An Efficient Swimming Machine

Triantafyllou, Michael S.; Triantafyllou, George S.

doi:10.1038/scientificamerican0395-64

Cited by 809 publications

(403 citation statements)

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“…This Strouhal number is also near the range in which aquatic animals are known to swim (Triantafyllou et al 1991(Triantafyllou et al , 1993, forming a reverse Kármán pattern in the symmetry plane (Triantafyllou & Triantafyllou 1995). The significant change in performance between the low-and moderate-Reynoldsnumber cases is attributed to the relative magnitude of surface pressures from which thrust is generated, to viscous shear stresses which primarily produce drag (note that separated flows may produce small shear stresses that make a positive contribution to the thrust).…”

Section: Sensitivity Of Wake Structure To Reynolds Numbermentioning

confidence: 87%

The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel

2008

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Thrust performance and wake structure were investigated for a rigid rectangular panel pitching about its leading edge in a free stream. For Re C = O(10 4 ), thrust coefficient was found to depend primarily on Strouhal number St and the aspect ratio of the panel AR. Propulsive efficiency was sensitive to aspect ratio only for AR less than 0.83; however, the magnitude of the peak efficiency of a given panel with variation in Strouhal number varied inversely with the amplitude to span ratio A/S, while the Strouhal number of optimum efficiency increased with increasing A/S. Peak efficiencies between 9 % and 21 % were measured. Wake structures corresponding to a subset of the thrust measurements were investigated using dye visualization and digital particle image velocimetry. In general, the wakes divided into two oblique jets; however, when operating at or near peak efficiency, the near wake in many cases represented a Kármán vortex street with the signs of the vortices reversed. The three-dimensional structure of the wakes was investigated in detail for AR = 0.54, A/S = 0.31 and Re C = 640. Three distinct wake structures were observed with variation in Strouhal number. For approximately 0.20 < St < 0.25, the main constituent of the wake was a horseshoe vortex shed by the tips and trailing edge of the panel. Streamwise variation in the circulation of the streamwise horseshoe legs was consistent with a spanwise shear layer bridging them. For St > 0.25, a reorganization of some of the spanwise vorticity yielded a bifurcating wake formed by trains of vortex rings connected to the tips of the horseshoes. For St > 0.5, an additional structure formed from a perturbation of the streamwise leg which caused a spanwise expansion. The wake model paradigm established here is robust with variation in Reynolds number and is consistent with structures observed for a wide variety of unsteady flows. Movies are available with the online version of the paper.

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Section: Sensitivity Of Wake Structure To Reynolds Numbermentioning

confidence: 87%

The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel

2008

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“…Because of this and the fact that the oscillation frequency was matched to that of the swimming shark, there was no variation possible in Strouhal number. Flexible foil shark tails nonetheless swam at Strouhal numbers in the range observed for swimming fishes [30,31]. The wakes of both the robotic flapping foil and the sharks consisted of linked vortex rings, and in both cases the vortex ring structure induced a substantial downwash at an angle of 2328 to 2508 to the horizontal, indicating that considerable lift forces were generated by both propulsive surfaces (figure 1 and shark tail-like foil (figure 1) with the inclined trailing edge produced one large ring (mean vorticity of 11.6-12.5 s 21 ; table 2) with a much weaker inner vortex ring (mean vorticity of 1.8 s 21 ; table 2).…”

