Drag and wakes of freely falling 60° cones at intermediate Reynolds numbers

Abstract

The drag coefficient for freely falling cones with a vertex angle of 60°was determined experimentally in the Reynolds number range from 90 to 8 ϫ 10 3 and described by empirical equations. The drag was determined by measurement of the terminal velocity of the cones falling through water. Flow-visualization experiments showed the different regimes of the wake structure for a wide range of the Reynolds numbers covering the successive destabilizations of the wake on the way to turbulence. Especially, a very regular staggered array of two rows of ring-shaped hairpin vortices appeared behind the cones in the Reynolds number range from 170 to 235. The Strouhal number was determined in the Reynolds number range from 170 to 1.2ϫ 10 3 . The arrangement of the double row of vortex rings and the oscillatory motion of the cones were given in some detail.

The wake of falling disks at low Reynolds numbers

“…6 Visualization of the two-thread wake behind a falling thin disk (D = 7 mm, t = 55 µm) at Re = 112. Modulation of the twothread wake was observed, the Strouhal number is calculated to be 0.12 from the image close to the value 0.113 calculated by Shenoy and Kleinstreuer [12] for the fixed χ = 1/10 disk and 0.122 found in experiment of freely rising disks by Fernandes et al The oscillation of the two-thread wake was also mentioned in studies of other bodies as in sphere [4,5,7] and cone [14]. Especially, Gumowski et al [8] observed a "three dimensional peristaltic" oscillation which modulated the counter rotating vortices behind a sphere to develop at Re = 266, the shedding of hairpin-like vortices was proposed resulting from the oscillations.…”

“…To make a comparison between various body geometries, we considered the normalized distance L/D, L was defined as the distance between the vortex cores of the two-thread wake at the same downstream location behind the bodies. The value of L/D was directly obtained from the visualization images of a disk, sphere [6] and 60 • cone [14]. However, the value of L/D depended both on the choice of downstream location and Reynolds number, so L were all measured at downstream position 4D as the two-thread wake was clearly far away from the recirculation region.…”

“…Another remarkable feature, in the transition process with a disk, was that the difference of Re c 1 and Re c 2 seemed much smaller compared with that for a sphere or a cone. The value Re c 2 − Re c 1 was typically about 10 as reported for a disk [11,16], but was found to be 60-90 for a sphere [3,4,6] and 70 for a 60 • cone [14].…”

“…These bodies spanned from spheres [1][2][3][4][5][6][7][8], disks [9][10][11][12], cones [13,14] to immiscible fluid drops [15]. A series of bifurcations were found en route the transition process from laminar states to turbulence.…”

“…Yaginuma and Itō [14] studied the free falling motion of a 60 • cone. The two-thread wake was observed behind the cone for 100 < Re < 170.…”