Abstract A three-by-three grid of submersible mussel rafts was analyzed using an experimentally validated dynamic numerical modeling approach. When submerged, the rafts’ pontoons are flooded, and they are held vertically by lines attached to surface floats and horizontally by a mooring grid. The rafts’ decreased waterplane area and increased inertia reduce the heave and pitch natural frequencies so that they are below the frequencies associated with the greatest wave energy. This has been found to significantly reduce the motion of the rafts compared to the surfaced configuration. The nine submersible rafts were anchored with 16 anchors and mooring lines. These mooring lines were connected to a grid of adjacent rectangular bays, with each corner (node) supported by a grid float. Each bay contains a raft connected to the submerged nodes of the grid by four bridle lines. The dynamics of the full system were modeled using a combined multibody and Finite Element Analysis (FEA) approach with dynamic loads computed using a modified Morison formulation. This model was implemented in the commercial code OrcaFlex. A similar model for a single submersible raft was previously validated with full-scale field experiments. The full dynamic system was simulated in the maximum expected waves and currents. Mean and maximum tensions in each grid line were quantified. Accelerations and velocities at the mussel rope attachment points were also examined, since these relate to mussel drop-off.

Abstract Tsunami waves pose a threat to the coastal zone and numerous studies have been carried out in the past to understand them. The present study — carried out in the 2D wave flume at the Ocean Engineering Laboratory of IIT Bombay — focusses on the interaction and run-up of solitary waves on coastal protection structures in the form of thin, rigid vertical porous barriers with special attention given to the degree of energy dissipation. In order to understand the physics of the energy dissipation problem, the propagation of the solitary wave and its interaction with the porous barrier has been studied from the viewpoint of energy balance. Based on this, a proper relationship for the wave energy dissipated by the barrier has been developed. Using this relationship, the experimental data has been analyzed and we have determined that the plate porosity that gives the optimal energy dissipation characteristics lies within the 10–20% range. In addition, using the experimental data, we have derived a formula for calculating the maximum wave run-up on the porous barrier models which should be useful in the planning, design, construction and maintenance of coastal protection structures.

Abstract Direct numerical simulation (DNS), based on solution of the Navier Stokes equations, is used to study the characteristics of the transformation of monochromatic waves over a simplified fringing reef, including wave shoaling, and wave breaking that occurs under certain circumstances. The reef geometry involves a sloped plane beach extended with a simple submerged horizontal reef flat. The characteristics are studied for several case studies involving a selection of submergence depths on the reef flat and for a range of incident wave conditions, corresponding to nonbreaking, a spilling breaker and a plunging breaker, are considered. The results are compared with those of laboratory experiments (Kouvaras and Dhanak, 2018). Consistent with other studies, generation of harmonics of the fundamental wave frequency is found to accompany the wave transformation over the reef and the process of transfer of energy through wave breaking. The energy flux decreases dramatically in the onshore direction when the waves break. The more severe the wave breaking process, the greater the decrease in energy flux, particularly in the wave shoaling process. Most of the wave energy is carried by the first harmonic throughout its passage over the fringing reef. In nonbreaking waves, the energy gradually transfers from the first harmonic to the second harmonic due to bottom effects in terms of flat wave troughs and secondary waves. The further the distance away from the fore edge of the reef, the larger the percentage of the transmission, resulting in a single dominant harmonic frequency at the end of the wave surfing zone. For breaking waves, the energy carried by the first harmonic gradually decreases in the onshore direction. Energy transmission between harmonics is not as efficient as nonbreaking waves, while wave dissipation is significant in the wave breaking process.

Abstract Oscillating Water Column (OWC) wave energy device is one of the most studied and applied wave energy converters (WECs). The survivability of WECs is a major concern in the OWC design. In this study, the wave dynamics of a dual-chamber OWC device is numerically and experimentally investigated. The experimental tests were carried out in the wave-current flume at the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology. A fully nonlinear numerical wave flume based on potential-flow theory and time-domain higher-order boundary element method (HOBEM) is developed and applied to simulate the interaction between air, wave and the dual-chamber OWC device. The numerical model is validated by comparing the simulated wave induced pressure on the barrier walls with the measurements. Then the wave forces and the moment on the device is numerically investigated. The model and experimental results indicate that the horizontal wave force on the front barrier wall is much larger than that on the internal barrier wall. The joint between the back wall and the ground withstands the largest bending moment, therefore, is most vulnerable to structure damage and fatigue.

