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.

Drag coefficient of a sphere in a non-stationary flow: new results

2007 ◽  
Vol 463 (2088) ◽  
pp. 3323-3345 ◽  
Author(s):  
G Jourdan ◽  
L Houas ◽  
O Igra ◽  
J.-L Estivalezes ◽  
C Devals ◽  
...  
Keyword(s):  
Drag Coefficient ◽  
Stationary Flow ◽  
Reynolds Numbers ◽  
Spherical Particles ◽  
Steady Flows ◽  
Two Phase ◽  
Spider Web ◽  
Wide Range ◽  
The Difference ◽  
Sphere Drag

The drag coefficient of a sphere placed in a non-stationary flow is studied experimentally over a wide range of Reynolds numbers in subsonic and supersonic flows. Experiments were conducted in a shock tube where the investigated balls were suspended, far from all the tube walls, on a very thin wire taken from a spider web. During each experiment, many shadowgraph photos were taken to enable an accurate construction of the sphere's trajectory. Based on the sphere's trajectory, its drag coefficient was evaluated. It was shown that a large difference exists between the sphere drag coefficient in steady and non-steady flows. In the investigated range of Reynolds numbers, the difference exceeds 50%. Based on the obtained results, a correlation for the non-stationary drag coefficient of a sphere is given. This correlation can be used safely in simulating two-phase flows composed of small spherical particles immersed in a gaseous medium.

scholarly journals Graupel and Hail Terminal Velocities: Does a “Supercritical” Reynolds Number Apply?

2014 ◽  
Vol 71 (9) ◽  
pp. 3392-3403 ◽  
Author(s):  
Andrew Heymsfield ◽  
Robert Wright
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Critical Reynolds Number ◽  
Terminal Velocity ◽  
Ice Crystals ◽  
Particle Sizes ◽  
Model Simulations ◽  
Ice Particles ◽  
Wide Range ◽  
Large Spherical

Abstract This study characterizes the terminal velocities of heavily rimed ice crystals and aggregates, graupel, and hail using a combination of recent drag coefficient and particle bulk density observations. Based on a nondimensional Reynolds number (Re)–Best number (X) approach that applies to atmospheric temperatures and pressures where these particles develop and fall, the authors develop a relationship that spans a wide range of particle sizes. The Re–X relationship can be used to derive the terminal velocities of rimed particles for many applications. Earlier observations suggest that a “supercritical” Reynolds number is reached where the drag coefficient for large spherical ice—hail—drops precipitously and the terminal velocities increase rapidly. The authors draw on observations and model simulations for slightly roughened large ice particles that suggest that the critical Reynolds number is dampened and that the rapid increase in the terminal velocity of smooth spherical ice particles rarely occurs for natural hailstones.

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.

Numerical investigation of anguilliform locomotion by the SPH method

2019 ◽  
Vol 30 (1) ◽  
pp. 328-346 ◽  
Author(s):  
Amin Rahmat ◽  
Hossein Nasiri ◽  
Marjan Goodarzi ◽  
Ehsan Heidaryan
Keyword(s):  
Drag Coefficient ◽  
Numerical Investigation ◽  
Sph Method ◽  
Content Type ◽  
Aquatic Locomotion ◽  
Wide Range ◽  
Particle Hydrodynamics ◽  
Dummy Particles ◽  
Smoothed Particle ◽  
Sph Algorithm

Purpose This paper aims to introduce a numerical investigation of aquatic locomotion using the smoothed particle hydrodynamics (SPH) method. Design/methodology/approach To model this problem, a simple improved SPH algorithm is presented that can handle complex geometries using updatable dummy particles. The computational code is validated by solving the flow over a two-dimensional cylinder and comparing its drag coefficient for two different Reynolds numbers with those in the literature. Findings Additionally, the drag coefficient and vortices created behind the aquatic swimmer are quantitatively and qualitatively compared with available credential data. Afterward, the flow over an aquatic swimmer is simulated for a wide range of Reynolds and Strouhal numbers, as well as for the amplitude envelope. Moreover, comprehensive discussions on drag coefficient and vorticity patterns behind the aquatic are made. Originality/value It is found that by increasing both Reynolds and Strouhal numbers separately, the anguilliform motion approaches the self-propulsion condition; however, the vortices show different pattern with these increments.

