The following report presents the results of the experimental testing of the Exowave wave energy converter (WEC) performed in September 2023 at the Ocean and Coastal Engineering Laboratory at Aalborg University, Denmark. The model tests are performed based on the current design of the WEC35 Exowave floater as part of the project 250 MW bølgekraft I den danske Nordsø før 2030 – fase 1 supported by the Danish Energy Agency under the Energy Technology Development and Demonstration Program (EUDP) contract number 64022-1062.
Wave excitation tests on a fixed sphere with the center at the still water level were carried out with three different physical wave basin setups. The tests were completed as a continued effort of the working group OES Wave Energy Converters Modeling Verification and Validation to increase confidence in numerical models of wave energy converters by generation of accurate benchmarks datasets for numerical model validation. An idealized test case with wave excitation of a fixed sphere to be used with the benchmarks was formulated. The three investigated physical wave basin setups included: 1) a six degree-of-freedom load cell mounted to the top of the sphere, 2) a bending beam force transducer mounted to the top of the sphere, and 3) a system of six pretensioned wires mounted to the top and bottom of the sphere with force transducers attached to each wire. The aim of the present paper is to identify the best representation of the idealized test case. To this end, the three experimental setups are inter-compared in terms of dynamic properties, sensitivity, and disturbances of the water phase from the presence of measurement equipment. Low inter-experiment variability was disclosed, ie, 5-8% depending on wave-nonlinearity, indicating accurate representations of the idealized test case across all setups. Setup 3 was found to be the more accurate representation and further work with this setup to release a public benchmark dataset was planned.
High-fidelity simulations using computational fluid dynamics (CFD) for wave-body interaction are becoming increasingly common and important for wave energy converter (WEC) design. The open source finite volume toolbox OpenFOAM® is one of the most frequently used platforms for wave energy. There are currently two ways to account for moving bodies in OpenFOAM: (i) mesh morph-ing, where the mesh deforms around the body; and (ii) an overlooked mesh method where a separate body mesh moves on top of a background mesh. Mesh morphing is computationally efficient but may introduce highly deformed cells for combinations of large translational and rotational motions. The overlooked method allows for arbitrarily large body motions and retains the quality of the mesh. However, it comes with a substantial increase in computational cost and possible loss of energy conservation due to the interpolation. In this paper we present a straightforward extension of the spherical linear interpolation (SLERP) based mesh morphing algorithm that increases the stability range of the method. The mesh deformation is allowed to be interpolated independently for different modes of motion, which facilitates tailored mesh motion simulations. The paper details the implementation of the method and evaluates its performance with computational examples of a cylinder with a moonpool. The examples show that the modified mesh morphing approach handles large motions well and provides a cost effective alternative to overlooked mesh for survival conditions.
Since time-domain simulations of wave energy converters are computationally expensive, how can we analyse their dynamics and test wide ranges of design variables, without simplifying the physics involved? One possible solution is the use of General Polynomial Chaos (gPC). GPC provides computationally efficient surrogate models for partial differential equation based models, which are particularly useful for sensitivity analysis and uncertainty quantification. We demonstrate the application of gPC to study the dynamics of a wave energy converter in an operational sea-state, when there is uncertainty in the values of the stiffness and damping coefficient of the power take-off.
The wave loads and the resulting motions of floating wave energy converters are traditionally computed using linear radiation–diffraction methods. Yet for certain cases such as survival conditions, phase control and wave energy converters operating in the resonance region, more complete mathematical models such as computational fluid dynamics are preferred and over the last 5 years, computational fluid dynamics has become more frequently used in the wave energy field. However, rigorous estimation of numerical errors, convergence rates and uncertainties associated with computational fluid dynamics simulations have largely been overlooked in the wave energy sector. In this article, we apply formal verification and validation techniques to computational fluid dynamics simulations of a passively controlled point absorber.
The phase control causes the motion response to be highly nonlinear even for almost linear incident waves. First, we show that the computational fluid dynamics simulations have acceptable agreement to experimental data. We then present a verification and validation study focusing on the solution verification covering spatial and temporal discretization, iterative and domain modelling errors. It is shown that the dominating source of errors is, as expected, the spatial discretization, but temporal and iterative errors cannot be neglected. Using hexahedral cells with low aspect ratio and 30 cells per wave height, we obtain results with less than 5% uncertainty in motion response (except for surge) and restraining forces for the buoy without phase control. The amplified nonlinear response due to phase control caused a large increase in numerical uncertainty, illustrating the difficulty to obtain reliable solutions for highly nonlinear responses, and that much denser meshes are required for such cases.
Mooring systems are required to keep floating wave energy converters (WECs) on station. The mooring concept might impact the performance of the WEC, its cost and its integrity. With the aim of clarifying the pros and cons of different mooring designs, we present the results from physical model experiments of three different mooring concepts in regular and irregular waves, including operational and survival conditions. The parameters investigated are the tension in the cables, the motions of the device in the different degrees of freedom and the seabed footprint in each case. We can see that the mooring system affects the performance of the wave energy converter, but the magnitude of the impact depends on the parameter analysed, on the mode of motion studied and on the conditions of the sea. Moreover, different configurations have similar performances in some situations and the choice of one over another might come down to factors such as the type of soil of the seabed, the spacing desired between devices, or environmental impacts. The results of our experiments provide information for a better selection of the mooring system for a wave energy converter when several constraints are taken into account (power production, maximum displacements, extreme tensions, etc).