A Surface Panel Method for Design of Hydrofoils

Abstract

A surface panel method treating a boundary-value problem of the Dirichlet type is presented to design a hydrofoil corresponding to a prescribed pressure distribution. An integral equation is derived from Green's theorem, giving a relation between the total potential of known strength and the unknown local flux. Upon discretization, a system of linear simultaneous equations is formed and solved for an assumed geometry. The pseudo local flux, present due to the incorrect positioning of the assumed geometry, plays a role of the geometry corrector, with which the new geometry is computed for the next iteration. Sample designs for a series of pressure distributions of interest are performed to demonstrate the fast convergence, effectiveness and robustness of the procedure. The method is shown equally applicable to designing two- and three-dimensional hydrofoil geometry.