Inversion of the source and vorticity equations for supercavitating hydrofoils

Abstract

The problem of a supercavitating hydrofoil of general shape with leading edge cavity detachment is addressed in linear theory in terms of unknown source and vorticity distributions on the foil and cavity. The related singular integral equations are inverted analytically and the cavitation number, the source and vorticity distributions are expressed in terms of integrals of quantities which depend only on the hydrofoil shape and the cavity length. Numerical algorithms for computing these integrals accurately and efficiently are given.

Cavitating and Non-cavitating Lumped Vortex Element under a Free Surface

“…The hydrodynamic characteristics of cavitating flat-plate was also given in [22]. An additional angle of attack in fully wetted solution can be defined to solve the cavitating flat-plate problem by considering these equations given in [22,23]. In this study both the cavitating and non-cavitating flat-plate moving steadily under a free surface have been represented by a lumped vortex element and closed-form solutions have been developed by using these equations.…”