Numerical Investigation of Curved Tip Effect on the Performance of 3-D Cavitating Hydrofoils Moving under Free Surface

Curved tip effect on the performance of three-dimensional (3-D) cavitating hydrofoils moving steadily under a free water surface has been investigated numerically by an iterative boundary element method (IBEM) developed before. The IBEM has been modified and extended to solve this problem. The fluid is assumed to be inviscid, incompressible and the flow irrotational. All variables and equations are made non-dimensional to achieve a very quick and consistent numerical scheme. The IBEM is based on the Green’s theorem. The hydrofoil problem and the free surface problem are solved separately with the effects of each other via their potential values in an iterative manner. Both the 3-D hydrofoil surface and the free surface are modelled with constant strength source and constant strength doublet panels. The kinematic boundary condition is applied on the hydrofoil surface while the linearized kinematic and dynamic combined condition is applied on the free water surface. The method was validated extensively before for cavitating hydrofoils but not when combined with tip curvature. It is first applied to a tapered wing and the results are compared with those of experiments. Later, it is applied to a tapered hydrofoil with curved tip upwards or downwards. The effects of curved tip shape on cavitating hydrofoil performance have been investigated. It is found that the curved tip caused an increase in loading and cavitation volume in unbounded flow domain. It is also obtained that curved tip caused a decrease in loading on the hydrofoil for lower chord-based Froude numbers than 0.8.