Numerical and experimental investigation of natural flow-induced vibrations of flexible hydrofoils

The objective of this work is to present combined numerical and experimental studies of natural flow-induced vibrations of flexible hydrofoils. The focus is on identifying the dependence of the foil’s vibration frequencies and damping characteristics on the inflow velocity, angle of attack, and solid-to-fluid added mass ratio. Experimental results are shown for a cantilevered polyacetate (POM) hydrofoil tested in the cavitation tunnel at the French Naval Academy Research Institute (IRENav). The foil is observed to primarily behave as a chordwise rigid body and undergoes spanwise bending and twisting deformations, and the flow is observed to be effectively two-dimensional (2D) because of the strong lift retention at the free tip caused by a small gap with a thickness less than the wall boundary layer. Hence, the viscous fluid-structure interaction (FSI) model is formulated by coupling a 2D unsteady Reynolds-averaged Navier-Stokes (URANS) model with a two degree-of-freedom (2-DOF) model representing the spanwise tip bending and twisting deformations. Good agreements were observed between viscous FSI predictions and experimental measurements of natural flow-induced vibrations in fully turbulent and attached flow conditions. The foil vibrations were found to be dominated by the natural frequencies in absence of large scale vortex shedding due to flow separation. The natural frequencies and fluid damping coefficients were found to vary with velocity, angle of attack, and solid-to-fluid added mass ratio. In addition, the numerical results showed that the in-water to in-air natural frequency ratios decreased rapidly, and the fluid damping coefficients increased rapidly, as the solid-to-fluid added mass ratio decreases. Uncoupled mode (UM) linear potential theory was found to significantly over-predict the fluid damping for cases of lightweight flexible hydrofoils, and this over-prediction increased with higher velocity and lower solid-to-fluid added mass ratio.