A three-dimensional vortex method for the hydrodynamic solution of planing cambered dihedral surfaces

A new numerical approach based on the Vortex Lattice Method (VLM) for the solution of the hydrodynamic performances of cambered hulls in steady planing is formulated and validated. Due to its fully 3D formulation, the method can be applied to both cambered and un-cambered dihedral planing surfaces of any shape without any further approximation. The exact three-dimensional wetted surface of the hull is where the body boundary condition is fulfilled. The sprays region detaching both in front of the stagnation root line and from the wet portion of the chine are modeled in the numerical scheme by means of additional vortex lattice regions. The dynamic boundary condition at the stern of the hull is non-linear with respect to the perturbation potential. Results show the dynamic pressure consistently accounts for the 3D features of the flow especially in the case of cambered planing surfaces. The numerical method is verified by a systematic analysis against semi-empirical methods and it is finally validated with experimental results on prismatic as well as cambered dihedral planing surfaces. Excellent correlations are found for both types of planing surfaces that range in the same confidence interval of higher fidelity numerical models, such as RANSE solvers.