Until now, wave-energy developers have focused on designing large machines for utility-scale electricity generation. While many concepts with good capture performance have been devised, significant commercial success has yet to be achieved in this market. Smaller wave energy converters (WECs) for specialist uses have received less attention. Emerging applications for these machines include powering sensors for ocean monitoring and providing energy for recharging maritime autonomous vehicles. Small reliable floating WECs can provide both the low levels of power required for these applications, and a surface platform for satellite
communications. Here, the key idea is to reduce costs and increase human safety by deploying small WECs to perform tasks that would otherwise require a ship. Developing small WECs for specialist uses provides a fast route to market, thereby creating a viable financial and technical base for the development of larger devices for applications where more power is required. This paper reports early results of time- and frequency-domain simulations of a compact WEC designed for monitoring the ocean environment.
High-fidelity models become more and more used in the wave energy sector. They offer a fully nonlinear simulation tool that in theory should encompass all linear and nonlinear forces acting on a wave energy converter (WEC). Studies using high-fidelity models are usually focusing on validation of the model. However, a validated model does not necessarily provide reliable solutions. Solution verification is the methodology to estimate the numerical uncertainties related to a simulation. In this work we test four different approaches: the classical grid convergence index (GCI); a least-squares version (LS-GCI); a simplified version of the least-square method (SLS-GCI); and the ITTC recommended practice. The LS-GCI requires four or more solutions whereas the other three methods only need three solutions. We apply these methods to four different high-fidelity models for the case of a heaving sphere. We evaluate the numerical uncertainties for two parameters in the time domain and two parameters in the frequency domain. It was found that the GCI and ITTC were hard to use on the frequency domain parameters as they require monotonic convergence which sometimes does not happen due to the differences in the solutions being very small. The SLS-GCI performed almost as well as the SL-GCI method and will be further investigated.
For design validation of offshore structures and conceptualisation of wave energy converters, physical model testing performed in wave basin laboratories is often applied. In such cases, knowledge about the wave conditions is of great significance. For validation of the wave condition in such tests, different methods for estimation of the directional wave spectra may be applied. However, different assumptions are imposed in the methods and deviations here from providing uncertainties in the results. The following paper quantifies the influence of nonlinear effects on the accuracy of the estimated directional wave spectra. This is done by analysis of idealised, synthetically generated waves based on second order wave theory and secondly with simplified amplitude dispersion included. The present analyzes show that the uncertainties of the directional wave spectra are proportional to the level of nonlinearity present in the wave field.
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.
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.
Computational fluid dynamics (CFD) is becoming an increasingly popular tool in the wave energy sector, and over the last five years we have seen many studies using CFD. While the focus of the CFD studies have been on the validation phase, comparing numerically obtained results against experimental tests, the uncertainties associated with the numerical solution has so far been more or less overlooked. There is a need to increase the reliability of the numerical solutions in order to perform simulation based optimization at early stages of development. In this paper we introduce a well-established verification and validation (V&V) technique. We focus on the solution verification stage and how to estimate spatial discretization errors for simulations where no exact solutions are available. The technique is applied to the cases of a 2D heaving box and a 3D moored cylinder. The uncertainties are typically acceptable with a few percent for the 2D box, while the 3D cylinder case show double digit uncertainties. The uncertainties are discussed with regard to physical features of the flow and numerical techniques.
A numerical model (MOODY) for the study of the dynamics of cables is presented in Palm et al. (2013), which was developed for the design of mooring systems for floating wave energy converters. But how does it behave when it is employed together with the tools used to model floating bodies? To answer this question, MOODY was coupled to a linear potential theory code and to a computational fluid dynamics code (OpenFOAM), to model small scale experiments with a moored buoy in linear waves. The experiments are well reproduced in the simulations, with the exception of second order effects when linear potential theory is used and of the small overestimation of the surge drift when computational fluid dynamics is used. The results suggest that MOODY can be used to successfully model moored floating wave energy converters.