INVESTIGATIONS OF THE STEADY AND UNSTEADY MOTION OF FREELY FALLING DISKS
Interim technical rept.
MICHIGAN UNIV ANN ARBOR
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The motions and wakes of freely falling disks have been studied and it has been found that the diverse motions of the disks exhibit a systematic dependence on the Reynolds number, Re, and the dimensionless moment of inertia, I. The relation between I and Re along the boundary separating stable and unstable pitching oscillations of the disk has been determined. The Reynolds number for stable motion of a disk with large I is 100 in agreement with the Reynolds number for stability of the wake of a fixed disk. Slightly unstable disks of large I were stabilized by reducing the moment of inertia. The highest Reynolds number for stable disk motion was 172. At higher Reynolds numbers the disks exhibited periodic pitching and translational oscillations. The laminar wake behind certain of the oscillating disks consisted of a staggered arrangement of two rows of regularly spaced vortex rings similar to the wake observed behind liquid drops by Margarvey and Bishop. The dependence of the dimensionless frequency of oscillation on I and Re was determined along the boundary for stable motion and at higher Reynolds numbers when the wake was turbulent. Tumbling motions of the disks were observed when the Reynolds number was large Re2000 and I was greater than a certain value, I 10 to the minus 2 power.
- Theoretical Mathematics