Abstract Linear diffraction modelling of irregular wave structure interaction is standard practice in both the frequency and time domains for fixed and floating bodies. This has been extended for the modular wave energy converter M4 with multiple floats and power take offs. In the time domain second-order forces assuming a stationary body have been added for floating wind energy platforms. This misses second-order, including mean, effects due to radiation damping, drag forces and the mechanical damping of wave energy conversion. If these are linearized they may be included in a frequency domain analysis. However mechanical damping and mooring forces on slack-moored platforms are generally highly nonlinear and time domain analysis is required. In this paper response is first computed with linear analysis and mechanical damping which has been shown to give reasonable prediction of experimental measurement for the response and power output of M4. The response gives the absorbed energy flux due to mechanical and radiation damping which is converted into a mean force through an average wave celerity. The model is extended to include a mooring and these mean forces; the computation is then repeated. The mean forces have negligible effect on response and associated power take off but determine the mooring forces. For a slack mooring zero stiffness is assumed. Comparing with wave basin experiments for the 6-float M4 configuration in operational conditions, mean mooring forces are generally underestimated, markedly for larger periods.

Abstract The majority of wave energy devices operate close to resonant conditions to enhance energy conversion resulting in large displacements. As a result, nonlinearities significantly contribute to the dynamics of the system. A typical approach to predict the behavior of the system and power output relies on the derivation of a mathematical model in the time domain to simulate the dynamics through some numerical codes. However, a relatively high computational demand is required for those simulations. In this regard, the present work deals with the nonlinearities in the frequency domain via Statistical Linearization. Two different power-take-off systems are investigated, a linear and a hydraulic one, and their mean power calculations are derived based on the Statistical Linearization. The reliability of the method is verified against the Power Spectrum Density (PSD) of nonlinear time domain simulations. Only the heave motion is analyzed, and several nonlinearities commonly reported for Point Absorbers (PA) were considered, such as cubic stiffness, geometric nonlinearities, drag forces, and Coulomb forces. The approach employed in this work offers a reliable estimation of body dynamics for all nonlinearities considered. In addition, the present method produced a fast estimation, which can be valuable for the assessment of several designs and sea load conditions.

Abstract Water wave propagation over shallowly submerged structures is of much interest in the context of submerged wave energy devices, breakwaters or barrier reefs. This work examines waves passing over a two-dimensional shallowly submerged fixed step extending to the seabed. The problem has been modelled in CFD using the open source toolbox OpenFoam utilising the Reynolds Averaged Navier-Stokes Equations. These simulations are compared to experimental work from a previous study as means of validation and extended to larger amplitude waves for a single incident wave frequency. The flow over the step is characterised and examined in the context of developing an efficient hybrid numerical model for the problem.

Abstract Using marine renewable energy can contribute providing the energy instead of using fossil fuel. There are some types of marine renewable energy. Wave energy is one of these and no one doubts its vast potential once they glance the sea. The object of this paper is an array of Point Absorber Wave Energy Converters (PA-WECs). In the array, complex hydrodynamic interactions among the array will occur. The interaction influences the wave power density among the array both increase and decrease. When we consider the maximization of generated electric power of the array, the suitable choice of the control force of the generator taken into a positive effect of the hydrodynamic interactions is the key. In the past research, as for a detection of the suitable control force of a single PA-WEC it has been shown the analytical solution within linear system. In this paper, we show the numerical solution of the control force parameter for maximizing the generated electric power of the array taking the hydrodynamic interaction among the array both in diffraction and radiation problem into account. Then we carried out the numerical examination and discussed the good arrangement of an array in waves based on the proposed method and an effect of the choice of the best and better control force.

Abstract In this paper, we report the proposal and development of the numerical model. The model applies to two and three dimensional problems. We introduce the model to the MPS method which is a kind of particle method, and discuss applicability of the model on numerical test of aerial physical pendulum in free torque load; the present model was compared with the theoretical solution by the 4th order Runge-Kutta method. As a result, we confirmed the good reproducibility of the model. And we can say that the model is suitable for analyzing the problem of physical pendulum. Secondary, we examine the practicability of this model in the regular wave from the calculation results. The tests are examined by a two-dimensional problem in order to reduce calculation cost. In addition, we conducted fluid-structure interaction analysis using the present model and confirmed the applicability of its model to fluid field analysis.

