CFD–DEM investigation of particle separations using a sinusoidal jigging profile

This paper presents a numerical investigation of solid separation in jigging device. Jigging is a gravity separation method commonly used by the minerals industry to separate coal, iron ore, diamonds and other minerals on the basis of particle size and/or density. Separation is recognised as being heavily dependent on fluid motion in the jig. This study explores the effects of the inlet time dependent velocity profile in relation to a wide criterion on jigging performance. Modelling of the liquid–solid system is performed through a combination of computational fluid dynamics (CFD) to simulate liquid flow and discrete element method (DEM) to resolve particle motion. The initial packing conditions consist of a binary-density particle system of 1130 particles each 1 cm in diameter. A range of jigging profiles have been implemented in mineral processing. In this study the sinusoidal pulsation profile is selected adopting variations in both amplitude and frequency. The performance of profile variants are compared in terms of solid flow patterns, separation kinetics, energy, and mean particle position. These quantitative comparisons demonstrate significant differences in the segregation rate, energy, and solid phenomena, helping find an alternative optimum operating setting for the system. In addition, boundaries of operation are found in terms of frequency and amplitude limits and the concentration mechanics are investigated in these regions.     

Resolved CFD–DEM coupling simulation using Volume Penalisation method

A resolved CFD–DEM coupling model for the simulation of particulate flows is proposed in this work. The Volume Penalisation (VP) method, which is a family of the continuous forcing Immersed Boundary (IB) method, is employed to express the particle–fluid interaction. A smooth mask function is used to avoid sharp transition between the solid (particle) and fluid domains that may cause numerical oscillation with moving particles. Optimal permeability is employed to reduce the model error associated with the VP method. It is determined as a function of only the interface thickness and fluid kinematic viscosity. The proposed model is accurate, easy to implement with any discretisation scheme, and only requires small computational overhead for particle–fluid interaction. Several simulations are performed to test the validity of the proposed model in various systems, i.e. from dilute to relatively dense flows, and the results show good agreement with the exact solution or empirical correlation. It is found that the error can be scaled with the ratio between the gap and interface thickness. The proposed model is also applied to predict the relative viscosity of suspensions and the density segregation in fluidised beds.     

On the particle–particle contact effects on the hole cleaning process via a CFD–DEM model

ABSTRACT

The accurate and precise computational models in order to predict the hole cleaning process is one of the helpful assets in drilling industries. Besides the bulk properties such as the flow velocity, particles average size, cleaning fluid properties, etc., that will affect the cleaning process, there is an unanswered question about the microscopic properties of the particles, particularly those which determines the contact characteristics: Do those play a major role or not? The rudimentary answer is not. The first purpose of the present work is to answer this question via a developed computational fluid dynamics coupled with discrete element method (CFD–DEM) in which the six unknown rolling and sliding friction coefficients of particle–particle contact, particle–wall contact, and particle–drill contact are considered as the main microscopic properties of the contacts. The second purpose is to search for optimum values of these coefficients in order to calibrate the CFD–DEM model with the experimental data for a near horizontal well cleaning available in the literature. The verification of the calibrated CFD–DEM model is checked by simulation of the hole cleaning process for different inclination angles of the deviated well. The results indicate the pivotal role of the microscopic properties of the particles on the characteristics of the particle transport mechanism.     

DEM simulation of single bubble flotation: Implications for the hydrophobic force in particle–bubble interactions

A 3D Discrete Element Method simulation model for a single bubble was developed in order to investigate the capture of hydrophobic particles. The bubble was considered stationary at the centre of the working space. Particle–particle and particle–bubble contacts were simulated using a linear spring-dashpot model. Gravitational, buoyancy, drag and hydrophobic forces were taken into account. The hydrophobic force was estimated through a single exponential decay law which depends on a pre-exponential parameter K and a decay length λ. It was observed that when λ was less than 10 nm, the number of the particles that were collected was independent of the strength of the hydrophobic force. In contrast, for values of λ within the range of 10–500 nm, the capture efficiency increased significantly with the strength of the hydrophobic force and λ. We have also demonstrated how these two parameters affect the particle trajectory around the bubble and thus produce a significant difference in particle collection when the strength and range of the hydrophobic force were varied.     

Implementation of design of experiments approach for the micronization of a drug with a high brittle–ductile transition particle diameter

Objective: To optimize air-jet milling conditions of ibuprofen (IBU) using design of experiment (DoE) method, and to test the generalizability of the optimized conditions for the processing of another non-steroidal anti-inflammatory drug (NSAID).

Methods: Bulk IBU was micronized using an Aljet mill according to a circumscribed central composite (CCC) design with grinding and pushing nozzle pressures (GrindP, PushP) varying from 20 to 110?psi. Output variables included yield and particle diameters at the 50th and 90th percentile (D₅₀, D₉₀). Following data analysis, the optimized conditions were identified and tested to produce IBU particles with a minimum size and an acceptable yield. Finally, indomethacin (IND) was milled using the optimized conditions as well as the control.

