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    • A numerical study on the effect of aspect-ratio and density ratio on the dynamics of freely falling plate in the flutter-to-tumble transition regime


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      The motion of a freely falling thin aluminium plate in water is studied using two-dimensional numerical simulations. The fluid-solid interface is treated using the diffuse interface immersed boundary method. Periodic side-to-side fluttering motion at the small dimensionless moment of inertia (I*) becomeschaotic in the intermediate range which finally settles for pure tumbling at high I*). Even the stable flutter trajectories exhibit significant sensitivity to incremental deviation in fluid forces brought in by inaccurate time marching. The maximum instantaneous inclination angle of the plate increases with I*) during flutter with the uniform multilevel distribution. At larger I*) , such distribution collapses to nearly a single level indicating the ability of the plate to autorotate under the influence of turning moment created by the neighbouring fluid. The plate is observed to retain the initial orientation during its flight in the tumbling regime. The range of I*) for chaotic motion is found to extend with the increase in initial inclination angle. Tests on the effect of initial conditions on the trajectories of the plate indicate while the chaotic regime is mostly affected by initial orientation and velocity of release, flutter and tumble motions converge for a variety of initial states. The chaotic motion transforms into a flutter or tumbles depending on the solid-to-fluid density ratio for a fixed geometry of the plate. However, with a fixed solid-to-fluid density ratio, aspect-ratio of the plate does not alter the stable trajectories appreciably.

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