(a) Wind tunnel built at the University of Geneva; (b) schematic of the wind circuit.
Circular contraction cone with square section; (a) front view, dimensions are in mm; (b) perspective view.
Schematic of experimental setup. The shadow image of one irregular particle inside the test section is sketched in three successive recording frames. The particle projected area and shape vary in different views and frames since the particle is irregular; (a) side view (yz plane); (b) front view (xy plane) which is the camera view with z being the perspective direction of the camera.
(a) Schematic of the pendulum experiment setup; (b) acceleration of pendulum in x direction calculated with the PTV code from movies recorded with recording speeds between 25 and 200 fps. The results show that increasing recording speed leads to the amplification of numerical noise in the calculation of the pendulum acceleration especially when the pendulum speed is small (t < 0.15 s).
Computer vision algorithms are used to calculate particle projection area from a random-orientation database of the particle; (a) shadow image of the particle C3 (see Table I ) recorded by the camera during its suspension in the wind tunnel test section; (b) the closest image to particle shadow image (a) found by the PTV code from 500 images in the random-orientation database of particle C3; (c) top view of image (b) in the database of particle C3 whose area is used as the projected area, A projected , of particle C3 of image (a).
Relative velocity, v r , of particles calculated by the PTV code before and after applying shadow and acceleration filters. (a) Relative velocity of particle S5 (standard deviation and range are 0.34 ms−1 and 2.0 ms−1 before applying filters, and 0.26 ms−1 and 1.1 ms−1, after applying filters); (b) relative velocity of particle C2 (standard deviation and range are 0.57 ms−1 and 3.5 ms−1 before applying filters, and 0.53 ms−1 and 2.4 ms−1, after applying filters).
Comparison of drag coefficient of spherical particles measured in the present study with those reported in literature. The measurements of the present work are shown by boxplots: the ends of the bars represent the smallest and the largest measurements, the box thickness indicates the first and the third quartiles and the horizontal line is the median (second quartile) of the measurement.
Comparison of drag coefficient of cylindrical particles measured in the present study with those reported in literature using Ld as A in the calculation of drag coefficient; Wieselsberger 6 results are from wind tunnel measurements on fixed cylinders with two free ends; Christiansen and Barker 12 data are from measurements on cylinders (E = 1.75) falling freely in the air (1000 < S < 2800); Isaacs and Thodos 13 data are from measurements on cylinders (E = 2.0) falling freely in the water (1.05 < S < 11.27).
Variation of drag coefficient of cylindrical particles with respect to (S/E)0.5 measured in the present study with those reported in literature using Ld as A in the calculation of drag coefficient; values of (S/E)0.5 for particles C1, C2, and C3 are 23, 16, and 12, respectively; Chow and Adams 3 experimental data are from measurements on cylinders (2 < E < 100) falling freely in the water (1.1 < S < 8.5).
Histograms of area ratio of cylindrical particles after applying filters. No preferred orientation can be found for particle C1, while particles C2 and C3 in more than 60% of the cases are suspended with A * > 0.9.
Variation of A * versus cylinder axis angle. A * is calculated from Eq. (5) and A projected (=Ldcos (α) + π(d/2)2sin (α)) is the area of the particle projected on the projection plane.
Properties of the particles used in our experiments and air in the wind tunnel.
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