There are many uncertainties associated with the estimation of extreme loads acting on a wave energy converter (WEC). In this study we perform a sensitivity analysis of extreme loads acting on the Uppsala University (UU) WEC concept. The UU WEC consists of a bottom-mounted linear generator that is connected to a surface buoy with a taut mooring line. The maximum stroke length of the linear generator is enforced by end-stop springs. Initially, a Variation Mode and Effect Analysis (VMEA) was carried out in order to identify the largest input uncertainties. The system was then modeled in the time-domain solver WEC-SIM coupled to the dynamic mooring solver Moody. A sensitivity analysis was made by generating a surrogate model based on polynomial chaos expansions, which rapidly evaluates the maximum loads on the mooring line and the end-stops. The sensitivities are ranked using the Sobol index method. We investigated two sea states using equivalent regular waves (ERW) and irregular wave (IRW) trains. We found that the ERW approach significantly underestimates the maximum loads. Interestingly, the ERW predicted wave height and period as the most important parameters for the maximum mooring tension, whereas the tension in IRW was most sensitive to the drag coefficient of the surface buoy. The end-stop loads were most sensitive to the PTO damping coefficient.
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.
This paper presents the methods developed and key findings of the IWEC project performed by Ocean Harvesting Technologies AB (OHT). It aimed to reduce the levelized cost of energy (LCoE) of OHT’s wave energy converter InfinityWEC, by analysing how different key parameters impact cost and annual output using a model of a 100-MW array installation. Component-level cost functions were developed and mapped to key parameters and constraints of the system. A large number of system configurations were then evaluated with a numerically efficient 3 degree-of-freedom (DoF) nonlinear radiationdiffraction model in WEC-Sim along with OHT’s sea statetuned polynomial reactive control (PRC). The most promising configurations were identified and investigated in more detail. The configuration with the best LCoE were finally identified and analysed further, including estimation of the effect of changing the PRC to model predictive control, which resulted in 17-34% higher annual output and 12-23% lower LCoE. The final LCoE was found to be 93-162 EUR MWh at 100 MW installed capacity. An important finding from the study is that using simplified metrics such as CAPEX/ton was found to be irrelevant. Numerical wave tank testing, high-fidelity computational fluid dynamics (CFD), were used to tune the viscous drag of the 3 DoF WEC-Sim model. Applying verification and validation (V&V) techniques the CFD simulations showed a relatively large numerical uncertainty, but the average power and the motion responses were found to be sufficiently accurate.
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.
Floating Power Plant (FPP) develops a hybrid floating wind and wave energy device. Pitching Wave Energy Converters (WECs) interact with the supporting structure, amplifying the motion of the WECs within the design wave frequency range. In this work we focus on the effect of the chamber geometry – without the WEC – in amplifying the waves inside the chamber. The simulations are carried out using two-phase Navier-Stokes simulations. We investigate the wave propagation and the interaction between waves and the fixed support structure. The simulations are compared to experimental tests performed in the wave basin at Aalborg University.
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.
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 International Energy Agency Technology Collaboration Program for Ocean Energy Systems (OES) initiated the OES Wave Energy Conversion Modeling 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 modeling 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.
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.
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.