor buoy, and numerical modelling of the decay of a sphere was completed as an initial test case [6][7][8]. The resulting simulations from the different members showed widespread simulation results, which highlighted the need for knowing the true, real-world results for the considered test case together with the associated measurement uncertainties. ...

Highly accurate and precise heave decay tests on a sphere with a diameter of 300 mm were completed in a meticulously designed test setup in the wave basin in the Ocean and Coastal Engineering Laboratory at Aalborg University, Denmark. The tests were dedicated to providing a rigorous benchmark dataset for numerical model validation. The sphere was ballasted to half submergence, thereby floating with the waterline at the equator when at rest in calm water. Heave decay tests were conducted, wherein the sphere was held stationary and dropped from three drop heights: a small drop height, which can be considered a linear case, a moderately nonlinear case, and a highly nonlinear case with a drop height from a position where the whole sphere was initially above the water. The precision of the heave decay time series was calculated from random and systematic standard uncertainties. At a 95% confidence level, uncertainties were found to be very low—on average only about 0.3% of the respective drop heights. Physical parameters of the test setup and associated uncertainties were quantified. A test case was formulated that closely represents the physical tests, enabling the reader to do his/her own numerical tests. The paper includes a comparison of the physical test results to the results from several independent numerical models based on linear potential flow, fully nonlinear potential flow, and the Reynolds-averaged Navier–Stokes (RANS) equations. A high correlation between physical and numerical test results is shown. The physical test results are very suitable for numerical model validation.

... Indeed, in recent years, the NLFK modeling approach has been employed to many WEC application cases, too numerous to collate in this review. For example, 9 of the 25 models submitted in the first joint reference paper for the International Energy Agency Ocean Energy Systems Task 10 WEC Modeling Verification and Validation group [200], utilize partially nonlinear models with NLFK forces. ...

This review focuses on the most suitable form of hydrodynamic modeling for the next generation wave energy converter (WEC) design tools. To design and optimize a WEC, it is estimated that several million hours of operation must be simulated, perhaps one million hours of WEC simulation per year of the R&D program. This level of coverage is possible with linear potential flow (LPF) models, but the fidelity of the physics included is not adequate. Conversely, while Reynolds averaged Navier-Stokes (RANS) type computational fluid dynamics (CFD) solvers provide a high fidelity representation of the physics, the increased computational burden of these models renders the required amount of simulations infeasible. To scope the fast, high fidelity options, the present literature review aims to focus on what CFD theories exist intermediate to LPF and RANS as well as other modeling options that are computationally fast while retaining higher fidelity than LPF.

... Model verification and validation are essential for numerical method development, which is commonly used to evaluate the confidence and accuracy of the model. Often, in lieu of validation through comparison to experimental data, numerical models go through verification via comparison to other numerical models (i.e., a code-to-code comparison (Combourieu et al., 2015;Wendt et al., 2017)). On the other hand, to ensure the numerical model accurately represents the physical system, a validation study is often carried out by comparing the numerical solutions to measurements from experimental tests. ...

The floating oscillating surge wave energy converter (FOSWEC) is a wave energy converter that was designed, built, and tested to develop an open-access data set for the purpose of numerical model validation. This paper details the experimental testing of the 1:33-scale FOSWEC in a directional wave basin, and compares experimental data to numerical simulations using the wave energy converter simulator (WEC-Sim) open-source code. The FOSWEC consists of a floating platform moving in heave, pitch, and surge, and two pitching flaps. Power is extracted through relative motion between each of the flaps and the platform. The device was designed to constrain different degrees of freedom so that it could be configured into a variety of operating conditions with varying dynamics. The FOSWEC was tested in a range of different conditions including: static offset, free decay, forced oscillation, wave excitation, and dynamic response to regular waves. In this paper, results from the range of experimental tests are presented and compared to numerical simulations using the WEC-Sim code.

... In addition, there is a very limited amount of experimental data that has been published and is high enough quality for code validation. However, some research groups, like OES Task 10 [8], are working towards the goal of building confidence in numerical estimations of loads and power production [9]. There are three categories to group the variety of approaches to simulating WECs: linear codes, quasi-linear codes and non-linear codes [10]. ...

