Swimming performance, resonance and shape evolution in heaving flexible panels

Abstract

Many animals that swim or fly use their body to accelerate the fluid around them, transferring momentum from their flexible bodies and appendages to the surrounding fluid. The kinematics that emerge from this transfer result from the coupling between the fluid and the active and passive material properties of the flexible body or appendages. To elucidate the fundamental features of the elastohydrodynamics of flexible appendages, recent physical experiments have quantified the propulsive performance of flexible panels that are actuated on their leading edge. Here we present a complementary computational study of a three-dimensional flexible panel that is heaved sinusoidally at its leading edge in an incompressible, viscous fluid. These high-fidelity numerical simulations enable us to examine how propulsive performance depends on mechanical resonance, fluid forces, and the emergent panel deformations. Moreover, the computational model does not require the tethering of the panel. We therefore compare the thrust production of tethered panels to the forward swimming speed of the same panels that can move forward freely. Varying both the passive material properties and the heaving frequency of the panel, we find that local peaks in trailing edge amplitude and forward swimming speed coincide and that they are determined by a non-dimensional quantity, the effective flexibility, that arises naturally in the Euler–Bernoulli beam equation. Modal decompositions of panel deflections reveal that the amplitude of each mode is related to the effective flexibility. Panels of different material properties that are actuated so that their effective flexibilities are closely matched have modal contributions that evolve similarly over the phase of the heaving cycle, leading to similar vortex structures in their wakes and comparable thrust forces and swimming speeds. Moreover, local peaks in the swimming speed and trailing edge amplitude correspond to peaks in the contributions of the different modes. This computational study of freely swimming flexible panels gives further insight into the role of resonance in swimming performance that is important in the engineering and design of robotic propulsors. Moreover, we view this reduced model and its comparison to laboratory experiments as a building block and validation for a more comprehensive three-dimensional computational model of an undulatory swimmer that will couple neural activation, muscle mechanics and body elasticity with the surrounding viscous, incompressible fluid.

Effect of actuation method on hydrodynamics of elastic plates oscillating at resonance

“…Fluid viscosity affects the forced resonance frequency, although for low fluid damping the resonance frequency overlays with the natural (undamped) frequency. Note that Quinn et al (2014) and Hoover et al (2018) have shown for elastic plates that the maxima of the thrust and tip deflection occur for the same effective flexibility. Thus, the values of D * corresponding to the maximum thrust match the forced resonance frequency.…”

“…(2014) and Hoover et al. (2018) have shown for elastic plates that the maxima of the thrust and tip deflection occur for the same effective flexibility. Thus, the values of corresponding to the maximum thrust match the forced resonance frequency.…”

“…Furthermore, elasticity can be used to optimize fin performance (Hoover et al. 2018). Comparison of cruising speed of elastic plates with different shapes revealed that the contracting fin shape facilities a faster swimming in comparison to fins with the diverging shape (Engels et al.…”

“…Such studies showed that resonance oscillations of elastic fins promote propulsion speed and thrust generation (Yeh & Alexeev 2014;Paraz, Schouveiler & Eloy 2016;Yeh & Alexeev 2016b). Furthermore, elasticity can be used to optimize fin performance (Hoover et al 2018). Comparison of cruising speed of elastic plates with different shapes revealed that the contracting fin shape facilities a faster swimming in comparison to fins with the diverging shape (Engels et al 2017).…”

Effect of trailing-edge shape on the self-propulsive performance of heaving flexible plates

“…Quinn, Lauder & Smits (2014 experimentally investigated the combined impact of St and resonance to improve the propulsive Effect of trailing-edge shape on self-propulsive performance 887 A7-3 performance of a flapping plate. Besides, theoretical works (Alben 2008;Michelin & Llewellyn Smith 2009;Paraz, Schouveiler & Eloy 2016), experiments (Heathcote & Gursul 2007;Heathcote, Wang & Gursul 2008) and numerical simulations (Michelin & Llewellyn Smith 2009;Eldredge, Toomey & Medina 2010;Ferreira de Sousa & Allen 2011;Kang et al 2011;Zhu, He & Zhang 2014;Hoover et al 2018) have been performed to investigate the effect of flexibility on the dynamic performance of plates. In addition, the effect of trailing-edge shape on the self-propulsive speed of flapping flexible plates was investigated experimentally by Lauder et al (2011).…”