Drag Coefficient Of Spherical Particle Research Articles

A Novel Prediction Model of the Drag Coefficient of Irregular Particles in Power-Law Fluids

The settlement drag coefficient of irregular particles in power-law fluids is a crucial parameter in the field of petroleum engineering. However, the irregular shape of the particle and the non-Newtonian rheological properties of the fluid make it challenging to predict the settlement drag coefficient. In this study, the spherical and irregular particle sedimentation processes in power-law fluids have been analyzed using a visual device and a high-speed camera system. A mechanical model dependent on the force balance of settlement particles was adopted to conduct a detailed statistical analysis of 114 spherical particle experimental results, and a prediction model of the drag coefficient of spherical particles in the power-law fluid was established with a mean relative error of 3.85%. On this basis, considering the influence of geometric shape on the law of particle sedimentation, a new irregular particle sedimentation resistance coefficient model in power-law fluid is established via the incorporation of the parameter circularity of 2D shape description c into the spherical particle sedimentation resistance coefficient predictive model. The parameters in the new irregular particle sedimentation resistance coefficient predictive model can be obtained via nonlinear data fitting of the 211 groups of irregular particles using experimental results in the power-law fluid. The model has high prediction accuracy for the drag coefficient of irregular particles in power-law fluid, with a mean relative error of 4.47, and expands the scope of engineering applications, which is of great significance for fracturing scheme design and wellbore cleaning.

New Model for Non-Spherical Particles Drag Coefficients in Non-Newtonian Fluid

The settlement drag coefficient of non-spherical particles (SDCNPs) is a crucial parameter in the field of petroleum engineering. Accurately predicting the SDCNPs in the fluid is essential to the selection and design of proppant and hydraulic design in the fracturing scheme. Although many models for anticipating the SDCNPs have been proposed, none of them can be adopted for non-Newtonian fluid (NNF) and Newtonian fluid (NF). In the investigation, the SDCNPs in NF and NNF are studied experimentally, and the anticipation mode of the settlement drag coefficient of spherical particles (SDCSPs) in different fluids (including Newton, Herschel-Bulkley and power law) is proposed. On this basis, the shape depiction parameter circularity is introduced to develop the SDCNPs. The results exhibit that the predicted values of the SDCNPs model perfectly align with the experimental values, and the average relative errors are 5.70%, 6.24% and 6.72%, respectively. The mode can accurately describe the settlement behavior of non-spherical particles (NSPs) and provide a basis for the application of NSPs in petroleum engineering.

A Novel Prediction Model of the Drag Coefficient of Shale Cuttings in Herschel–Bulkley Fluid

In the drilling industry, it is of great significance to accurately predict the drag coefficient and settling velocity of drill cuttings falling in the non-Newtonian drilling fluid. However, the irregular shape of drill cuttings and the non-Newtonian rheological properties of drilling fluid (e.g., shear-thinning and yield stress behavior) make it challenging to predict the settling velocity. In this study, the velocity of particle settlement was studied by a visual device and high-speed camera system. Experimental data of the free settlement of 224 irregular drilling cuttings and 105 spherical particles in the Herschel–Bulkley fluid were obtained. A mechanical model dependent on the force balance of settlement particles was adopted to conduct a detailed statistical analysis of the experimental results, and a prediction model of the drag coefficient of spherical particles in the Herschel–Bulkley fluid was established. A two-dimensional shape description parameter is introduced to establish a model for predicting the drag coefficient of irregular-shaped cuttings in a Herschel–Bulkley fluid. The model has high prediction accuracy for the settling velocity of irregular shale cuttings in Herschel–Bulkley fluid. The average relative error is 7.14%, verifying the model’s accuracy.

General Drag Coefficient for Flow over Spherical Particles

A generalized physics-based expression for the drag coefficient of spherical particles moving in a fluid is developed. The proposed correlation incorporates essential rarefied effects, low-speed hydrodynamics, and shock-wave physics to accurately model the particle-drag force for a wide range of Mach and Knudsen numbers (and therefore Reynolds number). Owing to the basis of the derivation in physics-based scaling laws, the proposed correlation embeds gas-specific properties and has explicit dependence on the ratio of specific heat capacities. The correlation is applicable for arbitrary particle relative velocity, particle diameter, gas pressure, gas temperature, and surface temperature. Compared with existing drag models, the correlation is shown to more accurately reproduce a wide range of experimental data. Finally, the new correlation is applied to simulate particle trajectories in high-speed dusty flows, relevant to a spacecraft entering the Martian atmosphere. The enhanced surface heat flux due to particle impact is found to be sensitive to the particle drag model.

