On the drag–thrust transition of a pitching foil

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 Re_D=255, the fluid dynamics around the oscillated foil at a series of values for the chord-based Reynolds number, Re_c, are investigated. The various values of Re_c 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 Sr_A to the Re_c at the drag–thrust transition boundary, which is briefly expressed as Sr_A∼Re_c⁻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.