Calculation of the primary trajectories of seeds and other particles in strong winds

1983 ◽  
Vol 219 (1215) ◽  
pp. 217-217
Keyword(s):  
Equations Of Motion ◽  
Aerodynamic Resistance ◽  
Reynolds Numbers ◽  
Spherical Particles ◽  
Spores And Pollen ◽  
General Terms ◽  
Wide Range ◽  
Strong Winds ◽  
Dispersal Distances ◽  
Enormous Number

The movement of variously dense spherical particles representing a variety of seeds, fruits, spores and pollen, and released from rest into arbitrary winds and a gravitational field is discussed in general terms that account in detail for changes in the quasi-static aerodynamic resistance to motion experienced by such particles during aerial flight. A hybrid analytical-empirical law is established which describes this resistance fairly accurately for particle Reynolds numbers in the range 0—60 000 and that allows for the numerical integration of the equations of motion so as to cover a very wide range of flight conditions. This makes possible the provision of a set of four-parameter universal range tables from which the dispersal distances for an enormous number of practical cases may be estimated. One particular case of particle movement in a region of pseudo-thermal convection is also discussed and this shows how a marked degree of deposition concentration may be induced in some circumstances by such a flow. Botanists and ecologists concerned with seed and particle dispersal in the environment may find the universal range tables of particular interest and use. This is because the tables obviate the need for the integration of the equations of motion when dealing with individual cases and permit an estimation of range purely on the basis of the specified quantities of particle size, density and altitude of release, atmospheric wind speed, density and viscosity, and the acceleration due to gravity.

Settling Behavior of Particles in Bubble Containing Newtonian Fluids: Experimental Study and Model Development

2021 ◽  
Author(s):  
Silin Jing ◽  
Xianzhi Song ◽  
Zhaopeng Zhu ◽  
Buwen Yu ◽  
Shiming Duan
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Volume Concentration ◽  
Settling Velocity ◽  
Particle Density ◽  
Particle Diameter ◽  
Newtonian Fluids ◽  
Spherical Particles ◽  
Bubble Volume ◽  
Particle Reynolds Number

Abstract Accurate description of cuttings slippage in the gas-liquid phase is of great significance for wellbore cleaning and the control accuracy of bottom hole pressure during MPD. In this study, the wellbore bubble flow environment was simulated by a constant pressure air pump and the transparent wellbore, and the settling characteristics of spherical particles under different gas volume concentrations were recorded and analyzed by highspeed photography. A total of 225 tests were conducted to analyze the influence of particle diameter (1–12mm), particle density (2700–7860kg/m^3), liquid viscosity and bubble volume concentration on particle settling velocity. Gas drag force is defined to quantitatively evaluate the bubble’s resistance to particle slippage. The relationship between bubble drag coefficient and particle Reynolds number is obtained by fitting the experimental results. An explicit settling velocity equation is established by introducing Archimedes number. This explicit equation with an average relative error of only 8.09% can directly predict the terminal settling velocity of the sphere in bubble containing Newtonian fluids. The models for predicting bubble drag coefficient and the terminal settling velocity are valid with particle Reynolds number ranging from 0.05 to 167 and bubble volume concentration ranging from 3.0% to 20.0%. Besides, a trial-and-error procedure and an illustrative example are presented to show how to calculate bubble drag coefficient and settling velocity in bubble containing fluids. The results of this study will provide the theoretical basis for wellbore cleaning and accurate downhole pressure to further improve the performance of MPD in treating gas influx.

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.

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