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REVIEW ARTICLES

Review of Hydrodynamic Scaling Laws in Aquatic Locomotion and Fishlike Swimming

[+] Author and Article Information
M. S. Triantafyllou

Department of Ocean Engineering,  Massachusetts Institute of Technology, Cambridge, MA 02139

F. S. Hover

Department of Ocean Engineering,  Massachusetts Institute of Technology, Cambridge, MA 02139

A. H. Techet

Department of Ocean Engineering,  Massachusetts Institute of Technology, Cambridge, MA 02139

D. K. Yue

Department of Ocean Engineering,  Massachusetts Institute of Technology, Cambridge, MA 02139

Appl. Mech. Rev. 58(4), 226-237 (Jul 01, 2005) (12 pages) doi:10.1115/1.1943433 History:

We consider observations and data from live fish and cetaceans, as well as data from engineered flapping foils and fishlike robots, and compare them against fluid mechanics based scaling laws. These laws have been derived on theoretical/numerical/experimental grounds to optimize the power needed for propulsion, or the energy needed for turning and fast starting. The rhythmic, oscillatory motion of fish requires an “impedance matching” between the dynamics of the actively controlled musculature and the fluid loads, to arrive at an optimal motion of the fish’s body. Hence, the degree to which data from live fish, optimized robots, and experimental apparatus are in accordance with, or deviate from these flow-based laws, allows one to assess limitations on performance due to control and sensing choices, and material and structural limitations. This review focuses primarily on numerical and experimental studies of steadily flapping foils for propulsion; three-dimensional effects in flapping foils; multiple foils and foils interacting with bodies; maneuvering and fast-starting foils; the interaction of foils with oncoming, externally-generated vorticity; the influence of Reynolds number on foil performance; scaling effects of flexing stiffness of foils; and scaling laws in fishlike swimming. This review article cites 117 references.

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Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Motion definitions: Surge—rowing motion along the x-axis, heave—linear up-and-down motion about the z-axis, and roll—motion causing equivalent heave motion at any specific spanwise location about the x-axis, pitch—motion about the y-axis

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Figure 2

Angle-of-attack definition for a two-dimensional foil traveling at constant forward speed U and oscillating in a heave-and-pitch motion

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Figure 3

Wake patterns as functions of the Strouhal number and maximum angle of attack for ho∕c=1. Points mark the experiments conducted by Anderson (28).

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Figure 4

Mean lift and mean thrust coefficient of a three-dimensional pitching and rolling foil, for bias angle from −10to30deg. Equivalent heave is defined at 0.75 of the radius; the curve marked Static provides the data for a steadily towed foil at an angle of attack (88).

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Figure 5

Kinematics of fast-starting two-dimensional foil in heave and pitch motion (29)

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Figure 6

Heave and pitch velocity (upper figure) and resulting thrust and lift forces (lower figure), as functions of time for the kinematics shown in Fig. 6(29)

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Figure 7

Thrust coefficient as function of Strouhal number for 15deg angle of attack and h∕c=0.75. Triangles denote experimental data, solid line linear inviscid theory, circles nonlinear inviscid theory (28)

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Figure 8

Power coefficient as function of Strouhal number for 15deg angle of attack and h∕c=0.75. For symbols, see Fig. 7.

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Figure 9

Thrust coefficient (left) and propulsive efficiency (right) as functions of the maximum angle of attack for several foils of varying flexibility, classified according to Shore toughness: X30 is most flexible, A10 to A70 denotes increasing stiffness. Solid line is for rigid foil, while vertical bars express experimental accuracy (104).

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Figure 10

Turbulence intensity in the axial direction (upper) and the transverse direction (lower graph) as functions of the phase velocity cp for a two-dimensional flexible plate undergoing harmonic wave oscillation with a linearly tapered amplitude from leading to trailing edge (114).

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