Edge effects on the fluttering characteristics of freely falling planar particles

Abstract

The effect of particle edge geometry on the descent motion of free falling planar particles is examined through experiments. Various planar particles, such as disk and polygons, with identical frontal areas (A p ) and different number of edges (or perimeter) are used. All particles are designed such that their values of Galileo number (G) and dimensionless moment of inertia (I * ) correspond to the previously identified fluttering regime of particle motion. Several modes of secondary motion are observed for the same particle and conditions, and these are not equally probable. This probability depends on the particle shape. Disks and heptagons were found to prefer a 'planar zig-zag' behaviour. These planar motions are composed of gliding sweeps and turning sections. As the number of sides in the polygon decreases, i.e. for hexagons and pentagons, the trajectory transition to a more three-dimensional form. These trajectories were found to be restricted to one plane per swing but the subsequent swings are in other planes. Further decrease in number of sides to a square results in the trajectories having a severe out-of-plane motion. These sub-regimes of particle motion within the fluttering regime are consistent with those reported for disks in previous studies.Based on this information, a new length scale that accounts for the frontal area of the particles and its edge geometry (i.e. perimeter) is proposed. This length scale represents the first approach to determine an equivalent disks for planar particles such that the phase digram in the Reynolds number (Re) -dimensionless moment of inertia (I * ) domain can be used to characterise the motion of planar particles with different frontal geometries. However further experiments covering other domains of the regime map are needed to verify its universality. *

Three dimensional wakes of freely falling planar polygons

“…3. We observe that different trajectories show strong differences in the relevance of the out-of-plane motion, as observed experimentally and in simulations for disks with different dimensionless inertia I * [Zhong et al 2011[Zhong et al , 2013Zhong and Lee 2012;Chrust et al 2013;Auguste et al 2013 among others] and experimentally for planar polygon particles (Esteban et al 2018). Thus, in here 'planar zig-zag' motion refers to trajectories with two trajectory sections that repeat periodically; gliding sections where the particle oscillates within a X − Y plane and turning sections where the particle shows small…”

“…Trajectories describing highly 3D motion are named 'spiral' motion; the X − Y footprint of these trajectories shows a particle describing a sequence of circles with a finite offset between consecutive loops. These trajectories also show a much steadier descent Esteban et al (2018). The solid and broken lines define the regimes and subregimes found in Field et al (1977) and Zhong et al (2011), respectively.…”

“…In each frame the dark particle projection is recorded onto the white background and the position of the particle centre of mass was obtained by locating the geometric centre of each particle projection. The image processing was performed using an in-house script developed in MATLAB, as in Esteban et al (2018) and Esteban et al (2019). The method to obtain the particle position from the grey-scale image is a threshold-based method, where raw images are converted into black and white images after applying a user-defined intensity threshold.…”

“…The V3V system acquires triplets of images that are later used to reconstruct the velocity field around the falling particle the equivalent particle diameter. Thus, we use the approach proposed in Esteban et al (2018) to obtain a new particle characteristic length-scale from which to obtain an equivalent Reynolds number and dimensionless moment of inertia. Thus, the dimensionless moment of inertia is defined as where = D c ∕Q , with D c the diameter of the circumscribed circle and Q = 4 A p ∕P 2 is the isoperimetric quotient.…”

Laboratory experiments on the temporal decay of homogeneous anisotropic turbulence

“…A key reason for this is the difficulty of obtaining a large enough volume of near HIT turbulence in a stationary frame within which the 3D motion of particles can be studied. We believe the facility presented in here could also be used to understand the dispersion of inertial solid particles under background turbulence in a controlled environment, extending the recent work on the settling dynamics of large irregular particles in quiescent flow in Esteban et al (2018a) and Esteban et al (2018b) among others.…”