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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 finโfin 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 threefoil 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 โ2Pโ wake structure behind the three-foil system with the optimal phase differences instead of a โ2Sโ 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 โ2Pโ 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.
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Lateral stability and wake analysis of tri-foil system pitching in-line
In recent years, there has been a growing interest in using tandem foils to mimic and study fish swimming, and to inform underwater vehicle design. Though much effort has been put to understanding the propulsion mechanisms of a tandem-foil system, the stability of such a system and the mechanisms for maintaining it remain an open question. In this study, a 3-foil system in an in-line configuration is used towards understanding the hydrodynamics of lateral stability. The foils actively pitch with varying phase. To quantify lateral force oscillation, the standard deviation of the lateral force, ๐๐๐๐, calculated over one typical flapping cycle is used, to account for the amount of variation in the lateral force experienced by the system of 3 foils. The higher the standard deviation, the more the spread in the lateral force cycle data, the more lateral momentum exchanged between the flow and the foils, and the less stable the system is. Through phase variations, it is found that the lateral force is minimized when the phases of the three foils are approximately, though not exactly, evenly distributed. The least stable system is found to be the one with the foils all in phase. Systems that are more laterally stable are found to tend to have narrower envelopes of regions around the foils with high momentum. Near-wake of the foils, the envelopes of stable systems are also found to have pronounced convergent sections, whereas the envelope of the less stable systems are found to diverge without much interruption. In the far wake, coherent, singular thrust jets, along with orderly 2-S vortices are found to form in the two best performing cases. In less stable cases, the thrust jets are found to be branched. Corresponding to the width of the high-momentum envelopes, lateral jets are found to exist in the gaps between neighboring foils, the strengths of which vary based on stability, with the lateral jets being more pronounced in the less stable cases (cases with high amount of lateral force oscillation). Peak lateral forces are found to coincide with moments of pressure gradient build-up across the foils. The pressure-driven flow near the trailing edge of the foils then creates trailing-edge vortices, and correspondingly, lateral gap flows. Moments of peak and plateau lateral force on an individual foil in the system are found to coincide with the initiation and shedding of trailing-edge vortices, respectively. The formation of trailing-edge vortices, lateral jets and cross-stream flows in gaps are closely intertwined, and all are 1. Indicative of large lateral momentum oscillation, and 2. The results of pressure gradient build-up across foils.
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- Award ID(s):
- 1931929
- PAR ID:
- 10473221
- Publisher / Repository:
- American Institute of Aeronautics and Astronautics
- Date Published:
- ISBN:
- 978-1-62410-699-6
- Format(s):
- Medium: X
- Location:
- National Harbor, MD & Online
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.2514/6.2023-1973
