Particle screening phenomena in an oblique multi-level tumbling reservoir: a numerical study using discrete element simulation

Due to their wide usage in industrial and technological processes, granular materials have captured great interest in recent research. The related studies are often based on numerical simulations and it is challenging to investigate computational phenomena of granular systems. Particle screening is an essential technology of particle separation in many industrial fields. This paper presents a numerical model for studying the particle screening process using the discrete element method that considers the motion of each particle individually. Dynamical quantities like particle positions, velocities and orientations are tracked at each time step of the simulation. The particular problem of interest is the separation of round shape particles of different sizes using a rotating tumbling vertical cylinder while the particulate material is continuously fed into its interior. This rotating cylinder can be designed as a uniform or stepped multi level obliqued vertical vessel and is considered as a big reservoir for the mixture of particulate material. The finer particles usually fall through the sieve openings while the oversized particles are rebounded and ejected through outlets located around the machine body. Particle–particle and particle–boundary collisions will appear under the tumbling motion of the rotating structure. A penalty method, which employs spring-damper models, will be applied to calculate the normal and frictional forces. As a result of collisions, the particles will dissipate kinetic energy due to the normal and frictional contact losses. The particle distribution, sifting rate of the separated particles and the efficiency of the segregation process have been studied. It is recognized that the screening phenomenon is very sensitive to the machines geometrical parameters, i.e. plate inclinations, shaft eccentricities and aperture sizes in the sieving plates at different levels of the structure. The rotational speed of the machine and the feeding rate of the particles flow have also a great influence on the transportation and segregation rates of the particles. In an attempt to better understand the mechanism of the particle transport between the different layers of the sifting system, different computational studies for achieving optimal operation have been performed.     

Vortex motion in the early stages of unsteady flow around a circular cylinder

In this paper, processes in the early stages of vortex motion and the development of flow structure behind an impulsively-started circular cylinder at high Reynolds number are investigated by combining the discrete vortex model with boundary layer theory, considering the separation of incoming flow boundary layer and rear shear layer in the recirculating flow region. The development of flow structure and vortex motion, particularly the formation and development of secondary vortex and a pair of secondary vortices and their effect on the flow field are calculated. The results clearly show that the flow structure and vortices motion went through a series of complicated processes before the symmetric main vortices change into asymmetric: development of main vortices induces secondary vortices; growth of the secondary vortices causes the main vortex sheets to break off and causes the symmetric main vortices to become “free” vortices, while a pair of secondary vortices is formed; then the vortex sheets, after breaking off, gradually extend downstream and the structure of a pair of secondary vortices becomes relaxed. These features of vortex motion look very much like the observed features in some available flow field visualizations. The action of the secondary vortices causes the main vortex sheets to break off and converts the main vortices into free vortices. This should be the immediate cause leading to the instability of the motion of the symmetric main vortices. The flow field structure such as the separation position of boundary layer and rear shear layer, the unsteady pressure distributions and the drag coefficient are calculated. Comparison with other results or experiments is also made. This work was presented at the First Asian Congress of Fluid Mechanics, Bangalore in December 1980.     

Capturing non-Brownian particle transport in periodic flows

In this paper we computationally examine the motion of a dilute suspension of slightly non-neutrally buoyant solid spheres as they migrate across the curved fluid streamlines of a viscous cellular flow. This is done by incorporating particle-fluid interactions into a continuum-based Lagrangian advection model derived from the Basset–Boussinesq–Oseen (BBO) equation, where the flow field is mimicked by using a perturbed streamfunction. Although the purely regular cellular flow is able to capture maximum velocity and particle diameter effects that are observed experimentally, it has several shortcomings. Most significantly, it is unable to capture the secondary island structures that exist in many rotating flow systems, nor the impact that these structures are observed to have on particle migration. Our results in this work demonstrate significant interplay between the underlying fluid structure and the non-trivial equilibrium locations of the non-Brownian particles, in agreement with previous experimental work. We also evaluate the effect of the Saffman lift force on the lateral migration of the solid spheres.     

Quantitative simulation of gas-particle two phase plane mixing layer using discrete vortex method

The gas and particle phase in a two-phase plane mixing layer flow are numerically simulated using the discrete vortex method and a trajectory tracking method. It is shown that the number of vortex elements contained in two semi-infinite discrete vortex sheet and the method of generating control volumes for statistical calculation of the particle phase have important effects on the predicted results of particle phase, especially for quantitative prediction. By adopting different number of vortex elements for two semi-infinite discrete vortex sheet and overlapping the control volumes, predicted results including streamwise velocity, fluctuating velocity and Reynolds shear stress of both phases are obtained and agree well with experimental measurements quantitatively. It shows that the discrete vortex method can achieve the accurate quantitative simulation of two-phase flow.     