Abstract Wave energy converters (WECs) are often subject to large displacements during operating conditions. Hence, nonlinearities present in numerical methods to estimate the performance of WECs must be considered for realistic predictions. These large displacements occur when the device operates on resonant conditions, which results in maximum energy conversion. The system dynamics are usually simulated via time domain models in order to being able to capture nonlinearities. However, a high computational cost is associated with those simulations. Alternatively, the present work treats the nonlinearities in the frequency domain via Statistical Linearization (SL). The SL results are compared to the Power Spectrum Density (PSD) of time domain simulations to verify the reliability of the proposed method. In this regard, the work initiates with the derivation of the governing equations of the air-chamber and the Oscillating Water Column (OWC). Then, the SL technique is presented and applied. The SL results show a satisfactory agreement for the system dynamics, mean surface elevation, mean pressure, and mean power compared to time domain simulations. Also, the SL technique produces a rapid estimation of the response, which is an effective approach for the evaluation of numerous environmental conditions and design, and further optimization procedures.

Abstract A series of cabin-suspended ships, named Wave Harmonizer, has been developed since 2008. The model ship consists of cabin part, hull part and conjunction part which is mounted in-between the cabin and the hull. The possibility and feasibility of introducing suspensions into small vessels are investigated. Effectiveness evaluations are made in two aspects: motion reduction of the cabin and wave energy harvesting through the oscillating cabin. According to the research results obtained in 2015 and 2016, it was found that the deck of the cabin may bear obvious inclination while weights were loading or unloading from it. Moreover, in relative long waves, the effectiveness of the motion reduction of the skyhook controller was insufficient. To solve those problems, an attitude control strategy is proposed. It is adopted as an outer-loop of the existing controller. Inclination sensors are employed to collect the rotational angle of the cabin in terms of pitch and roll. After finishing the design and construction of the double-loop control system, open loop tests are carried out in dry and wet conditions. The chain mechanism of the ship is investigated. Then a bench test is operated to validate the control concept and performance of the double-loop control system. Finally, tank tests are implemented to examine the inclination reduction of the cabin at regular head waves. In this paper, the development of the double-loop control system is described, experimental results are demonstrated with respect to the heave and pitch motion reduction of the cabin at the condition of with/without the outer control loop. It shows that the inclination reduction at the loading/unloading condition and the walking-on-deck condition are significant. However, in waves the effectiveness is not clearly verified. It suggests that the influence of the apparent gravity on the inclination measurement in waves should be investigated and solutions to accurately detect the inclination of the cabin should be sought.

Abstract This article presents a data-efficient learning approach for the complex-conjugate control of a wave energy point absorber. Particularly, the Bayesian Optimization algorithm is adopted for maximizing the extracted energy from sea waves subject to physical constraints. The algorithm learns the optimal coefficients of the causal controller. The simulation model of a Wavestar Wave Energy Converter (WEC) is selected to validate the control strategy for both the regular and irregular waves. The results indicate the efficiency and feasibility of the proposed control system. Less than 20 function evaluations are required to converge towards the optimal performance of each sea state. Additionally, this model-free controller can adapt to variations in the real sea state and be insensitive and robust to the WEC modeling bias.

Abstract The study presents analyses of key parameters that affect the performance of the point absorbing wave energy converter (WEC). Performance is assessed by running hydrodynamic and structural response simulations and calculating the power absorption of the WEC and fatigue damage in the mooring lines from the output data. The baseline model of the WEC input to the simulation is modelled after the WaveEL 3.0 device, designed by Waves4Power and installed in Runde, Norway. Simulations are run for single buoy and small array configurations, varying environmental conditions, mooring system, and WEC buoy shaft length. Environmental conditions are chosen to reflect locations studied as potential future installation sites. Select configurations are further analyzed through an analysis of LCOE and LCA. The results show that optimal mooring line geometry depends on water depth, and that optimal shaft length depends on the average sea conditions at the location. The array simulations show that small WEC separating distances will limit the mooring line length, which will result in lower power absorption and lower fatigue lives in the mooring lines. The LCOE shows that the four-buoy array configuration is the most profitable, and both the LCOE and LCA show that the main process contribution to climate change and the total product cost is the manufacturing of the WEC buoy itself. The research in this study demonstrates the importance of using simulations to make effective WEC design choices for a given environment.

