On the forced flow around a flapping foil

The two dimensional incompressible viscous flow past a flapping foil immersed in a uniform stream is studied numerically. Numerical simulations were performed using a Lattice-Boltzmann model for moderate Reynolds numbers. The computation of the hydrodynamic force on the foil is related to the the wake structure. In particular, when the foil's centre of mass is fixed in space, numerical results suggest a relation between drag coefficient behaviour and the flapping frequency which determines the transition from the von K\'arm\'an (vKm) to the inverted von K\'arm\'an wake. Beyond the inverted vKm transition the foil was released. Upstream swimming was observed at high enough flapping frequencies. Computed hydrodynamic forces suggest the propulsion mechanism for the swimming foil.