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First published online June 13, 2008
Journal of Experimental Biology 211, 2087-2100 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.016279

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Propulsion performance of a skeleton-strengthened fin

Qiang Zhu^* and Kourosh Shoele

Department of Structural Engineering, University of California, San Diego, La Jolla, CA 92093, USA

View larger version (22K): [in this window] [in a new window]   Fig. 1. (A) Schematic showing a typical ray-strengthened caudal fin [modified from Alben et al. (Alben et al., 2007)]. We note that the rays are segmented and are tapered and branched near the trailing edge. (B) The dorsal view of the internal structure of a ray [courtesy of S. Alben and the Royal Society (Alben et al., 2007)]. (C) A geometrically and structurally simplified fin employed in the present modeling study. See List of symbols and abbreviations for definitions.

View larger version (15K): [in this window] [in a new window]   Fig. 2. Deformation of the fin in the homocercal mode within period. The arrow illustrates the direction of sway. The forward motion is subtracted. St=0.2, 0=10°. t, time; T, period.

View larger version (5K): [in this window] [in a new window]   Fig. 3. The y-displacements (normalized by c) of the trailing ends of Ray 1 and Ray 5 during a period in the homocercal mode. St0.2, 0=10°. t, time; T, period.

View larger version (25K): [in this window] [in a new window]   Fig. 4. Distribution of the pressure coefficient Cp=p/U2 on (A) the left side and (B) the right side of the surface of a flexible fin in the homocercal mode at t=T/8. St=0.2, 0=10°. t, time; T, period.

View larger version (14K): [in this window] [in a new window]   Fig. 5. The thrust coefficient of (A) a rigid fin and (B) a flexible fin as a function of the Strouhal number, St, and the yaw amplitude, 0, in the homocercal mode.

View larger version (17K): [in this window] [in a new window]   Fig. 6. The propulsion efficiency of (A) a rigid fin and (B) a flexible fin as a function of the Strouhal number, St, and the yaw amplitude, 0, in the homocercal mode.

View larger version (9K): [in this window] [in a new window]   Fig. 7. The transverse force coefficient of (A) a rigid fin and (B) a flexible fin as a function of the Strouhal number, St, and the yaw amplitude, 0, in the homocercal mode.

View larger version (11K): [in this window] [in a new window]   Fig. 8. (A) The thrust coefficient, (B) the transverse force coefficient and (C) the propulsion efficiency of rigid and flexible fins in the homocercal mode at St=0.3.

View larger version (12K): [in this window] [in a new window]   Fig. 9. Deformation of the fin in the heterocercal mode within period. The arrow demonstrates the direction of sway. The forward motion is subtracted. St=0.2, 0=35°. t, time; T, period.

View larger version (5K): [in this window] [in a new window]   Fig. 10. The y-displacements (normalized by c) of the trailing ends of Ray 1, Ray 5, and Ray 9 during a period in the heterocercal mode. St=0.2, 0=35°. t, time; T, period.

View larger version (28K): [in this window] [in a new window]   Fig. 11. (A) Thrust coefficient, (B) propulsion efficiency, (C) transverse force coefficient and (D) lifting coefficient of a flexible fin in the heterocercal mode. St, Strouhal number; 0, yaw amplitude.

View larger version (38K): [in this window] [in a new window]   Fig. 12. Inplane streamlines on z=0 (plane a) and z=0.3c (plane b) around (A) a rigid fin and (B) a flexible fin in the homocercal mode. St=0.3, 0=0°. The streamlines are plotted in a reference system moving with the forward and the sway motions. The locations of plane a and plane b are illustrated in the inset.

View larger version (41K): [in this window] [in a new window]   Fig. 13. Iso-surfaces of vorticity in the wakes behind (A) a rigid fin in the homocercal mode, (B) a flexible fin in the homocercal mode and (C) a flexible fin in the heterocercal mode. The iso-surfaces are plotted at the level of 0.9 (after normalization by U/c). St=0.3. For the homocercal mode, 0=10°; for the heterocercal mode, 0=35°. U, forward speed; c, chord length of the foil.

View larger version (90K): [in this window] [in a new window]   Fig. 14. Flow field within the y=0 plane behind a flexible fin in (A) the homocercal mode and (B) the heterocercal mode. xl is the x-location of the leading edge. The contour displays the y-component of the vorticity (normalized by U/c). St=0.3. For the homocercal mode, 0=10°; for the heterocercal mode, 0=35°.

View larger version (22K): [in this window] [in a new window]   Fig. B1. Distribution of boundary elements on the fin surface and the wake.

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