Periodic Reporting for period 1 - OpenWave (Validation and Optimization of an Open-Source Novel Nonlinear Froude-Krylov Model for Advanced Design of Wave Energy Converters) Reporting period: 2019-05-01 to 2021-04-30 Summary of the context and overall objectives of the project The European Commission sets ambitious goals towards the build-up of a sustainable and resilient society, ensuring that human activities and search for prosperity are compatible with our natural environment and ecosystem, now and, more importantly, in the future. A key role is played by renewable energy technologies, essential to meet carbon neutrality targets in the European agenda. Ocean energy is recognized as one of the largest but still untapped potential, essential to contribute and diversify the future energy system. Among offshore renewable energy sources, wave energy is in rapid development, with a common effort to accelerate the development to increase performance and reduce costs, in the pathway towards economic viability. A major tool in such a continuous refinement process is numerical modelling, enabling engineers to evaluate, quantify, and predict. Moreover, the accuracy of such models is crucial for the effectiveness of the design and operation of wave energy converters. Due to the inherent highly nonlinear nature of wave-structure interactions, especially for wave energy converters deemed to experience large movements in order to increase power capture, traditional mathematical models are often inapt to fulfil expectations. Higher-fidelity models, on the other hand, have often too high demands for computational time, becoming inapplicable for certain studies. This project aimed at bridging the gap between mathematical model fidelity and computational burden, developing a modelling approach with a better compromise between accuracy and computational time. The model was developed for a range of popular wave energy device concepts, namely axisymmetric and prismatic floaters. The objectives of the project, all successfully achieved, encompassed the experimental validation of the modelling approach with wave tank testing, the expansion of the pre-existing methodology to a wider class of devices, the further computational time requirement reduction, and the publication of an open-source tool for implementing the proposed model. The conclusions of the project were aligned with its objectives, demonstrating a better fidelity and computational performance with respect to other similar models, showing the ability to appreciate and replicate highly-nonlinear phenomena founded in experimental and offshore installation. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far All of the project’s activities were centred around a novel mathematical framework for the computation of nonlinear Froude-Krylov forces, particularly useful when applied to wave energy converters. Main objectives involved the validation of the methodology via comparison with data gathered during experimental campaigns, the expansion of the methodology to a wider class of floaters (starting form axisymmetric and expanding to prismatic), and the computational burden reduction. The first activities were focused on the Sparbuoy floating oscillating water column, invented at Instituto Superior Tecnico de Lisboa, Portugal, also the secondment institution of the project. The novel mathematical model was implemented, after adaptation to match the Sparbuoy characteristics, also including case-specific description of the water column, air turbine and mooring system (modelled both in quasi-static in-house code, Moordyn, and Orcaflex). As a main result, the code was validated thanks to good comparison with experimental data; in particular, the code was shown able to detect and correctly articulate parametric resonance, which is a highly-nonlinear phenomenon, unperceived by conventional linear models, decreasing power extraction and potentially threatening survivability. A second major activity performed during the project focused on expanding the range of applicability of the proposed modelling approach, namely from only axisymmetric (widely used, but not covering the totality of wave energy converters) to also prismatic floaters. As major application case, the Inertial Sea Wave Energy Converter (ISWEC) device was considered, invented at the Marine Offshore Renewable Energy Lab of Politecnico di Torino, Italy, which was the host institution. After successful comparison with experimental data and existing state of the art codes, the influence of nonlinearity on the device performance was investigated, focusing on the interplay between model accuracy and energy-maximising control strategies. Furthermore, devices realizing direct and indirect extraction from hydrodynamically-excited modes were critically compared. Finally, the computational effort was reduced by optimizing the numerical integration algorithms and switching to object-oriented programming, resulting in a computational speed-up of at least two order of magnitudes with respect to versions prior to this project, in line with objectives. Finally, such results were disseminated within the scientific community by means of peer-reviewed journal papers and conference papers and, most importantly, an open source toolbox for the seamless implementation of the proposed novel method. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) Several progresses beyond the state of the art were achieved within the lifetime of this project. Nonlinear Froude-Krylov forces were widely recognized as important in the development of floating wave energy converters. However, state of the art numerical models, before the fellow’s activities, relied on mesh-based descriptions of the floater, hence requiring a high computational time and making extensive application unfeasible: in particular, optimization and control have such a tight computational demand that made the application of traditional nonlinear Froude-Krylov models unfeasible. Conversely, thanks to this project, a computational alternative is now available, providing a speedup of about 3 orders of magnitude with respect to previous mesh-based approaches. Moreover, the modelling approach was validated during the project, confirming the accuracy of its results. Such results will have impacts on optimal design of wave energy converters, improved power extraction assessment, load assessment, and energy-maximisation control strategies. Overall, this project’s results will contribute to speedup the process towards commercial viability of wave energy technologies.