An official website of the United States government
The interaction between a pair of tandem in-line oscillating hydrofoils is presented. The hydrofoils undergo sinusoidal pitching about their leading edges with a fixed Strouhal number of [Formula: see text] and a Reynolds number of 10,000. The streamwise spacing, spanwise spacing, and phase offset between the hydrofoils are varied. Force measurements are employed to investigate changes in thrust, lift, spanwise force, power consumption, and propulsive efficiency. A method to mitigate confounding factors from connecting rod drag is employed using streamlined fairings. Near and far streamwise spacing regions are identified with a transition occurring near 0.875 chord lengths downstream. Decreasing streamwise spacing in the far region causes a rise in the maximum power consumption of the follower hydrofoil. Decreasing streamwise spacing in the near region results in an opposite trend, with a sharp drop in maximum average power consumption by the follower. An empirical model for power consumption of the follower is developed. Increased spanwise spacing is found to weaken the interaction between the hydrofoils, driving them toward their isolated performance. This phenomenon is related to the spanwise contraction of the wake shed by the leader and is a function of the overlap of the wake region impacting the follower.
more »
« less
Flow Interactions Between Low Aspect Ratio Hydrofoils in In-line and Staggered Arrangements
Many species of fish gather in dense collectives or schools where there are significant flow interactions from their shed wakes. Commonly, these swimmers shed a classic reverse von Kármán wake, however, schooling eels produce a bifurcated wake topology with two vortex rings shed per oscillation cycle. To examine the schooling interactions of a hydrofoil with a bifurcated wake topology, we present tomographic particle image velocimetry (tomo PIV) measurements of the flow interactions and direct force measurements of the performance of two low-aspect-ratio hydrofoils ( A R = 0.5 ) in an in-line and a staggered arrangement. Surprisingly, when the leader and follower are interacting in either arrangement there are only minor alterations to the flowfields beyond the superposition of the flowfields produced by the isolated leader and follower. Motivated by this finding, Garrick’s linear theory, a linear unsteady hydrofoil theory based on a potential flow assumption, was adapted to predict the lift and thrust performance of the follower. Here, the follower hydrofoil interacting with the leader’s wake is considered as the superposition of an isolated pitching foil with a time-varying cross-stream velocity derived from the wake flow measurements of the isolated leader. Linear theory predictions accurately capture the time-averaged lift force and some of the major peaks in thrust derived from the follower interacting with the leader’s wake in a staggered arrangement. The thrust peaks that are not predicted by linear theory are likely driven by spatial variations in the flowfield acting on the follower or nonlinear flow interactions; neither of which are accounted for in the simple theory. This suggests that unsteady potential flow theory that does account for spatial variations in the flowfield acting on a hydrofoil can provide a relatively simple framework to understand and model the flow interactions that occur in schooling fish. Additionally, schooling eels can derive thrust and efficiency increases of 63-80% in either a in-line or a staggered arrangement where the follower is between two branched momentum jets or with one momentum jet branch directly impinging on it, respectively.
more »
« less
- Award ID(s):
- 1653181
- PAR ID:
- 10189016
- Date Published:
- Journal Name:
- Biomimetics
- Volume:
- 5
- Issue:
- 2
- ISSN:
- 2313-7673
- Page Range / eLocation ID:
- 13
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)New experiments examine the interactions between a pair of three-dimensional (AR = 2) non-uniformly flexible pitching hydrofoils through force and efficiency measurements. It is discovered that the collective efficiency is improved when the follower foil has a nearly out-of-phase synchronization with the leader and is located directly downstream with an optimal streamwise spacing of X*=0.5. The collective efficiency is further improved when the follower operates with a nominal amplitude of motion that is 36% larger than the leader’s amplitude. A slight degradation in the collective efficiency was measured when the follower was slightly-staggered from the in-line arrangement where direct vortex impingement is expected. Operating at the optimal conditions, the measured collective efficiency and thrust are ηC=62% and CT,C=0.44, which are substantial improvements over the efficiency and thrust of ηC=29% and CT,C=0.16 of two fully-rigid foils in isolation. This demonstrates the promise of achieving high-efficiency with simple purely pitching mechanical systems and paves the way for the design of high-efficiency bio-inspired underwater vehicles.more » « less
-
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
-
We study the problem of online learning in a two-player decentralized cooperative Stackelberg game. In each round, the leader first takes an action, followed by the follower who takes their action after observing the leader’s move. The goal of the leader is to learn to minimize the cumulative regret based on the history of interactions. Differing from the traditional formulation of repeated Stackelberg games, we assume the follower is omniscient, with full knowledge of the true reward, and that they always best-respond to the leader’s actions. We analyze the sample complexity of regret minimization in this repeated Stackelberg game. We show that depending on the reward structure, the existence of the omniscient follower may change the sample complexity drastically, from constant to exponential, even for linear cooperative Stackelberg games.more » « less
-
Abstract The goal of this work is to present a method based on fluid–structure interactions to enforce a desired trajectory on a passive double pendulum. In our experiments, the passive double pendulum represents human thigh and shank segments, and the interaction between the fluid and the structure comes from a hydrofoil attached to the double pendulum and interacting with the vortices that are shed from a cylinder placed upstream. When a cylinder is placed in flow, vortices are shed in the wake of the cylinder. When the cylinder is forced to rotate periodically, the frequency of the vortices that are shed in its wake can be controlled by controlling the frequency of cylinder’s rotation. These vortices exert periodic forces on any structure placed in the wake of this cylinder. In our system, we place a double pendulum fitted with a hydrofoil at its distal end in the wake of a rotating cylinder. The vortices exert periodic forces on this hydrofoil which then forces the double pendulum to oscillate. We control the cylinder to rotate periodically, and measure the displacement of the double pendulum. By comparing the joint positions of the double pendulum with those of human hip, knee and ankle joint positions during walking, we show how the system is able to generate a human walking gait cycle on the double pendulum only using the interactions between the vortices and the hydrofoil.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/biomimetics5020013
