Effects of Viscosity and Free-Surface Nonlinearity on the Wave Motion Generated by an Oscillating Twin Hull

Abstract

The hydrodynamics of a rectangular, floating twin hull under heave oscillation is analyzed to determine viscous and nonlinear effects on the radiation hydrodynamics of multi-hulls, in particular, at the resonant frequency corresponding to the piston (Helmholtz) mode of wave motions. A second-order finite-difference method based on boundary-fitted coordinates is used for the solution of the incompressible Navier-Stokes equations together with exact nonlinear viscous boundary conditions. To separate the viscosity effects from the nonlinear free-surface effects, through comparison of results, nonlinear inviscid results are also obtained using a boundary-fitted curvilinear coordinates based finite difference method. The nonlinear inviscid algorithm is based on the Eulerian-Lagrangian formulation of the nonlinear free-surface flow. The nonlinear results are compared with the linear potential-flow results obtained by Yeung and Seah [20] to quantify the combined nonlinear and viscous effects on the wave forces. The present results show the overall behavior of the wave motion to be similar to that predicted by the linear potential-flow theory [20]. Our results show that the effects of nonlinearity and viscosity on the wave motion can be significant for the Helmholtz mode, particularly for small separation distance between the hulls, which result in large vertical oscillation of the mean surface between the hulls. For small amplitudes of oscillation, the hydrodynamic pressure forces computed in the present analysis are in striking agreement with that given by the linear potential-flow analysis of Yeung and Seah [20].