Investigations of the Steady and Unsteady Motion of Freely Falling Disks

Willmarth, William W.; Hawk, Norman E.; Harvey, Robert L.

doi:10.21236/ad0420913

Cited by 5 publications

(6 citation statements)

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“…However, Field et al (1997) found that, for low Reynolds numbers, a disc dropped with any initial orientation would adjust itself until it fell with its face perpendicular to its motion. Similar results were found by Willmarth et al (1963Willmarth et al ( , 1964 for Re d between 1 and 100. Higher Reynolds numbers lead to chaotic motion where the disc may tumble, rotate, or pitch side to side.…”

Section: Crystal Buoyancysupporting

confidence: 88%

Ice Growth and Platelet Crystals in Antarctica

Crook¹

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<p>First-year land-fast sea ice growth in both the Arctic and the Antarctic is characterised by the formation of an initial ice cover, followed by the direct freezing of seawater at the ice-water interface. Such growth usually results, through geometric selection, in congelation ice. This is, in general, the typical crystal structure observed in first-year ice growth in the Arctic. However, in certain regions of the Antarctic, platelet crystals are observed to contribute significantly to the ice growth, beyond a depth of 1 m. This thesis will investigate a number of ideas as to why the platelet crystals only appear in the ice after a significant amount of congelation growth has occurred. One of the key premises will be that platelet ice forms when smaller frazil crystals, beneath the ice, rise up and attach to the interface. They are then incorporated into the ice cover and become the platelets seen in ice cores. The Shields criterion is used to find the strength of turbulence, associated with tidal flow, required to keep a frazil crystal from adhering to the interface. It is shown that the sub-ice flow is sufficient to keep most crystals in motion. However, this turbulence may weaken or dissipate completely as the tide turns. The velocity associated with brine rejection is suggested as an alternative to keep the crystals in suspension during these periods of low shear turbulence. Brine rejection occurs as the sea ice grows, rejecting salt into the seawater below. By comparing this velocity with a model for the frazil rise velocity it is shown that brine rejection has sufficient strength to keep crystals in suspension. This effect weakens as the ice gets thicker, allowing larger frazil crystals to rise to the interface. The early work in this thesis shows that a flow can keep a single crystal from adhering to the interface. This can be regarded as the competence of a flow to keep a crystal in suspension. However, of equal importance is the capacity of a flow to keep a mass of crystals in suspension. It is shown that, given a sufficiently large mass of crystals beneath the ice, the same flow that can hold a single crystal in suspension will not be able to keep all the crystals in motion. The deposition of crystals is predicted to occur in a gradual manner if there is a steady build-up of crystals beneath the ice. The largest crystals, close to the interface, will settle against the ice as the flow is unable to support the entire mass of crystals Also considered is whether frazil crystals may be similar to cohesive sediments. If this is the case, a sudden influx of crystals from outside of the system may lead to the formation of a layer of unattached crystals beside the ice-water interface. This can cause a critical collapse of the turbulent field, resulting in the settling of a large quantity of frazil crystals. Though the emphasis of much of this thesis is on the effect of the flow on the crystals, it is also found that a mass of crystals can have a stabilising effect on the flow. The change in the density profile induced by an increase in the frazil concentration towards the ice-water interface (and hence a decrease in the density of the ice-water mixture) damps the turbulence produced by shear. The mass and size of crystals in suspension play major roles in the strength of stabilisation. Measurements of turbulence and the suspension of frazil crystals beneath sea ice are difficult to make. This thesis aims to present and analyse a number of models which may explain the platelet puzzle - the delayed appearance of the platelet crystals in ice cores. These are compared with the observations which are available, and conclusions made on the validity of the theories presented.</p>

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Section: Crystal Buoyancysupporting

confidence: 88%

Ice Growth and Platelet Crystals in Antarctica

Crook¹

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“…Another issue on the measurement of drag coefficient of irregular particles is due to their secondary motion when they are freely transported in a fluid. 2,3,10,[12][13][14][15][16][17][18][19][20][21][22][23][24] Secondary motions have significant effect on the drag coefficient of the particles in the direction of their primary motion. 2,3,10,[12][13][14]23 A.…”

Section: Drag Coefficientmentioning

confidence: 99%

“…Secondary motions of particles Different types of particle secondary motion are reported for different particle shapes, ranging from small oscillation and rotation to tumbling and chaotic motions. 2,3,10,[12][13][14][15][16][17][18][19][20][21][22][23][24] Two main sources are known to be responsible for secondary motions of particles. The first source is the way that hydrodynamical forces and torques evolve when particle degrees of freedom change.…”

