Numerical Prediction of Skin Friction Coefficient by Coupling a Bem with X-Foil: Effect on the Hydrofoil and Propeller Performance

Abstract

A boundary element method (BEM) has been commonly used in a hydrofoil or propeller performance analysis. The effect of viscosity is often considered by applying a constant empirical friction coefficient over the blade, which does not fully consider the development of the boundary layer. In this paper, a three-dimensional (3D) low-order BEM is coupled with an originally two-dimensional boundary layer solver, X-foil, to evaluate the effect of viscosity on the blade surface and predict the open water characteristics of the 3D hydrofoil and propeller. During the process, the boundary layer equations are solved at each section, where the 2D influence coefficients in X-foil have been replaced by the 3D influence coefficients, corresponding to the panels at each strip, with the effect of the boundary layer sources from the other sections and the other blades being considered, in an iterative sense. Then, the viscous/inviscid interactive method is employed to calculate the skin friction coefficient, which significantly improves the prediction of friction and pressure distribution on the blade, and the efficiency of the propeller. Subsequently, full-blown Reynolds Averaged Navier-Stokes (RANS) simulations are conducted to validate the predicted results under various conditions. The results demonstrate that the skin friction coefficient correlates well with RANS results. This model was shown to be robust and efficient for predicting viscous effects while requiring less computational effort than an arduous 3D meshwork in RANS.