Density difference-driven segregation in a dense granular flow

2013 ◽  
Vol 717 ◽  
pp. 643-669 ◽  
Author(s):  
Anurag Tripathi ◽  
D. V. Khakhar
Keyword(s):  
Distinct Element ◽  
Tracer Particle ◽  
Packing Fraction ◽  
Heavy Particles ◽  
Drag Forces ◽  
Fluctuation Dissipation ◽  
Granular Mixtures ◽  
Inclination Angles ◽  
Tangential Forces ◽  
Dense Granular Flow

AbstractWe consider the segregation of spheres of equal size and different density flowing over an inclined plane, theoretically and computationally by means of distinct element method (DEM) simulations. In the first part of the work, we study the settling of a single higher-density particle in the flow of otherwise identical particles. We show that the motion of the high-density tracer particle can be understood in terms of the buoyancy and drag forces acting on it. The buoyancy force is given by Archimedes principle, with an effective volume associated with the particle, which depends upon the local packing fraction, $\phi $. The buoyancy arises primarily from normal forces acting on the particle, and tangential forces have a negligible contribution. The drag force on a sphere of diameter $d$ sinking with a velocity $v$ in a granular medium of apparent viscosity $\eta $ is given by a modified Stokes law, ${F}_{d} = c\pi \eta dv$. The coefficient ($c$) is found to decrease with packing fraction. In the second part of the work, we consider the case of binary granular mixtures of particles of the same size but differing in density. A continuum model for segregation is presented, based on the single-particle results. The number fraction profile for the heavy particles at equilibrium is obtained in terms of the effective temperature, defined by a fluctuation–dissipation relation. The model predicts the equilibrium number fraction profiles at different inclination angles and for different mass ratios of the particles, which match the DEM results very well. Finally, a complete model for the theoretical prediction of the flow and number fraction profiles for a mixture of particles of different density is presented, which combines the segregation model with a model for the rheology of mixtures. The model predictions agree quite well with the simulation results.

Euler–Lagrange Two-Phase Model for Simulating Live-Bed Scour Beneath Marine Pipelines

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
A. Yeganeh-Bakhtiary ◽  
M. Zanganeh ◽  
E. Kazemi ◽  
L. Cheng ◽  
A. K. Abd Wahab
Keyword(s):  
Numerical Model ◽  
Granular Media ◽  
Fluid Shear Stress ◽  
Distinct Element ◽  
Fluid Phase ◽  
Point Of View ◽  
Two Dimensional ◽  
Two Phase ◽  
Drag Forces ◽  
Bed Scour

In this study, an Euler–Lagrange coupling two-phase flow model, namely movable bed simulator (MBS)-two-dimensional (2D) model was employed to explore the current-induced live-bed scour beneath marine pipelines. The fluid phase characteristics, such as velocity and pressure, were obtained by the Reynolds-averaged Navier–Stokes (RANS) equations with a k-ε turbulence closure model in a two-dimensional Eulerian grid, whereas the seabed beneath pipelines was traced as an assembly of discrete sand grains from the Lagrangian point of view. The live-bed scour was evolved as the motion of a granular media based on distinct element method (DEM) formulation, in which the frequent interparticle collision was described with a spring and dashpot system. The fluid flow was coupled to the sediment phase, considering the acting drag forces between. Comparison between the numerical result and experimental measurement confirms that the numerical model successfully estimates the bed profile and flow velocity field. It is evident that the fluid shear stress decreases with the increasing of gap ratio e/D. The numerical model provides a useful approach to improve mechanistic understanding of hydrodynamic and sediment transport in live-bed scour beneath a marine pipeline.

On the dynamics of buoyant and heavy particles in a periodic Stuart vortex flow

1993 ◽  
Vol 254 ◽  
pp. 671-699 ◽  
Author(s):  
Kek-Kiong Tio ◽  
Amable Liñán ◽  
Juan C. Lasheras ◽  
Alfonso M. Gañán-Calvo
Keyword(s):  
Dynamical System ◽  
Computational Study ◽  
Mass Density ◽  
Order Term ◽  
Equilibrium Points ◽  
Density Ratio ◽  
Viscous Drag ◽  
Perturbation Scheme ◽  
Heavy Particles ◽  
Drag Forces

In this paper, we study the dynamics of small, spherical, rigid particles in a spatially periodic array of Stuart vortices given by a steady-state solution to the two-dimensional incompressible Euler equation. In the limiting case of dominant viscous drag forces, the motion of the particles is studied analytically by using a perturbation scheme. This approach consists of the analysis of the leading-order term in the expansion of the ‘particle path function’ Φ, which is equal to the stream function evaluated at the instantaneous particle position. It is shown that heavy particles which remain suspended against gravity all move in a periodic asymptotic trajectory located above the vortices, while buoyant particles may be trapped by the stable equilibrium points located within the vortices. In addition, a linear map for Φ is derived to describe the short-term evolution of particles moving near the boundary of a vortex. Next, the assumption of dominant viscous drag forces is relaxed, and linear stability analyses are carried out to investigate the equilibrium points of the five-parameter dynamical system governing the motion of the particles. The five parameters are the free-stream Reynolds number, the Stokes number, the fluid-to-particle mass density ratio, the distribution of vorticity in the flow, and a gravitational parameter. For heavy particles, the equilibrium points, when they exist, are found to be unstable. In the case of buoyant particles, a pair of stable and unstable equilibrium points exist simultaneously, and undergo a saddle-node bifurcation when a certain parameter of the dynamical system is varied. Finally, a computational study is also carried out by integrating the dynamical system numerically. It is found that the analytical and computational results are in agreement, provided the viscous drag forces are large. The computational study covers a more general regime in which the viscous drag forces are not necessarily dominant, and the effects of the various parametric inputs on the dynamics of buoyant particles are investigated.

