Drag Coefficient Of Particles Research Articles

Influence of Particle Shape on the Drag Coefficient for Isometric Particles

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.

A rational approach to drag prediction of spherical and nonspherical particles

In the past, general formulas for calculating the drag coefficient for both spherical and nonspherical particles have involved a dependence on a Reynolds number ( Re) and one or more shape descriptors resulting in complicated functions of at least two variables. This paper shows that both the Stokes' shape factor ( K 1) and the Newton's shape factor or scruple ( K 2) are important for the prediction of drag. However, instead of requiring a function of three variables ( Re, K 1, K 2) to predict drag, a function only of the generalized Reynolds number ReK 1 K 2 is needed. The shape factors K 1 and K 2 are then modeled as functions of the geometric shape descriptors' sphericity and the projected area in the direction of motion. Goodness of fit to experimental data is calculated and compared with a recently determined formula.

Flow of slightly settling slurries in a horizontal rotary drum

AbstractAn experimental study was conducted to examine the flow of slightly settling slurries in a horizontal rotary drum. The effects of the slurry flow rate, feed solids concentration, particle settling velocity and drum rotational speed on the hold‐up solids concentration were investigated.At low drum speeds, the hold‐up solids concentration was much higher than that of the feed. However, at higher drum speeds, the hold‐up solids concentration approached that in the feed. At a given drum speed, the hold‐up solids concentration was found to vary linearly with the feed solids concentration. A semi‐empirical correlation was developed to predict the hold‐up solids concentration using the drum Froude number, the single particle drag coefficient and a dimensionless slurry feed rate.

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)

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

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

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

A holistic approach to particle drag prediction

Although perfect spherical particles are not often encountered in the practical engineering world, most particle drag research to date has centered around spherical particles. Unfortunately, there has been no other way to predict irregular particle drag accurately due to the lack of reliable shape descriptors for rough particles. This paper presents a unified diagram (analogous to the Moody diagram for pipe friction factors) to predict particle drag coefficients. The diagram developed presents particle drag as a function of Reynolds number and a hydrodynamic particle shape descriptor, called scruple ( Z), which characterizes the shape, roughness, or irregularity, of a particle. Several methods of calculating scruple are presented. It may be found from such shape descriptors as sphericity, aspect ratio or harmonic persistence, since data exist to relate these descriptors to drag coefficient. Also, it may be presented directly as an approximate value for some given ore, object or shape, as found from experimental data. Future experimental work on drag coefficients will serve to expand our prediction of scruple and extend this simple approach to the prediction of particle drag.

Drag Coefficient and Fall Velocity of nonspherical particles

The most commonly encountered particles in the areas of sediment transport, fluidization, sedimentation, etc. are nonspherical. The role of these particles can be ascertained only through the knowledge of drag coefficient and fall velocity. Graphical relationships for the determination of drag coefficient and fall velocity are available in the literature. The graphical relationships are less accurate because they are subject to errors of judgment. Furthermore, these relationships cannot be used for any analytical purposes. In 1954, Schulz et al. collected extensive data for the drag coefficient and fall velocity of nonspherical particles. Based on these data, empirical equations for the drag coefficient and fall velocity of nonspherical particles of natural and mechanical origin are derived from curve fittings and presented. It is hoped that these equations will find use in the analytical modeling of various engineering problems involving fluid‐nonspherical particles interaction.

The effect of particle shape on the spouting properties of non-spherical particles

The spouting properties of thirteen types of particles (twelve being agricultural seeds) were measured in a 150-mm diameter cylindrical column with a 60° conical base. The particles, with sphericities varying from 0.39 to 1 (one being 0.39, others being in the range of 0.66–1.0), were investigated to determine the effect of shape factor on the minimum spouting velocity and the fountain height of non-spherical particles. By using the effective particle size, ϕ d v, in the Mathur-Gishler correlation, the minimum spouting velocity was predicted within ±20%. Using the volume equivalent size d v, overpredicted the minimum spouting velocity for particles with sphericities less than 0.75. The fountain height is calculated by first solving the mass and momentum balance equations in the spout to calculate the particle velocity at the bed surface. By including the effect of particle shape on the particle drag coefficient in the spout, the fountain height could be predicted reasonably well (within ±40% for 12 of the 13 types of particles). If the effect of particle shape was ignored, the predicted fountain heights were much lower than the experimental values.

Application of an electrodynamic balance to the study of particle-fluid interactions

An electrodynamic balance was used to study the aerodynamics and mass transfer characteristics of spherical and nonspherical particles up to 200 μm in size. The balance uses an electric field established by a DC potential to a pair of end electrodes and an AC potential to the central electrode to suspend single changed particles. The suspended particle is then subjected to a steady and/or oscillating air jet. Results from this study indicate that the drag coefficient of irregular-shaped particles was greater than that for spheres, and was unaffected by rotation. Measured mass transfer rates for irregular-shaped naphthalene particles were consistently higher than values predicted for equivalent spheres. These results suggest a strong influence of mass transfer on particle shape and particle Reynolds number.

雪氷粒子の水力輸送に関する基礎的研究 氷粒子の抗力係数

In this paper, drag coefficients of sphere and non-sphere ice particles and its effects on pressure loss in icewater two-phase flow were described. Drag coefficients of sphere ice particles fell close to the previous CD-Res curve (drag coefficient-particle Reynolds number), while those of non-sphere ice particles were in the range of 1-6 in this experiment.Particle motion in water was analyzed by the equation of motion taking into account Basset term. By comparing the experimented particle trajectories with calculated ones, it was confirmed that the Basset term played an important role in motion of particles with densities near that of water such as snow, ice and polystyrene.Pressure loss for ice-water two-phase flow was measured and compared with the results calculated by Durand'sand Newitt's equation. The use of adequate drag coefficient in Durand's equation gave a good agreement between the experimental results and calculated ones at low velocities. At high velocities, a discrepancy was observed because Durand's equation always gave positive values, but negative values of pressure loss coefficients were obtained in this experiment. Newitt's equation showed larger values than the experiments because this equation was applicable to the flow with a moving bed.

