An official website of the United States government
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.
more »
« less
Revealing the mechanism and scaling laws behind equilibrium altitudes of near-ground pitching hydrofoils
A classic lift decomposition is conducted on potential flow simulations of a near-ground pitching hydrofoil. It is discovered that previously observed stable and unstable equilibrium altitudes are generated by a balance between positive wake-induced lift and negative quasi-steady lift while the added mass lift does not play a role. Using both simulations and experiments, detailed analyses of each lift component's near-ground behaviour provide further physical insights. When applied to three-dimensional pitching hydrofoils the lift decomposition reveals that the disappearance of equilibrium altitudes for AR < 1.5 occurs due to the magnitude of the quasi-steady lift outweighing the magnitude of the wake-induced lift at all ground distances. Scaling laws for the quasi-steady lift, wake-induced lift and the stable equilibrium altitude are discovered. A simple scaling law for the lift of a steady foil in ground effect is derived. This scaling shows that both circulation enhancement and the velocity induced at a foil's leading edge by the bound vortex of its ground image foil are the essential physics to understand steady ground effect. The scaling laws for unsteady pitching foils can predict the equilibrium altitude to within 20% of its value when St < 0.45. For St > 0.45, there is a wake instability effect, not accounted for in the scaling relations, that significantly alters the wake-induced lift. These results not only provide key physical insights and scaling laws for steady and unsteady ground effects, but also for two schooling hydrofoils in a side-by-side formation with an out-of-phase synchronization.
more »
« less
- Award ID(s):
- 2040351
- PAR ID:
- 10559516
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 978
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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
-
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
-
We present experiments on oscillating hydrofoils undergoing combined heaving and pitching motions, paying particular attention to connections between propulsive efficiency and coherent wake features extracted using modal analysis. Time-averaged forces and particle image velocimetry measurements of the flow field downstream of the foil are presented for a Reynolds number of Re=11000 and Strouhal numbers in the range St=0.16--0.35. These conditions produce 2S and 2P wake patterns, as well as a near-momentumless wake structure. A triple decomposition using the optimized dynamic mode decomposition method is employed to identify dominant modal components (or coherent structures) in the wake. These structures can be connected to wake instabilities predicted using spatial stability analyses. Examining the modal components of the wake provides insightful explanations into the transition from drag to thrust production, and conditions that lead to peak propulsive efficiency. In particular, we find modes that correspond to the primary vortex development in the wakes. Other modal components capture elements of bluff body shedding at Strouhal numbers below the optimum for peak propulsive efficiency and characteristics of separation for Strouhal numbers higher than the optimum.more » « less
-
We present experiments on oscillating hydrofoils undergoing combined heaving and pitching motions, paying particular attention to connections between propulsive efficiency and coherent wake features extracted using modal analysis. Time-averaged forces and particle image velocimetry measurements of the flow field downstream of the foil are presented for a Reynolds number of Re=11000 and Strouhal numbers in the range St=0.16–0.35 . These conditions produce 2S and 2P wake patterns, as well as a near-momentumless wake structure. A triple decomposition using the optimized dynamic mode decomposition method is employed to identify dominant modal components (or coherent structures) in the wake. These structures can be connected to wake instabilities predicted using spatial stability analyses. Examining the modal components of the wake provides insightful explanations into the transition from drag to thrust production, and conditions that lead to peak propulsive efficiency. In particular, we find modes that correspond to the primary vortex development in the wakes. Other modal components capture elements of bluff body shedding at Strouhal numbers below the optimum for peak propulsive efficiency and characteristics of separation for Strouhal numbers higher than the optimum.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2023.1004