Free-floating bodies are commonly modelled using Cummins’ equation based on linear potential flow theory and including non-linear forces when necessary. In this paper, this methodology is applied to a body pitching around a fixed hinge (not free-floating) located close to a second bottom-fixed body. Due to the configuration of the setup, strong hydrodynamic interactions occur between the two bodies. An investigation is made into which non-linear forces need to be included in the model in order to accurately represent reality without losing computational efficiency. The non-linear forces investigated include hydrostatic restoring stiffness and different formulations of excitation forces and quadratic drag forces. Based on a numerical comparison, it is concluded that the different non-linear forces, except for the quadratic drag force, have a minor influence on the calculated motion of the pitching body. Two formulations of the quadratic drag force are shown to result in similar motions, hence the most efficient one is preferred. Comparisons to wave basin experiments show that this model is, to a large extent, representative of reality. At the wave periods where the hydrodynamic interactions between the bodies are largest, however, the amplitudes of motion measured in the wave basin are lower than those calculated numerically.

... Therefore, such a method has the potential to run roughly in real time, or a little slower, depending on the particular implementation. However, these considerations are for computations performed in Matlab, which is between one and two orders of magnitude slower than lower level coding languages, such as C or Fortran (Wendt et al., 2017). With C or Fortran implementation, therefore, real time execution is easily achievable. ...

Wave energy devices are designed, and controlled, in order to be extremely responsive to incoming wave excitation, hence maximising power absorption. Due to the consequent large motion excursions, highly nonlinear behaviour is likely to occur, especially in relation to variations in wetted surface. Moreover, nonlinearities may induce parametric instability, or activate internal mechanisms for exchanging energy between different degrees of freedom (DoFs), usually affecting the overall efficiency of the device. Consequently, single-DoF linear models may produce overly optimistic power production predictions, and neglect important dynamics of the system. One highly nonlinear phenomenon, particularly detrimental to power absorption for several wave energy converters, is parametric roll, which internally diverts part of the energy flow, from the axis where the power take-off is installed, to a secondary axis, generating parasitic motion. This paper proposes a computationally efficient multi-DoFs nonlinear model, which can effectively describe nonlinear behaviour, such as parametric pitch and roll, and their impact on motion prediction, power production assessment, and optimal control parameters.

... Therefore, such a method has the potential to run roughly in real time, or a little slower, depending on the particular implementation. However, the computation times given are for computations performed in Matlab, which is between one and two orders of magnitude slower than lower level coding languages, such as C or Fortran (Wendt et al., 2017). With C or Fortran implementation, therefore, real time execution is easily achievable. ...

Parametric resonance is a highly nonlinear phenomenon, difficult to model and foresee , with often detrimental consequences on the power production efficiency of wave energy converters. Parametric excitation, due to time-varying parameters of the system, activates an internal excitation mechanism, which diverts part of the energy from the principal degree of freedom, consequently generating parasitic motions. Although the ability of a mathematical model to articulate parametric instability is beneficial for design and control purposes, the increase in computational burden and complexity is often unacceptable. However, using computationally frugal nonlinear Froude-Krylov force calculations, applicable to axisymmetric devices, it is possible to define mathematical models fast enough for computation in real time. The focus of the paper is a floating oscillating water column device, inspired by the Sparbuoy device, in order to demonstrate the ability of such a mahematical model to describe parametric roll responses.

... Therefore, such a method has the potential to run roughly in real time, or a little slower, depending on the particular implementation. However, these considerations are for computations performed in Matlab, which is between one and two orders of magnitude slower than lower level coding languages, such as C or Fortran (Wendt et al., 2017). With C or Fortran implementation, therefore, real time execution is easily achievable. ...

Wave energy devices are designed, and controlled, in order to be extremely responsive to incoming wave excitation, hence maximising power absorption. Due to the consequent large motion excursions, highly nonlinear behaviour is likely to occur, especially in relation to variations in wetted surface. Moreover, nonlinearities may induce parametric instability, or activate internal mechanisms for exchanging energy between different degrees of freedom (DoFs), usually affecting the overall efficiency of the device. Consequently, single-DoF linear models may produce overly optimistic power production predictions, and neglect important dynamics of the system. One highly nonlinear phenomenon, particularly detrimental to power absorption for several wave energy converters, is parametric roll, which internally diverts part of the energy flow, from the axis where the power takeoff is installed, to a secondary axis, generating parasitic motion. This paper proposes a computationally efficient multi-DoFs nonlinear model, which can effectively describe nonlinear behaviour, such as parametric pitch and roll, and their impact on motion prediction, power production assessment, and optimal control parameters.

