Abstract
Herein, the dynamics and flow fields of an inverted flag are studied using hydrogen bubble flow visualization and particle image velocimetry technologies at different height-to-length ratios and flow velocities in a water tunnel. Results show that the height-to-length ratio of the inverted flag at which the critical flow velocity remains nearly constant is approximately 1.4. Moreover, a nonperiodic flapping phenomenon is observed under various height-to-length ratios. This phenomenon may be attributed to the existence of multiple equilibrium solutions to the self-excited vibration system, thus engendering chaos in the system comprising an inverted flag and surrounding fluid. Other indications that the system has entered chaos include multiple frequencies, non-overlapping phase diagram, and positive Lyapunov exponent. Further discussion of the flow fields around the inverted flag reveals that the large-amplitude oscillation is due to the flow separation, while the flapping instability is a static divergence instability. In the large flapping mode, the starting leading-edge vortex (LEV) is wrapped by Kelvin-Helmholtz instabilities, which are arranged at almost uniform spacing along a circular path. In addition, the variation in position, circulation, and radius of the starting LEV are discussed in detail.
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