Section: Drag Coefficientmentioning

confidence: 99%

“…2,3,[10][11][12][13][14][15][16][17] However, the measurements of the drag coefficient strongly depend on the nature of particle secondary motions, which are different for different density ratios. 2,3,10,[12][13][14][15][16][17][18][19][20][21][22][23][24] Besides, it is found that the drag coefficient of particles of any shape at intermediate Reynolds numbers (1 < Re < 10 4 ) is related to values of their drag coefficient at very low (Re 1) and at very high Reynolds numbers (10 4 < Re < 10 5 ). 25,26 Therefore, characterization of drag coefficient of particles at both high Reynolds number and high density ratios can be used either directly or to be used for estimating particle drag coefficient at intermediate Reynolds numbers.…”

Section: Introductionmentioning

confidence: 99%

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Dedicated vertical wind tunnel for the study of sedimentation of non-spherical particles

Bagheri

Bonadonna

Manzella

et al. 2013

Review of Scientific Instruments

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A dedicated 4-m-high vertical wind tunnel has been designed and constructed at the University of Geneva in collaboration with the Groupe de compétence en mécanique des fluides et procédés énergétiques. With its diverging test section, the tunnel is designed to study the aero-dynamical behavior of non-spherical particles with terminal velocities between 5 and 27 ms(-1). A particle tracking velocimetry (PTV) code is developed to calculate drag coefficient of particles in standard conditions based on the real projected area of the particles. Results of our wind tunnel and PTV code are validated by comparing drag coefficient of smooth spherical particles and cylindrical particles to existing literature. Experiments are repeatable with average relative standard deviation of 1.7%. Our preliminary experiments on the effect of particle to fluid density ratio on drag coefficient of cylindrical particles show that the drag coefficient of freely suspended particles in air is lower than those measured in water or in horizontal wind tunnels. It is found that increasing aspect ratio of cylindrical particles reduces their secondary motions and they tend to be suspended with their maximum area normal to the airflow. The use of the vertical wind tunnel in combination with the PTV code provides a reliable and precise instrument for measuring drag coefficient of freely moving particles of various shapes. Our ultimate goal is the study of sedimentation and aggregation of volcanic particles (density between 500 and 2700 kgm(-3)) but the wind tunnel can be used in a wide range of applications.

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“…The aerodynamic moment on an inclined body at low Reynolds numbet -_ at most small. Willmarth (10), et al, in their investigation of freely falling disks refers to the work of Gans, who was able to show that for low Reynolds number creeping motion there is no aerodynamic moment produced by fluid pressure on a body that has three mutually perpendicular planes of symmetry. For higher Reynolds numbers no direct computation of the aerodynamic moment as a fuitction oi body incidence has been reported; thus, ore is led to consider more general analyses of body angular motion.…”

Section: P CDmentioning

confidence: 99%

Chaff Aerodynamics

Brunk¹,

Mihora²,

Jaffé³

1975

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depend greatly upon the principal cross-section dimensions of the filaments. Aerodynamic forces and moment coefficients for each dipole configuration were computed from the photographic multi-image motion data using photogrammetric and aerodynamic data reduction programs developed as part of the effort. The resulting aerodynamic coefficient data were successfully correlated with Reynolds number, angle of attack, and various other parameters. While the force coefficients were found to be large and in general agreement with the various theories for creeping flow, the moment coefficients were extremely small and resulted primarily from configurational asymmetries. Using both the experimental data and theory, aerodynamic coefficient tables for representative dipole configurations, suitable for 6-DOF simulation of dipole motion, were prepared. These aerodynamic data were subsequently used in co, junction with a 6-DOF Monte Carlo trajectory program, modified for inclusion of stochastic atmospheric turbulence, for preliminary simulation of chaff dipole motion in both quiescent and turbulent atmospheres. Turbulence was found to have a large effect on the translational motion of the dipole, but only a small effect on its angular motion.

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Investigations of the Steady and Unsteady Motion of Freely Falling Disks

Cited by 5 publications

References 1 publication

Ice Growth and Platelet Crystals in Antarctica

Ice Growth and Platelet Crystals in Antarctica

Dedicated vertical wind tunnel for the study of sedimentation of non-spherical particles

Chaff Aerodynamics

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