... Using a constant time step second-order Runge-Kutta scheme, varying the time step from 0.005 s to 0.025 s, for a regular wave of period about 0.7 s, the resulting run time is between one and three times the simulation time for a Matlab implementation. Therefore, such a method has the potential to run roughly in real time, or a little slower, depending on the particular implementation, given that Matlab is between one and two orders of magnitude slower than lower level coding languages, such as C or Fortran (Wendt et al. 2017). With a C or Fortran implementation, therefore, real-time execution is easily achievable. ...

Wave energy devices are designed, and controlled, to be extremely responsive to incoming wave excitation, hence, maximising power absorption. Due to the consequent large motion excursions, highly nonlinear behaviour is likely to occur, especially in relation to variations in wetted surface. Moreover, nonlinearities may induce parametric instability, or activate internal mechanisms for exchanging energy between different degrees of freedom (DoFs), usually affecting the overall efficiency of the device. Consequently, single-DoF linear models may produce overly optimistic power production predictions, and neglect important dynamics of the system. One highly nonlinear phenomenon, potentially detrimental to power absorption for several wave energy converters, is parametric roll/pitch; due to parametric excitation, part of the energy flow is internally diverted, from the axis where the power take-off is installed, to a secondary axis, generating parasitic motion. This paper proposes a computationally efficient multi-DoF nonlinear model, which can effectively describe nonlinear behaviour, such as parametric pitch and roll, and their impact on motion prediction, power production assessment, and optimal control parameters.

... This code competition was run by the Center for Ocean Energy Research at Maynooth University, the basis of which was detailed in an OMAE 2014 publication by Costello et al. on numerical model comparison to experimental data for a submerged horizontal cylinder [4,5]. Related to competitions are international code comparison efforts, such as the International Energy Agency (IEA) Ocean Energy Systems (OES) Task 10 effort on modeling WECs, and the IEA OES Offshore Code Comparison Collaboration (OC3) through Offshore Code Comparison Collaboration, Continued with Correlation (OC5) efforts on modeling floating offshore wind turbines [6,7]. ...

This paper details the development and validation of a numerical model of the Wavestar wave energy converter (WEC) developed in WEC-Sim. This numerical model was developed in support of the WEC Control Competition (WECCCOMP), a competition with the objective of maximizing WEC performance over costs through innovative control strategies. WECCCOMP has two stages: numerical implementation of control strategies, and experimental implementation. The work presented in this paper is for support of the numerical implementation, where contestants are provided a WEC-Sim model of the 1:20 scale Wavestar device to develop their control algorithms. This paper details the development of the numerical model in WEC-Sim and of its validation through comparison to experimental data.

... Note that option (a) is about 80 times slower than the algebraic integration. However, it is important to point out that all calculations are performed in Matlab, which is between one and two orders of magnitude slower than lower level coding languages, such as C or Fortran (Wendt et al., 2017). ...

... The linear, weakly nonlinear and fully nonlinear calculations show distinct grouping in their predictions. See Wendt et al. (2017) for more details on the comparisons. Phase II of the project is currently being defined. ...

COMMITTEE MANDATE
Concern for load analysis and structural design of offshore renewable energy devices.
Attention shall be given to the interaction between the load and structural response of fixed
and floating installations taking due consideration of the stochastic nature of the ocean
environment. Aspects related to prototype testing, certification, marine operations and total
cost of energy shall be considered.

... 3, it is found that the numerical integration scheme is, on average, about 80 times slower than the algebraic integration, where the computational time of the VFK method is of the order of magnitude of 10 −4 s. However, it is important to point out that all the calculations are performed in Matlab, which is between one and two orders of magnitude slower than lower level coding languages [8]. ...

Accurate and computationally efficient mathematical models are fundamental for designing, optimizing, and controlling wave energy converters. Wave energy devices are likely to exhibit significant nonlinear behaviour, over their full operational envelope, so that nonlinear models may become indispensable.
Froude-Krylov nonlinearities are of great importance in point absorbers but, in general, their calculation requires an often unacceptable increase in model complexity and computational time. However, if the body is assumed to be axisymmetric, it is possible to describe the whole geometry analytically, thereby allowing faster calculation of nonlinear Froude-Krylov forces.
In this paper, a convenient parametrization of axisymmetric body geometries is proposed, applicable to devices moving in surge, heave, and pitch. In general, the Froude-Krylov integrals must be solved numerically. Assuming small pitch angles, it is possible to further simplify the problem, and achieve an algebraic solution, which is considerably faster than numerical integration.