Pressure gradient and friction factor for sedimentation and fluidisation of uniform spheres in liquids

A new method is given for the calculation of the drag force, pressure gradient and friction factor for sedimenting suspensions and fluidised beds of uniform spherical particles in liquids. A comparison is made with previous methods of correlation. In addition, the relationship between the various drag coefficients for particles in concentrated suspensions is clarified. The importance of the particle-to-vessel diameter ratio in determining the value of the drag coefficient is established.

Drag coefficient and terminal velocity of spherical and nonspherical particles

Explicit equations are developed for the drag coefficient and for the terminal velocity of falling spherical and nonspherical particles. The goodness of fit of these equations to the reported experimental data is evaluated and is compared with that of other recently proposed equations. Accurate design charts for C D and u t are prepared and displayed for all particle sphericities.

Drag coefficient for axisymmetric flow around individual spheroidal particles

A correlation relating drag coefficients for spheroidal particles to Reynolds number and aspect ratio has been developed. Regression analysis was performed on available data; the resulting expression is capable of accurately predicting drag coefficients over a Reynolds number range of 1 to 200 with the aspect ratio varying from 0.2 to 5.

Settling Velocity of Variously Shaped Particles in Drilling and Fracturing Fluids

Summary The settling velocities of a variety of shaped particles to simulate drilled cuttings were measured in both Newtonian and non-Newtonian fluids. The results showed that the particle drag coefficient is a function of the particle Reynolds number and, in the case of power-law-model fluids, of the flow behavior index. A new generalized model has been developed for predicting the settling velocities of particles of various shapes in both Newtonian and power-law fluids over a range of flow regimes.

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

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 Improved Approach to Calculating Terminal Velocities of Plate-like Crystals and Graupel

Abstract Measurements of 461 planar crows and 312 graupel reported by Kajikawa have been used to develop equations for calculating the terminal velocity and mass of lump and conical graupel and of planar crystals of a variety of shapes and degrees of riming, the resultant equations being applicable to numerical modeling studies. Because all of the parameters required for the derivation of particle drag coefficients were known, the equations are more accurate than those previously used. The implications of the changed values for terminal velocity for these particle types are discussed with respect to the growth of particles through accretion.

Particle drag in a dilute turbulent two-phase suspension flow

The drag between phases plays an important role in the study of a turbulent two-phase suspension flow and its physical understanding will greatly promote progress in theoretical treatments of a whole range of important industrial and technical problems involving such a flow. The conventional practice of using the results of measurements based on a single particle in a laminar stream for the case of a turbulent flow of a dilute suspension is questioned. An analysis of the results of local measurements of upward turbulent flows of a solid particle-air two-phase suspension leads to the determination of the realistic particle drag coefficient over a wide range of flow conditions. It is established that the particle drag can be described by the simple Stokes law, based on an apparent turbulent viscosity of the fluid for the particles in the suspension flow. A correlation is provided for this apparent turbulent viscosity in terms of the particle size and concentration in the suspension, the local flow turbulence Reynolds number and the particle-to-fluid density ratio.

FREE SETTLING OF A NON-SPHERICAL PARTICLE IN A STAGNANT LIQUID

ABSTRACT The free settling behavior of the cylindrical particles made of four kinds of materials with horizontal motion in the stagnant water observed with an aid of the image sensor anemometer in the Reynolds number ranged from about 150 to 1000 was investigated in this paper. The four kinds of materials were finished into cylindrical specimens having the diameters “d” of 1.5 to 3.0 mm and the ratios of “d” to the length of specimen “1s” of d/1s = 1/2 to 1/3.5. From the experimental results, the settling behavior of the particles was found to be simply expressed by the equation of a simple harmonic motion. By correcting the drag coefficient of the cylindrical particles with a correction factor which is obtained from the simple harmonic motion, the relationship between the drag coefficient and Reynolds number for the cylindrical particles was found to be parallel to that for the spherical particles.

Dispersed powder flow through vertical pipes

In this study a novel transducer, based on an electrical capacitance principle, was used to measure the instantaneous volume-averaged in situ particle fraction and thereby determine the volume-averaged particle velocities. It was clear that the 450 μm diameter sand particles were being accelerated to a terminal slip velocity with respect to the gas phase. The static pressure drop over the same length was also measured and interpreted by means of a one-dimensional, two-phase model. The contributions to the overall pressure drop of gravitational forces on the particle, acceleration of gas and particles and the coupling force between gas and particles were calculated. The gas—particle drag coefficients were within 30% of those of single particles. A predictive model was also developed which yielded good results with the experimental data.

Hydrotransport of solids in horizontal pipes: Effects of solids concentration and particle size on the deposit velocity

AbstractCorrelations previously proposed in the literature for the deposit velocity in the flow of settling slurries in horizontal tubes generally predict increasing values with increasing solids concentration. However, the present comprehensive investigation which has drawn on data from a broad geographical base, confirms that the deposit velocity shows a maximum with respect to concentration and decreases above about 15% by volume solids. It is also shown that the presence of fine particles (&lt;75 μm) is particularly significant in determining the degree of the reduction in the deposit velocity for the higher concentrations. This reduction would appear to be due primarily to a significant increase in the drag coefficient for particles settling in a fine particle suspension, i.e. heavy medium. The data are summarized in graphs for a variety of materials including sand, gravel, iron ore and coal.