Three dimensional wakes of freely falling planar polygons

Abstract

The wake characteristics of various thin particles with identical material properties but different frontal geometries (disks, hexagonal plates and square plates) are examined by means of three dimensional measurements of the instantaneous velocity field. The reference particle is a circular disk that lies within the Reynolds number—dimensionless moment of inertia domain (Re- I^∗) corresponding to the fluttering regime, as defined by Willmarth et al. (Phys Fluids 7:197–208, 1964). Hexagonal and square plates are manufactured to have the same frontal area and material properties of the reference particle. Three dimensional trajectories obtained from high-speed imaging show that disks preferably adopt a quasi-2D oscillatory descent; i.e. ‘planar zig-zag’, whereas particles with less circularity adopt three dimensional trajectories more frequently; i.e. ‘transitional’ and ‘spiral’ descent. The wake behind free-falling disks is found to be a succession of hairpin vortices shed off at every turning point linked by a pair of counter rotating vortices that grow downstream from the leading edge of the disk. In contrast, square plates describing ‘spiral’ descent show an almost time-independent wake morphology with large-scale vortex shedding around the entire perimeter of the particle. The large-scale wake structures of hexagonal plates resemble either the disks’ or the squares’ depending on the falling regime that they adopt. Finally, we compare the dimensionless vorticity distribution in the wake of the particles and found that this also depends on the falling style that the particle adopts during the descent.

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