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.

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.

Drag Coefficient and Settling Velocity of Particles in Non-Newtonian Suspensions

1987 ◽  
Vol 109 (3) ◽  
pp. 319-323 ◽  
Author(s):  
M. Y. Dedegil
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Drag Coefficient ◽  
Yield Stress ◽  
Particle Velocity ◽  
Settling Velocity ◽  
Fluid Velocity ◽  
Newtonian Fluids ◽  
Drag Forces ◽  
Physical Composition

Drag forces on bodies in non-Newtonian fluids which are to be described by using the Reynolds number should only contain forces which are associated with the fluid velocity or particle velocity. Forces due to the yield stress τ0 must be considered separately. According to its physical composition, the Reynolds number must be calculated by means of the fully representative shear stress including the yield stress τ0. Then the drag coefficient cD as a function of the Reynolds number can be traced back to that of Newtonian fluids.

An Immersed Boundary Direct Numerical Simulation Study of the Wall Effect on the Dynamics of a Rigid Sphere

2017 ◽  
Author(s):  
Jason Gatewood ◽  
Zhi-Gang Feng
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Drag Coefficient ◽  
Particle Diameter ◽  
Laminar Flows ◽  
Wall Effect ◽  
Immersed Boundary ◽  
Rigid Sphere ◽  
Rigid Spheres

The presence of a wall near a rigid sphere is known to disturb the particle fore and aft flow field and thereby affect particle drag and lift. This effect has wide ranging implications in particulate flows such as the dynamics of blood cells in microvessels or the transport of particulates in channel and pipe flows. In this study, an Immersed Boundary Direct Numerical Simulation (IB-DNS) is used to predict the dynamics of a rigid spherical body in the presence of a wall at laminar flows. The wall effect is shown to be significant when the dimensionless ratio (L/D) of the particle diameter (D) to the wall distance (L) is less than 3, and when particle Reynolds number is less than 10. Based on the IB-DNS results, a correlation for the wall effect on drag coefficient is derived that can be used to predict the actual drag coefficient for rigid spheres under the influence of a wall for L/D between 0.75 and 3 and Reynolds number between 0.18 and 10. The data underlying the correlation developed herein is validated by comparison to published experimental, numerical, and analytical correlations. The application of the IB-DNS method to study the wall effect is both novel and significant. It is novel in that such an application is not yet demonstrated. It is significant in that it; (1) utilizes a uniform Cartesian fluid mesh and (2) requires no sub domains of higher grid resolution in the wall gap.

Effective Drag Coefficient for Gas-Particle Flow in Shock Tubes

1970 ◽  
Vol 92 (1) ◽  
pp. 165-172 ◽  
Author(s):  
George Rudinger
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Particle Motion ◽  
Gas Flow ◽  
Particle Concentration ◽  
Particle Diameter ◽  
Weak Shock ◽  
Average Particle ◽  
Particle Rotation ◽  
Lateral Velocity

Effective drag coefficients for flows of suspensions of spherical glass particles in air were derived from simultaneous measurements of pressure and particle concentration in the flow behind weak shock waves. Average particle diameters were 29 and 62μm. The instantaneous concentration was determined by light scattering, and the results agree well with earlier shock-tube data based on streak records. They exhibit several unexpected features: the correlation between drag coefficient and Reynolds number is much steeper (∝ Re−1.7) than the generally used “standard” curve but approaches it at Reynolds numbers of several hundred; the correlation is independent of the particle concentration over the range of the experiments, that is, for particle-to-gas flow rate ratios between about 0.05 and 0.36; if the Reynolds number immediately behind the shock front is changed by varying the shock strength, the points move along the correlation, but if it is changed by changing the particle size, the entire correlation is shifted although to a smaller extent than would correspond to the direct effect of particle diameter on the Reynolds number. To account for the observations, a flow model is developed which allows for microscopic longitudinal and lateral perturbations of the particle motion that are the result of various causes, such as particle interactions with wakes of other particles, lateral forces caused by particle rotation, or electrostatic forces. Because of the nonlinearity of the equation of motion, the averaged particle motion is different from that of a particle without perturbations. The effective drag coefficient for the average particle motion is therefore different from the standard drag coefficient applied along the actual motion. With this model and plausible assumptions for the average lateral velocity component of the particle motion, all features of the experimental data can be qualitatively explained.

