Blind test comparison of wave–structure interactions: A non-linear Froude–Krylov modelling approach

One of the essential stepping stones for reaching economic viability and industrial feasibility of the wave energy conversion sector is the effectiveness of the device design, which is dependent, among others, to the accuracy of mathematical models used for development. Despite being more than 45 years old, modelling is not mature yet and there is still a clear lack of standardisation of modelling techniques, and a need for increasing confidence in hydrodynamic models. The objective of the Collaborative Computational Project in Wave Structure Interaction is to critically compare and evaluate various different modelling techniques, under the same shared experimental conditions, and using clearly pre-defined metrics. This paper details a contribution implementing, in a computationally efficient way, non-linear Froude–Krylov forces and non-linear kinematics, with the goal to define a medium–high fidelity model, able to compute at a small fraction of the computational time typically required by fully non-linear models. The case study considers survivability-like wave conditions, represented by three steep focused waves, particularly challenging to be modelled using potential theory-based mathematical models. Despite a poor representation in pitch/surge, a good agreement with experimental heave response and mooring load is found, at small computation time, close to real-time computation

Nonlinear hydrodynamic modelling of wave energy converters under controlled conditions

One of the major challenges facing modern industrialized countries is the provision of energy: traditional sources, mainly based on fossil fuels, are not only growing scarcer and more expensive, but are also irremediably damaging the environment. Renewable and sustainable energy sources are attractive alternatives that can substantially diversify the energy mix, cut down pollution, and reduce the human footprint on the environment. Ocean energy, including energy generated from the motion of wave, is a tremendous untapped energy resource that could make a decisive contribution to the future supply of clean energy. However, numerous obstacles must be overcome for ocean energy to reach economic viability and compete with other energy sources. Energy can be generated from ocean waves by wave energy converters (WECs). The amount of energy extracted from ocean waves, and therefore the profitability of the extraction, can be increased by optimizing the geometry and the control strategy of the wave energy converter, both of which require mathematical hydrodynamic models that are able to correctly describe the WEC- uid interaction. On the one hand, the accuracy and representativeness of such models have a major in uence on the effectiveness of the WEC design. On the other hand, the computational time required by a model limits its applicability, since many iterations or real-time calculations may be required. Critically, computational time and accuracy are often mutually contrasting features of a mathematical model, so an appropriate compromise should be defined in accordance with the purpose of the model, the device type, and the operational conditions. Linear models, often chosen due to their computational convenience, are likely to be imprecise when a control strategy is implemented in a WEC: under controlled conditions, the motion of the device is exaggerated in order to maximize power absorption, which invalidates the assumption of linearity. The inclusion of nonlinearities in a model is likely to improve the model's accuracy, but increases the computational burden. Therefore, the objective is to define a parsimonious model, in which only relevant nonlinearities are modelled in order to obtain an appropriate compromise between accuracy and computational time. In addition to presenting a wider discussion of nonlinear hydrodynamic modelling for WECs, this thesis contributes the development of a computationally efficient nonlinear hydrodynamic model for axisymmetric WEC devices, from one to six degrees of freedom, based on a novel approach to the nonlinear computation of static and dynamic Froude-Krylov forces

Coexisting attractors in floating body dynamics undergoing parametric resonance

This study pertains to analysing the dynamical behaviour of a floating body undergoing parametric resonances. A simple vertical cylinder, representing a classical spar-buoy, is considered, limiting its motion to heave and pitch degrees of freedom. Its geometry and mass distribution are chosen such that a 2:1 ratio of heave to pitch/roll natural frequency makes the spar-buoy prone to parametric resonance. The system is then studied by the shooting method, combined with a pseudo-arclength continuation, and the harmonic balance procedure. Results show that an extensive bistable region exists, where stable parametric resonance coexists with a regular resonance response. The analysis also unveiled the existence of stable quasiperiodic motions existing in correspondence of both pitch and heave resonance. Results are qualitatively validated using a model based on the explicit nonlinear Froude–Krylov force calculation

Consistency of Viscous Drag Identification Tests for Wave Energy Applications

Viscous drag forces in mathematical models for wave energy converters are usually modelled by means of a term based on the Morison equation. Due to large relative velocities, induced by control strategies in order to increase the power absorption,viscous losses can have a high impact on the model accuracy and,in turn, on the model-based power optimization control strategies.Notwithstanding the importance of a reliable estimation of the drag coefficient in the Morison equation, much inconsistency and low trustworthiness is found in the literature, about both the values themselves, and the identification methods.Indeed, drag identification for wave energy applications is particularly challenging, mainly due to the device dimensions,characteristic flow regimes, large motions and, in particular, the presence of the free surface. An ideal identification test would be able to replicate the full complexity of the flow, and concurrently to isolate viscous forces from other forces and nonlinear effects.This paper seeks to discuss the inherent challenges to drag identification, proper to wave energy applications. Moreover,different identification techniques are implemented, evaluated and compared, with regard to the estimation of the drag coefficient for a floating heaving point absorber

Importance of Nonlinear Wave Representation for Nonlinear Froude-Krylov Force Calculations for Wave Energy Devices

