Fluid Forces and Vortex Wakes of a Flapping Foil

We present a combined numerical (particle vortex method) and experimental (soap film tunnel) study of a symmetric foil with pitching oscillations in a two-dimensional free stream. We vary the frequency and amplitude of the oscillations and observe von K{\'a}rm{\'a}n wake, inverted von K{\'a}rm{\'a}n wake, and wakes in which two vortex pairs form per oscillation period. We find a close correspondence between the numerically determined vortex structures and the thickness variations that visualize the flow in the soap film.\footnote{Schnipper, Andersen, and Bohr, J. Fluid Mech. {\bf 633}, 411--423 (2009).} Numerically we obtain systematic maps with $25 \times 40$ simulations in the frequency and amplitude plane of both wake type and average forces and moments, and we discuss the drag-thrust transition in relation to the changes in wake structure. Finally, we investigate the time evolution of the fluid forces and its link to the vortex formation near the round leading edge and the vortex shedding at the sharp trailing edge.