Results: CCC design included eight successful runs for milling IBU from the ten total runs due to powder “blowback” from the feed hopper. DoE analysis allowed the optimization of the GrindP and PushP at 75 and 65?psi. In subsequent validation experiments using the optimized conditions, the experimental D₅₀ and D₉₀ values (1.9 and 3.6?μm) corresponded closely with the DoE modeling predicted values. Additionally, the optimized conditions were superior over the control conditions for the micronization of IND where smaller D₅₀ and D₉₀ values (1.2 and 2.7?μm vs. 1.8 and 4.4?μm) were produced.

Conclusion: The optimization of a single-step air-jet milling of IBU using the DoE approach elucidated the optimal milling conditions, which were used to micronize IND using the optimized milling conditions.     

Extruder scale-up assessment in the process of extrusion–spheronization: comparison of radial and axial systems by a design of experiments approach

Scaling-up the extrusion–spheronization process involves the separate scale-up of each of the five process steps: dry mixing, granulation, extrusion, spheronization, and drying. The aim of the study was to compare two screw extrusion systems regarding their suitability for scaling-up. Two drug substances of high- and low-solubility in water were retained at different concentrations as formulation variables. Different spheronization times were tested. The productivity of the process was followed up using the extrusion rate and yield. Pellets were characterized by their size and shape, and by their structural and mechanical properties. A response surface design of experiments was built to evaluate the influence of the different variables and their interactions on each response, and to select the type of extrusion which provides the best results in terms of product quality, the one which shows less influence on the product after scale-up (“scalability”) and when the formula used changes (“robustness”), and the one which allows the possibility to adjust pellet properties with spheronization variables (“flexibility”). Axial system showed the best characteristics in terms of product quality at lab and industrial scales, the best robustness at industrial scale, and the best scalability, by comparison with radial system. Axial system thus appeared as the easiest scaled-up system. Compared to lab scale, the conclusions observed at industrial scale were the same in terms of product quality, but different for robustness and flexibility, which confirmed the importance to test the systems at industrial scale before acquiring the equipment.     

Simulation of the pressure drop across granulated mixtures using a coupled DEM – CFD model

The sinter process converts mixtures of iron ore, iron ore fines and fluxes into a fused aggregate (sinter) that is used as burden material in the blast furnace. The rate of this process is predicted by measuring the pressure drop across the green granulated mixture before ignition. A lower pressure drop corresponds with a higher permeability resulting in a higher sinter rate. The addition of fine material, such as concentrate or concentrate agglomerated into micropellets, to the sinter mixture affects the pressure drop. This study numerically predicts the pressure drop over several granulated mixtures in order to reduce the number of experimental measurements. The pressure drop was studied both experimentally using a pot grate and by coupled DEM (Discrete Element Method) – CFD (Computational Fluid Dynamics) simulations. The validation of the model was performed by comparing the measured and numerical values of the pressure drop across glass beads 3 and 6?mm in diameter respectively. The simulation of the pressure drop was extended to granulated mixtures that contain 0–40% concentrate or micropellets. DEM was also used to numerically simulate iron ore granules and relate their mechanical behaviour to particle size distribution, shape, friction coefficient, Young’s modulus and adhesion force.     

Three-dimensional numerical simulation of the exhaust stroke of a single-cylinder four-stroke ICE

In this paper an extensive CFD simulation of the exhaust stroke of a single-cylinder fourstroke ICE, including the entire exhaust manifold is described. Guidelines for the implementation of the full threedimensional model of the discussed process are included. The simulation involves the time-dependent flow of exhaust gases through the exhaust valve and the flow dynamics within the 2.2-m-long, straight exhaust pipe during the period when the valve is closed. Also the intake port with the intake valve is being coupled during the valves’ overlap period. The model geometry corresponds exactly to the actual engine geometry. The movement of the mesh follows the measured kinematics of the piston and the valves. The data obtained from the experimental environment was used for both the initialization and the validation of the computations. It was found that the phenomena affecting the dynamics of the exhaust flow are extremely three-dimensional and should be treated as such. In particular, the flow through the exhaust valve and the heat transfer along the exhaust pipe were influenced greatly by the effects of cold, fresh air breaking into the exhaust pipe in the period after the EVC. The presented study is the basis for future three-dimensional investigations of the entropy-generation rate along the exhaust system, including the exhaust valve.     

Computational and experimental studies on bed dynamics of a gas–solid fluidized bed using Geldart-A particle: A comparison

The bed dynamics of a two-dimensional gas–solid fluidized bed is studied experimentally and computationally using Geldart-A particles. