Linearized potential theory of flapping foils in tandem configuration*

A vortical impulse theory is used to compute the lift, thrust and moment of two-dimensional flapping foils in tandem configuration within the framework of unsteady linear potential theory. First, general expressions are derived for any set of oscillating foils of arbitrary chord lengths, taking into account the effect of their unsteady wakes and the interaction of any set of moving point vortices. Then, analytical explicit solutions for the lift, thrust and moment are obtained for the specific case of two oscillating airfoils in tandem configuration. In the limit of large separation distance, we recover the expressions of a single oscillating foil for the forewing, but the hindwing is always affected by the unsteady wake of the forewing. These potential results are compared with available experimental and numerical data, with good agreement for small amplitude of the oscillations and sufficiently high Reynolds numbers.