• Energy Research

A time domain model is applied to a three-dimensional point absorber wave energy converter. The dynamical properties of a semi-submerged hemisphere oscillating around a pivot point where the vertical height of this point is above the mean water level are investigated. The numerical model includes the calculation of the non-linear hydrostatic restoring moment by a cubic polynomial function fit to laboratory test results. Moreover, moments due to viscous drag are evaluated on the oscillating hemisphere considering the horizontal and vertical drag force components. The influence on the motions of this non-linear effect is investigated by a simplified formulation proportional to the quadratic velocity. Results from experiments are shown in order to validate the numerical calculations. All the experimental results are in good agreement with the linear potential theory as long as the waves are sufficiently mild i.e. H/λ≤0.02. For steep waves, H/λ≥0.04 however, the relative velocities between the body and the waves increase thus requiring inclusion of the non-linear hydrostatic restoring moment to effectively predict the dynamics of the wave energy converter. For operation of the device with a passively damping power take-off the moment due to viscous drag is found to be negligible

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 and are public as a benchmark dataset.

CFD-based numerical wave tank (CNWT) models, are a useful tool for the analysis of wave energy converters (WECs). During the development of a CNWT, model validation is vital, to prove the accuracy of the numerical solution. This paper presents an extensive validation study of a CNWT model for the 1:5 scale Wavestar point-absorber device. The previous studies reported by Ransley et al. [1] and Windt et al. [2] are extended in this paper, by including cases in which the power-take off (PTO) system is included in the model. In this study, the PTO is represented as a linear spring-damper system, providing a good approximation to the full PTO dynamics. The spring stiffness and damping coefficients in the numerical PTO model are determined through a linear least squares fit of the experimental PTO position, velocity and force data. The numerical results for free surface elevation, PTO data (position, velocity, force), generated power and pressure on the WEC hull are shown to compare well with the experimental measurements.

The levelized cost of energy (LCOE) from wave energy converters (WECs) needs to be decreased in order to be able to become competitive with other renewable electricity sources. Probabilistic reliability methods can be used to optimize the structure of WECs. Optimization is often performed for critical structural components, like welded details, bolts or bearings. This paper considers reliability studies with a focus on plain bearings available from stock for the Wavestar device, which exists at the prototype level. The Wavestar device is a point absorber WEC. The plan is to mount a new power take-off (PTO) system consisting of a discrete displacement cylinder (DDC), which will allow different hydraulic cycles to operate at constant pressure levels. This setup increases the conversion efficiency, as well as decouples the electricity production from the pressure variations within the hydraulic cycle when waves are passing. The new PTO system leads to different load characteristics at the floater itself compared to the actual setup where the turbine/generator is directly coupled to the fluctuating hydraulic pressure within the PTO system. This paper calculates the structural reliability of the different available plain bearings planned to be mounted at the new PTO system based on a probabilistic approach, and the paper gives suggestions for fulfilling the minimal target reliability levels. The considered failure mode in this paper is the brittle fatigue failure of plain bearings. The performed sensitivity analysis shows that parameters defining the initial crack size have a big impact on the resulting reliability of the plain bearing.

The paper deals with the optimal feedback control and sub-optimal causal feedback control of an array of wave energy point absorbers using the reactive forces from the power take-off systems on the point absorbers as control forces. The dynamic coupling of the absorbers via the radiation wave forces and control forces are taken into account. Assuming linear wave mechanics the optimal control law is shown to be a non-causal feedback controller with feedback from measurement of the displacement, velocity, and acceleration of all floaters. i.e no wave load estimation or prediction is assumed. The control law will be optimal for any 2D or 3D irregular sea-state, as well as during the transient phase. To circumvent the non-causality problem related to the optimal controller law, a causal closed loop controller is suggested based on a slightly modified optimal control law. The controller contains an undetermined symmetric positive definite gain matrix. Since, the response of the array is narrow-banded at optimal control, this matrix has been chosen as the radiation damping matrix at the peak angular frequency. The causal controller is optimal under monochromatic wave excitation and close to optimal for irregular sea-states.

The top-mounted pitching point absorber is one of the most promising wave energy converters in that it can be easily attached to an existing offshore structure. However, it is difficult to predict accurately its energy conversion performance because of the strongly nonlinear hydrodynamic behaviour. Herein, smoothed particle hydrodynamics (SPH) is used to solve this wave-structure interaction problem. The SPH method is first validated against free surface deformation measurements obtained from a wedge water entry experiment. SPH simulations of regular wave interaction with fixed and freely pitching devices agree well with measured data, providing confidence in the prediction of power conversion performance. Absorbed power and capture width ratio exhibit uni-modal behaviour with wave period. The wave period of peak power within this distribution increases with PTO damping. According to the observed scaling behaviour with device scale, an optimally damped larger scale device is effective at absorbing energy from incident waves of longer wavelength. In finite deep water, the larger device achieves higher efficiency compared with the smaller ones, and its peak efficiency at 2πh/λ=1.1 provides reference for siting.

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.