Propulsion performance of tandem flapping foils with chordwise prescribed deflection from linear potential theory.

Abstract

The effect of prescribed flexural deflection on the propulsive performance of tandem- arranged flapping foils is analyzed by using the vortex impulse formulation in the limit of two-dimensional, linear potential flow theory. Analytical expressions are given for a general configuration of tandem foils undergoing a quadratic flexural deflection coupled with heaving and pitching motions about arbitrary pitching and deflection axes, although quantitative results are focused to the cases pivoting about their leading edges. Flexural deflection may augment not only the thrust and the propulsive efficiency of the individual foils in relation to an otherwise identical rigid-foil configuration, it also modifies the wake behind the front foil, changing the wake interaction with the trailing foil and, consequently, modifying the tandem propulsive performance. The effect of the upstream wake on the thrust force of the trailing foil is analyzed by using the vorticity distributions obtained an- alytically. Patterns of propulsive performance enhancement in both the spacing-frequency and the spacing-phase shift planes are analyzed and discussed in relation to previous available experimental and numerical results. The present theoretical results provide some new insights for the design of small aerial or aquatic vehicles using biomimetic tandem propulsors.