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A NACA0012 airfoil undergoing pitching and plunging motion at Re = 20,000-40,000 was simulated using a two-dimensional Navier-Stokes flow solver. Results were compared with experimental measurements in the literature and those from an inviscid analytical method and an unsteady panel method code. Although the peak in propulsive efficiency with Strouhal number demonstrated in the experimental results was predicted by the inviscid methods, it was found to be significantly modified by leading-edge vortex shedding and viscous drag at low Strouhal numbers. The occurrence and influence of vortex shedding is controlled by both the motion of the airfoil (amplitudes and phases of plunging and pitching) and the flapping frequency, which limits the time available for vortex formation and convection over the airfoil surface. Thus, Strouhal number alone is insufficient to characterize the efficiency of flapping-foil propulsion.
Young et al. (Tue,) studied this question.