... The consequent run time for computing the response of the device to incoming wave is about 1.2 times the simulation time, effectively allowing the model to run almost in real time. However, it is important to point out that all calculations are performed in Matlab, which is between one and two orders of magnitude slower than lower level coding languages, such as C or Fortran [17]. Nevertheless, although the mesh-based LAMSWEC nonlinear FK model is coded in Fortran (which is a significantly faster implementation than Matlab), it has a run time about 10 times longer than the simulation time [8], therefore about one order of magnitude slower than the method proposed in this paper. ...

High accuracy, with low computational time is likely to be a fundamental requirement for mathematical models for wave energy converters, in order to be effective tools for reliable motion prediction and power production assessment, device and controller design, and load estimation. Wave energy converters are particularly prone to complex nonlinear behavior, which are difficult to model efficiently. Highly-nonlinear effects, related to nonlinear Froude-Krylov forces, include nonlinear coupling, instability, and parametric resonance, which may detract from or improve converted power production. It is therefore essential to be able to describe such nonlinearities, in order to assess their repercussion on the performance of the device, and eventually design the system in order to exploit them. This paper provides a computationally efficient, compact, and flexible modelling approach for describing nonlinear Froude-Krylov forces for axisymmetric wave energy devices, in 6 degrees of freedom. Unlike other nonlinear Froude-Krylov models, based on a mesh discretization of the geometry, the analytical formulation of the wetted surface allows the dynamical model to run almost in real time. The model is shown capable of appreciating pitching instability and parametric resonance, whose conditions for existence, and repercussion on converted power are discussed, for a heaving wave energy converter.

3.1 MODELLING OF WAVE ENERGY CONVERTER DYNAMICS Currently, several WECs exist with different absorption mechanisms and subsystems. Hence, a general formulation to describe the dynamics of all possible devices is a non- trivial task. This section provides practical, condensed information, and derivations for the dynamics of oscillating bodies, as this category comprises most WECs, and relevant literature is recommended for more technical information. The approaches described here can be extended to the analysis of other WECs systems and examples of these are given throughout the book.
3.2 PRINCIPLES AND BOUNDS OF WAVE POWER ABSORPTION Understanding the principles and limits in WEC power absorption is crucial for efficient PTO system design. To avoid losing generality, this section treats the PTO system (a complex and multi-functional sub-system of WEC as detailed in Section 3.3) as a generic feedback control system that generates a PTO control force modifying the power absorption performance of the WEC system.
3.3 CONTROL SYSTEM AND POWER TAKE-OFF DESIGN
The PTO system is the core of a WEC, and has multiple functions: 1) most obviously, it converts the mechanical power of the WEC mechanism into electricity; 2) it enhances the hydrodynamic efficiency of the WEC and thus maximises its power absorption in varying sea states; and 3) it ensures safe operation of the WEC in the harsh sea environment.

Multi-mode Wave Energy Converters (WECs) are able to harvest energy from multiple Degrees-of-Freedom (DOFs) simultaneously, which increases the power that can be absorbed from the incident wave compared to single-DOF WECs. However, nonlinear coupling between hydrodynamic modes, which occurs when the WEC oscillates simultaneously in multiple directions, means that simply applying the typical control strategies used for single-DOF WECs can lead to sub-optimal performance. This study investigates the multi-DOF dynamic control of a submerged, flat cylindrical WEC subjected to hydrodynamic coupling effects modelled under the weakly nonlinear potential flow theory based on the weak-scatterer approximation. Results show that, at low incident wave frequencies, tuning the surge, heave and pitch modes of the WEC to the same natural frequency can result in power losses of up to 30% in the weakly nonlinear model compared to results obtained from a fully linear model. These discrepancies are attributed to the pitching motions of the WEC, which changes the projected surface area of the device relative to the equilibrium position and hence violates the assumptions of the linear theory. From these findings, a suggested design strategy where the surge, heave and pitch DOFs were all decoupled and tuned to different natural frequencies was therefore proposed. In the presence of weakly nonlinear hydrodynamic coupling, it was found that this design may result in significant improvements in power absorbed for the multi-mode WEC, compared to a case where all DOFs are simply tuned to match the peak frequency of a given sea state.

