Turning strategies for plunging elastic plate propulsor

We use three-dimensional computer simulations to examine turning strategies for a biomimetic oscillating elastic rectangular plate propulsor submerged in a viscous fluid. The elastic plate is actuated near the first natural frequency at the leading edge. Two kinematic actuation patterns are probed to produce both pitching and yaw moments: (1) periodic plunging with asymmetric velocities on the upstroke and downstroke and (2) combined sinusoidal plunging and twisting motion. Both strategies lead to net lateral forces and turning moments. For the first case, we find that the magnitudes of the force and turning moment increase with the degree of asymmetry in the stroke. For the second case, our simulations reveal a range of optimal phase angles and twisting amplitudes that lead to the maximum yaw moment.

Figure 1

Schematics of (a) asymmetric plunging actuation and (b) combined plunging and rotation as turning strategies for a biomimetic flexible plate swimmer. The black outline indicates the zero-displacement plate position. (c) Plots of the leading edge displacement for different values of velocity ratio $v_1/v_2$ as asymmetric plunging strategy.

Figure 2

(a) Lift force and (b) thrust force generated by asymmetric plunging swimmer as a function of the velocity ratio.

Figure 3

(a) Maximum trailing edge displacement and (b) difference between root-mean-square trailing edge upstroke and downstroke velocity as a function of the velocity ratio.

Figure 4

Turning moment on asymmetric plunging swimmer as a function of the velocity ratio.

Figure 5

(a) Thrust and (b) pitching moment efficiency on asymmetric plunging swimmer as a function of the velocity ratio.

Figure 6

(a) Displacement time history with (b) bending profile at times A, B, and C, corresponding to times $t/\tau =0$, 0.16, and 0.5, respectively. The asymmetry in the bending pattern is mainly caused by the quick movement from A to B.

Figure 7

Surface of constant vorticity magnitude ($\omega =20$ normalized by leading edge frequency) plotted for $\chi =1.0$, (a) ${\mathcal{A}}_{\mathcal{R}}=2.5$ and (b) ${\mathcal{A}}_{\mathcal{R}}=1.0$ at time $t/\tau =0.16$, which corresponds to point B of Fig. 6 (top view).

Figure 8

(a) Propulsive and (b) lateral forces for combined plunging and rotating swimmer. Propulsive forces decrease with increasing ${\alpha }_0$, which is related to the smaller projected areas for increasing ${\alpha }_0$. Lateral force is maximized in a range of phase values $\psi =-\pi /12$ and $\psi =5\pi /12$.

Figure 9

Turning moment for a combined plunging and rotating swimmer. The moment follows similar trends to lateral force.

Figure 10

(a) Propulsive and (b) lateral forces for combined plunging and rotating swimmer for ${\alpha }_0=\pi /4$ and several fluid-solid and aspect ratios.

Figure 11

Turning moment for combined plunging and rotating swimmer for ${\alpha }_0=\pi /4$ and several fluid-solid and aspect ratios.

Figure 12

(a) Schematic showing rotating ${\left(xyz\right)}^{\prime }$ axes relative to the fixed $\left(xyz\right)$ axes. (b) Perspective of swimmer in ${\left(xyz\right)}^{\prime }$ axes. (c) Absolute and relative deflections of the trailing edge corner points. The relative deflection of the corner points nearly coincide, showing that the swimmer has negligible twist motion.

Figure 13

Time histories of relative trailing edge velocity for a plunging plate with no rotation showing the time of maximum vertical force production relative to the maximum trailing edge velocity.

Figure 14

Time histories for multiple quantities for ${\alpha }_0=\pi /4$ and $\psi =\pi /6$. Large lateral force and turning moment are produced because the time of maximum force production based on the relative trailing edge velocity is tuned to the maximum of $\alpha$.

Figure 15

Time histories for multiple quantities for ${\alpha }_0=\pi /4$ and $\psi =7\pi /12$. Little lateral force and moment production is due to the time of maximum force production occurring when $\alpha \approx 0$, so force is directed vertically, not laterally.

Figure 16

(a) Propulsive and (b) lateral forces efficiency for combined plunging and rotating swimmer for ${\alpha }_0=\pi /4$ and several fluid-solid and aspect ratios.

Figure 17

Turning moment efficiency for combined plunging and rotating swimmer for ${\alpha }_0=\pi /4$ and several fluid-solid and aspect ratios.