The effect of Stefan flow on Nusselt number and drag coefficient of spherical particles in non-isothermal gas flow

A Stefan flow can be generated during a phase change or reactions of a particle immersed in a fluid. This study investigates the effect of Stefan flow on the exchange of momentum (drag coefficient (CD)) and heat transfer (Nusselt number (Nu)) between the particle and bulk-fluid. Fully resolved simulations were carried out for a flow near a spherical particle immersed in a uniform bulk flow. The immersed boundary method is used for implementing fluid-solid interactions and the particle is considered as a static boundary with fixed boundary conditions. In a non-isothermal flow, the changes in thermophysical properties at the boundary layer played a role in the variation of CD and Nu by a Stefan flow further. The previously developed model for the drag coefficient of a spherical particle in a uniform isothermal flow was modified for a uniform non-isothermal flow. The model is developed based on physical interpretation. A new model is developed for the Nusselt number for a spherical particle with a uniform Stefan flow combining available models in literature. The models are validated for Stefan Reynolds number −8⩽Resf,p⩽25 and particle Reynolds number of 2⩽Ref⩽30 in gas flow (i.e. Pr≈0.7).

The effect of Stefan flow on the drag coefficient of spherical particles in a gas flow

Particle laden flows with reactive particles are common in industrial applications. Chemical reactions inside the particle can generate a Stefan flow that affects heat, mass and momentum transfer between the particle and the bulk flow. This study aims at investigating the effect of Stefan flow on the drag coefficient of a spherical particle immersed in a uniform flow under isothermal conditions. Fully resolved simulations were carried out for particle Reynolds numbers ranging from 0.2 to 14 and Stefan flow Reynolds numbers from (−1) to 3, using the immersed boundary method for treating fluid-solid interactions. Results showed that the drag coefficient decreased with an increase of the outward Stefan flow. The main reason was the change in viscous force by the expansion of the boundary layer surrounding the particle. A simple model was developed based on this physical interpretation. With only one fitting parameter, the performance of the model to describe the simulation data were comparable to previous empirical models.

Technique for measurements of the drag coefficient of spherical particle at condition of gas injection from its surface

A new technique for measurement of the drag coefficient of spherical particle at condition of gas injection from its surface is presented. Results of investigation of the effect of the gas injection from a surface of a solid spherical particle on the drag coefficient are presented. In the investigation, the ratio of the gas injection rate and the velocity of the flow blowing around the particle was varied. Based on the obtained results, it is shown that the drag coefficient in condition the absence of the gas injection from the particle surface in the examined range of the Reynolds numbers are consistent with the standard drag dependence for the turbulent flow regime. At the same time, when at condition of gas injection from the particle surface, the drag coefficient is decreased (this effect is more pronounced with a decrease in the flow rate). The dependences of the change in the drag coefficient on the Reynolds number with changing the rate of the gas injection from the particle surface.

The method for studying the drag coefficient of spherical particles under non-isothermal conditions

A method and results of an experimental studying the sedimentation of solid spherical particles in a viscous liquid under non-isothermal conditions at low Reynolds numbers (Re<1) are presented. To determine the dependence of the drag coefficient on the temperature difference between the particles and liquid, a special setup has been developed. The experimental setup for determining the effect of non-isothermal conditions on the gravitational sedimentation of solid spherical particles in a viscous liquid consists of a prismatic cell with a viscous liquid, a particle heating device, a device for incorporating the reference and heated particles into the liquid, and a system for visualization of the particle sedimentation. In the experimental setup, two particles of the same diameter, made of the same material, are introduced into the cell at a zero initial velocity. Immediately before introduction into the liquid, one of the particles is heated (or cooled) to a temperature different from the temperature of the other (reference) particle, equal to the temperature of the liquid. The deposition rate of each of the particles is measured by the time-of-flight method using video of the deposition process through the transparent walls of the cell. As a result of a series of experiments, a decrease in the drag coefficient by 38% was obtained at a maximum temperature difference between the particles and liquid of 280°C.

General formulas for drag coefficient and settling velocity of sphere based on theoretical law

The settlement of particles is of great importance in many areas. The accurate determination of drag coefficient and settling velocity in wide Reynolds number (Re) range remains a problem. In this paper, a series of new formulas for drag coefficient of spherical particles based on theoretical laws, such as the Stokes law, the Oseen law, and the Goldstein law, were developed and fitted using 480 groups of experimental data (Re<2×105). The results show that the 2nd approximation of a rational function containing only one parameter can describe CD–Re relationship accurately over the whole Re range of 0–2×105. The new developed formulas containing five parameters show higher goodness over wide Re range than presently existing equations. The introduction of the Oseen law is helpful for improving the fitting goodness of the empirical formulas. On the basis of one of the Oseen-based CD–Re formulas giving the lowest sum of squared relative errors Q over the whole Re range (Re<2×105), a general formula for settling velocity ut based on dimensionless parameters was proposed showing high goodness.

