Developing Computational Methods for Moored Floating Wave Energy Devices
Licentiate thesis, 2014
Floating point absorbers are a common class of wave-power devices typically designed to move with large amplitude in energetic waves. This stands in sharp contrast to traditional marine design, where the wave-excited motions of the structure are preferably kept to a minimum. Large motions in relatively shallow water increase the risk of slack in the mooring cables, which in turn causes snap loads of large amplitude that might affect the design loads of the moorings. Thus, a high level of non-linearity is introduced in both the mooring force response and the device motion in waves. Furthermore, there is a strong coupling between the two problems, so they cannot be solved independently. These requirements are not fully covered by conventional methods of marine design, implying a need for further development of methods.
This thesis describes the development of MooDy, a modular, Finite Element (FE) code for mooring cable dynamics. The spatial discretisation is realised by a modified version of the Local Discontinuous Galerkin method with high-order polynomial basis functions. Further, a coupled computational method for the dynamics of moored, floating wave energy converters (WECs) is presented, and applied to two generic WECs in regular waves. MooDy interacts with a separate solver for the hydrodynamic problem through an Automated Program Interface (API) communicating fair-lead position and tension force at each time step. The API is used to communicate with both a standard, linear potential flow solver and a Reynolds Averaged Navier Stokes (RANS) solver. The RANS simulations are done with the OpenFOAM platform, and the free surface is captured using the Volume of Fluid (VoF) method. This approach has the potential to encompass effects from viscous forces, instantaneous water level, green water and breaking, non-linear waves; all the while taking non-linear mooring restraint into account. Thus, the suggested method strives for completeness, although it comes at a high computational cost.
Results from MooDy exhibit the theoretically predicted exponential convergence for smooth solutions, and compare well with experimental data. The model supports propagating tension-waves with very little numerical damping; a feature that is not available in commercial codes. However, some numerical fluctuations in the tension force are noted, due to the numerical implementation of the sea-bed interaction and the loss of structural stiffness in the slacking of the cable. The computational cost of the coupled RANS-Mooring solver is very high, and preliminary results show large deviations from the predictions by linear theory for the resonance region of a generic WEC. As the body moves with large amplitude, the deviation is the combined effect of fully non-linear exciting wave force, viscous forces, non-linear mooring restraint and numerical damping due to an under-resolved boundary layer around the structure. Work with the quantification of the individual importance of these effects is ongoing.