Experiments and computations are presented for a foil pitching about its leading edge near a planar, solid boundary. The foil is examined when it is constrained in space and when it is unconstrained or freely swimming in the cross-stream direction. It was found that the foil has stable equilibrium altitudes: the time-averaged lift is zero at certain altitudes and acts to return the foil to these equilibria. These stable equilibrium altitudes exist for both constrained and freely swimming foils and are independent of the initial conditions of the foil. In all cases, the equilibrium altitudes move farther from the ground when the Strouhal number is increased or the reduced frequency is decreased. Potential flow simulations predict the equilibrium altitudes to within 3 %–11 %, indicating that the equilibrium altitudes are primarily due to inviscid mechanisms. In fact, it is determined that stable equilibrium altitudes arise from an interplay among three time-averaged forces: a negative jet deflection circulatory force, a positive quasistatic circulatory force and a negative added mass force. At equilibrium, the foil exhibits a deflected wake and experiences a thrust enhancement of 4 %–17 % with no penalty in efficiency as compared to a pitching foil far from the ground. These newfound lateral stability characteristics suggest that unsteady ground effect may play a role in the control strategies of near-boundary fish and fish-inspired robots.
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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, 𝝈𝝈𝒀𝒀, 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
- NSF-PAR ID:
- 10473221
- Publisher / Repository:
- American Institute of Aeronautics and Astronautics
- Date Published:
- 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