Section: Resultsmentioning

confidence: 99%

Volumetric imaging of shark tail hydrodynamics reveals a three-dimensional dual-ring vortex wake structure

et al. 2011

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Understanding how moving organisms generate locomotor forces is fundamental to the analysis of aerodynamic and hydrodynamic flow patterns that are generated during body and appendage oscillation. In the past, this has been accomplished using two-dimensional planar techniques that require reconstruction of three-dimensional flow patterns. We have applied a new, fully three-dimensional, volumetric imaging technique that allows instantaneous capture of wake flow patterns, to a classic problem in functional vertebrate biology: the function of the asymmetrical (heterocercal) tail of swimming sharks to capture the vorticity field within the volume swept by the tail. These data were used to test a previous three-dimensional reconstruction of the shark vortex wake estimated from two-dimensional flow analyses, and show that the volumetric approach reveals a different vortex wake not previously reconstructed from two-dimensional slices. The hydrodynamic wake consists of one set of dual-linked vortex rings produced per half tail beat. In addition, we use a simple passive shark-tail model under robotic control to show that the three-dimensional wake flows of the robotic tail differ from the active tail motion of a live shark, suggesting that active control of kinematics and tail stiffness plays a substantial role in the production of wake vortical patterns.

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“…At typical swimming speeds (2.5 m/sec and above) of dolphins, such as Tursiops truncatus (Williams et al, 1999;Fish and Rohr, 1999;Rohr et al, 2002), the maximum angle of attack is close to or below the 17 degrees stall angle for the NACA 63-021 foil (Fish, 1993). Indeed, angles of attack up to 30 degrees may be sustained by oscillating hydrofoils similar to dolphin flukes without stalling (Triantafyllou and Triantafyllou, 1995;Anderson et al, 1998). An oscillating foil can function at high angles of attack because of unsteady effects that enhance the pressure difference between the two sides of the foil and result in greater lift production.…”

Section: Discussionmentioning

confidence: 99%

“…Interest in the development of biorobots and nonpropeller propulsive systems has focused on an examination of animal systems and locomotor performance (Triantafyllou and Triantafyllou, 1995;Taubes, 2000;Fish, 2006;Fish and Lauder, 2006). The paucity of detailed three-dimensional data on control surfaces has meant that engineers based predictive models and robotic designs on flat plates or standard foils.…”

Section: Discussionmentioning

confidence: 99%

Examination of the three‐dimensional geometry of cetacean flukes using computed tomography scans: Hydrodynamic implications

Fish

Beneski

Ketten

2007

The Anatomical Record

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The flukes of cetaceans function in the hydrodynamic generation of forces for thrust, stability, and maneuverability. The three-dimensional geometry of flukes is associated with production of lift and drag. Data on fluke geometry were collected from 19 cetacean specimens representing eight odontocete genera (Delphinus, Globicephala, Grampus, Kogia, Lagenorhynchus, Phocoena, Stenella, Tursiops). Flukes were imaged as 1 mm thickness cross-sections using X-ray computer-assisted tomography. Fluke shapes were characterized quantitatively by dimensions of the chord, maximum thickness, and position of maximum thickness from the leading edge. Sections were symmetrical about the chordline and had a rounded leading edge and highly tapered trailing edge. The thickness ratio (maximum thickness/chord) among species increased from insertion on the tailstock to a maximum at 20% of span and then decreasing steadily to the tip. Thickness ratio ranged from 0.139 to 0.232. These low values indicate reduced drag while moving at high speed. The position of maximum thickness from the leading edge remained constant over the fluke span at an average for all species of 0.285 chord. The displacement of the maximum thickness reduces the tendency of the flow to separate from the fluke surface, potentially affecting stall patterns. Similarly, the relatively large leading edge radius allows greater lift generation and delays stall. Computational analysis of fluke profiles at 50% of span showed that flukes were generally comparable or better for lift generation than engineered foils. Tursiops had the highest lift coefficients, which were superior to engineered foils by 12-19%. Variation in the structure of cetacean flukes reflects different hydrodynamic characteristics that could influence swimming performance. Anat Rec, 290:614-623, 2007Rec, 290:614-623, . 2007 Wiley-Liss, Inc.

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An Efficient Swimming Machine

Cited by 809 publications

References 0 publications

The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel

The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel

Volumetric imaging of shark tail hydrodynamics reveals a three-dimensional dual-ring vortex wake structure

Examination of the three‐dimensional geometry of cetacean flukes using computed tomography scans: Hydrodynamic implications

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