The correlation between wake transition and propulsive efficiency of a flapping foil: A numerical study

We study numerically the propulsive wakes produced by a flapping foil. Both pure pitching and pure heaving motions are considered, respectively, at a fixed Reynolds number of Re = 1700. As the major innovation of this paper, we find an interesting coincidence that the efficiency maximum agrees well with the 2D-3D transition boundary, by plotting the contours of propulsive efficiency in the frequency-amplitude parametric space and comparing to the transition boundaries. Although there is a lack of direct 3D simulations, it is reasonable to conjecture that the propulsive efficiency increases with Strouhal number until the wake transits from a 2D state to a 3D state. By comparing between the pure pitching motion and the pure heaving motion, we find that the 2D-3D transition occurs earlier for the pure heaving foil than that of the pure pitching foil. Consequently, the efficiency for the pure heaving foil peaks more closely to the wake deflection boundary than that of the pure pitching foil. Furthermore, since we have drawn the maps on the same parametric space with the same Reynolds number, it is possible to make a direct comparison in the propulsive efficiency between a pure pitching foil and a pure heaving foil. We note that the maximum efficiency for a pure pitching foil is 15.6%, and that of a pure heaving foil is 17%, indicating that the pure heaving foil has a slightly better propulsive performance than that of the pure pitching foil for the currently studied Reynolds number. Published by AIP Publishing.