Closure to “Drag Coefficient and Fall Velocity of Nonspherical Particles” by Prabhata K. Swamee and Chandra Shekhar P. Ojha (May, 1991, Vol. 117, No. 5)

1992 ◽  
Vol 118 (11) ◽  
pp. 1591-1592 ◽  
Author(s):  
Prabhata K. Swamee ◽  
Chandra Shekhar P. Ojha
1991 ◽  
Vol 117 (5) ◽  
pp. 660-667 ◽  
Author(s):  
Prabhata K. Swamee ◽  
Chandra Shakhar P. Ojha

2021 ◽  
pp. 1-20
Author(s):  
Ozan Sayman ◽  
Eduardo Pereyra ◽  
Cem Sarica

Summary The objective of this study is the experimental and theoretical investigation of the fall mechanics of continuous flow plungers. Fall velocity of the two-piece plungers with different sleeve and ball combinations and bypass plungers are examined in both static and dynamic conditions to develop a drag coefficient relationship. The dimensionless analysis conducted included the wall effect, inclination, and the liquid holdup correction of the fall stage. A fall model is developed to estimate fall velocities of the ball, sleeve, and bypass plungers. Sensitivity analysis is performed to reveal influential parameters to the fall velocity of continuous flow plungers. In a static facility, four sleeves with different height, weight, and outer diameter (OD); three balls made with different materials; and a bypass plunger are tested in four different mediums. The wall effect on the settling velocity is defined, and it is used to validate the ball drag coefficient results obtained from the experimental setup. Two-phase flow experiments were conducted by injecting gas into the static liquid column, and the liquid holdup effect on the drag coefficient is observed. Experiments in a dynamic facility are used for liquid holdup and deviation corrections. The fall model is developed to estimate fall velocities of the continuous flow plungers against the flow. Dimensionless parameters obtained in the experiments are combined with multiphase flow simulation to estimate the fall velocity of plungers in the field scale. Reference drag coefficient values of plungers are obtained for respective Reynolds number values. Experimental wall effect, liquid holdup, and inclination corrections are provided. The fall model results for separation time, fall velocity, total fall duration, and maximum flow rate to fall against are estimated for different cases. Sensitivity analysis showed that the drag coefficient, the weight of plungers, pressure, and gas flow rate are the most influential parameters for the fall velocity of the plungers. Furthermore, the fall model revealed that plungers fall slowest at the wellhead conditions for the range of gas flow rates experienced in field conditions. Lower pressure at the wellhead had two opposing effects; namely, reduced gas density, thereby reducing the drag and gas expansion that increased the gas velocity, which in turn increased the drag. Estimating fall velocity of continuous flow plungers is crucial to optimize ball and sleeve separation time, plunger selection, and the gas injection rate for plunger-assisted gas lift (PAGL). The fall model provides maximum flow rate to fall against, which is defined as the upper operational boundary for continuous flow plungers. This study presents a new methodology to predict fall velocity using the drag coefficient vs. Reynolds number relationship, wall effect, liquid holdup, deviation corrections, and incorporating multiphase flow simulation.


1994 ◽  
Vol 59 (12) ◽  
pp. 2583-2594 ◽  
Author(s):  
Miloslav Hartman ◽  
Otakar Trnka ◽  
Karel Svoboda ◽  
Václav Veselý

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.


1993 ◽  
Vol 58 (5) ◽  
pp. 961-982 ◽  
Author(s):  
Miroslav Hartman ◽  
John G. Yates

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.


Atmosphere ◽  
2020 ◽  
Vol 11 (5) ◽  
pp. 494
Author(s):  
Alexander Theis ◽  
Stephan Borrmann ◽  
Subir Kumar Mitra ◽  
Andrew J. Heymsfield ◽  
Miklós Szakáll

The complex surface geometries of hailstones affect their fall behavior, fall speeds, and growth. Systematic experimental investigations on the influence of the number and length of lobes on the fall velocity and the drag coefficient of hailstones were performed in the Mainz vertical wind tunnel to provide relationships for use in numerical models. For this purpose, 3D prints of four artificial lobed hailstone models as well as spheres were used. The derived drag coefficients show no dependency in the Reynolds number in the range between 25,000 and 85,000. Further, the drag coefficients were found to increase with increasing length of lobes. All lobed hailstones show higher or similar drag coefficients than spheres. The terminal velocities of the the hailstones with short lobes are very close to each other and only reduced by about 6% from those of a sphere. The terminal velocities from the long lobed hailstones deviate up to 21% from a sphere. The results indicate that lobes on the surface of hailstones reduce their kinetic energy by a factor of up to 3 compared to a sphere. This has important consequences for the estimation of the destructive potential of hailstones.


1983 ◽  
Vol 105 (2) ◽  
pp. 174-178 ◽  
Author(s):  
K. W. Ragland ◽  
M. A. Mason ◽  
W. W. Simmons

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.


2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Zegao Yin ◽  
Zhenlu Wang ◽  
Bingchen Liang ◽  
Li Zhang

A spherical particle’s acceleration fall through still fluid was investigated analytically and experimentally using the Basset-Boussinesq-Oseen equation. The relationship between drag coefficient and Reynolds number was studied, and various parameters in the drag coefficient equation were obtained with respect to the small, medium, and large Reynolds number zones. Next, some equations were used to derive the finite fall time and distance equations in terms of certain assumptions. A simple experiment was conducted to measure the fall time and distance for a spherical particle falling through still water. Sets of experimental data were used to validate the relationship between fall velocity, time, and distance. Finally, the initial velocity effect on the total fall time and distance was discussed with different terminal Reynolds numbers, and it was determined that the initial velocity plays a more important role in the falling motion for small terminal Reynolds numbers than for large terminal Reynolds number scenarios.


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