Parametric design of a resonant point absorber with a fully submerged toroidal shape
Introduction
In the last decade the interest in the marine renewable energy sector by governmental institutions, stakeholders and researchers grew fast throughout the world, as proved by the deployment of the first marine energy prototypes in the real environment and the increasing number of funding opportunities. In this respect, in March 2018 the European Commission endorsed the “Ocean Energy Implementation Plan” (EU, 2018), developed by the Temporary Working Group for Ocean Energy, where a set of technical, financial and environmental actions, devoted to support the deployment of marine energy converters, are provided. Besides, the document furnishes a strategic roadmap with several key-action plans, in order to ensure the clean energy transition of the European countries and develop well-established and mature technologies, capable of covering a significant amount of the EU power demand over the next 35 years.
Among the various marine renewable sources, wave energy probably represents the most promising one, with a theoretical annual potential in Europe of about 2800 TWh (Magagna, 2019). Anyway, the Levelised Cost of Energy ( is still high, if compared with other renewable technologies, such as the solar or the onshore wind ones, with a reference value equal to 0.720 and 0.560 €/kWh in 2015 and 2018 respectively, so proving that the marine energy sector is not mature enough for the international market. In this respect, the European Commission has set ambitious targets for WEC devices which are expected to reach a of 0.200 €/kWh by 2025, 0.150 €/kWh by 2030 and 0.100 €/kWh by 2035. This roadmap towards the commercial phase reveals to be ambitious, as WEC devices still need to achieve a significant amount of operational hours in real environment, combined with a reasonable level of power production, in order to gain the trust of investors and manufactures. Indeed, the pathway towards the cost-reduction needs to combine economies of scale, based on large industrial production and optimised maintenance operations, and learning by research through the improvement of currently embodied technologies.
Among the variety of WEC devices, point absorbers represent one of the most promising technologies, due to the relatively simple working principle. Since the pioneering work by Budal and Falnes (1975), considerable improvements have been gained from both theoretical and experimental point of views. The hydrodynamic modelling of this WEC device, coupled with electric or hydraulic Power Take-Off (PTO) units, has been widely investigated by several researchers thorough the world (Pastor and Liu, 2014; Piscopo et al., 2016; Do et al., 2018; Kolios et al., 2018 among others). Recently, attention has been also paid to improve the hydrodynamic performances by increasing the freedom degrees (Al Shami et al., 2019), applying a tuned inertial mass (Haraguchi and Asai, 2020) or developing novel layouts to enhance the survivability in extreme sea state conditions (Zheng et al., 2020). In current analysis the floating buoy layout, recently developed by Piscopo and Scamardella (2019) and consisting of a hemispherical buoy connected by means of a deep-draught vertical cylinder to a fully submerged toroidal shape, is assumed as reference design to maximize the power production and decrease the cost of energy. The new point absorber allows increasing the power production, as regards a similarly sized single-body WEC device, consisting of a hemispherical floating buoy, by properly tuning the heave natural period with the prevailing sea states at the deployment site. In this respect, based on the main outcomes by Piscopo and Scamardella (2019), the new layout allows: (i) obtaining an appreciable increase of the Annualised Energy Production up to 60% for low and medium energy power production site, as regards conventional single-body point absorbers, and (ii) properly tuning the main dimensions of the toroidal shape, depending on the wave climate at the deployment site. The point absorber is connected by means of a tensioned wire rope to a Permanent Magnet Linear Generator (PMLG) equipped with a gravity-based foundation, such as that one developed at the Uppsala University (Sjökvist and Göteman, 2017). Particularly, a parametric analysis is performed, by systematically varying the height of the fully submerged volume, in order to properly tune the heave natural period of the WEC device with the prevailing sea states at the deployment site. In this respect, the main aims of current research can be summarized as follows:
- (i)
The Annualised Energy Production () of the new WEC device is systematically assessed based on the met-ocean conditions at the candidate deployment site, located in the western Mediterranean Sea, in order to carry out a comparative analysis with a reference WEC device, consisting of a hemispherical buoy with the same waterplane area. Besides, the hydrodynamic behaviour of the WEC device in extreme sea state conditions is investigated and the scantling of the tensioned wire rope, connecting the floating buoy to the PMLG translator mass, is performed based on both Ultimate (ULS) and Fatigue (FLS) Limit State design conditions;
- (ii)
A comparative analysis, in terms of , is performed between the new and the reference WEC device, in order to further investigate the effectiveness of the new layout;
- (iii)
A sensitivity analysis is performed to explore a possible reduction pathway of the , by combining both economical, operational and technological aspects, with the main aim of gaining the EU target that should be reached by 2025.