Abstract Wave energy is sustainable and clean energy, so it has great potential to be an eco-friendly and lasting renewable energy resource in the future. Recently, a number of researchers have investigated different types of wave energy converters (WECs) using numerical models such as potential theory and Computational Fluid Dynamics (CFD) to enhance the efficiency of such devices. In this paper, a validation of a point absorber type WECs is investigated to capture the movement of the WEC system and to measure the moment on the WEC system. The WEC consists of a lever and a buoy. The geometry is the same as the existing experimental geometry of the reference in order to validate the present numerical simulation. The buoy is connected to the lever and has a hinge on the connection point. Besides, another hinge is installed in the middle of the lever, and the WEC system rotates in the pitch direction. The commercial CFD package Star-CCM+, which solves Reynolds-Averaged Navier-Stokes equations, is employed in this study. In the initial stages of this research, a validation study against published experimental results was conducted. The rotational displacement and the moment on the buoy were compared with the existing experimental data of the reference. The result shows good agreement. In the near future, a study on a new pivoted point absorber WEC device regarding the buoy shape of the WEC device and an operation principle will be performed based on this numerical study.

Abstract This paper explores the response of a wave energy device during extreme and operational conditions and the effect of this response on the geotechnical stability of the associated taut moorings. The non-hydrostatic wave-flow model SWASH is used to simulate the response of a taut-moored wave energy converter. The predicted forces acting on the mooring system are used to compute the build-up of excess pore pressures in the soil around the mooring anchor and the resulting changes in strength and capacity. An initial loss of strength is followed by a subsequent increase in capacity, associated with long-term cyclic loading and hardening due to consolidation. The analyses show how cyclic loading may actually benefit and reduce anchoring requirements for wave energy devices. It demonstrates the viability of a close interdisciplinary approach towards an optimized and cost-effective design of mooring systems, which form a significant proportion of expected capital expenditures.

Abstract The design of a 1/15 th geometrically scaled wave tank model of the Azura™ commercial-scale wave energy device is presented. The objectives of the wave tank tests, conducted at the University of Maine Harlod Alfond Wind/Wave Ocean Engineering Lab (W 2 ), included verification of the Azura’s energy capture in irregular waves, evaluation of performance in survival wave conditions, and testing of two advanced control algorithms. Due to the difficulty in properly Froude Scaling a hydraulic system, the model used a direct-drive rotary motor/generator power takeoff (PTO), with the dynamics of the hydraulic PTO included via a hardware-in-the-loop simulation. This PTO implementation led to additional design requirements being imposed on the model drivetrain. In addition to the model PTO design, the instrumentation design, structural design, and test plans are presented. The resulting model and PTO achieved a high level of controllability, and accurately emulated the dynamics of the hydraulic PTO of the full-scale Azura prototype.

Abstract This article describes the model development and preliminary progress of an on-going research study on the effects of nonlinearities in ocean wave input and power-take-off (PTO) control on wave energy conversion system dynamics and efficiency. The model system employed and progress on recent developments are: (1) nonlinear wave modeling in the ocean, generation and propagation in a wave basin, and (2) nonlinear PTO control algorithm. An overview of the holistic analytical, numerical and experimental research approach/work plan is presented. To provide a simple means for analysis, comparison and performance evaluation, the WEC-Sim numerical platform is used for model implementation and system dynamic simulation. Analytical and numerical predictions of the nonlinear wave fields in a wave basin using the nonlinear Fourier analysis (NLFA) technique and corresponding nonlinear wavemaker theory and a plan for future validation using a comprehensive series of experimental test data as well as ocean wave measurements are described. Efficiency of the nonlinear PTO control and a future evaluation work plan by comparing numerical simulations with results of WEC model test data under corresponding wave conditions of the experimental studies without the presence of the WEC system are also presented.