Due to their computational convenience, mathematical models for wave energy converters are usually linear. Including nonlinearities may improve the accuracy of the results, but often at the price of an additional computational and complexity burden, which can be justified only if nonlinearities are significant. One of the sources of nonlinearity in fluid-body interactions is the wave field itself. Different wave models exist, among which are linear Airy’s theory, the Wheeler stretching approach, and the nonlinear Rienecker-Fenton method, which achieve a different compromise of accuracy and complexity. The impact of the accuracy of such wave theories strongly depends on the specific device (operating principle, power production region and survivability mode), and installation site (water depth, occurrences of each sea state in the scatter diagram of the installation site). This paper evaluates the performance of different wave field representations, firstly in absolute terms, and secondly in relation to the associated computation of nonlinear Froude-Krylov forces for different wave energy devices

Comparing nonlinear hydrodynamic forces in heaving point absorbers and oscillating wave surge converters

Two of the most common modes of oscillation of single degree of freedom wave energy converters are heave and surge, which are, respectively, exploited by heaving point absorbers (HPAs), and oscillating wave surge converters (OWSCs). Given major hydrodynamic differences between HPAs and OWSC, different nonlinear forces may be more or less relevant. Likewise, the scaling properties of such nonlinear forces may be different, according to the type of device, introducing uncertainties. This paper studies different nonlinear effects, and the relevance of different hydrodynamic force components, in HPAs and OWSCs. Nonlinear Froude–Krylov forces, as well as viscous drag effects, are represented and both prototype and full-scale device sizing are considered. Results show that HPAs are predominantly affected by nonlinear Froude–Krylov forces, while the most important hydrodynamic forces in OWSCs are diffraction and radiation effects. In addition, viscous drag appears to have little relevance in HPAs, but a significant influence in OWSCs. Finally, nonlinearities are shown to significantly affect the phase of the different force components

Analytical Formulation of Nonlinear Froude-Krylov Forces for Surging-Heaving-Pitching Point Absorbers

Accurate and computationally efficient mathematical models are fundamental for designing, optimizing, and controlling wave energy converters. Wave energy devices are likely to exhibit significant nonlinear behaviour, over their full operational envelope, so that nonlinear models may become indispensable. Froude-Krylov nonlinearities are of great importance in point absorbers but, in general, their calculation requires an often unacceptable increase in model complexity and computational time. However, if the body is assumed to be axisymmetric, it is possible to describe the whole geometry analytically, thereby allowing faster calculation of nonlinear Froude-Krylov forces. In this paper, a convenient parametrization of axisymmetric body geometries is proposed, applicable to devices moving in surge, heave, and pitch. In general, the Froude-Krylov integrals must be solved numerically. Assuming small pitch angles, it is possible to further simplify the problem, and achieve an algebraic solution, which is considerably faster than numerical integration

A Compact 6-DoF Nonlinear Wave Energy Device Model for Power Assessment and Control Investigations

High accuracy at a low computational time is likely to be a fundamental trait for mathematical models for wave energy converters, in order to be effective tools for reliable motion prediction and power production assessment, device and controller design, and loads estimation. Wave energy converters are particularly prone to exhibit complex and nonlinear behaviours, which are difficult to be modelled efficiently. Highlynonlinear effects, related to nonlinear Froude-Krylov forces, are nonlinear coupling, instability, and parametric resonance, which may damage or improve the power production. It is therefore fundamental to be able to describe such nonlinearities, in order to assess their repercussion on the performance of the device, and eventually design the system in order to exploit them. This paper provides a computationally efficient, compact, and flexible modelling approach for describing nonlinear Froude- Krylov forces for axisymmetric wave energy devices, in 6 degrees of freedom. Unlike other similar models, based on a mesh discretization of the geometry, the analytical formulation of the wetted surface allows the dynamical model to run almost in real time

Consistency of Viscous Drag Identification Tests for Wave Energy Applications

Viscous drag forces in mathematical models for wave energy converters are usually modelled by means of a term based on the Morison equation. Due to large relative velocities, induced by control strategies in order to increase the power absorption,viscous losses can have a high impact on the model accuracy and,in turn, on the model-based power optimization control strategies.Notwithstanding the importance of a reliable estimation of the drag coefficient in the Morison equation, much inconsistency and low trustworthiness is found in the literature, about both the values themselves, and the identification methods.Indeed, drag identification for wave energy applications is particularly challenging, mainly due to the device dimensions,characteristic flow regimes, large motions and, in particular, the presence of the free surface. An ideal identification test would be able to replicate the full complexity of the flow, and concurrently to isolate viscous forces from other forces and nonlinear effects.This paper seeks to discuss the inherent challenges to drag identification, proper to wave energy applications. Moreover,different identification techniques are implemented, evaluated and compared, with regard to the estimation of the drag coefficient for a floating heaving point absorber

Optimization and Energy Maximizing Control Systems for Wave Energy Converters

In recent years, we have been witnessing great interest and activity in the field of wave energy converters’ (WECs) development, striving for competitiveness and economic viability via increasing power conversion while decreasing costs and ensuring survivability [...