On the Interfoil Spacing and Phase Lag of Tandem Flapping Foil Propulsors

Abstract

The aim of this article is to provide a theoretical basis upon which to advance and deploy novel tandem flapping foil systems for efficient marine propulsion. We put forth three key insights into tandem flapping foil hydrodynamics related to their choreography, propulsive efficiency, and unsteady loading. In particular, we propose that the performance of the aft foil depends on a new nondimensional number, s/U τ , which is the inter-foil separation s normalized by the distance that the freestream U advects in one flapping period τ. Additionally, we show how unsteady loading can be mitigated through choice of phase lag. Research with isolated flapping foils has demonstrated up to 87% propulsive efficiency [Anderson et al, 1998], nearly achieving the ideal efficiency of an actuator disk. However, single-foil propulsion is not practical due to shortcomings such as large oscillations in thrust, large unsteady side forces, and no mechanical redundancy. Many other non-traditional propulsors also suffer these flaws or are simply inefficient. Biomimetic concept designs and trade-offs have recently been reviewed by Fish [2013]. One promising non-traditional propulsor concept involves in-line tandem flapping foils (two hydrofoils, one aft of the other). Recent research indicates that the high efficiency of a single flapping foil may be possible with a tandem foil arrangement [Akhtar et al, 2007; Boschitsch et al, 2014]. Tandem flapping foils may also solve the operational problems associated with a single foil,