General Electric, the National Renewable Energy Laboratory (NREL), the University of Massachusetts Amherst (UMass), and Glosten have recently completed a US Department of Energy (DOE)-funded research program to study technologies for mitigating loads on floating offshore wind turbines through the use of advanced turbine controls and tuned mass dampers (TMDs). The analysis was based upon the Glosten PelaStar tension leg platform (TLP) with GE Haliade 150 turbine, a system developed in a previous front end engineering design (FEED) study funded by the Energy Technology Institute (ETI) in the UK. The platform was designed for the WaveHub wave energy research site, with a mean water depth of 59-m. Loads were analyzed by running time-domain simulations in four 50-year return period (50-YRP) ultimate load state (ULS) conditions and 77 fatigue load state (FLS) environmental conditions. In 50-YRP conditions advanced controls are not active. The influence of TMDs on ULS loads have been reported previously (Park et al. [2]). In FLS conditions advanced controls and TMDs afford dramatic reductions in fatigue damage, offering the potential of significant savings in tower structural requirements. Simulations in turbine idling conditions were run in OrcaFlex , and simulations in operating conditions were run in FAST . Simulations were run with a baseline turbine controller, representative of the current state of the art, and an advanced controller developed by NREL to use collective and individual blade pitch control to maintain rotor speed and reduce tower loads. UMass developed a number of TMD types, with varying system configurations, including passive nonlinear dampers and semi-actively controlled dampers with an inverse velocity groundhook control algorithm. Loads and accelerations in FLS conditions were evaluated on the basis of damage equivalent loads (DELs), and fatigue damage was computed by Miner’s summations of stress cycles at the tower base. To study sensitivity to water depth, loads were analyzed at both the 59-m WaveHub depth and a more commercially realistic depth of 100 m. TMDs reduce fatigue damage at the tower-column interface flange by up to 52% in 59-m water depth and up to 28% in 100 m water depth. Advanced controls reduce fatigue damage at the tower-column flange by up to 22% in 59-m water depth and up to 40% in 100 m water depth. The most effective load-mitigation strategy is combining advanced controls with TMDs. This strategy affords a 71% reduction in fatigue damage in both 59-m and 100-m water depths.

Industrial realization of both floating offshore wind and wave energy technologies requires reductions in the current high levelized cost of energy. Reducing mooring fatigue loads could decrease levelized cost of energy, as mooring is expected to be a major cost of these systems. Previous work on improving mooring reliability and costs has focused on material and design. In this exploratory study, we quantify how placing WECs in front of a FOWT could reduce fatigue damage incurred by FOWT mooring cables in long-crested wave conditions. We use SWAN to quantify the WEC-induced sea state modifications and obtain wave spectra at the FOWT location. The spectra are then input into WEC-Sim and MooDy to model the mooring cable behavior. Fatigue analysis with Rainflow Counting is used to quantify the fatigue loading on the mooring cables. Results from this study show a 8% reduction in fatigue damage to mooring cables over the lifetime of the structure. These results indicate that co-location could have a beneficial effect on FOWT mooring cable fatigue. In future work, these results will be leveraged to perform optimal O&M planning and reliability-based design optimization of floating offshore wind turbines.

Circular cylinders are one of the most common geometries used in many structures, such as fixed platforms, risers, umbilical cables, offshore fish farms, floating offshore wind turbines, wave energy devices, plastic cleanup booms, and oil containment booms. Although partially submerged horizontal circular cylinders can be found in many offshore and marine structures, few works have investigated the influence of their positions beneath the free surface and the resulting wave force. The present work aimed to numerically study the wave force acting on a fixed horizontal circular cylinder near the free surface for different depths. The wave flow was modeled using a viscous model available in the StarCCM+ software using a two-dimensional numerical wave tank. The governing equations were solved using the finite volume in an unstructured mesh. A circular cylinder with a diameter (D) of 0.10 m and a regular wave with a steepness (H/L) of 0.025 were used in the present study. In this case, the cylinder diameter is much smaller than the wave length. Three different submerged depths were investigated, and the numerical results were compared with experimental data extracted from Dixon [1]. Good agreement was found for the first two cylinder positions (z c /D = 0 and −0.3). For the last case (z c /D = −0.5), a phase shift was observed. However, by correcting it, the agreement between the numerical and experimental data was also good.