Free-Surface Effects on Two-Dimensional Hydrofoils by RANS-VOF Simulations

Abstract

Foiling yachts and crafts are both very sensitive to the flying height in terms of stability and performance, raising the scientific issue of the influence of the free-surface when the foil is at low submergence. This work presents numerical simulations of a 2D hydrofoil section NACA0012 at 5° angle of attack in the vicinity of the free-surface, for different values of the submergence depth, for a chord-based Froude number of 0.571 and a Reynolds number of 159,000. Unsteady-Reynolds Averaged Navier-Stokes (URANS) equations are solved with a mixture model to capture the free surface (Volume Of Fluid method), and using an automatic grid refinement. Verification of the numerical model and validation with data from the literature are presented. Deformation of the free surface and alteration of the hydrodynamic forces compared to the deep immersion case are observed for a submergence depth-to-chord ratio ℎ/𝑐 lower than 2. The foil drag increases up to more than three times the infinite-depth value at ℎ/𝑐≈0.5. The lift force slightly increases until ℎ/𝑐 around 1, and then decreases sharply. For ℎ/𝑐<0.5, the pressure field around the foil is totally modified and the lift is swapped to downward. The study highlights the importance of considering the effect of finite submergence to compute foils’ hydrodynamic forces, for example to be used in Velocity Prediction Programs (VPP) of foiling crafts.