Propulsive performance and vortex shedding of a foil in flapping flight

The propulsive performance and vortex shedding of an oscillating foil, which mimics biological locomotion, are investigated based on a computational fluid dynamics analysis. The objectives of this study are to investigate unsteady forces, in particular a thrust force, for the foil in pitching and plunging motion, and to deal with the relations of the propulsive performance with leading-edge vortex structure and vortex shedding in the near wake. The two-dimensional incompressible Navier-Stokes equations in the vorticity and stream-function formulation are solved by fourth-order essentially compact finite difference schemes for the space derivatives and a fourth-order Runge-Kutta scheme for the time advancement. To reveal the mechanism of the propulsive performance, the unsteady forces and the shedding of the leading- and trailing-edge vortices of the foil in the pitching and plunging motion are analyzed. Based on our calculated results, three types of the leading-edge vortex shedding, which have an effective influence on the vortex structures in the wake of the oscillating foil, are identified. The effects of some typical factors, such as the frequency and amplitude of the oscillation, the phase difference between the pitching and plunging motions, and the thickness ratio of the foil, on the vortex shedding and the unsteady forces are discussed.