Computational Modeling of Rolling Cams for Wave-Energy Capture in a Viscous Fluid

The performance of an unsymmetrical rolling cam as an ocean-wave energy extractor was studied experimentally by Salter (1974) and then analyzed from the hydrodynamics standpoint by a number of workers in the 70’s (e.g. Evans, 1976). The analysis was carried out on the basis of inviscid-fluid theory and the energy-absorbing efficiency was found to approach 100%. This well-known result did not account for the presence of viscosity, which alters not only fluid damping but also, to some extent, the added-inertia characteristics. How fluid viscosity may alter these conclusions and reduce the energy-extraction effectiveness is examined in this paper, for two rolling-cam shapes: a smooth “Eyeball Cam” with a simple mathematical form and a “Keeled Cam” with a single sharp-edged bilge keel. The solution methodology involved the Free-Surface Random-Vortex Method (FSRVM), reviewed by Yeung (2002). Frequency-domain solutions in inviscid fluid were first sought for these two shapes as baseline performance metrics. As expected, without viscosity, both shapes perform exceedingly well in terms of extraction efficiency. The hydrodynamic properties of these two shapes were then examined in a real, viscous fluid, under a high Reynolds-number assumption. The added moment of inertia and damping are noted to be changed, especially for the Keeled Cam. With the power-take-off (PTO) damping chosen based on the viscous-fluid results, time-domain solutions are developed to understand the behavior of the rolling motion, the effects of PTO damping, and the effects of the cam shapes. These assessments can be effectively made with FSRVM as the computational engine, even at motion of fairly large amplitude, for which an actual system may need to be designed.