scholarly journals Forced segregation in binary granular mixtures

2021 ◽  
Vol 249 ◽  
pp. 02001
Author(s):  
Salvatore Pillitteri ◽  
Geoffroy Lumay ◽  
Éric Opsomer ◽  
Nicolas Vandewalle
Keyword(s):  
Experimental Data ◽  
Analytical Solutions ◽  
Physical Interpretation ◽  
Packing Fraction ◽  
Granular Mixtures ◽  
Large Particles ◽  
Granular Particles

Mixing granular particles of di erent sizes is a common way of increasing the packing fraction. Recently, a model predicting the packing fraction, taking into account the inhomogeneity of the mixed small and large particles, has been proposed by S. Pillitteri et al. Under certain conditions, this model can be simpli ed and analytical solutions can be found. We present here these solutions, compared to experimental data, and the physical interpretation they can bring.

scholarly journals How size ratio and segregation affect the packing of binary granular mixtures

Soft Matter ◽  
2020 ◽  
Vol 16 (39) ◽  
pp. 9094-9100
Author(s):  
Salvatore Pillitteri ◽  
Eric Opsomer ◽  
Geoffroy Lumay ◽  
Nicolas Vandewalle
Keyword(s):  
Packing Fraction ◽  
Size Ratio ◽  
Granular Mixtures ◽  
Granular Segregation ◽  
Small Grains

For reaching high packing fractions, grains of various sizes are often mixed together allowing the small grains to fill the voids created by the large ones. However, in most cases, granular segregation occurs leading to lower packing fractions. We show how a layered packing or a gradient segregation affects the global packing fraction.

scholarly journals Some Notes on Granular Mixtures with Finite, Discrete Fractal Distribution

2021 ◽  
Author(s):  
Emoke Imre ◽  
István Talata ◽  
Daniel Barreto ◽  
Maria Datcheva ◽  
Wiebke Baille ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Distinct Element ◽  
Fractal Dimensions ◽  
Internal Stability ◽  
Size Distributions ◽  
Entropy Theory ◽  
Micro Computed Tomography ◽  
Fractal Distribution ◽  
Granular Mixtures ◽  
Grain Size Distributions

Why fractal distribution is so frequent? It is true that fractal dimension is always less than 3? Why fractal dimension of 2.5 to 2.9 seems to be steady-state or stable? Why the fractal distributions are the limit distributions of the degradation path? Is there an ultimate distribution? It is shown that the finite fractal grain size distributions occurring in the nature are identical to the optimal grading curves of the grading entropy theory and, the fractal dimension n varies between –¥ and ¥. It is shown that the fractal dimensions 2.2–2.9 may be situated in the transitional stability zone, verifying the internal stability criterion of the grading entropy theory. Micro computed tomography (μCT) images and DEM (distinct element method) studies are presented to show the link between stable microstructure and internal stability. On the other hand, it is shown that the optimal grading curves are mean position grading curves that can be used to represent all possible grading curves.

scholarly journals AN IMPROVED DISTINCT ELEMENT METHOD FOR HIGH PACKING FRACTION STOCHASTIC MEDIA MODELING

2021 ◽  
Vol 247 ◽  
pp. 04026
Author(s):  
Zhiyuan Feng ◽  
Nan An ◽  
Kan Wang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Random Media ◽  
Particle System ◽  
Neutron Transport ◽  
Distinct Element ◽  
Packing Fraction ◽  
Distinct Element Method ◽  
Stochastic Media ◽  
Element Method

Due to the generality and flexibility of Monte Carlo method in geometric modeling, Monte Carlo method plays an important role in accurate simulation of random media. At present, rand om sequential addition method (RSA) and distinct element method (DEM) are more accurate and mature explicit modeling methods. The former approach has the problem of upper limit of packing fraction, which is suitable for stochastic geometry with lower filling rate. DEM method can fill random medium model with packing fraction higher than 60%, but DEM is not suitable for non-contact dispersed particles based on the interaction between particles. There fore, an improved DEM method is proposed to solve the problem of modeling non-contact p articles dispersed in the stochastic media with high packing fraction. The virtual surfaces are constructed outside of the outer layer of particles to make them in contact with each other. Thus, the particle system is suitable for DEM method. The construction of virtual surface does not affect the neutron transport process. The correctness of the improved DEM is verified by comparing the total filling particle number and calculation results ofkeffwith RSA method. At the same time, according to the distribution of filling particles, the improved DEM method fills the particles more uniformly.

