Fig 1.
Physical model and coordinate systems.
(a) Top view and (b) perspective view.
Fig 2.
Details of the area around the first two links are given by a closer look.
Fig 3.
The midlines of the flexible, undulating body during one period.
Since the front part of the swimmer makes no undulation, only the rear is shown. The red line shows the motion trajectory of the tail peduncle end.
Fig 4.
The prerscribed motion of the thunniform swimmer in one cycle.
(a) t/T = 1/8, (b) 1/4, (c) 3/8, (d) 1/2, (e) 5/8, (f) 3/4, (g) 7/8 and (h) 1.0.
Fig 5.
Zone 1 contains front body and Zone 2 contains rear body and caudal fin. Zone 3 denotes the large peripheral area that contains no fish.
Fig 6.
Mesh distribution for one swimming cycle.
(a) t/T = 1/4, (b) 1/2, (c) 3/4, (d) 1.0.
Fig 7.
Grid and time-step sensitivity study for thunniform fish.
Change on the crusing velocity with Ap for (a) three different grids and (b) three different time-step sizes.
Fig 8.
Validation of the numerical method.
(a) Comparison of computed cruising velocity with established experimental results for different motion frequencies. (b) Falling speed of the sphere reaching an asymptotic value of 1.005.
Fig 9.
Temporal variation of forward velocity Vf, transverse velocity uTY and yawing angular velocity ΩZ.
The cruising velocity Vs at the fully developed state is denoted by the horizontal dashed line. The balance positions of transverse velocity uTY and yawing angular velocity ΩZ are represented by the horizontal solid lines.
Fig 10.
Time history of total longitudinal force Fl.
Fig 11.
Fluid forces (moments) of front body, rear body and caudal fin during cruising in one specific cruising period.
(a) Longitudinal force, (b) transverse force and (c) yawing moment.
Fig 12.
Pressure contours on the fish body and selected sectional planes at four instants during one specific cycle at the cruising stage.
The color scheme for pressure contours is such that red colors denote the highest pressure and blue the lowest pressure.
Fig 13.
Vorticity contours for different swimming stages.
(a) Starting stage, (b) accelerating stage and (c) cruising stage.
Fig 14.
Pressure distribution of the tail with mid-depth-plane vorticity field during accelerating stage.
(a) t = 5.5s and (b) t = 6.0s.
Fig 15.
Variation in (a) forward velocity and (b) longitudinal force with time for various Ap.
For all these cases, θm = 25° and f = 1.0Hz.
Fig 16.
Temporal variation of (a) transverse force and (b) yawing moment for various Ap.
For all these cases, θm = 25° and f = 1.0Hz.
Table 1.
Power requirement for various tail undulating amplitudes.
Fig 17.
Variation in output power and efficiency of caudal fin and the whole-fish efficiency with Ap.
For all these cases, θm = 25° and f = 1.0Hz.
Fig 18.
Vorticity field at four discrete phases during one period for various Ap.
For all these cases, θm = 25° and f = 1.0Hz. (a) Ap = 0.4C and (b) Ap = 0.6C.
Fig 19.
Mid-depth-plane vorticity contours with pressure distribution of the tail for various Ap.
For all these cases, θm = 25° and f = 1.0Hz. (a) Ap = 0.4C and (b) Ap = 0.6C.
Fig 20.
Iso-surface of the square of velocity in the transverse direction for different Ap.
For all these cases, θm = 25° and f = 1.0Hz. The blue region means |uTY| = 0.05 m/s; the green region means |uTY| = 0.1 m/s and the fish is drawn in red. (a) Ap = 0.4C and (b) Ap = 0.6C.
Fig 21.
Time history of (a) forward velocity and (b) longitudinal force for different oscillating amplitudes of the caudal fin.
For all these cases, Ap/C = 0.6 and f = 1.0Hz.
Fig 22.
Variation in (a) transverse force and (b) yawing moment with time for various oscillating amplitudes of the caudal fin.
For all these cases, Ap/C = 0.6 and f = 1.0Hz.
Table 2.
Power requirement for different θm.
Fig 23.
Variation in output power and efficiency of caudal fin and the whole-fish efficiency with θm.
For all these cases, Ap/C = 0.6 and f = 1.0Hz.
Fig 24.
Vorticity contours at four instants in one period for different oscillating amplitudes of the caudal fin.
For all these cases, Ap/C = 0.6 and f = 1.0Hz. (a) θm = 15° and (b) θm = 35°.
Fig 25.
Iso-surface of the square of the transverse velocity for different θm.
For all these cases, Ap/C = 0.6 and f = 1.0Hz. The blue region means |uTY| = 0.1 m/s; the green region means |uTY| = 0.2 m/s and the fish is drawn in red. (a) θm = 15° and (b) θm = 35°.
Fig 26.
Fish postures with pressure distribution of the tail and mid-depth-plane vorticity field for various θm.
For all these cases, Ap/C = 0.6 and f = 1.0Hz. (a) θm = 15° and (b) θm = 35°.