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.

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.

scholarly journals A SIMILARITY CRITERION FOR SPHERICAL FUEL ELEMENTS FREE FALL VELOCITY IN CYLINDRICAL CHANNELS WITH VISCOUSE LIQUID

2021 ◽  
pp. 64-69
Author(s):  
Oksana L. Andrieieva ◽  
Leonid A. Bulavin ◽  
Victor I. Tkachenko
Keyword(s):  
Experimental Data ◽  
High Temperature ◽  
Active Zone ◽  
Similarity Criterion ◽  
Free Fall ◽  
Reynolds Numbers ◽  
Cylindrical Vessel ◽  
Fall Velocity ◽  
Fuel Elements ◽  
High Temperature Gas

The introduction of nuclear high-temperature gas-cooled reactors (HTGR) with an active zone based on spherical fuel elements (SFE) poses the task of determining the velocity of their free fall in cylindrical channels with a viscous liquid. To solve it, the experimental data of other researchers are generalized, and for a certain range of Reynolds numbers the criterion of similarity for the velocity of free fall of spheres in cylindrical channels with water is found. The criterion is formulated on the basis of the Freud number. It is shown that from the dependence of the velocity of falling of the model sphere in a cylindrical vessel with water on the dimensionless diameter of the sphere, it is possible to determine the velocity of falling of the sphere in water, arbitrary.

A numerical study on free-fall of a torus with initial inclination angle at low Reynolds numbers

2021 ◽  
Vol 107 ◽  
pp. 103389
Author(s):  
Tao Huang ◽  
Haibo Zhao ◽  
Sai Peng ◽  
Jiayu Li ◽  
Yang Yao ◽  
...  
Keyword(s):  
Inclination Angle ◽  
Numerical Study ◽  
Free Fall ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Low Reynolds

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.

scholarly journals Fluid Dynamics Properties of Barium Hexaferrite Particle

2014 ◽  
Vol 17 (49) ◽  
Author(s):  
Perdamean Sebayang ◽  
Muljadi ◽  
Anggito Tetuko ◽  
Priyo Sardjono
Keyword(s):  
Particle Size ◽  
Bulk Density ◽  
Barium Hexaferrite ◽  
Reynolds Numbers ◽  
Terminal Velocity ◽  
Size Estimation ◽  
Floc Size ◽  
Ethanol Medium ◽  
Lower Bulk Density ◽  
Relationship Of

Particle size distribution of Barium Hexaferrite sample has been performed with commonly used methods of mathematical models by Rosin-Rammler (RR model) distribution. By using sieving method from 20-400 mesh, the basis of network analysis distribution function F(d) and density function, f(d) were obtained. Particle size estimation was performed using sedimentation gravitation based on Stokes law to obtained Reynolds numbers and terminal velocity of flocs in medium value has been calculated. The results of Reynolds numbers shows that Barium hexaferrite flocs in ethanol medium in laminar flow, whereas terminal velocity increases as larger particle size and density, however, bulk density reduce due to contained highly porous in the sample which yields lower bulk density. The relationship of turbidity with the floc size has been evaluated. The results show that turbidity and bulk density increases as smaller particle size, meanwhile, terminal velocity reduced. Differences in turbidity for each sample (20-400 mesh) has been determined which shows two region instead, with first region from 150-850 µm yields larger differences compared to the second region: 37-105 µm.  

The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields

1987 ◽  
Vol 174 ◽  
pp. 441-465 ◽  
Author(s):  
M. R. Maxey
Keyword(s):  
Settling Velocity ◽  
High Strain ◽  
Free Fall ◽  
Terminal Velocity ◽  
Homogeneous Turbulence ◽  
Mean Flow ◽  
Particle Inertia ◽  
The Mean ◽  
Random Flow ◽  
Flow Particle

The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, is shown to depend on the particle inertia and the free-fall terminal velocity in still fluid. With no inertia the particle settles on average at the same rate as in still fluid, assuming there is no mean flow. Particle inertia produces a bias in each trajectory towards regions of high strain rate or low vorticity, which affects the mean settling velocity. Results from a Gaussian random velocity field show that this produces an increased settling velocity.

Numerical Simulation of Heavy Particle Dispersion Time Step and Nonlinear Drag Considerations

1992 ◽  
Vol 114 (1) ◽  
pp. 100-106 ◽  
Author(s):  
Lian-Ping Wang ◽  
D. E. Stock
Keyword(s):  
Numerical Simulation ◽  
Numerical Experiments ◽  
Heavy Particle ◽  
Free Fall ◽  
Particle Dispersion ◽  
Integration Time ◽  
Fall Velocity ◽  
Time Step ◽  
Physical Experiments ◽  
Total Integration

Numerical experiments can be used to study heavy particle dispersion by tracking particles through a numerically generated instantaneous turbulent flow field. In this manner, data can be generated to supplement physical experiments. To perform the numerical experiments efficiently and accurately, the time step used when tracking the particles through the fluid must be chosen correctly. After finding a suitable time step for one particular simulation, the time step must be reduced as the total integration time increases and as the free-fall velocity of the particle increases. Based on the numerical calculations, we suggest that the nonlinear drag be included in a numerical simulation if the ratio of the particle’s Stokes free-fall velocity to the fluid rms velocity is greater than two.

