Role of the near-tip region of a fin in fish propulsion

Fish combine a wide variety of passive and active control mechanisms to generate thrust. Muscle actuation is used by fish in order to dynamically alter the shape or the stiffness of different parts of the body, to ultimately control propulsion. We uncover the effects of locally altering the tip region of a flapping fin system, by using a low-order robotic model. We show how the actuation of this region can largely modify propulsion. Detailed forces and torque measurements and a low-order eigenmode reconstruction of the flow around the flapping fin show the effects of varying the phase difference between the tip region and the body of the fin on the propulsive performance. Kinematics that force the trailing edge to move behind the main body of the fin are beneficial in terms of efficiency and thrust generation. For a very small range of phase differences, large thrusts can be combined with large side forces that could be used by fish to increase maneuverability.

Figure 1

Lateral schematic of the robotic fin used for the experiments.

Figure 2

Lateral schematic view of the experimental setup. The robotic fin appears hanging from a six-axis load cell installed in an air-bearing system. A uniaxial load cell is used to have redundant measurements of the thrust forces generated by the system.

Figure 3

Schematic of the robotic fin including the definition of the main kinematic variables.

Figure 4

Schematic of the kinematics of the robotic fin flapping in four phase difference configurations: (a) for $\varphi =-{180}^{\circ }$ (out of phase), (b) for $\varphi =-{90}^{\circ }$, (c) for $\varphi =0^{\circ }$ (in phase), and (d) for $\varphi ={90}^{\circ }$

Figure 5

Mean thrust coefficient ($C_T$), standard deviation of the side force ($C_S$), main shaft torque ($C_M$), mean power coefficient ($C_P$), efficiency ($\eta$), and ratio of thrust to side force ($\zeta$) as a function of the phase difference imposed between the main body of the fin and the tip. The dashed horizontal line in all plots is used to indicate the results obtained with the reference rigid case.

Figure 6

Time-averaged cycles for the thrust, side force, and power for the rigid case and for cases with phase differences of $-{180}^{\circ }$, $-{90}^{\circ }$, $0^{\circ }$, and ${90}^{\circ }$. Time is in dimensionless form $t^{*}=tf$.

Figure 7

Time evolution of the total force coefficient $\overrightarrow{C_F}$ for the cases presented in Fig. 6.

Figure 8

(a)–(c) Magnitude of the mean in line with the flow velocity field ($\overline{u}/\overline{V}$) for the rigid case and for two cases with $-{90}^{\circ }$ and ${90}^{\circ }$ phase differences. (d)–(f) First POD mode (${\psi }^1$) of the in-line velocity for the same cases.

Figure 9

POD modal kinetic energy (${\epsilon }_n$) spectra for all phase differences investigated. Inset: The kinetic energy in cumulative form.

Figure 10

Momentum flux coefficient $C_{f_x}$ as a function of $x$ in the region near the tip of the flapping system. Distributions of $\rho {\overline{u}}^2$ along the $y$ direction, at $x/D=0.75$ and $x/D=1.25$.