Influence of platform design and power take-off characteristics on the performance of the E-Motions wave energy converter

Highlights

• Numerical model of E-Motions calibrated and validated with experimental data.

• The hydrodynamic and power performance of eight E-Motions variants assessed.

• The trapezoidal prism and half-sphere geometries yielded the best average power outputs.

• Improved designs of E-Motions were simulated for different power take-off characteristics.

Abstract

E-Motions wave energy converter is a promising device capable of harnessing energy from wave/wind induced roll oscillations onto a generic floating platform, whose development was initiated with an experimental proof-of-concept study that, despite demonstrating the potentialities of the device, also highlighted the need for further developments, aimed at improving its performance and efficiency. This justified a new phase of numerical modelling, where E-Motions was reproduced within the ANSYS® AQWA™ environment, a potential theory-based numerical model widely used in the field of wave energy converter development. The model was setup (first stage) and calibrated (second stage) with experimental data from a proof-of-concept study, carried out on a 1:40 geometric scale, with a good agreement being obtained for the hydrostatic properties (difference below 5%) and hydrodynamic roll response (minimum average error of 2.83°). From a follow-up third stage, focused on comparing eight different hull solutions with similar natural roll periods, it was determined that the half-sphere and trapezoidal prism geometries produced the highest power outputs for the studied conditions (maximum average outputs of nearly 5 kW/m and 8 kW/m, respectively). These two designs were then adapted to a 1:20 geometric scale alongside an updated version of the half-cylinder, which served as a “control” case, and subjected to a final stage of numerical modelling centered on assessing the Power Take-Off’s influence (namely through variable damping and mass) in their performance. Outcomes from this stage denote the necessity of a careful selection of Power Take-Off mass/damping combinations, as a disproportionate relationship could lead to scenarios where the conversion system would stall on one of the superstructure’s sides, moving within a very limited range of the available sliding amplitude. Maximum average power output values reach nearly 24 kW, 30 kW and 18 kW for the half-cylinder, half-sphere and trapezoidal prism, respectively, with a follow-up experimental study being planned for the near future, in order to evaluate the validity of these results.

Introduction

Wave energy is one of the major constituents of marine renewable energy sources (MRES), with an estimated global theoretical resource of about 32 000 TWh/year [1], higher than the global electricity consumption (about 23 000 TWh/year, according to data from 2019 [2]). Wave energy presents certain advantages over solar and wind energy, for instance, such as greater resource persistency, predictability, more uniformly distributed and energetically denser (3 kW/m², double during storms [3]) than wind and solar energy (500 W/m² [3] and 170 W/m², respectively [4]). Overall, however, wave energy harvesting technologies have not yet reached the required maturity level to be competitive with other energy sectors. High energy costs inherent to maintenance and operation expenditures, the ocean environment (biofouling and wave loads), the irregular nature of waves [5] and upscaling were identified as major issues that must be tackled [6]. Supported by the lessons learned from other concepts, the latest generation of wave energy harvesting devices may be able to tackle these challenges. This includes several roll/pitch-based devices, including the SEAREV [7], the Salter’s Duck [8], the Backward Bent Duct Buoy (BBDB) [9] or the Whatever Input to Torsion Transfer (WITT) [10].

E-Motions is a novel wave energy converter (WEC) concept envisioned from the observation of floating platforms, such as ships and other types of vessels, subjected to wave action. Many WECs convert energy from the wave-induced excitation of particular degrees of freedom (DoF), namely heave and surge, but E-Motions harnesses energy from wind and/or wave-induced roll oscillations of a floating platform, Fig. 1. Unlike many WECs, it is expected to be versatile, adaptable to a wide range of floating platforms and capable of protecting sensitive electronics from degradation caused by the surrounding sea environment, thus mitigating the aforementioned maintenance and replacement requirements. These characteristics combine into a unique WEC concept that has already been subjected to a successful proof-of-concept study [11]. The next stage of development of E-Motions requires a better understanding of the hydrodynamic response of different designs of floating platform, the influence of the Power Take-Off (PTO) system, the non-linear interactions between the platform and mobile PTO components and the estimated power output from a wider range of wave conditions. By expanding the number of hull designs, assessing different PTO mass-damping combinations, considering a more realistic mooring system and simulating a greater number of wave conditions, a convergence towards an improved E-Motions technological solution (from the non-optimized proof-of-concept study design) can be achieved.

