The effect of gravity and cavitation on a hydrofoil near-the free surface

A nonlinear analysis has been made to determine the effects of the free surface and transverse gravity field on the steady cavity flow past a shaped hydrofoil beneath the free surface. A closed cavity wake model has been proposed, and a method for the determination of an analytical function from its modulus and argument on the region boundary has been employed to derive the complex flow potential in a parameter plane. The boundary-value problem is reduced to a system of integral and integro-differential equations in the velocity modulus along the free boundaries and the velocity angle along the hydrofoil surface, both written as a function of parametric variables. The system of equations is solved through a numerical procedure, which is validated in the cases of a cavitating flat plate and non-cavitating shaped hydrofoils by comparison with data available in the literature. The results are presented in a wide range of Froude numbers and depths of submergence in terms of the cavity and free-surface shapes and force coefficients. The influences of the free surface and gravity on the aforementioned quantities are discussed. The limiting cavity size corresponding to zero cavitation number in the presence of gravity is found for various initial flow parameters.