Experimental Simulation of Fish-Inspired Unsteady Vortex Dynamics on a Rigid Cylinder

Abstract

The unsteady hydrodynamics of the tail flapping and head oscillation of a fish, and their phased interaction, are considered in a laboratory simulation. Two experiments are described where the motion of a pair of rigid flapping foils in the tail and the swaying of the forebody are simulated on a rigid cylinder. Two modes of tail flapping are considered: waving and clapping. Waving is similar to the motion of the caudal fin of a fish. The clapping motion of wings is a common mechanism for the production of lift and thrust in the insect world, particularly in butterflies and moths. Measurements carried out include dynamic forces and moments on the entire cylinder-control surface model, phase-matched laser Doppler velocimetry maps of vorticity-velocity vectors in the axial and cross-stream planes of the near-wake, as well as dye flow visualization. The mechanism of flapping foil propulsion and maneuvering is much richer than reported before. They can be classified as natural or forced. This work is of the latter type where discrete vortices are forced to form at the trailing edge of flapping foils via salient edge separation. The transverse wake vortices that are shed, follow a path that is wider than that given by the tangents to the flapping foils. The unsteady flap-tip axial vortex decays rapidly. Significant higher order effects appear when Strouhal number (St) of tail flapping foils is above 0.15. Efficiency, defined as the ratio of output power of the flapping foils to the power input to the actuators, reaches a peak below the St range of 0.25–0.35. Understanding of two-dimensional flapping foils and fish reaching their peak efficiency in that range is clarified. Strouhal number of tail flapping does emerge as an important parameter governing the production of net axial force and efficiency, although it is by no means the only one. The importance of another Strouhal number based on body length and its natural frequency is also indicated. The relationship between body length and tail flapping frequency is shown to be present in dolphin swimming data. The implication is that, for aquatic animals, the longitudinal structural modes of the body and the head/tail vortex shedding process are coupled. The phase variation of a simulated and minute head swaying, can modulate axial thrust produced by the tail motion, within a narrow range of ±5 percent. The general conclusion is that, the mechanism of discrete and deterministic vortex shedding from oscillating control surfaces has the property of large amplitude unsteady forcing and an exquisite phase dependence, which makes it inherently amenable to active control for precision maneuvering. [S0098-2202(00)00102-4]