Abstract When swimming near a solid planar boundary, bio-inspired propulsors can naturally equilibrate to certain distances from that boundary. How these equilibria are affected by asymmetric swimming kinematics is unknown. We present here a study of near-boundary pitching hydrofoils based on water channel experiments and potential flow simulations. We found that asymmetric pitch kinematics do affect near-boundary equilibria, resulting in the equilibria shifting either closer to or away from the planar boundary. The magnitude of the shift depends on whether the pitch kinematics have spatial asymmetry (e.g. a bias angle, θ 0 ) or temporal asymmetry (e.g. a stroke-speed ratio, τ ). Swimming at stable equilibrium requires less active control, while shifting the equilibrium closer to the boundary can result in higher thrust with no measurable change in propulsive efficiency. Our work reveals how asymmetric kinematics could be used to fine-tune a hydrofoil’s interaction with a nearby boundary, and it offers a starting point for understanding how fish and birds use asymmetries to swim near substrates, water surfaces, and sidewalls.
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Swimming freely near the ground leads to flow-mediated equilibrium altitudes
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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- NSF-PAR ID:
- 10112213
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 875
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract A transient two-dimensional acoustic boundary element solver is coupled to a potential flow boundary element solver via Powell's acoustic analogy to determine the acoustic emission of isolated hydrofoils performing biologically-inspired motions. The flow-acoustic boundary element framework is validated against experimental and asymptotic solutions for the noise produced by canonical vortex-body interactions. The numerical framework then characterizes the noise production of an oscillating foil, which is a simple representation of a fish caudal fin. A rigid NACA 0012 hydrofoil is subjected to combined heaving and pitching motions for Strouhal numbers ($0.03 < St < 1$) based on peak-to-peak amplitudes and chord-based reduced frequencies ($0.125 < f^* < 1$) that span the parameter space of many swimming fish species. A dipolar acoustic directivity is found for all motions, frequencies, and amplitudes considered, and the peak noise level increases with both the reduced frequency and the Strouhal number. A combined heaving and pitching motion produces less noise than either a purely pitching or purely heaving foil at a fixed reduced frequency and amplitude of motion. Correlations of the lift and power coefficients with the peak root-mean-square acoustic pressure levels are determined, which could be utilized to develop long-range, quiet swimmers.
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null (Ed.)Animals and bio-inspired robots can swim/fly faster near solid surfaces, with little to no loss in efficiency. How these benefits change with propulsor aspect ratio is unknown. Here we show that lowering the aspect ratio weakens unsteady ground effect, thrust enhancements become less noticeable, stable equilibrium altitudes shift lower and become weaker and wake asymmetries become less pronounced. Water-channel experiments and potential flow simulations reveal that these effects are consistent with known unsteady aerodynamic scalings. We also discovered a second equilibrium altitude even closer to the wall ( ${<}0.35$ chord lengths). This second equilibrium is unstable, particularly for high-aspect-ratio foils. Active control may therefore be required for high-aspect-ratio swimmers hoping to get the full benefit of near-ground swimming. The fact that aspect ratio alters near-ground propulsion suggests that it may be a key design parameter for animals and robots that swim/fly near a seafloor or surface of a lake.more » « less
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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 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 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 ‘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.more » « less
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null (Ed.)Scaling laws for the thrust production and power consumption of a purely pitching hydrofoil in ground effect are presented. For the first time, ground-effect scaling laws based on physical insights capture the propulsive performance over a wide range of biologically relevant Strouhal numbers, dimensionless amplitudes and dimensionless ground distances. This is achieved by advancing previous scaling laws (Moored & Quinn ( AIAA J. , 2018, pp. 1–15)) with physics-driven modifications to the added mass and circulatory forces to account for ground distance variations. The key physics introduced are the increase in the added mass of a foil near the ground and the reduction in the influence of a wake-vortex system due to the influence of its image system. The scaling laws are found to be in good agreement with new inviscid simulations and viscous experiments, and can be used to accelerate the design of bio-inspired hydrofoils that oscillate near a ground plane or two out-of-phase foils in a side-by-side arrangement.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2019.540
