Unsteady aerodynamics of a general tandem of heaving and pitching foils from linear potential theory.

Abstract

We derive general expressions for the aerodynamic force and moment on an arbitrary set of pitching and heaving foils from the vortical impulse theory in the limit of linearized potential, two-dimensional flow. Of special interest for studying the propulsion of some aquatic and aerial animals and small unmanned vehicles is the case of two oscillating foils in an aligned tandem configuration, for which analytical explicit expressions for the lift, thrust and moment are obtained. 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 in the present inviscid model. Relatively simple expressions are obtained in the cases of two heaving foils and of two pitching foils, for which the optimal conditions generating a maximum thrust force and a maximum propulsion efficiency are mapped in terms of the non- dimensional separation distance, reduced frequency and phase shift, and discussed physically in relation to the optimal results for a single oscillating foil. The present theoretical results are compared with available experimental and numerical data, with good agreement for small amplitude of the oscillations and sufficiently high Reynolds numbers.