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.

scholarly journals A Wind Tunnel Investigation into the Aerodynamics of Lobed Hailstones

Atmosphere ◽  
2020 ◽  
Vol 11 (5) ◽  
pp. 494
Author(s):  
Alexander Theis ◽  
Stephan Borrmann ◽  
Subir Kumar Mitra ◽  
Andrew J. Heymsfield ◽  
Miklós Szakáll
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Kinetic Energy ◽  
Drag Coefficient ◽  
Numerical Models ◽  
Complex Surface ◽  
Experimental Investigations ◽  
Fall Velocity ◽  
Drag Coefficients ◽  
Destructive Potential

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.

scholarly journals Experimental modeling of the interaction of hard and aeriform body and the onset of a drag crisis with a significant change in velocity

2021 ◽  
Vol 2131 (2) ◽  
pp. 022124
Author(s):  
N V Kudinov ◽  
A M Atayan
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Drag Coefficient ◽  
Air Flow ◽  
Aerodynamic Characteristics ◽  
Spherical Body ◽  
Experimental Modeling ◽  
Numerical Information ◽  
Physical Experiments ◽  
Glue Method

Abstract The paper deals with the possibilities and prospects of experimental modeling of the interaction of a solid and a gaseous body. It is assumed that reliable experimental data have already been obtained and published. The problem of approximating the complex aerodynamic characteristics of air flow around a spherical body is posed and solved. The study was carried out using the «Cut-Glue» method for approximating numerical information about blowing experiments. Generally, this information reflects the dependence of the drag coefficient on the Reynolds number. The choice of the Cut-Glue method for the approximation of complex, multiextremal characteristics that can be obtained in physical experiments is substantiated.

A strong-interaction theory for the motion of arbitrary three-dimensional clusters of spherical particles at low Reynolds number

1988 ◽  
Vol 197 ◽  
pp. 1-37 ◽  
Author(s):  
Qaizar Hassonjee ◽  
Peter Ganatos ◽  
Robert Pfeffer
Keyword(s):  
Exact Solution ◽  
Reynolds Number ◽  
Low Reynolds Number ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Particle Diameter ◽  
Simple Expression ◽  
Spherical Particles ◽  
Solution Technique ◽  
Low Reynolds

This paper contains an ‘exact’ solution for the hydrodynamic interaction of a three-dimensional finite cluster at arbitrarily sized spherical particles at low Reynolds number. The theory developed is the most general solution to the problem of an assemblage of spheres in a three-dimensional unbounded media. The boundary-collocation truncated-series solution technique of Ganatos, Pfeffer & Weinbaum (1978) for treating planar symmetric Stokes flow problems has been extensively modified to treat the non-symmetric multibody problem. The orthogonality properties of the eigenfunctions in the azimuthal direction are used to satisfy the no-slip boundary conditions exactly on entire rings on the surface of each particle rather than just at discrete points.Detailed comparisons with the exact bipolar solutions for two spheres show the present theory to be accurate to five significant figures in predicting the translational and angular velocity components of the particles at all orientations for interparticle gap widths as close as 0.1 particle diameter. Convergence of the results to the exact solution is rapid and systematic even for unequal-sized spheres (a1/a2 = 2). Solutions are presented for several interesting and intriguing configurations involving three or more spherical particles settling freely under gravity in an unbounded fluid or in the presence of other rigidly held particles. Advantage of symmetry about the origin is taken for symmetric configurations to reduce the collocation matrix size by a factor of 64. Solutions for the force and torque on three-dimensional clusters of up to 64 particles have been obtained, demonstrating the multiparticle interaction effects that arise which would not be present if only pair interactions of the particles were considered. The method has the advantage of yielding a rather simple expression for the fluid velocity field which is of significance in the treatment of convective heat and mass transport problems in multiparticle systems.

scholarly journals Slipping motion of large neutrally buoyant particles in turbulence

2013 ◽  
Vol 735 ◽  
Author(s):  
Mamadou Cisse ◽  
Holger Homann ◽  
Jérémie Bec
Keyword(s):  
Reynolds Number ◽  
Fluid Velocity ◽  
Particle Diameter ◽  
Viscous Sublayer ◽  
Energy Dissipation Rate ◽  
Spherical Particles ◽  
Viscous Boundary Layer ◽  
Average Value ◽  
Wall Flows ◽  
Shadowing Effect

AbstractDirect numerical simulations are used to investigate the individual dynamics of large spherical particles suspended in a developed homogeneous turbulent flow. A definition of the direction of the particle motion relative to the surrounding flow is introduced and used to construct the mean fluid velocity profile around the particle. This leads to an estimate of the particle slipping velocity and its associated Reynolds number. The flow modifications due to the particle are then studied. The particle is responsible for a shadowing effect that occurs in the wake up to distances of the order of its diameter: the particle calms turbulent fluctuations and reduces the energy dissipation rate compared to its average value in the bulk. Dimensional arguments are presented to draw an analogy between particle effects on turbulence and wall flows. Evidence is obtained for the presence of a logarithmic sublayer at distances between the thickness of the viscous boundary layer and the particle diameter ${D}_{p} $. Finally, asymptotic arguments are used to relate the viscous sublayer quantities to the particle size and the properties of the outer turbulence. It is shown in particular that the skin-friction Reynolds number behaves as $R{e}_{\tau } \propto {({D}_{p} / \eta )}^{4/ 3} $.

Sign in / Sign up

Export Citation Format

Share Document