Influence of Tip Clearance on the Hydrodynamic Damping Characteristics of a Hydrofoil

Tip clearance in hydraulic machines may complicate the fluid–structure interaction (FSI) effects. In this investigation, a mode-based approach (modal work) is evaluated and employed to quantitatively predict the added mass, added stiffness, and hydrodynamic damping ratio, in relation to the first-order bending mode of a vibrating hydrofoil. The investigated relative tip clearance ranges from 0.067% to 2% of the span length. The predicted vortex shedding frequency, natural frequency, and hydrodynamic damping ratio of the hydrofoil are in good agreement with the previously published experimental results, with relative deviations within 9.92%, 6.97%, and 11.23%, respectively. Simulation results show that the added mass, added stiffness, and hydrodynamic damping ratio increase inversely as the tip clearance increases. In particular, as the relative tip clearance increases from 0.067% to 2%, the added mass in still water, the added stiffness, and hydrodynamic damping ratio at a velocity of 10 m/s decrease by 18.66%, 9.36%, and 27.99%, respectively. As the tip clearance increases, the inversely increased pressure difference between the upper and lower surfaces of the vibrating hydrofoil is the main reason for the inversely increased hydrodynamic damping ratio. This is due to the energy leakages via the tip clearance region increase as the tip clearance increases, which may cause less fluid force to resist the vibration of the hydrofoil, resulting in less negative modal work done by the fluid load on the hydrofoil.