Development of efficient hydrodynamic models for the simulation and optimisation of jointed wave energy converters

Abstract

Jointed wave energy converters are often conceived as an extension to a prior design in order to improve the efficiency of power extraction. However, by moving towards larger numbers of degrees of freedom, optimising their performance becomes increasingly constrained by the computational efficiency of the hydrodynamic numerical models. Metaheuristic optimisation methods, such as genetic algorithms, often provide a very effective search through the design space, but require many executions of the hydrodynamic analysis. Frequency-domain models based on linear hydrodynamics are reasonably accurate and fast enough to enable a suitably broad search for optimal designs. They also require the use of so-called generalised modes to account for types of body motion beyond the standard six degrees of freedom of a rigid body, as is the case in a jointed body. However, the scarcity of implementation details and simplicity of applications in the literature would suggest that there exist barriers to the widespread use of generalised modes for jointed bodies. Motivated by two distinct optimisation problems, the difficulties in constructing models using these modes are exposed in the present work, and a recommended approach is presented in a didactic manner. This approach is then applied to each of two applications in turn. The first application is motivated by the fact that a wave energy device whose motion is confined to a sloped direction can efficiently absorb energy over a wide range of wave periods. However, sustaining this performance in a deep water environment would normally require a costly support structure. This problem has been addressed by a new device concept called the WaveTrain, which comprises a series of sloped modules, interlinked by struts and rotational joints. This configuration aims to restrict the module motion to the inclined plane, by enabling an exchange of restorative forces amongst neighbouring modules. Whereas the requirement for stable, sloped motion partly specifies the design, other aspects of the geometry and the mass distribution are best investigated through an optimisation study. Using bespoke genetic algorithms, the effects of the geometry and mass distribution on the power extraction are investigated herein, with additional consideration for the cyclic loadings in a multi-objective version. Since the objective functions are computed using a numerical hydrodynamic model (involving generalised modes), and due to the discontinuous nature of the search space that results from a set of nonlinear constraints, some specialised modifications are first required to ensure the correct and efficient operation of the genetic algorithms. Using four variants of the objective functions, a series of criteria have been found, which inform the design of the WaveTrain device. The second application is a freely-floating spine of ten Edinburgh duck modules, whose two-degree-of-freedom spine joints aim to mitigate unwanted loadings, whilst increasing the efficiency of power extraction from a given area of sea or ocean. Whilst the shape of the duck is itself a result of careful design for energy absorption effi ciency, coordinated control of the moments imparted to the ducks about the joints is required for optimal performance of the full spine. Again exploiting an efficient model enabled by the use of generalised modes, several variants of a frequency-domain control strategy are used to investigate the dynamics and performance under conditions of optimal power extraction. In particular, the effects of constraining the motions of the five uncontrolled (not power-extracting) degrees of freedom in addition to the 28 controlled (power-extracting) degrees of freedom is investigated, by way of a theoretical development. The power extraction, motions, control moments and joint shear forces are analysed in a variety of monochromatic wave periods and heading angles, to provide a better understanding of the context for the full-scale design. A series of irregular seas based on a real wave climate are then used to infer how the scaling of the device affects the performance, along with obtaining further understanding of the effects of wave direction, directional spreading and the variant of the control strategy employed.