For the proof-of-concept study [11], a physical modelling approach was selected, following on the example of other WECs, such as CECO [12] or Inertial Sea Wave Energy Converter (ISWEC) [13]. It was possible to evaluate the influence of several variables (e.g., wave conditions and PTO damping) on the E-Motion’s hydrodynamic response and power performance. However, this approach requires considerable resources and time, respecting similarity criteria (geometric, kinematic and dynamic [14]) and is susceptible to laboratory and scale effects [15], including PTO downscaling [16]. These limitations can be overcome by a complementary numerical modelling approach, thus combining into an increasingly applied composite modelling [17]. The data attained from physical modelling can be used to calibrate numerical models of WECs, which do not have the resource and time requirements inherent to physical modelling. Moreover, additional variable combinations can be studied more efficiently [18]. As discussed in [19], development cost reduction may be achieved by pursuing a Performance before Readiness approach, which should increase the likelihood of successful market entry. By conducting a thorough performance evaluation of several design alternatives, a WEC concept can be optimized before proceeding to higher Technology Readiness Levels (TRL), where the flexibility to introduce changes is far lower [20]. To obtain reliable and affordable performance estimates, numerical models can be employed as a time and resource-efficient solution [19].

Currently, two main families of numerical approaches are commonly applied to develop WECs: Computational Fluid Dynamics (CFD), based on solving the Navier-Stokes Equations (NSE), and linear potential flow-based codes associated with the Boundary Element Method (BEM) [19]. CFD tools can be either Eulerian [21] or Lagrangian [22], depending on their treatment and discretization of the domain. They are used to solve complex non-linear hydrodynamics without neglecting terms associated with surface deformation, viscous and turbulence effects, wave breaking [23] and overtopping [24]. This improved treatment gives CFD tools a high accuracy, yet the computational cost is often very high, making them unpractical for a thorough study of WEC solutions, large domains and/or lengthy simulations. Commonly, CFD is employed at later development stages for analyzing a device’s survivability capabilities under extreme wave-action [25], where non-linear effects associated with high wave amplitudes and WEC motions cannot be neglected [24]. Alternatively, BEM tools have been successfully applied in the offshore industry for several decades [19], being recommended for WEC development at early to intermediate stages of development [26], when the systematic study of several alternative designs is required. A priori, they do not account for the non-linear terms considered in CFD, and discretize the body wetted surfaces into panels (diffracting and non-diffracting, being the former required to solve the wave-structure interactions problem). Accuracy is lower, in comparison with CFD, but for operational conditions, where wave amplitudes and WEC motions are relatively small, the simplifications are accurate enough at a far lower computational cost. Depending on the case study and the degree of reduction on the computational effort, the simplifications can range from minor (fully non-linear, based on Rankine singularities with non-linear free surface) to major (fully linear, based on Green functions with linearized free-surface and body-boundary conditions) [27]. Consequently, they are preferable, at a low TRL, for carrying out an exhaustive optimization study of WEC designs [24].

One of the most commonly used BEM softwares is ANSYS® AQWA™ [28]. It permits modelling of wave-structure interactions and can include mooring systems or articulations (joints and hinges). Simulations are carried out in either frequency or time-domain, providing data on hydrostatic properties, frequency-dependent coefficients (added mass and radiation damping), excitation forces and hydrodynamic response to various wave conditions and sea-states, whether regular or irregular. Ma et al. [29] applied this software to a pitching float WEC with a built-in pendulum, denoting increased device stability when the mooring point positions were closer to the centre of mass. A spherical-bottom shape float yielded improved pitching performance, namely through width tuning and side radius increment. Bracco et al. [13] analysed the ISWEC by also applying AQWA™, supported by data from a small-scale physical model. From the parametric study it was concluded that the optimized variant of the ISWEC allowed for as much as three times the power to be absorbed, with cost reductions of about one order of magnitude. Lastly, the CECO was subjected to various numerical studies [30], including an offshore version [31]. WAMIT® [32] and ANSYS® AQWA™ were the selected BEM-based software. It was possible to validate the numerical model [12] and systematically test CECO variants towards an improvement of the hydrodynamic response and energy conversion efficiency. An annual energy production (AEP) and capture width ratio (CWR) of up to 1 040 MWh and 52% were obtained, respectively. Other similar studies where AQWA™ was applied include a multi-DoF point absorber [33] and a barge for WEC installment procedures [34].

Following on the outlined examples of WEC development, this paper addresses the numerical study of design solutions for the E-Motions device. The goal is to determine a combination of variables, namely those related to the PTO and the floating platform’s shape and mass distribution that maximizes the power performance and hydrodynamic response of this WEC. In Section 2, the E-Motions concept is described both mechanically and mathematically, as to provide a better understanding of the operation mode. Section 3 follows with the description and setup of the numerical model of E-Motions (Stage 1), as well as the calibration supported by the experimental proof-of-concept’s results (Stage 2). In Section 4, the main results of the numerical optimization strategy are presented and discussed. This section is divided into two parts: Stage 3, which focuses on the hydrodynamic response and power output performance for different geometric designs, aimed at selecting the two most promising solutions; and Stage 4, where the selected designs are subjected to a parametric study related to PTO properties, namely mass and damping, with a steel chain catenary-based mooring system. Lastly, Section 5 presents some remarks on the drawn conclusions and recommendations for following developments of E-Motions.