Effects of Reynolds number and thickness on an undulatory self-propelled foil

The effects of the Reynolds number (Re) and thickness on an undulatory self-propelled foil were numerically investigated using the immersed boundary method. Re varied from 50 to 2 × 10⁵, which encompasses the viscous, intermediate, and inertial regimes using a NACA 0012 airfoil. An investigation of the thickness was performed on NACA airfoils with maximum thicknesses of 0.04 ∼ 0.24 at two Re values (5 × 10⁴ and 500). The results indicated that the foil can achieve a higher forward velocity, perform less work, and exhibit a higher propulsive efficiency with increasing Re. However, the effect of Re is asymptotic beyond 5 × 10⁴. Four types of vortex structures exist, and the transition from one regime to another is closely related to hydrodynamic changes. In the thickness study, thinner foils outperformed thicker foils in terms of the forward velocity and input power at both Re values. However, the efficiency related to the conversion of input power into kinetic energy for NACA 0004 was the lowest. An optimum thickness exists that depends on Re. At higher Re, the vortical structure differs for each thickness with the deflection angle, whereas at low Re, the location of the separation point strongly influences the hydrodynamics.