Free-Fall of Solid Particles through Fluids

1993 ◽  
Vol 58 (5) ◽  
pp. 961-982 ◽  
Author(s):  
Miroslav Hartman ◽  
John G. Yates
Keyword(s):  
Drag Coefficient ◽  
Newtonian Fluid ◽  
Free Fall ◽  
Terminal Velocity ◽  
Solid Particles ◽  
Fall Velocity ◽  
Predictive Relationships ◽  
Implicit And Explicit

A comprehensive, up-to-date review is presented of predictive relationships for the terminal, free-fall velocity of solid particles falling in an infinite Newtonian fluid. The study explores accuracy of the implicit and explicit equations in terms of the drag coefficient and the terminal velocity. Problems of predicting the terminal velocity of non-spherical, isometric as well as non-isometric, particles is discussed.

Explicit relationships for the terminal velocity of spherical particles

1990 ◽  
Vol 55 (2) ◽  
pp. 403-408 ◽  
Author(s):  
Miloslav Hartman ◽  
Václav Veselý ◽  
Karel Svoboda ◽  
Vladimír Havlín
Keyword(s):  
Drag Coefficient ◽  
Free Fall ◽  
Terminal Velocity ◽  
Spherical Particles ◽  
Wide Range ◽  
Archimedes Number

The Turton-Levenspiel correlation for the drag coefficient of a sphere is employed to compare recently proposed explicit equations to predict the free-fall conditions. Predictions of four different expressions are explored over a wide range of Archimedes number.

Influence of Particle Shape on the Drag Coefficient for Isometric Particles

1994 ◽  
Vol 59 (12) ◽  
pp. 2583-2594 ◽  
Author(s):  
Miloslav Hartman ◽  
Otakar Trnka ◽  
Karel Svoboda ◽  
Václav Veselý
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Drag Coefficient ◽  
Fluidized Beds ◽  
Fluid Velocity ◽  
Particle Diameter ◽  
Free Fall ◽  
Fall Velocity ◽  
Gas Cleaning ◽  
Explicit Formulae

A comprehensive correlation has been developed of the drag coefficient for nonspherical isometric particles as a function the Reynolds number and the particle sphericity on the basis of data reported in the literature. The proposed formula covers the Stokes, the transitional and the Newton region. The predictions of the reported correlation have been compared to experimental data measured in this work with the dolomitic materials in respect to their use in calcination and gas cleaning processes with fluidized beds. Approximative explicit formulae have also been reported that make it possible to estimate the terminal free-fall velocity of a given particle or to predict the particle diameter corresponding to a fluid velocity of interest.

Effect of Tumbling and Burning on the Drag of Bluff Objects

1983 ◽  
Vol 105 (2) ◽  
pp. 174-178 ◽  
Author(s):  
K. W. Ragland ◽  
M. A. Mason ◽  
W. W. Simmons
Keyword(s):  
Drag Coefficient ◽  
Solid Fuel ◽  
Flat Surface ◽  
Free Fall ◽  
Wood Chips ◽  
Fall Velocity ◽  
Fuel Particles

The drag on various tumbling, nonburning wooden plates, cubes, rods, and wood chips was determined by measuring the free-fall velocity. The drag coefficient was reduced by a factor of 0.46 to 0.72 compared to the drag coefficient with the largest flat surface oriented perpendicular to the flow. The drag coefficient of burning wooden cubes and disks which are not tumbling was half that of identical nonburning, nontumbling cubes and disks. The drag coefficient of burning wooden cylinders with axes normal to the flow was slightly larger than nonburning cylinders with the same orientation. The information was obtained in order to better model the trajectory of solid fuel particles in furnaces.

The behaviour of clusters of spheres falling in a viscous fluid Part 1. Experiment

1964 ◽  
Vol 20 (1) ◽  
pp. 121-128 ◽  
Author(s):  
K. O. L. F. Jayaweera ◽  
B. J. Mason ◽  
G. W. Slack
Keyword(s):  
Regular Polygon ◽  
Free Fall ◽  
Isosceles Triangle ◽  
Reynolds Numbers ◽  
Terminal Velocity ◽  
Horizontal Line ◽  
Fall Velocity ◽  
Left Behind ◽  
Initial Spacing ◽  
Small Clusters

The sedimentation of small clusters of uniform spheres, falling freely through a viscous liquid, has been studied with Reynolds numbers (based on diameter of the sphere and its velocity of free fall in the unbounded fluid) of individual spheres ranging from 10−4 to 10. The fall velocity of a cluster is, in all cases, greater than that of individual spheres, the more so when the spheres are closer together. Two spheres falling side-by-side rotate inwards and separate as they fall if Re > 0·05, but no rotation nor separation is observed for Re < 0·03. When equal-sized spheres of Re > 1 fall vertically one behind the other, the rear sphere is accelerated into the wake of the leader, rotates, round it and separates from it when the line of centres is horizontal. If two spheres of unequal size but the same individual terminal velocity fall together, the smaller always travels faster than the larger. When three similar equally spaced spheres are dropped in a horizontal line, they interchange positions but do not separate when 0·06 < Re < 0·16. But, if 0·16 < Re < 3, one sphere is always left behind; which sphere depends critically upon the initial spacing. If three to six equal spheres, of 0·06 < Re < 7, start falling as a compact cluster, they eventually draw level and arrange themselves in the same horizontal plane at the vertices of a regular polygon. The polygon expands at a decreasing rate during fall. When three spheres are arranged initially in a horizontal isosceles triangle, the spheres oscillate about their equilibrium positions but eventually the spheres form a stable equil triagnle. If Re > 7, or the cluster contains 7 or more equal spheres, it shows no tendency to form a regular polygon but breaks up into two or more groups. A regular heptagon, and a hexagon with an additional sphere at its centre, are also unstable.

