A Vortex-Lattice Modeling Approach for Free-Surface Effects on Submerged Bodies and Propellers

A vortex-lattice modeling approach is proposed for investigating the free-surface effects on the hydrodynamics of submerged moving bodies and the propeller in the frame of the potential flow theory. The bodies, the propeller, and the free surface waves generated by them are modeled uniformly by vortex lattices. By fulfilling simultaneously the non-penetration boundary condition on the body surface (or on the camber surface for a propeller) and the linearized free-surface boundary condition, a set of linear algebraic equations can be established and solved for the vortex strengths. The vortex lattices for modeling the body- or propeller-generated waves are located slightly above the still water surface, while those for modeling the body are located on the exact body surface. In the case of the propeller, the vortex-lattice lifting-surface model is employed at present and combined with the vortex-lattice free-surface model. A number of test cases are given to investigate the convergence property and accuracy of the proposed approach, in terms of body-surface velocity or pressure distributions, as well as the lift and the wave-making resistance. Then the free-surface effects on quasi-steady propeller hydrodynamics are simulated and investigated at different submerged depths.