Abstract
The boundary element method is widely used in solving potential flow problems. This paper uses Taylor expansion boundary element method (TEBEM) to analyze hydrodynamic characteristics of hydrofoils under the free surface, which mainly applies the Taylor expansion to the dipole strength of the boundary integral equation (BIE), and then keeps the first-order derivatives, finally takes the two tangential derivatives with respect to the field points on the boundary to form the closed equations. Combine the equations then solve the potential and its tangential derivatives. The method is applied to three dimensional hydrofoil of the asymmetric NACA4412 profile moving beneath the free surface with constant speed. The free surface condition is linearized in terms of the Double-Body method. Upstream waves are prevented by the use of a one-sided, upstream, finite difference operator for the free surface condition. After solving the doublets on the foil and sources on the free surface, the numerical results of pressure, lift and resistance coefficients and also wave profiles can then be evaluated for different Froude numbers and depths of submergence to demonstrate the influence of free surface and aspect ratio effects on performance of the hydrofoil. Compared to traditional constant panel method (CPM) method, the TEBEM method can extremely improve the accuracy of the tangential derivatives on the non-smooth body surface.