A new model for predicting drag coefficient and settling velocity of spherical and non-spherical particle in Newtonian fluid

2017 ◽  
Vol 321 ◽  
pp. 242-250 ◽  
Author(s):  
Xianzhi Song ◽  
Zhengming Xu ◽  
Gensheng Li ◽  
Zhaoyu Pang ◽  
Zhaopeng Zhu
Keyword(s):  
Drag Coefficient ◽  
Spherical Particle ◽  
Newtonian Fluid ◽  
Settling Velocity ◽  
New Model

Refinements to Ice Particle Mass Dimensional and Terminal Velocity Relationships for Ice Clouds. Part II: Evaluation and Parameterizations of Ensemble Ice Particle Sedimentation Velocities

2007 ◽  
Vol 64 (4) ◽  
pp. 1068-1088 ◽  
Author(s):  
Andrew J. Heymsfield ◽  
Gerd-Jan van Zadelhoff ◽  
David P. Donovan ◽  
Frederic Fabry ◽  
Robin J. Hogan ◽  
...  
Keyword(s):  
Climate Models ◽  
Doppler Radar ◽  
Terminal Velocity ◽  
Fall Velocity ◽  
Particle Sedimentation ◽  
Cloud Properties ◽  
Wide Range ◽  
Single Moment ◽  
Ice Water Content ◽  
Ice Water

Abstract This two-part study addresses the development of reliable estimates of the mass and fall speed of single ice particles and ensembles. Part I of the study reports temperature-dependent coefficients for the mass-dimensional relationship, m = aDb, where D is particle maximum dimension. The fall velocity relationship, Vt = ADB, is developed from observations in synoptic and low-latitude, convectively generated, ice cloud layers, sampled over a wide range of temperatures using an assumed range for the exponent b. Values for a, A, and B were found that were consistent with the measured particle size distributions (PSD) and the ice water content (IWC). To refine the estimates of coefficients a and b to fit both lower and higher moments of the PSD and the associated values for A and B, Part II uses the PSD from Part I plus coincident, vertically pointing Doppler radar returns. The observations and derived coefficients are used to evaluate earlier, single-moment, bulk ice microphysical parameterization schemes as well as to develop improved, statistically based, microphysical relationships. They may be used in cloud and climate models, and to retrieve cloud properties from ground-based Doppler radar and spaceborne, conventional radar returns.

scholarly journals SEDIGISM: the kinematics of ATLASGAL filaments

2018 ◽  
Vol 619 ◽  
pp. A166 ◽  
Author(s):  
M. Mattern ◽  
J. Kauffmann ◽  
T. Csengeri ◽  
J. S. Urquhart ◽  
S. Leurini ◽  
...  
Keyword(s):  
Unit Length ◽  
Dust Emission ◽  
Free Fall ◽  
Outer Radius ◽  
Line Of Sight ◽  
Fall Velocity ◽  
Automated Algorithm ◽  
Power Law Exponent ◽  
Continuum Data ◽  
Self Gravity

Analyzing the kinematics of filamentary molecular clouds is a crucial step toward understanding their role in the star formation process. Therefore, we study the kinematics of 283 filament candidates in the inner Galaxy, that were previously identified in the ATLASGAL dust continuum data. The 13CO(2 – 1) and C18O(2 – 1) data of the SEDIGISM survey (Structure, Excitation, and Dynamics of the Inner Galactic Inter Stellar Medium) allows us to analyze the kinematics of these targets and to determine their physical properties at a resolution of 30′′ and 0.25 km s−1. To do so, we developed an automated algorithm to identify all velocity components along the line-of-sight correlated with the ATLASGAL dust emission, and derive size, mass, and kinematic properties for all velocity components. We find two-third of the filament candidates are coherent structures in position-position-velocity space. The remaining candidates appear to be the result of a superposition of two or three filamentary structures along the line-of-sight. At the resolution of the data, on average the filaments are in agreement with Plummer-like radial density profiles with a power-law exponent of p ≈ 1.5 ± 0.5, indicating that they are typically embedded in a molecular cloud and do not have a well-defined outer radius. Also, we find a correlation between the observed mass per unit length and the velocity dispersion of the filament of m ∝ σv2. We show that this relation can be explained by a virial balance between self-gravity and pressure. Another possible explanation could be radial collapse of the filament, where we can exclude infall motions close to the free-fall velocity.

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