Propulsive performance and vortex wakes of multiple tandem foils pitching in-line

Abstract

Numerical studies are presented on the propulsive performance and vortex dynamics of multiple hydrofoils pitching in an in-line configuration. The study is motivated by the quest to understand the hydrodynamics of multiple fin–fin interactions in fish swimming. Using the flow conditions (Strouhal and Reynolds numbers) obtained from a solitary pitching foil of zero net thrust, the effect of phase differences between neighboring foils on the hydrodynamic performance is examined both in position-fixed two- and three-foil systems at Reynolds number Re=500. It is found that the three-foil system achieves a thrust enhancement up to 118% and an efficiency enhancement up to 115% compared to the two-foil system. Correspondingly, the leading-edge vortex (LEV) and the trailing-edge vortex (TEV) of the hindmost foil combine to form a ‘2P’ wake structure behind the three-foil system with the optimal phase differences instead of a ‘2S’ wake, a coherent wake pattern observed behind the optimal two-foil system. The finding suggests that a position-fixed three-foil system can generate a ‘2P’ wake to achieve the maximum thrust production and propulsive efficiency simultaneously by deliberately choosing the undulatory phase for each foil. When increasing Reynolds number to 1000, though the maximum thrust and propulsive efficiency are not achieved simultaneously, the most efficient case still produces more thrust than most of the other cases. Besides, the study on the effects of three-dimensionality shows that when the foils have a larger aspect ratio, the three-foil system has a better hydrodynamic performance, and it follows a similar trend as the two-dimensional (2D) foil system. This work aids in the future design of high-performance underwater vehicles with multiple controlled propulsion elements.