Abstract
Computationally fast and accurate mathematical models are essential for effective design, optimization, and control of wave energy converters. However, the energy-maximising control strategy, essential for reaching economic viability, inevitably leads to the violation of linearising assumptions, so the common linear models become unreliable and potentially unrealistic. Partially nonlinear models based on the computation of Froude–Krylov forces with respect to the instantaneous wetted surface are promising and popular alternatives, but they are still too slow when floaters of arbitrary complexity are considered; in fact, mesh-based spatial discretisation, required by such geometries, becomes the computational bottle-neck, leading to simulations 2 orders of magnitude slower than real-time, unaffordable for extensive iterative optimizations. This paper proposes an alternative analytical approach for the subset of prismatic floating platforms, common in the wave energy field, ensuring computations 2 orders of magnitude faster than real-time, hence 4 orders of magnitude faster than state-of-the-art mesh-based approaches. The nonlinear Froude–Krylov model is used to investigate the nonlinear hydrodynamics of the floater of a pitching wave energy converter, extracting energy either from pitch or from an inertially coupled internal degree of freedom, especially highlighting the impact of state constraints, controlled/uncontrolled conditions, and impact on control parameters’ optimization, sensitivity and effectiveness.
Highlights
Wave-structure interactions are complex physical phenomena, often difficult to model and predict with a degree of confidence satisfactory for several non-trivial ocean engineering applications
In the regions of operational wave periods (Tw > 5.5s) of this wave energy converters (WECs), and especially in the working DoF, the diffraction component is considerably smaller than the Froude–Krylov part, which is a promising hint for the effectiveness of the nonlinear Froude-Krylov force (NLFK) approach
In order to verify the correctness of the timedomain implementation and the accuracy of the state space approximation of the radiation forces, the response amplitude operator (R AO) in heave and pitch is computed under linear conditions, both with linear and nonlinear time domain models, and compared with independent frequency domain calculation
Summary
Wave-structure interactions are complex physical phenomena, often difficult to model and predict with a degree of confidence satisfactory for several non-trivial ocean engineering applications. Further examples of software including NLFK computation via a mesh are SIMDYN (Somayajula and Falzarano 2015; Wang et al 2019), as well as various other in-house implementations (Guerinel et al 2013; Jang and Kim 2019, 2020) Such NLFK models are already faster than weakly- or fully-nonlinear potential flow models (Penalba et al 2017), where the potential problem is solved for each time-domain simulation at each time step on a continuously updating wetted surface (Letournel et al 2014). 2 presents the definition of nonlinear Froude–Krylov forces and the mathematical formulation of the computationally efficient computation for generic prismatic floaters; Section 3 presents the case study considered in this paper to quantify different nonlinear effects and their impact on the behaviour and performance of the WEC; in particular, two scenarios are considered, where energy is directly extracted from the pitching motion, in Sect.
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