A numerical study on the effect of aspect-ratio and density ratio on the dynamics of freely falling plate in the flutter
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Sådhanå (2020)45:259 https://doi.org/10.1007/s12046-020-01487-y
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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 A RANA, V K KUSHWAHA and ARNAB KUMAR DE* Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Assam 781039, India e-mail: [email protected] MS received 19 March 2020; revised 28 May 2020; accepted 23 July 2020 Abstract. 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 ðI Þ becomes chaotic 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. Keywords.
Flutter; tumble; chaotic regime; Froude number; turning moment; initial condition.
1. Introduction Objects like thin paper cards, plates, and leaves do not fall straight to the ground. Instead, they follow complex trajectories owing to the coupling between their motion and surrounding fluid. The forces which act on objects such as drag, lift, buoyancy and weight need to be accounted for to study their trajectories. The equations of motion of the freely falling objects under their own weight depend mainly on the solid-to-fluid density ratio ðqs =qf Þ and thickness-towidth ratio ðbÞ. The object undergoes different types of motions such as stable fall (straight downward), flutter (oscillating from one side to another), tumble (end-overend rotation) or combination of any of these depending upon the above-mentioned ratios. Moreover, it is a classic example of two-way coupling between fluid and solid, which requires an understanding of aerodynamic forces
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