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

Can Tidal Current Energy Provide Base Load?

Tidal energy belongs to the class of intermittent but predictable renewable energy sources. In this paper, we consider a compact set of geographically diverse locations, which have been assessed to have significant tidal stream energy, and attempt to find the degree to which the resource in each location should be exploited so that the aggregate power from all locations has a low variance. An important characteristic of the locations chosen is that there is a good spread in the peak tidal flow times, though the geographical spread is relatively small. We assume that the locations, all on the island of Ireland, can be connected together and also assume a modular set of tidal turbines. We employ multi-objective optimisation to simultaneously minimise variance, maximise mean power and maximise minimum power. A Pareto front of optimal solutions in the form of a set of coefficients determining the degree of tidal energy penetration in each location is generated using a genetic algorithm. While for the example chosen the total mean power generated is not great (circa 100 MW), the case study demonstrated a methodology that can be applied to other location sets that exhibit similar delays between peak tidal flow times

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

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

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

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

Viscoelastic and Electromagnetic Materials with Nonlinear Memory

A method is presented for generating free energies relating to nonlinear constitutive equations with memory from known free energies associated with hereditary linear theories. Some applications to viscoelastic solids and hereditary electrical conductors are presented. These new free energies are then used to obtain estimates for nonlinear integro-differential evolution problems describing the behavior of nonlinear plasmas with memory

Identification of Nonlinear Excitation Force Kernels Using Numerical Wave Tank Experiments

This paper addresses the mathematical modelling of the relationship between the free surface elevation (FSE) and the excitation force for wave energy devices (excitation force model). While most studies focus on the model relating the FSE to the device motion, the excitation force model is required to complete the mathematical wave energy system description and also plays an important role in excitation force observer design. In the paper, a range of linear and nonlinear modelling methodologies, based on system identification from numerical wave tank tests, are developed for a range of device geometries. The results demonstrate a significant benefit in adopting a nonlinear parameterisation and show that models are heavily dependent on incident wave amplitude