Predicting the drag coefficient and settling velocity of spherical particles

Abstract This paper presents a relationship for calculating the drag coefficient of a spherical particle. The results obtained were validated using experimental data, including comparison with results from other relationships such as certainty analysis. The validation indicated that the proposed relationship is easier to apply and produces the best results. In addition, a relationship based on the characteristics of both the fluid and the particles was established to calculate directly the settling velocity of a spherical particle in a fluid at rest. The settling velocity values obtained with the proposed relationship were validated using experimental data and the model proved to be reliable and precise.

Drag Coefficient in Solid–Fluid System Modeling with the Eulerian Multiphase Model

This article reviews the formulas determining the drag coefficient of spherical particles moving in a fluid system in the context of numerical modeling of spouted bed grain dryers. The study describes several formulas that have been implemented in code Fluent 6.3, in a simulation model of a spouted bed based on the Eulerian multiphase model. The article also analyzes the voidage function that accounts for the effect of particle density on the value of the drag coefficient. Simulation results were compared with the basic model, which has been discussed in detail in a different study carried out by the author. This study investigates the computer model's response to changes in the manner of computing the drag coefficient and the possibility of applying various computational formulas in spouted bed modeling. The experiment was conducted by the author in view of the scarcity of publications on the subject and the need to organize the existing knowledge on drag coefficient modeling, which is the main contribution of the article.

Calculation of the Velocity of Free Settling of Solid Particles in a Newtonian Liquid

A cubic equation for the velocity of free settling of solid particles in a Newtonian liquid is derived on the basis of a simple approximate expression for the drag coefficient of spherical particles as a function of the Reynolds number using the concept of the effective diameter of a particle of arbitrary shape, which characterizes the surface, volume, and midsection of the particle. The exact and approximate solutions are compared, and some experimental data are analyzed.

516 管壁面上を転動する球粒子の非定常抗力係数 : 粒子密度と圧力波範囲を拡張した場合

516 管壁面上を転動する球粒子の非定常抗力係数 : 粒子密度と圧力波範囲を拡張した場合

Measurement of the Drag Coefficient of Spherical Particles Attached to Fluid Interfaces

The drag coefficient, β, of spherical particles attached to a pure air-water interface is determined. The method is based on the measurement of the particle velocity V, under the action of a well-defined lateral capillary force F. The capillary force is created by controlled deformation of the water surface by means of a Teflon barrier whose vertical position can be precisely adjusted. The magnitude of the force is calculated by means of the theory of capillary interaction between a sphere and a vertical wall (Kralchevsky et al., J. Colloid Interface Sci. 167, 47, 1994). The drag coefficient is calculated from the ratio β = F/V at small Reynolds numbers. The dependence of the drag coefficient on the particle size and the three-phase contact angle is determined. For small spheres, which do not create substantial deformation of the fluid interface, β is always smaller than the Stokes coefficient, βs - 6 πηa (η is the water viscosity and a is the particle radius). For large spheres, however, β can be greater than βs. This higher hydrodynamic resistance can be explained by the presence of a curved meniscus around heavier particles. The measured values of β are compared with theoretical calculations and very good agreement is reached. It is demonstrated that the method is sensitive to the presence of adsorbed surfactants and that it can be used for the determination of the surface viscosity of adsorbed layers.

PARTICLE SIZE CLASSIFICATION BY DEPOSITION ANGLE IN A GAS CENTRIFUGE AT REDUCED PRESSURE

Centrifugal particle size classification by a gas centrifuge which produces a forced vortex was investigated at reduced pressures. In this method, different particle trajectories cause the formation of a continuous gradation of particle size on the rotor wall. Here, particles in the subsieve and submicron ranges were classified with good resolution because the ''Cunningham correction'' increases as pressure decreases. Also, the computed solutions gave excellent agreement with the experimental results. The numerical solutions with and without the integral term for non-uniform motion have been compared, the approximate equation of best fit for the drag coefficient of spherical particles being used in both cases.

NEW APPROXIMATE EQUATION OF DRAG COEFFICIENT FOR SPHERICAL PARTICLES

An approximate equation for the drag coefficient of spherical particles is proposed in the form of a quadratic equation in logarithmic co-ordinates. The constants of the equation have been determined by the least square method from experimental values5). This equation gives better agreement with experimental values than the equations proposed previously by other authors. The constants of the equation and the comparison of its accuracy are summarized in Tables I and 2. This equation is valid even at Reynolds numbers between O and 70, 000, the standard deviation of the relative error being 5%.