A Numerical Formulation Applicable to Surface Piercing Hydrofoils and Propellers

The flow field around a fully ventilated two-dimensional hydrofoil of arbitrary geometry is considered. The presented theory is a non-linear, time marching, potential based boundary element method. The perturbation potential on the cavity is a function of submergence and time. The non-linear cavity geometry is determined iteratively within the solution at each timestep. A linearized free surface condition, at infinite Froude number, is enforced by using the “negative image” approach. The developed analysis is shown to converge well with iterations per timestep, even though the cavity geometry has been found to be sensitive to the panel arrangement at the foil leading edge. Pressure distributions compare very well with linearized analytical results at small angles of attack, but the non-linear effects are noticeable at larger angles of attack.