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.
Mooring systems for floating wave energy converters often rely on floaters to allow for minimum restraints of the body motion in heavy. However, the inclusion of floaters also introduce possible slack-taut scenarios induced by the dynamic response of the floater in relation to the fair-lead point of the mooring. This can increase the occurrence of snap loads. The present study outlines the work to include floaters and sinks into a high-order discontinuous Galerkin model for mooring cable dynamics. Numerical simulations of a mooring leg adapted from the Waves4Power full-scale device are performed, and the results from varying the floater geometry are analyzed.
For this case the floater influence on the occurrence of snap loads was clearly evident. There is a strong correlation between floater pitch response and cable slack in the upper mooring cable. For a floater with constant buoyancy, increasing the floater height and thereby increasing the pitch inertia of the floater is shown to decrease the range of frequencies where cable slack occurs. It is illustrated that for some cases, changing floater geometry can avoid slack altogether. A careful design of the floater geometry can thus make a large difference for the dynamic load factor of the mooring system.
The power output from many wave energy converters (WECs) is limited by a finite stroke length in the power take-off (PTO) mechanism. As the PTO approaches its maximum stroke length, an end-stop system needs to be engaged to avoid damage to the machinery. Still the on-set of the end-stop is a nonlinear trigger force, a stiff point in the system. In this respect it is similar to how snap loads in the mooring cables affect the system after a period of cable slack. This paper presents a detailed study into the dynamics of end-stop events and snap loads for a WEC. The WEC is a bottom-mounted linear generator connected to a surface buoy via a steel wire. By comparing a linear spring model with three dynamic mooring line models we conclude that large differences are observed in the low-tension and slack regions of the cable during moderate wave loads, while minor differences are seen in the estimated peak tension. By further varying end-stop parameters we observe that the peak tension in the line changes mildly with the axial stiffness for moderate wave heights. The peak tension is surprisingly unaffected by the introduction of a critical damping level to the end-stop system, despite the significant increase in end-stop force which causes the translator to come to a sudden stop. We discuss how the connection between maximum line force and end-stop parameters is highly dependent on the buoy position in the wave at the instant of end-stop onset.
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.
The paper presents incompressible Navier-Stokes simulations of the dynamics of a floating wave energy converter (WEC) coupled to a high-order finite element solver for cable dynamics. The coupled model has very few limiting assumptions and is capable of capturing the effects of breaking waves, green water loads on the WEC as well as non-linear mooring forces and snap loads, all of which are crucial for correct estimates of the extreme loads acting on the system in violent seas. The cable dynamics model has been developed as a stand-alone library that can be coupled to any body motion solver. In this study the open-source CFD package OpenFOAM has been employed. Preliminary test cases using incident regular Stoke's 5th order waves are presented, both for wave heights corresponding to operational conditions of the WEC as for a more severe condition in survival mode. It is illustrated that the coupled model is able to capture the complicated force propagation in the mooring cables.
Floating wave energy converters (WECs) operating in the resonance region are strongly affected by non-linearities arising from the interaction between the waves, the WEC motion and the mooring restraints. To compute the restrained WEC motion thus requires a method which readily accounts for these effects. This paper presents a method for coupled mooring analysis using a two-phase Navier-Stokes (VOF-RANS) model and a high-order finite element model of mooring cables. The method is validated against experimental measurements of a cylindrical buoy in regular waves, slack-moored with three catenary mooring cables. There is overall a good agreement between experimental and computational results with respect to buoy motions and mooring forces. Most importantly, the coupled numerical model accurately recreates the strong wave height dependence of the response amplitude operators seen in the experiments.
The paper discusses the use of CFD simulations to analyse the parametric excitation of moored, full scale wave energy converters in six degrees of freedom. We present results of VOF-RANS and VOF-Euler simulations in OpenFOAM!R for two body shapes: (i) a truncated cylinder; and (ii) a cylinder with a smooth hemispherical bottom. Flow characteristics show large differences in smoothness of flow between the hull shapes, where the smoother shape results in a larger heave response. However the increased amplitude makes it unstable and parametric pitch excitation occurs with amplitudes up to 30". The responses in surge, heave and pitch (including the transition to parametric motion) are found to be insensitive to the viscous effects. This is notable as the converters are working in resonance. The effect of viscous damping was visible in the roll motion, where the RANS simulations showed a smaller roll. However, the roll motion was found to be triggered not by wave-body interaction with the incident wave, but by reflections from the side walls. This highlights the importance of controlling the reflections in numerical wave tanks for simulations with WEC motion in six degrees of freedom.
The present paper describes the work carried out in the project ’Mooring Solutions for Large Wave Energy Converters’, which is a Danish research project carried out in a period of three years from September 2014, with the aim of reducing cost of the moorings for four wave energy converters and improving the applied design procedure. The paper presents the initial layouts and costs and illustrates which solutions could potentially reduce cost. Different methods for analysis of the systems were applied, ranging from simple quasi-static analysis to full dynamic analysis and experimental work. The numerical methods were compared to the experimental data, and results showed significant underestimation of tensions in the quasi-static model while reasonable overestimation was found in the dynamic analysis even without major tuning of the model. The dynamic analysis has then been implemented in a meta-model based optimization process with the aim of optimizing the mooring layout for each WEC according to cost of the systems.
Physical wave basin tests with a focus on uncertainty estimation have been conducted on a sphere subjected to wave loads at Aalborg University as part of the effort of the OES Wave Energy Converters Modeling Verification and Validation (formerly, OES Task 10) working group to increase credibility of numerical modeling of WECs. The tests are referred to as the Kramer Sphere Cases, and the present note is dealing with wave excitation force tests on a fixed model. The present note is including details to facilitate CFD models which replicate the physical setup in detail.
Physical wave basin tests with a focus on uncertainty estimation have been conducted on a fixed sphere subjected to wave loads at Aalborg University as part of the effort of the OES Wave Energy Converters Modeling Verification and Validation (formerly, OES Task 10) working group to increase credibility of numerical modeling of WECs.
The present note defines an idealized test case formulated to accurately represent the physical tests in a simple way. The test case consists of a fixed, rigid sphere half submerged in water subjected to regular waves of three different levels of linearity. The objective of the present note is to allow for numerical tests of the idealized test case.