This paper proposes a simulation technique to real-time control hydrostatic and hydrodynamic forces acting on pack ices depending on a user-subroutine of an explicit finite element code. By controlling the buoyancy for the wet elements, the hydrostatic force was possible in terms of a nonlinear restoring force. The hydrodynamic force acting on a pack ice was expressed as a drag force. The CFD analyses for a single pack ice under constant surge speed were carried out to estimate the total resistance and accordingly to calibrate the average drag coefficient. The proposed approach with the average drag coefficient produced same results with the CFD analyses. The user-subroutine with the drag coefficient was used to simulate the towing tests of an icebreaker in the pack ice condition. There were different ice resistances between the test and simulations. This forced to recalibrate the drag coefficient considering the difference of the stiffnesses in the towing test and simulations. After recalibration of the drag coefficient to 2.0, there were successful coincidences between the towing tests and simulations in terms of the ice resistances. The radiation effects were critical in the motion of pack ice, so the radiation force should be considered for future study.

Our communal global ocean energy resources are substantial and, perhaps even, one of the last untapped significant renewable resources which has the ability to assist in global decarbonization efforts. As we globally move towards a renewable energy future, ocean energy (e.g. waves, tides, currents and offshore winds) need to be considered in the suite of energy supply options to create a resilient, affordable and reliable future energy system. Estimates suggest global wave resources could theoretically generate 32,000 terawatt-hours (TWh) annually. As such, the opportunity associated with the responsible development of the wave energy sector can not be overstated. For context, the total United States of America electrical demand was approximately 3.8 TWh in 2019. This chapter provides an overview of the latest efforts of characterize and parameterize our global wave energy resources, a review of the fundamental operating principles of wave energy converter (WEC) technologies, and best practices to predict the ultimate performance and power production from the wave energy sector.

This paper explores how to achieve a fair equilibrium between conventional and renewable energy on the global energy market by integrating economic, social and environmental factors. It also seeks to analyze the effect of technology on the advancement of clean energy on increasing the efficiency of renewable energy and reducing costs. This paper uses the prospective approach as a research method to describe the essence of the demand for traditional and renewable energy and to extrapolate its trends. The results show that the current energy situation is not sustainable and leads to an increase in environmental pollution and an increase in dependence on fossil fuels. The findings also demonstrate that the technological development of renewable energy technologies allows it to gain an important position on the global energy market. The results of this study provide a scientific basis for drawing up energy policies in both the producing countries and the countries and countries importing oil. In addition, the current study provides managers of international energy firms with the advancement of investment plans in the field of clean energy to respond to the needs of the global energy industry both today and in the future.

A submerged wave device generates energy from the relative motion of floating bodies. In WaveSub, three floats are joined to a reactor; each connected to a spring and generator. Electricity generated damps the orbital movements of the floats. The forces are non-linear and each float interacts with the others. Tuning to the wave climate is achieved by changing the line lengths so there is a need to understand the performance trade-offs for a large number of configurations. This requires an efficient, large displacement, multidirectional, multi-body numerical scheme. Results from a 1/25 scale wave basin experiment are described. Here we show that a time domain linear potential flow formulation (Nemoh, WEC-Sim) can match the tank testing provided that suitably tuned drag coefficients are employed. Inviscid linear potential models can match some wave device experiments, however, additional viscous terms generally provide better accuracy. Scale experiments are also prone to mechanical friction and we estimate friction terms to improve the correlation further. The resulting error in mean power between numerical and physical models is approximately 10%. Predicted device movement shows a good match. Overall, drag terms in time domain wave energy modelling will improve simulation accuracy in wave renewable energy device design.

Numerical modelling of wave energy converters (WECs) can provide insights into device performance at an early stage and help de-risk projects before progressing to more advanced, costlier stages of development. Several software packages have been made available for this purpose in recent years. However, the lack of design convergence in the wave energy industry, with its wide range of working principles and mechanisms, means that many developers have been unable use these tools. Here we show that some limitations can be overcome by using an alternative multibody dynamics approach. A third party multibody dynamics code based on the Lagrange multiplier method, Hotint, has been coupled to Innosea’s existing WEC modelling code, InWave, and verified using existing test cases. This has made the modelling of many new types of mechanisms possible – include closed mechanical loops.

This paper describes work performed during the first half of Phase I of the Offshore Code Comparison Collaboration Continuation, with Correlation project (OC5). OC5 is a project run under the International
Energy Agency Wind Research Task 30, and is focused on validating the tools used for modeling offshore wind systems. In this first phase, simulated responses from a variety of offshore wind modeling tools were validated against tank test data of a fixed, suspended cylinder (without a wind turbine) that was tested under regular and irregular wave conditions at MARINTEK. The results from this phase include an examination of different approaches one can use for defining and calibrating hydrodynamic coefficients for a model, and the importance
of higher-order wave models in accurately modeling the hydrodynamic loads on offshore substructures.

