On the drag–thrust transition of a pitching foil

Abstract

The drag–thrust transition of a symmetric foil undergoing pitching oscillation in a uniform flow is numerically studied in the present work. Under a certain thickness-based Reynolds number ReD=255, the fluid dynamics around the oscillated foil at a series of values for the chord-based Reynolds number, Rec, are investigated. The various values of Rec are obtained by keeping the maximum thickness of the foil fixed while rhythmically changing the chord length of the foil. Depending on the numerical results, we uncover a scaling relation that links the amplitude-based Strouhal number SrA to the Rec at the drag–thrust transition boundary, which is briefly expressed as SrA∼Rec−1. Through analysing the velocity field of the foil, it is found that the drag–thrust transition of the pitching foil is closely associated with the critical velocity of the latest vortex produced by the foil. These findings helps in understanding the kinematic behaviour of aquatic animals and designing bio-inspired underwater robots.