scholarly journals Designing non-segregating granular mixtures

2021 ◽  
Vol 249 ◽  
pp. 03011
Author(s):  
Yifei Duan ◽  
Paul B. Umbanhowar ◽  
Richard M. Lueptow
Keyword(s):  
Particle Size ◽  
Equilibrium Condition ◽  
Density Ratio ◽  
Heavy Particles ◽  
Dem Simulations ◽  
Particle Size Ratio ◽  
Granular Mixtures ◽  
Mixture Concentration ◽  
Large Particles ◽  
Density Ratios

In dense flowing bidisperse particle mixtures varying in size or density alone, large particles rise (driven by percolation) and heavy particles sink (driven by buoyancy). When the two particle species differ from each other in both size and density, the two segregation mechanisms either enhance (large/light and small/heavy) or oppose (large/heavy and small/light) each other. In the latter case, an equilibrium condition exists in which the two mechanisms balance and the particles no longer segregate. This leads to a methodology to design non-segregating particle mixtures by specifying particle size ratio, density ratio, and mixture concentration to achieve the equilibrium condition. Using DEM simulations of quasi-2D bounded heap flow, we show that segregation is significantly reduced for particle mixtures near the equilibrium condition. In addition, the rise-sink transition for a range of particle size and density ratios matches the predictions of the combined size and density segregation model.

scholarly journals Computational Fluid Dynamics Modelling and Simulation of an Inclined Horizontal Axis Hydrokinetic Turbine

Energies ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 3151 ◽  
Author(s):  
Leidy Contreras ◽  
Omar Lopez ◽  
Santiago Lain
Keyword(s):  
Three Dimensional ◽  
Horizontal Axis ◽  
Power Coefficient ◽  
Navier Stokes ◽  
Main Stream ◽  
Transient Model ◽  
Drag Forces ◽  
Operation Conditions ◽  
Hydrokinetic Turbine ◽  
Inclination Angles

In this contribution, unsteady three-dimensional numerical simulations of the water flow through a horizontal axis hydrokinetic turbine (HAHT) of the Garman type are performed. This study was conducted in order to estimate the influence of turbine inclination with respect to the incoming flow on turbine performance and forces acting on the rotor, which is studied using a time-accurate Reynolds-averaged Navier-Stokes (RANS) commercial solver. Changes of the flow in time are described by a physical transient model based on two domains, one rotating and the other stationary, combined with a sliding mesh technique. Flow turbulence is described by the well-established Shear Stress Transport (SST) model using its standard and transitional versions. Three inclined operation conditions have been analyzed for the turbine regarding the main stream: 0° (SP configuration, shaft parallel to incoming velocity), 15° (SI15 configuration), and 30° (SI30 configuration). It was found that the hydrodynamic efficiency of the turbine decreases with increasing inclination angles. Besides, it was obtained that in the inclined configurations, the thrust and drag forces acting on rotor were lower than in the SP configuration, although in the former cases, blades experience alternating loads that may induce failure due to fatigue in the long term. Moreover, if the boundary layer transitional effects are included in the computations, a slight increase in the power coefficient is computed for all inclination configurations.

The E-ring: interactions with plasma and implications for its evolution

1984 ◽  
Vol 75 ◽  
pp. 599-602
Author(s):  
T.V. Johnson ◽  
G.E. Morfill ◽  
E. Grun
Keyword(s):  
Time Scale ◽  
Particle Density ◽  
High Energy ◽  
Particle Removal ◽  
Density Region ◽  
Drag Forces ◽  
Orbit Evolution ◽  
History Of ◽  
Ring Particle ◽  
Ring Material

A number of lines of evidence suggest that the particles making up the E-ring are small, on the order of a few microns or less in size (Terrile and Tokunaga, 1980, BAAS; Pang et al., 1982 Saturn meeting; Tucson, AZ). This suggests that a variety of electromagnetic and plasma affects may be important in considering the history of such particles. We have shown (Morfill et al., 1982, J. Geophys. Res., in press) that plasma drags forces from the corotating plasma will rapidly evolve E-ring particle orbits to increasing distance from Saturn until a point is reached where radiation drag forces acting to decrease orbital radius balance this outward acceleration. This occurs at approximately Rhea's orbit, although the exact value is subject to many uncertainties. The time scale for plasma drag to move particles from Enceladus' orbit to the outer E-ring is ~104yr. A variety of effects also act to remove particles, primarily sputtering by both high energy charged particles (Cheng et al., 1982, J. Geophys. Res., in press) and corotating plasma (Morfill et al., 1982). The time scale for sputtering away one micron particles is also short, 102 - 10 yrs. Thus the detailed particle density profile in the E-ring is set by a competition between orbit evolution and particle removal. The high density region near Enceladus' orbit may result from the sputtering yeild of corotating ions being less than unity at this radius (e.g. Eviatar et al., 1982, Saturn meeting). In any case, an active source of E-ring material is required if the feature is not very ephemeral - Enceladus itself, with its geologically recent surface, appears still to be the best candidate for the ultimate source of E-ring material.

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