Hydrodynamic wake resonance as an underlying principle of efficient unsteady propulsion

Abstract

A linear spatial stability analysis is performed on the velocity profiles measured in the wake of an actively flexible robotic elliptical fin to find the frequency of maximum spatial growth, that is, the hydrodynamic resonant frequency of the time-averaged jet. It is found that: (i) optima in propulsive efficiency occur when the driving frequency of a flapping fin matches the resonant frequency of the jet profile; (ii) there can be multiple wake resonant frequencies and modes corresponding to multiple peaks in efficiency; and (iii) some wake structures transition from one pattern to another when the wake instability mode transitions. A theoretical framework, termed wake resonance theory, is developed and utilized to explain the mechanics and energetics of unsteady self-propulsion. Experimental data are used to validate the theory. The analysis, although one-dimensional, captures the performance exhibited by a three-dimensional propulsor, showing the robustness and broad applicability of the technique.

Hydrodynamic Performance of Aquatic Flapping: Efficiency of Underwater Flight in the Manta

“…Experiments with rigid pitching and heaving airfoils, which mimic the unsteady propulsion generated by fish tail and wing motion, have demonstrated that optimal conditions exist for thrust production when the oscillation of the foils coincides with the maximum amplification of disturbances in the wake [21]. This result has been further demonstrated for three-dimensional ray-like fins [56] and two-dimensional flexible pitching panels [57].…”

Analytical insights into optimality and resonance in fish swimming

“…Because this peak is purely owing to fluid effects, we call it a hydrodynamic resonance. However, its relation to the socalled wake resonance [12] is not obvious, because the latter is unrelated to muscle bending moment.…”

Coupling Motion and Energy Harvesting of Two Side-by-Side Flexible Plates in a 3D Uniform Flow

“…Regarding the applications, the underlying hydrodynamic principles also inspire researchers to develop advanced equipment involving the interactions of unsteady flows and deformable bodies. Recently, the robotic models of fish swimming have been of great interest in ocean engineering, and a wide diversity of approaches have been taken for the mechanical design of fish-inspired systems [9][10][11], such as a carangiform fish robot [12,13] and a batoid-inspired robot [14][15][16]. Besides the active flow control mechanisms used in bionic propulsion, passive flapping or vibrating dynamics have also been applied in developing renewable energy harvesters, which are usually based on compliant materials, such as elastic-mounted cylinders and piezoelectric membranes [17][18][19].…”