The development of a laboratory drip rig for performing reproducible comparisons on different precipitation sensors by correcting for environmental conditions and rig set up

2020 ◽  
Author(s):  
Ginger Frame ◽  
Erin Spencer
Keyword(s):  
Water Droplet ◽  
Terminal Velocity ◽  
Test Method ◽  
Small Scale ◽  
Rain Event ◽  
Test Scenario ◽  
Fall Velocity ◽  
Sensing Technology ◽  
Set Up ◽  
The Impact

&lt;p&gt;Assessing the accuracy of precipitation sensors can prove very challenging due to the lack of a universal test standard, stemming from difficulties in creating a controlled test scenario. We propose a refined method of testing that is highly reproducible and can be applied to any precipitation sensor regardless of sensing technology.&lt;/p&gt;&lt;p&gt;It is widely understood that two identical disdrometers mounted close together in a real rain event are not likely to report the same precipitation measurements due to the small scale spatial variation of rain. This makes it difficult to draw comparisons between sensors of the same type and even more difficult to compare rain sensors that have different sensing areas and use different sensing technologies. It is therefore desirable to simulate rainfall in the laboratory that is representative of real world conditions but this presents its own set of challenges, primarily in creating rain drops that travel at terminal velocity. This test method significantly reduces the impact of this issue.&lt;/p&gt;&lt;p&gt;This is particularly important for sensors such as optical, acoustic, radar or impact, where the calculations used to obtain rainfall accumulation and drop size distribution assume that the droplets are at terminal velocity. Even for sensors such as capacitive rain gauges and tipping buckets, where the velocity of fall is not directly related to the measurements, more valid conclusions can be drawn about the sensor&amp;#8217;s ability to measure precipitation when the droplets imitate real rainfall as closely as possible.&lt;/p&gt;&lt;p&gt;Here, the development of a drip rig capable of creating raindrops of a controlled size is documented. The drip rig can be mounted at a known height and used to test a variety of different precipitation sensors. However, due to height restrictions in the laboratory, it is not possible to get larger raindrops to terminal velocity. Mounted at a height of 7.4m, drops above 2 mm in diameter do not reach 99% terminal velocity, and drops above 3 mm do not reach 95%. For this reason, corrections must be applied to the calculations. It is therefore essential to have an understanding of the change in fall velocity of a water droplet with fall distance.&lt;/p&gt;&lt;p&gt;This work documents the equations used to calculate drop velocity with fall distance for different drop masses. Temperature, humidity and air pressure define air density, which has a significant impact on the velocity of a falling water droplet. The effect of each of these environmental factors has been investigated in order to allow for further corrections. Performing these corrections greatly improves the validity and repeatability of the tests carried out on precipitation sensors.&lt;/p&gt;

Secondary Ice Production upon Freezing of Freely Falling Drizzle Droplets

2020 ◽  
Vol 77 (8) ◽  
pp. 2959-2967 ◽  
Author(s):  
Alice Keinert ◽  
Dominik Spannagel ◽  
Thomas Leisner ◽  
Alexei Kiselev
Keyword(s):  
Pure Water ◽  
Free Fall ◽  
Terminal Velocity ◽  
Sea Salt ◽  
Ice Formation ◽  
Formation Mechanisms ◽  
Ice Multiplication ◽  
Ice Production ◽  
Droplet Shattering ◽  
Droplet Fragmentation

Abstract Ice multiplication processes are known to be responsible for the higher concentration of ice particles versus ice nucleating particles in clouds, but the exact secondary ice formation mechanisms remain to be quantified. Recent in-cloud observations and modeling studies have suggested the importance of secondary ice production upon shattering of freezing drizzle droplets. In one of our previous studies, four categories of secondary ice formation during freezing of supercooled droplets have been identified: breakup, cracking, jetting, and bubble bursts. In this work, we extend the study to include pure water and an aqueous solution of analog sea salt drizzle droplets moving at terminal velocity with respect to the surrounding cold humid air. We observe an enhancement in the droplet shattering probability as compared to the stagnant air conditions used in the previous study. Under free-fall conditions, bubble bursts are the most common secondary ice production mode in sea salt drizzle droplets, while droplet fragmentation controls the secondary ice production in pure water droplets.

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