Leading-Edge Corrections to the Linear Theory of Partially Cavitating Hydrofoils

Abstract

In this work, first, the partially cavitating hydrofoil problem is formulated in linear theory in terms of vorticity and source distributions on the projection of the hydrofoil to the free-stream direction. The resulting system of integral equations is inverted and the solution is expressed in terms of integrals of the horizontal perturbation velocity in fully wetted flow, multiplied by weighting functions that are independent of the shape of the hydrofoil. Second, the linearized dynamic boundary condition on the cavity is modified so that the total velocity on the cavity as predicted by applying Lighthill's leading-edge corrections is a constant. This results in a varying horizontal perturbation velocity on the cavity rather than a constant as required by conventional linear theory. The modified system of integral equations is inverted and the solution is expressed in terms of integrals of known quantities. The present linearized theory with the leading-edge corrections included, predicts a finite cavitation inception number as well as the correct effect of foil thickness on cavity size.