Boundary Element Method Analysis of 3D Effects and Free-Surface Proximity on Hydrofoil Lift and Drag Coefficients in Varied Operating Conditions

Abstract

The use of hydrofoils to enhance ship performance raises the scientific issue of free-surface proximity, which is important to consider during the design stage, to feed velocity prediction programs, for instance. Typically, the flow over a shallowly submerged hydrofoil is characterized by the Froude number, the submergence depth-to-chord ratio, the angle of attack, and geometric parameters of the lifting surface. Among these parameters, the present paper investigates the influence of the wing aspect ratio on the lift and drag coefficients of hydrofoils operating near a free surface. For this purpose, rectangular wings with an H105 profile at 2° angle of attack and aspect ratios ranging from 4 to 20 are systematically analyzed using a 3D boundary element method. The free surface is modeled using a linearized Neumann-Kelvin boundary condition. Chord-based Froude numbers of 0.5, 1.1, and 6.3 are studied. The submersion depth is swept between 0.1 and 30 times the foil chord length. The evolution of the normalized lift and drag coefficients with respect to the foil submersion and the aspect ratio is discussed in detail. Flow velocity is shown to play a significant role in the evolution of the lift and drag coefficients with submersion depth, close to the free surface, for all the aspect ratios. Its influence gets reduced by moving away from the free surface. The critical submersion depth, where the free-surface effects cease, is found to increase with higher flow velocity and aspect ratio. Furthermore, both positive and negative correlations between the force coefficients and the aspect ratio are identified, depending on the operating conditions. It is found that when the proximity to the free surface either enhances or impairs a force coefficient relative to its value in unbounded flow, increasing the aspect ratio amplifies this effect. Overall, this study confirms the effectiveness of steady boundary element methods for simulating the flow around hydrofoil wings in the vicinity of a free surface and contributes to further understanding the influence of geometric parameters on hydrofoil performance.