Hydrodynamic performance of pitching foils with two leading-edge protuberances

Abstract

Inspired by the tubercles on humpback whales, the ‘tubercle-effect’ first identified by (Fish and Battle, 1995; Fish and Lauder, 2006) had been studied extensively to understand their influence on overall efficiency for airfoils and wings. Pitching and/or heaving motion of foils produces net thrust inspired from fin-based locomotion of aquatic animals, and is often being proposed as a greener means of propulsion having reduced acoustic signature. With this aim in mind, the present work investigates the effect of using tubercles on pitching motion of foils. The hydrodynamic characteristics of finite aspect ratio pitching foils having leading-edge modifications in the form of two protuberances are investigated using experiments. The thrust and efficiency with and without protuberances are investigated for pure pitching motions at reduced frequencies (1.8 – 3.2) and pitching amplitudes (7.5°- 20°) for Reynolds number 2 × 104. The experimental results are compared with inviscid linear theory calculations which over-predict the mean thrust, while the amplitude of the lift force and its variation with reduced frequency is similar. The performance improvements in terms of thrust and efficiency for the modified design are restricted to ≥15° pitching amplitudes at higher reduced frequencies. The wake vorticity patterns obtained using Computational Fluid Dynamics investigations show the influence of the leading-edge vortex, which gets modified when the protuberances are used. The transition from 2S wake to 2P wake with the increase in the amplitude of oscillation is captured. The reversal of von Kármán Vortex Street with the pitching frequency and thus the transition from drag to thrust generation is observed for both the baseline and modified foil designs. The results indicate that protuberances over the leading-edge of hydrofoils can influence the hydrodynamics during pitching motion and can be effectively employed for performance tailoring based on the geometry and motion characteristics. The simplified setup used here is also meant to serve as a basis towards future research including verification and validation work for numerical solvers.