The behaviour of freely falling cylinders and cones in a viscous fluid

Abstract

The terminal velocities, drag coefficients, and orientations of single cylinders falling in a large tank of viscous liquid have been determined for Reynolds numbers Re ranging from > 0·01 to 1000 to 1000. Stationary eddies appear in the wakes of cylinders at 26 > Re > 50, and the shedding of a Kármán vortex street at Re > 50 causes them to oscillate as they fall.

The interaction of two long, thin cylinders, which is largely determined by their initial relative positions, has been studied in some detail. One interesting result is that two equal cylinders, initially non-parallel and vertically separated by about 50 diameters, catch up and slide along each other until they bisect at right angles. When several cylinders are released in random orientations, they tend to cluster and then separate into pairs crossed at right angles and into trip-lets in the form of a symmetrical ++.

Cones with a flat base fall with apex upwards if the vertex angle θ < ¼π and with apex downwards if θ > ¼π. Double cones, cemented base to base, and with apex angles θ₁ and θ₂(θ₂ > θ₁), fall with acute apex upwards if $2\theta _1 + \theta_2 \textless \frac {3}{2} \pi$, the stable orientation being apex downwards if this condition is not satisfied. At Re ≃ 100, the shedding of a Kármán vortex street causes the cones to oscillate, while at Re > 800, the flow becomes highly turbulent and they tumble as they fall.