Numerical Simulation of the Potential Flow around a Submerged Hydrofoil with Fully Nonlinear Free-Surface Conditions

Hydrofoils have been utilized worldwide to facilitate coastal vessels for transportation, surveillance, and patrol with high speed. Inevitably, the free surface has a significant effect on the hydrofoils because of the shallow draft. In this paper, a numerical procedure based on a boundary-element method is developed for simulating a uniform incoming flow passing a two-dimensional submerged hydrofoil with free-surface effects. In the proposed technique, the boundaries of the computational domain are discretized by small elements over which the known and unknown variables are linearly distributed. To avoid the numerical instabilities induced by the sudden start of the flow through a sharp-edged foil, it is assumed that a vortex sheet with uniform strength C has been placed within the foil at the initial time step. The unknown vortex strength C, the velocity potential phi and phi(n) on the boundaries are obtained simultaneously by solving the boundary integral equation together with an added auxiliary function at each time step. The free surface is assumed to be undisturbed at the initial time step. Then, it is traced by a Eulerian scheme. Both linear and nonlinear free-surface conditions have been applied. Convergence studies with respect to the element size, the time step, and the size of far-field boundaries have been undertaken. Comparison of the present numerical results with experimental data and previous numerical results shows that the present method gives fairly good results on the force, circulation, and wave excitation of the foil.