This paper reports on a benchmark study based on small-scale (1:50) measurements of a single, oscillating water column chamber mounted sideways in a long flume. The geometry of the OWCchamber is extracted from a barge-like, attenuator- type floating concept “KNSwing” with 40 chambers targeted for deployment in the Danish part of the North Sea. In addition to traditional two-way energy extraction we also consider one-way energy extraction with passive venting and compare chamber response, pressures and total absorbed energy between the two methods. A blind study was established for the numerical modeling, with participants applying several implementations of weakly nonlinear potential flow theory and commercial Navier–Stokes solvers (CFD). Both compressible and incompressible models were used for the air phase. Potential flow calculations predict more energy absorption near the chamber resonance for one-way absorption than for two-way absorption, but the opposite is found from the experimental measurements. This outcome is mainly attributed to energy losses in the experimental passive valve system, but this conclusion must be confirmed by better experimental measurements. Modeling the one-way valve in CFD proved to be very challenging and only one team was able to provide results which were generally closer to the experiments. The study illustrates the challenges associated with both numerical and experimental analysis of OWC chambers. Air compressibility effects were not found to be important at this scale, even with the large volume of additional air used for the one-way case.
In a number of experiments and field tests of point absorbers, snap loads have been identified to cause damage on the mooring cables. Snap loads are basically propagating shock waves, which require special care in the numerical modeling of the mooring cable dynamics. In this paper we present a mooring cable model based on a conservative formulation, discretized using the Runge-Kutta discontinuous Galerkin method. The numerical model is thus well suited for correctly capturing snap loads. The numerical model is verified and validated using analytic and experimental data and the computed results are satisfactory.
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.
This paper analyzes the nonlinear forces on a moored point-absorbing wave energy converter (WEC) in resonance at prototype scale (1:1) and at model scale (1:16). Three simulation types were used: Reynolds Averaged Navier-Stokes (RANS), Euler and the linear radiation-diffraction method (linear). Results show that when the wave steepness is doubled, the response reduction is: (i) 3% due to the nonlinear mooring response and the Froude-Krylov force; (ii) 1-4% due to viscous forces; and (iii) 18-19% due to induced drag and non-linear added mass and radiation forces. The effect of the induced drag is shown to be largely scale-independent. It is caused by local pressure variations due to vortex generation below the body, which reduces the total pressure force on the hole. Euler simulations are shown to be scale-independent and the scale effects of the WEC are limited by the purely viscous contribution (1-4%) for the two waves studied. We recommend that experimental model scale test campaigns of WECs should be accompanied by RANS simulations, and the analysis complemented by scale-independent Euler simulations to quantify the scale-dependent part of the nonlinear effects.
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.