Design tools for wave energy converters with flexible membranes

Abstract

The Earth’s oceans contain vast amounts of energy in the form of ocean waves that propagate towards our shores. As we aim to meet the challenge of limiting global heating to, at most, 2 degrees Celsius the use of Wave Energy Converters (WECs), which convert the energy of ocean waves into electricity, could form an important part of the future global energy system. However, this is dependent on a step-change in the cost competitiveness of WECs relative to other, more mature, forms of renewable energy.

While solar, wind and tidal energy converters have seen a convergence on a single design and a reduction in cost, to date there has been a lack of convergence on a single design of WEC and no design has proven to be commercially viable. This has lead a number of organisations to look again at the WEC design space in order to see if there is a design type capable of providing the required change in cost. A set of WEC design types that have the potential to provide a step-change reduction in the cost of energy is devices that utilise flexible membranes as part of the main structure. In particular, there is a large potential cost reduction in devices where the power take-off (PTO) is integrated into the flexible membrane structure. However, while progress has been made in the analysis of individual flexible membrane WECs there has been limited analysis of the entire design space. One factor that has contributed to this, compared to their rigid body counterparts, is the lack of a general-purpose method or tool for analysis for these types of devices. Numerical analysis of flexible membrane devices differs from that of rigid body WECs as determining the shape of the device in still water is non-trivial, and the dynamic analysis must take into account the motion of the flexible structure itself, combined with any internal fluid contained in the flexible membrane device. While this type of analysis has been performed before, it has only been for individual devices where developers and academics have focused on developing tools and methods specific to that device. The result is that there is no general-purpose method for analysis of a WEC that utilises flexible membranes as part of the structure.

In this thesis, two questions are asked. One, is it possible to develop a general-purpose method for analysis of WECs with flexible membrane structures? Two, can the general-purpose method be used to develop a set of simulation tools for analysis of generic flexible membrane WECs? Where the developed tool will form the basis for the development of a commercial software tool-set for exploitation by wave energy consultancy firm Wave Venture.

The general-purpose method proposed here is made up of a non-linear static analysis and a linear dynamic analysis. The non-linear static analysis evaluates the static shape of the flexible membrane structure in its equilibrium position, in response to gravity, hydrostatic pressure, internal pressure and mechanical constraints. The linear dynamic analysis is based on the assumptions of small displacements of the device about the static shape configuration in response to small amplitude waves, and that the system can be treated as a mass-spring-damper system subject to sinusoidal forcing. The coupling of the effect of the water and waves in the external domain, the fluid in the internal domain, the flexible membrane structural components and any PTOs are dealt with by the use of generalised mode shapes throughout the analysis. A lumped parameter approach is used to calculate the force, mass, stiffness and damping coefficients for each generalised mode shape of each separate domain. These are summed across all domains to give the full system coefficients. The response of the device and the hydrodynamic power absorbed is then calculated in the frequency domain.

The general-purpose tool-set developed using this method is a combination of bespoke tools developed in Python and integration of third-party software, with modifications where required. The tool-set is developed as a proof of concept for a commercial version. As such, the separate tools have been developed with a level of integration to allow any combination of number or bodies, number of internal cells, type of internal cell fluids, levels of membrane elasticity and type of PTO to be analysed automatically based on only user inputs, including information stored with the geometry mesh.

The third-party software has been included where existing software performs the desired calculations (in some cases with modifications) and could be used as part of a commercial software package without licensing restrictions.

Validation of each individual simulation tool in the tool-set is presented, while the full general-purpose tool-set developed is used to analyse a number of flexible membrane WECs and other flexible membrane sea-faring structures. The results show the ability of the proposed general-purpose method and the developed tool-set to simulate the response of a range of different types of flexible membrane WECs.

The results also highlight the importance of appropriate generalised modes shape type selection for each analysis, and importance of adhering to the assumptions of both the general-purpose method and the tool-set that has been implemented.

Finally, areas for improvement are discussed where the tool-set developed could be improved to better represent the method proposed, and areas where the proposed method could be extended to give accurate results over a wider range of sea states and device types.