Steady and Unsteady Motions and Wakes of Freely Falling Disks

Abstract

Marching of freely falling plates" is a fluid dynamics video submitted to the Gallery of Fluid Motion in APS-DFD 2011 at Baltimore Maryland. The problem of a freely falling plate is of interest in both fluid mechanics and nonlinear dynamics. The trajectory of the plate can be regular (Willmarth et al., 1964) or chaotic (Aref and Jones, 1993). As long as Reynolds number is high enough, regular flutter and tumble motion can be obtained for plates with small and large Froude numbers respectively. Belmonte et al. (1998) conducted experimental study on thin flat strips falling in a vertical cell. They categorized the Froude number at which the transition from flutter to tumble occurs. analyzed the transitions between fluttering and tumbling using vorticity-stream function formulation and ODE dynamic equations based on quasi-steady models. They also found that the fluid circulation is mainly generated by the plate rotation and its angular velocity. However, the correlation among the plates motion, generated vortices, and aerodynamic forces is still not fully understood yet, especially in the case of multiple bodies. The DNS (Direct Numerical Simulation, Dong et al., 2006) of freely falling plates is conducted using our in-house CFD (Computational Fluid Dynamics) solver. Showcased examples in this video are a part of DNS results in the attempt to answer the above question. arXiv:1110.3819v1 [physics.flu-dyn]

Observations of the Falling Motion of Plate-Like Snow Crystals Part I: The Free-Fall Patterns and Velocity

“…The tumbling motion observed in laboratory tank experiments (Willmarth et al, 1964;Stringham et al, 1969) did not appear in the present observations.…”

“…Analogous to the results of tank experiments for disk-like particles (Willmarth et al, 1964;Stringham et al, 1969), it appears that over the range of unstable falling motion as the values of Re and I* increase, the more developed the unstable patterns become. Thus, the unstable pattern can be approx- groups.…”

“…The free-fall pattern of disk-like particles is generally affected by Re and the non-dimensional moment of inertia (I*, stability number), as pointed out by Willmarth et al (1964) and Stringham et al (1969). In the case of plate-like snow crystals, however, it has been shown that the limit of the onset of unstable falling motion is determined by the Best or Davis number (Be=CdRe2) eand I*=Ia/*d5, as shown in Fig.…”

Doppler lidar measurements of oriented planar ice crystals falling from supercooled and glaciated layer clouds

“…As the crystals grow bigger and the Reynolds number Re = vD/ν k increases to ∼ 1 (D here is the diameter of the crystal, v its fall speed and ν k the kinematic viscosity of the air), the time taken to fall a distance equal to the particle diameter t = D/v becomes comparable to the time taken for the vorticity generated at the crystal surface to diffuse that same distance, t ≈ D 2 /ν k , and the vorticity is 'left behind' as it falls. Stable, symmetrical vortices are formed behind falling discs (Willmarth et al, 1964;Pitter et al, 1973); numerical experiments by Wang and Ji (1997) confirm that these standing eddies also form behind hexagonal plate and broad-branch ice crystal shapes. If the crystal is inclined at an angle to the horizontal plane, the asymmetrical drag acts to reorient the plate into the horizontal position: this reorientation is stabilised by viscosity, so oscillations around the horizontal are damped, and the particle falls stably and steadily (Willmarth et al, 1964).…”

“…Stable, symmetrical vortices are formed behind falling discs (Willmarth et al, 1964;Pitter et al, 1973); numerical experiments by Wang and Ji (1997) confirm that these standing eddies also form behind hexagonal plate and broad-branch ice crystal shapes. If the crystal is inclined at an angle to the horizontal plane, the asymmetrical drag acts to reorient the plate into the horizontal position: this reorientation is stabilised by viscosity, so oscillations around the horizontal are damped, and the particle falls stably and steadily (Willmarth et al, 1964). Measurements of natural ice crystals by Kajikawa (1992) confirm that horizontal orientation occurs for a variety of planar crystal types (all of the P1 and P2 types defined by Magono and Lee, 1966).…”