Non-linear Theory for Partially Cavitating Hydrofoils

Abstract

Present linearized theories can not predict cavity flow around a hydrofoil with rounded nose. The authors propose a non-linear theory for a partially cavitating hydrofoil with arbitrary profile where cavity does not generate from the leading edge of the hydrofoil. Transient cavity flow model is adopted in the present theory. According to Hess and Smith's method for a two-dimensional steady flow, line sources and vortex are distributed on the surface of hydrofoil and that of cavity to treat the hydrofoil and cavity thickness exactly. Boundary conditions are as follows :
(1) flow direction is parallel to the surface on wetted portion of the hydrofoil
(2) flow velocity is constant on the cavity surface except for the collapsing region
(3) position of cavity tip coincides with laminar separation point or transition point of boundary layer on cavitating hydrofoil
The solution is derived by an iterative procedure. In the cavity collapsing region, cavity shape and collapsing length are determined by solving Rayleigh's equation for a single spherical bubble and connected to the constant velocity region. The laminar separation point and transition point are derived from theoretical calculation.
Experiments were made with a hydrofoil with symmetrical section whose chord was 150 mm and thickness was 12 mm. The position of cavity tip and end, cavity volume and cavity shape were measured. The results of present theory were found to be in good agreement with experimental results.