Motion of a condensed particle in a channel with injection

Consideration is given to problems associated with modeling of the motion of a condensed particle in a channel with injection with allowance for the action of different force factors (the hydrodynamic-drag force, the Saffman lift force, and the thermophoresis force). From the results of the numerical modeling, the author draws conclusions on the degree of influence of different force factors on the pattern of motion of the particle. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 79, No. 1, pp. 81–89, January–February, 2006.     

Numerical and physical modeling of a low-velocity air flow in a channel with a circular vortex cell

Based on a numerical solution, by the finite-volume method, of two-dimensional Reynolds equations that are closed using Menter’s two-parameter turbulence model and on physical modeling in a wind tunnel the authors analyze flow in a channel with a cylindrical vortex cell of circular cross section. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 2, pp. 346–353, March–April, 2000.     

A Model of Polydisperse Vapor–Droplet Mixture Flow in a Vortex Chamber

Journal of Engineering Physics and Thermophysics - A thermo- and hydrodynamic model of polydisperse vapor–droplet mixture flow in a vortex evaporation chamber has been described. The motion...     

On the interaction of a vortex pair and a vortex ring with a flat shield

The approximate method of calculation of nonstationary flow in the interaction of a vortex pair and a vortex ring with a parallel and respectively perpendicular flat shield is presented. It is shown that these primary vortices induce transverse wall flow on the shield in the ideal-fluid approximation; in this flow, with allowance for the fluid’s viscosity, a boundary layer is generated which represents vortex flow with sign opposite to that of the primary vortices. Boundary-layer separations occur on the portion of the shield with a positive longitudinal pressure gradient. Secondary flows interact with the primary ones due to which the flow is rearranged; the transverse displacement of the initial vortex pair with a loop-shaped trajectory of its motion is observed in the plane problem, whereas the formation of ascending flow along the axis of the vortex ring is observed in the axisymmetric problem. The effect found in the latter case in laminar and turbulent regimes of flow is confirmed for the laminar regime by experiment and by the data of numerical simulation of Navier–Stokes and Reynolds equations.     

Generation of intensive narrow-band disturbances in a flow with a large-scale hydrodynamic structure

This paper analyzes the reasons for the appearance of intensive narrow-band disturbances and self-sustained oscillations in a flow with an inhomogeneity on its boundary. It has been shown that self-sustained oscillations are due to the formation of large-scale cocurrent hydrodynamic systems with vortex structures and acoustic feedback. It is supposed that the vortex formed in the zone near the edge of the surface generates noise as a result of the involvement in the rotary motion of the azimuth-inhomogeneous structure. It is noted that self-sustained oscillations can be avoided or suppressed by disorganizing the elements of the large-scale hydrodynamic structure. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 4, pp. 682–689, July–August, 2008.     

The vibrations of pre-twisted rotating Timoshenko beams by the Rayleigh–Ritz method

A modeling method for flapwise and chordwise bending vibration analysis of rotating pre-twisted Timoshenko beams is introduced. In the present modeling method, the shear and the rotary inertia effects on the modal characteristics are correctly included based on the Timoshenko beam theory. The kinetic and potential energy expressions of this model are derived from the Rayleigh–Ritz method, using a set of hybrid deformation variables. The equations of motion of the rotating beam are derived from the kinetic and potential energy expressions introduced in the present study. The equations thus derived are transmitted into dimensionless forms in which main dimensionless parameters are identified. The effects of dimensionless parameters such as the hub radius ratio, slenderness ration, etc. on the natural frequencies and modal characteristics of rotating pre-twisted beams are successfully examined through numerical studies. Finally the resonance frequency of the rotating beam is evaluated.     

Study and optimization of flow field in a novel cyclone separator with inner cylinder

This paper presents a study of gas-solid flow in a novel cyclone separator with inner cylinder, compared with that in a conventional cyclone. The Reynolds stress model (RSM) is used to simulate fluid flow, and the discrete phase model (DPM) is selected to describe the motion behavior of particles. The experimental data measured by particle image velocimetry (PIV) is used to verify the reliability of the numerical model. The results show that in the novel cyclone, the cleaned gas can be quickly discharged from the vortex finder, the movement distance and residence time of fine particles are prolonged, the short-circuit flow and vertical vortex under the vortex finder are eliminated, the mutual interference between upflow and downflow in the cylinder is eliminated, and the region of quasi-free vortex in the cone is enlarged. Compared with the conventional cyclone, the novel cyclone has higher collection efficiency and lower pressure drop.     

Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall

The motion of a spherical particle in infinite linear flow and near a plane wall, subject to the slip boundary condition on both the particle surface and the wall, is studied in the limit of zero Reynolds number. In the case of infinite flow, an exact solution is derived using the singularity representation, and analytical expressions for the force, torque, and stresslet are derived in terms of slip coefficients generalizing the Stokes–Basset–Einstein law. The slip velocity reduces the drag force, torque, and the effective viscosity of a dilute suspension. In the case of wall-bounded flow, advantage is taken of the axial symmetry of the boundaries of the flow with respect to the axis that is normal to the wall and passes through the particle center to formulate the problem in terms of a system of one-dimensional integral equations for the first sine and cosine Fourier coefficients of the unknown traction and velocity along the boundary contour in a meridional plane. Numerical solutions furnish accurate predictions for (a) the force and torque exerted on a particle translating parallel to the wall in a quiescent fluid, (b) the force and torque exerted on a particle rotating about an axis that is parallel to the wall in a quiescent fluid, and (c) the translational and angular velocities of a freely suspended particle in simple shear flow parallel to the wall. For certain combinations of the wall and particle slip coefficients, a particle moving under the influence of a tangential force translates parallel to the wall without rotation, and a particle moving under the influence of a tangential torque rotates about an axis that is parallel to the wall without translation. For a particle convected in simple shear flow, minimum translational velocity is observed for no-slip surfaces. However, allowing for slip may either increase or decrease the particle angular velocity, and the dependence on the wall and particle slip coefficients is not necessarily monotonic.     

An investigation of segregation and mixing in dense phase pneumatic conveying

Pneumatic conveying of bulk materials has become an important technology in many industries: from pharmaceuticals to petro-chemicals and power generation. Particulate segregation has been investigated in many solids handling processes. However, little work has been published on the segregation and mixing in pneumatic conveying pipelines, particularly in dense phase pneumatic conveying. Due to the character of dense phase flow, it is difficult to investigate the segregation in a flowing plug. A sampling device was designed and built to take samples from the pneumatic conveying pipeline after “catching a plug”. Several experiments were conducted over a range of gas–solids flow conditions with 3 mm nylon pellets and 3 mm ballotini as a segregating mixture. Experimental data combined with video footage were analysed to describe the segregation and mixing of solids plugs in pipes. This investigation provides initial research on establishing a segregation index in a flowing plug. A gas–solids two-dimensional mathematical model was developed for plug flow of a nylon-glass particulate mixture in a horizontal pipeline in dense phase pneumatic conveying. The model was developed based on the discrete element method (DEM). The model was used to simulate the motion of particles both in a homogeneous flow and as binary mixtures taking into account the various interactions between gas, particles and pipe wall. For the gas phase, the Navier Stokes equations were integrated by the semi-implicit method for pressure-linked equations (SIMPLE) using the scheme of Patankar employing the staggered grid system. For the particle motion the Newtonian equations of motion of individual particles were integrated, where repulsive and damping forces for particle collision, the gravity force, and the drag force were taken into account. For particle contact, a model with a simple non-linear spring and dash pot model for both normal and tangential components was used. This model employed a mixture of 3 mm pellets and ballotini as virtual materials with properties of nylon and glass. The results from the model are discussed and compared with experimental work and show qualitative agreement. Further modelling and experimental work in key areas is proposed.     

On the mechanism of the Ranque–Hilsch effect

A model of flow in a Ranque vortex tube is suggested. It is based not on the thermal interaction between hot and cold flows, but rather on a mechanical one. It is shown that to describe the Ranque–Hilsch effect it is necessary, along with the radial flow, to take into account the uptake or addition of mass, as well as to ensure a smoother conjugation between a forced and a peripheral vortices, demanding the continuity not only of the tangential velocity component, but also of its first derivative with respect to the radius. In this case, the motion in the vortex tube is considered as a system of vortex flows and vortex sources interacting between themselves.     

Application of particle simulation methods to composite materials: a review

Particle simulation methods represent deformation of an object by motion of particles, and their Lagrangian and discrete nature is suitable for explicit modeling of the microstructure of composite materials. They also facilitate handling of large deformation, separation, contact, and coalescence. Mesh-free particle methods will thus be appropriate for a part of issues throughout the lifecycle of composite materials despite their high calculation cost. This study focuses on three particle simulation methods, namely, smoothed particle hydrodynamics, moving particle semi-implicit method, and discrete element method, and reviews approaches for modeling composite materials through these methods. Applicability of each method as well as advantages and drawbacks will be discussed from the viewpoint of engineering of composite materials. This reviewing study suggests capability of particle simulation methods to handle multiphysics and to predict various complex phenomena that necessitate explicit modeling of the material’s microstructure consisting of reinforcements (inclusions), matrix, and voids.     

