The inclusion of non-linearities in a mathematical model for U-Oscillating Water Column wave energy converters

A mathematical model for U-Oscillating Water Column (U-OWC) wave energy converters is developed and tested. The model is based on the linear irrotational wave theory but is able to treat different nonlinearities related to the physical processes involved in the U-OWC dynamics. These nonlinearities include those due to not small oscillations of the free surface in the air chamber and to the air transformation, as well as those related to the characteristics of the air turbine. An approach to include into the model the flow resistances encountered by the flow within the U-OWC is also presented. The model was tested using both laboratory and field experimental data. The latter were obtained using a physical model of a U-OWC installed on the coast. The results show that the model accurately computes the hydrodynamic quantities involved in the U-OWC dynamics. An application of the mathematical model to a real scale U-OWC subject to random waves compatible with a JONSWAP spectrum is presented. The nonlinear part of this model can be incorporated in other linear models of oscillating water column devices already appeared in the literature (H. Martins-Rivas and C.C. Mei, Journal Fluid Mech. 2009).