A Panel Method for the Potential Flow Around 2-D Hydrofoils

Authors: ŞAKİR BAL

Abstract: A potential-based panel method for the hydrodynamic analysis of 2-D hydrofoils moving under a free surface with constant speed without consideration of the cavitation phenomenon is described. By applying Green's theorem and choosing the value of internal potential as equal to the incoming flow potential, an integral equation for the total potential is obtained under the potential flow theory. The free surface condition is linearized and the Dirichlet boundary condition is used instead of the Neumann boundary condition. The 2-D hydrofoil is approximated by line panels on which there are only constant doublet distributions. The method of images is used for satisfying the linearized free surface condition and all the terms in the fundamental solution of total potential are integrated over a line panel. Pressure distribution, lift, wave resistance and free surface deformations are calculated for NACA4412, van de Vooren hydrofoils and a thin hydrofoil. Values obtained are higher than those in the literature, not only for the pressure distributions but also for the lift and wave resistance coefficients and wave elevations. The effect of free surface is examined by a parametric variation of the Froude number and depth of submergence.

Keywords: Potential Flow, 2D Hydrofoils, Free Surface

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