A comprehensive set of experimental and numerical comparisons of the performance of two self-reacting point absorber wave energy converter (WEC) designs is undertaken in typical operating conditions. The designs are either currently, or have recently been, under development for commercialization. The experiments consist of a series of 1:25 scale model tests to quantify hydrodynamic parameters, motion dynamics, and power conversion. Each WEC is given a uniquely optimized power take off damping level. For hydrodynamic parameter identification, an optimization based method to simultaneously extract Morison drag and Coulomb friction coefficients from decay tests of under-damped, floating bodies is developed. The physical model features a re-configurable reacting body shape, a feedback controlled power take-off, a heave motion constraint system, and a mooring apparatus. A theoretical upper bound on power conversion for single body WECs, called Budal's upper bound, is extended to two body WECs.
The numerical analyses are done in three phases. In the first phase, the WECs are constrained to heave motion and subjected to monochromatic waves. Quantitative comparisons are made of the WEC designs in terms of heave motion dynamics and power conversion with reference to theoretical upper bounds. Design implications of a reactive power take-off control scheme and relative motion constraints on the wave energy converters are investigated using an experimentally validated, frequency domain, numerical dynamics model. In the second phase, the WECs are constrained to heave motion and subjected to panchromatic waves. A time domain numerical model, validated by the experimental results, is used to compare the WECs in terms of power matrices, capture width matrices, and mean annual energy production. Results indicate that the second WEC design can convert 30% more energy, on average, than the first design given the conditions at a representative location near the West coast of Vancouver Island, British Columbia, Canada. In the last phase, the WECs are held with three legged, horizontal, moorings and subjected to monochromatic waves. Numerical simulations using panelized body geometries for calculations of Froude-Krylov, Morison drag, and hydrostatic loads are developed in ProteusDS. The simulation results---mechanical power, mooring forces, and dynamic motions---are compared to model test results. The moored WEC designs exhibit power conversion consistent with heave motion constrained results in some wave conditions. However, large pitch and roll motions severely degrade the power conversion of each WEC at wave frequencies equal to twice the pitch natural frequency. Using simulations, vertical stabilizing strakes, attached to the reacting bodies of the WECs are shown to increase the average power conversion up to 190% compared to the average power conversion of the WECs without strakes.

In this paper, the exemplary results of the IEA Wind Task 30 "Offshore Code Comparison Collaboration Continuation" (OC4) Project – Phase I, focused on the coupled simulation of an offshore wind turbine (OWT) with a jacket support structure, are presented. The focus of this task has been the verification of OWT modeling codes through code-to-code comparisons. The discrepancies between the results are shown and the sources of the differences are discussed. The importance of the local dy-namics of the structure is depicted in the simulation results. Furthermore, attention is given to aspects such as the buoyancy calculation and meth-ods of accounting for additional masses (such as hydrodynamic added mass). Finally, recommendations concerning the modeling of the jacket are given. KEYWORDS Offshore wind turbine; coupled simulation; aero-hydro-servo-elastic codes; jacket support structure; code verification; code-to-code compari-son; OC4 INTRODUCTION

This paper presents an analysis of a novel wave energy converter concept that combines an oscillating surge wave energy converter (OSWEC) with control surfaces. The control surfaces allow for a variable device geometry that enables the hydrodynamic properties to be adapted with respect to structural loading, absorption range and power-take-off capability. The device geometry is adjusted on a sea state-to-sea state time scale and combined with wave-to-wave manipulation of the power take-off (PTO) to provide greater control over the capture efficiency, capacity factor, and design loads. This work begins with a sensitivity study of the hydrodynamic coefficients with respect to device width, support structure thickness, and geometry. A linear frequency domain analysis is used to evaluate device performance in terms of absorbed power, foundation loads, and PTO torque. Previous OSWEC studies included nonlinear hydrodynamics, in response a nonlinear model that includes a quadratic viscous damping torque that was linearized via the Lorentz linearization. Inclusion of the quadratic viscous torque led to construction of an optimization problem that incorporated motion and PTO constraints. Results from this study found that, when transitioning from moderate-to-large sea states the novel OSWEC was capable of reducing structural loads while providing a near constant power output.

This book introduces the basic concepts of hydrodynamics and the study of water waves. Part 1 deals with the basic equations governing flow motion and indicates possible approximations; Part 2 covers general methods of integration and the mathematical treatment of these basic equations; Part 3 is concerned specifically with water wave theories. (C.M.W.)

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