Brownian motion and the drift of charged nanoparticles in laminar gas flow in a plane channel

Using two limiting cases (of adsorbing and reflecting channel walls), the influence of Brownian motion on the motion of nanoparticles in laminar gas flow under the action of an external electric field has been considered. Similarity criteria making it possible to classify experimental situations have been found. Numerical modeling of deposition from the flow has been carried out with the example of the motion of a monodisperse ensemble of spherical nanoparticles with a radius of 3 nm. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 2, pp. 215–220, March–April, 2009.     

Nonstationary radiation-gasdynamic model of a laser-plasma accelerator

Based on the system of two-dimensional axisymmetrical continuity equations, Navier-Stokes and energy equations, and the equations of selective heat radiation transfer, a computational model is constructed and conditions of unsteady subsonic flows in a cylindrical channel of a power unit of the laser-plasma accelerator type are investigated. The governing parameters of the model are calculated, at which numerical solutions can be obtained to describe steady laminar gas flow in the neighborhood of the region of heat release, nonstationary oscillatory motions, and nonstationary vortex motion. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 1, pp. 174–179, January–February, 2000.     

Quasistatic critical states of strings for deep drilling

We pose the problem of buckling of an elongated twisted rotating rod subjected to tension-compression and containing an internal flow of homogeneous fluid. We derive the resolving equations capable of modeling the stability of strings for deep drilling, propose a procedure for their solution, and consider typical examples. The critical values of the parameters of the system specifying its elastic equilibrium are determined and the stability loss modes of are established. __________ Translated from Problemy Prochnosti, No. 5, pp. 109–119, September–October, 2006.     

Dynamics of the viscous interaction of a ring vortex with a flat screen

A separation turbulent flow has been mathematically simulated on the basis of numerical solution of nonstationary Navier-Stokes equations for determining the dynamics of viscous interaction of a ring vortex with a flat screen. The problem was solved for an axisymmetric turbulent flow at Reynolds numbers falling within the range 10⁵–10⁷. On the basis of the calculation data obtained, the interaction of a ring vortex with a turbulent flow induced on the screen and with the secondary ring vortices was investigated. The data obtained are in qualitative agreement with the analogous data obtained by other authors with the use of the discrete-vortex method and the boundary-layer theory as well as with the available experimental and calculation data obtained for a laminar flow. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 1, pp. 184–190, January–February, 2008.     

Observed behavior of various oxide inclusions in front of a solidifying low-carbon steel shell

The engulfment and pushing (extrusion) of inclusions during solidification play an important role in the formation of a steel structure and, as a result, for the mechanical properties of the final steel product. The aim of this study is to gain knowledge about the behavior of non-metallic inclusions at the interface between a growing solid front and a liquid phase. The focus is on the effect of the titanium and titanium oxide content on the inclusions and the different phenomena, which occurs at the solid/liquid interface. This was studied in samples of low-carbon steels de-oxidized by different combinations of Al, Ca, and Ti. For this purpose, each metal sample of 0.19 g was melted at a temperature close to 1550 °C in an argon atmosphere and solidified under different solidification rates. A direct observation of inclusion behavior during solidification was made using a confocal scanning laser microscope equipped with an infrared gold image furnace. The alloying elements in the sample varied between: C 0.002–0.044; Si 0.02–1.33; Mn 0.12–1.33; P 0.003–0.016; S 0.003–0.01; Al 0.002–0,033; Ni 0–0.28; Cr 0–0.25; Ti 0.008–0.065; Ca 0.0007–0.002; O 0.002–0.0114 and N 0.0028–0.0056 (mass%). Several types of inclusions with different morphologies were found within the sample. The morphology of the observed inclusions on the molten steel surface varied from round alumina and calcium-oxide-rich inclusion to needle-shaped titanium oxide-rich inclusions. The observed motions of the inclusions at the vicinity of the front of the solidifying steels were classified. At a low solidifying velocity and a small inclusion size, inclusions flowed away from the solidifying front. Furthermore, they also or got pushed a distance and thereafter flowed away from the interface. At a medium velocity and a slightly bigger size, inclusions tend to get pushed in front of the solidifying front. Another observation was that at a high velocity and a large particle size, inclusions tend to get engulfed or pushed and then engulfed by the progressing front. The relationship among the morphology, chemical composition of inclusions and the solidifying velocity is discussed in this article.