Motion of freely falling spheres at moderate Reynolds numbers

Lee, D. A.; Viets, Hermann

doi:10.2514/3.6459

Cited by 9 publications

(5 citation statements)

References 9 publications

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“…A more general class of phenomena includes free-falling objects in a fluid. A falling object in a fluid exhibits a rich dynamical behaviour, such as fluttering (oscillation from side to side), tumbling (continuous rotation) and chaotic motions [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Maxwell [17] was among the first to attempt to explain the steady tumbling motion qualitatively.…”

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confidence: 99%

The kinematics of falling maple seeds and the initial transition to a helical motion

2011

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A maple seed falls in a characteristic helical motion. A crude analogy with autorotation of a wind turbine suggests that the torque due to the aerodynamic force would initiate the gyration of the seed. We were therefore surprised that a seed with a torn wing gyrates in a similar manner as a full-winged seed. In fact, a seed with only a sliver of leading edge can still gyrate. Thus the gyrating motion appears not to fully depend on the aerodynamic force. If, on the other hand, the aerodynamic force is completely absent, a seed would fall from rest like a rock in a vacuum.To investigate how the seed reaches its steady helical motion, we use a high-speed digital camera to film the intact and cut seeds at 1000 Hz. With a mirror, the camera records two views simultaneously so that we can extract the 3D kinematics of the wing. We tracked the centre of mass and quantified the descending speed, the azimuthal rotation, and the cone angle for seeds with wings of different shapes. We found that the initial transition from rest to a steady gyration occurs in three steps: a tumble about the span-wise direction, followed by a tilt towards the vertical axis, leading to the gyration about the vertical axis and an opening of the cone angle before settling into a steady state. We offer a new explanation for the cause of the auto-gyration that accounts for these three stages.

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The kinematics of falling maple seeds and the initial transition to a helical motion

2011

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“…This suggests that a Newtonian fluid cannot support transverse oscillations of a sphere. However, the rocking motion of falling spheres with slight transverse oscillations has been documented by Viets & Lee (1971), but this is due to the center of mass of the sphere being displaced from it geometric center.…”

Section: Transverse and Helical Oscillationsmentioning

confidence: 99%

On the Instability of Spheres Settling through a Vertical Pipe Filled with HPG

2012

JAFM

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An extensive set of experiments were performed to determine the stability boundary for the longitudinal oscillation of steel spheres settling through Hydroxy Propyl Guar (HPG) contained in long vertical tubes, a phenomenon first reported by Mollinger, et al. (1999). Results are reported in d/D-pH parameter space, where d is the sphere diameter and D is the internal diameter of a tube. Longitudinal oscillations, which owe their existence to the self-healing nature of the gel, occur over the region 0.48 < d/D < 0.86 and 8.31 < pH < 8.82. We discover that the upper pH limit of this stability domain is linked to the HPG gel point. During the course of experimentation, additional instabilities in the form of high-frequency transverse oscillations or helical motions were discovered and documented. The pure transverse oscillations found in the domain 8.035 < pH < 8.31 and 0.9 < d/D < 0.6 result from the elastic nature of the guar in this region. For 6.25 < pH < 8.035 transverse oscillations or stable descents are interspersed between bands of tight helical motion at large d/D and wide helical motion at low d/D. At the lowest value pH = 6.25 the guar is a Newtonian fluid, yet the spiral motion persists in small bands of d/D. We have verified, in the literature and through additional experiments using distilled water as the Newtonian liquid that the spiral motion of spheres falling inside vertical tubes does indeed exist. We undertook a repetition of the experiment reported in Mollinger, et al. (1999) to determine the entire region

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“…The study of the trajectories of falling non‐spherical bodies dates back to at least Newton (Viets & Lee 1971) and a vast body of experimental and theoretical work exists concerned with the behaviour of sedimenting bodies in viscous fluids (Leal 1980; Kim & Karrila 2005). Qualitative experimental observations of sinking ellipsoids were made by Pettyjohn & Christiansen (1948) and Becker (1959), but it was the theoretical work of Cox (1965) that first quantitatively described the effects of inertia on particle orientation during sinking.…”

Section: Model Backgroundmentioning

confidence: 99%

Are hydrodynamic shape effects important when modelling the formation of depositional remanent magnetization?

Heslop

2007

Geophysical Journal International

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A B S T R A C TRecent conceptual models have attributed the weak depositional remanent magnetizations observed in natural sediments to flocculation processes in the water column. Magnetic particles included into flocs have not only to rotate themselves into alignment with the geomagnetic field but also the larger particles to which they are attached, making remanence acquisition an inefficient process. Alignment is hindered further when the magnetization vectors of the particles in any given floc partially cancel, reducing the overall magnetic torque. Existing numerical simulations of flocculation effects on depositional remanence formation have been limited to spherical bodies with translational and rotational motion acting independently of each other. In the case of non-spherical flocs, the translational and rotational motion are coupled and such bodies will describe a complex trajectory through the water column. Calculations will be presented that show the torque exerted on a non-spherical floc by the surrounding water can be orders of magnitude greater than the magnetic torque. Non-spherical flocs will, therefore, align less efficiently with the geomagnetic field and hydrodynamic effects may play an important role in controlling the magnitude of sedimentary remanence.

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Motion of freely falling spheres at moderate Reynolds numbers

Cited by 9 publications

References 9 publications

The kinematics of falling maple seeds and the initial transition to a helical motion

The kinematics of falling maple seeds and the initial transition to a helical motion

On the Instability of Spheres Settling through a Vertical Pipe Filled with HPG

Are hydrodynamic shape effects important when modelling the formation of depositional remanent magnetization?

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