Abstract
Tomographic particle image velocimetry was used to explore the evolution of three-dimensional flow structures of revolving low-aspect-ratio flat plates in combination with force measurements at a Reynolds number of 10,000. Two motion kinematics are compared that result in the same terminal condition (revolution with constant angular velocity and $$45^{\circ }$$ angle of attack) but differ in the motion during the buildup phase: pitching while revolving at a constant angular velocity; or surging with a constant acceleration at a fixed angle of attack. Comparison of force histories shows that the pitching wing generates considerably higher forces during the buildup phase which is also predicted by a quasi-steady model quite accurately. The difference in the buildup phases affects the force histories until six chords of travel after the end of buildup phase. In both cases, a vortex system that is comprised of a leading-edge vortex (LEV), a tip vortex and a trailing edge vortex is formed during the initial period of the motion. The LEV lifts off, forms an arch-shaped structure and bursts into substructures, which occur at slightly different phases of the motions, such that the revolving–surging wing flow evolution precedes that of the revolving–pitching wing. The delay is shown to be in accordance with the behavior of the spanwise flow which is affected by the interaction between the tip vortex and revolving dynamics. Further analysis shows that the enhanced force generation of the revolving–pitching wing during the pitch-up phase originates from: (1) increased magnitude and growth rate of the LEV circulation; (2) relatively favorable position and trajectory of the LEV and the starting vortex; and (3) generation of bound circulation during the pitching motion, whereas that of the revolving–surging wing is negligible in the acceleration phase.
Highlights
The flapping flight of insects and birds is a three-dimensional unsteady phenomenon, which combines pitch, plunge and sweeping motions of the wing, with threedimensional effects being further enhanced by low values of the wing aspect ratio
The revolving–pitching motion kinematics used in the experiments can be described as follows (Fig. 2a): The motion is initiated by a constant acceleration from rest to Vt = 0.2 m/s at an angle of attack (α) of 0◦ over t∗ = 2 (d∗ = 1 and the revolution angle φ = 25.8◦); this is followed by a period in which the wing pitches up to α = 45◦ over t∗ = 1 (d∗ = 1) at a constant pitch rate (α = 3.14 rad/s corresponding to a nondimensional pitching rate of k = αc/(2Vt) = 0.39); and the wing continues to revolve at a constant rate at α = 45◦
Note that for sake of comparison, the origin for the horizontal axis (d∗) has been defined such that the start of the pitch-up phase for the pitching wing and start of the acceleration phase for the surging wing match and that for both cases the terminal condition is reached at d∗ = 1
Summary
The flapping flight of insects and birds is a three-dimensional unsteady phenomenon, which combines pitch, plunge and sweeping motions of the wing, with threedimensional effects being further enhanced by low values of the wing aspect ratio. One of the earlier studies to investigate the effect of wing rotation on the generation of forces was reported by Dickinson (1994) He performed experiments on a two-dimensional wing model to investigate the effect of wing rotation during the stroke reversal and showed that formation of vortical structures in the rotation phase of the motion increases forces considerably. Hamdani and Sun (2000) studied the fast pitching motion of a two-dimensional airfoil in a constant free-stream by Navier–Stokes simulations They reported that large aerodynamic forces are generated during the rapid pitch-up which they associated with the formation and motion of new vorticity layers in addition to the previously existing thick vorticity layers. Loading on a rapidly pitching nominally two-dimensional flat plate
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