On the Performance of a Dual-Cylinder Wave-Energy Converter: Single Versus Two Degrees of Freedom

A recently developed dual (coaxial-)cylinder wave-energy converter (WEC) consists of inner and outer-cylinders, with the outer one sliding over the inner one. An effective design was to tension-tether the inner cylinder (Son and Yeung, OMAE2014-#24582) while the outer cylinder acts as a floater heaving in response to incident waves. Even though the idea was a success, there was significant scientific curiosity in our early stage of the design in the following context: if both cylinders were allowed to heave simultaneously and independently, what would be the implications on the energy-extraction performance and power-take-off constraints? In this paper, we report the detailed analysis conducted at the time of the design. To begin with, the hydrodynamic coefficients, namely, the added mass, radiation-damping, and wave-exciting force for the individually moving cylinders were solved using the method of matched eigenfunction expansions (Chau and Yeung, OMAE2012-#83987). We expanded that capability to allow coupling or interference hydro-dynamic coefficients to be computed in the current work. This coupling is shown to lead to two degrees of freedom of motion, one for each cylinder, with excitation forces on each based on reciprocity (Haskind’s) relations. The resulting relative heave motion between the cylinders is used to drive the permanent magnet linear generator (PMLG) to capture electrical energy. The performance of the WEC, in terms of capture width, is calculated for both regular-wave and irregular-wave conditions and is compared with that for the one degree-of-freedom system, fixed inner cylinder and heaving outer cylinder. The change in WEC performance in response to changing generator damping was found to be very different for the two cases. This behavior leads to very different optimal generator damping values in regular and irregular waves. The advantages and shortcomings of the two systems are compared and explained.