The hydrodynamic analysis is carried out by a non-linear time-domain model, solved by a dedicated code developed in Matlab (MathWorks, 2018), including the heave, surge and pitch motions of the floating buoy and the vertical motion of the PMLG translator mass.
Section snippets
The WEC layout
The point absorber, recently designed by Piscopo and Scamardella (2019) and depicted in Fig. 1, is assumed as reference WEC device. It has a spar-type configuration, consisting of a floating hemisphere and a deep-draught vertical cylinder, connected to a fully submerged toroidal shape by means of 8 equally spaced bracings. The floating buoy is entirely built in Normal Strength Steel (NSS), apart from the toroidal shape which is made of marine concrete filled with polyurethane foam. Additional
Environmental loads
The parametric design performed in Section 4 is carried out assuming that the wave farm is deployed at Alghero, about 3 km off the Sardinia coastline, provided that this is one of the most energetic sites in the western Mediterranean Sea. The wave statistics are provided by the Italian Sea Wave Measurement Network (APAT, 2006), currently managed by the governmental institution ISPRA, namely “Istituto Superiore per la Protezione e la Ricerca Ambientale”. In this respect, Table 1 provides the
AEP assessment
The assessment of the WEC devices is carried out by the simplified heave model, as surge and pitch motions have an almost negligible impact on power production (Miquel et al., 2017; Piscopo et al., 2020). Based on the results outlined in Table 6, the new layout allows gaining an appreciable increase of the , ranging from 53% up to 70%, as regards the reference WEC device. This outcome is due to the improved hydrodynamic behaviour of the point absorber with the fully submerged toroidal
Discussion
By the hydrodynamic analysis carried out in Section 4, the WEC device with the fully submerged toroidal shape is effective to increase the power production and decrease the cost of energy. In this respect, by Fig. 7(a), it is gathered that the layout with a 2.0 m high toroidal shape maximises the , with a 70% increase as regards the reference configuration. Besides, by Fig. 7(b), the new point absorber allows gaining a 16% reduction of the , as regards the reference layout, almost
Conclusions
The parametric design of a resonant point absorber with a fully submerged toroidal shape has been performed with the main aim of comparing the hydrodynamic performances of the new WEC device with a reference layout consisting of a floating hemisphere. The point absorber is connected by means of a tensioned line to a PTO unit with gravity-based foundation and an increased upper free stroke length, in order to accomplish the large vertical motions of the translator mass in extreme sea state
Notes
The WEC device with the fully submerged toroidal shape is covered by the Italian patent demand number 102019000004221 pending at the Ministry of Economic Development (MISE).
CRediT authorship contribution statement
V. Piscopo: Conceptualization, Methodology, Software, Writing - original draft, Formal analysis, Visualization. A. Scamardella: Conceptualization, Validation, Supervision, Data curation, Project administration, Funding acquisition.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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2022, Ocean EngineeringCitation Excerpt :Al Shami et al. (2019a) studied the improvement of the hydrodynamic performance of a point absorber by increasing the freedom degrees of the submerged bodies. Piscopo and Scamardella (2021) conducted the parametric design of a resonant point absorber equipped with a fully submerged toroidal shape to investigate the effectiveness of the new WEC device in terms of power production and cost of energy. Normally, the natural frequency of the semi-submerged body is much higher than frequencies of incoming waves.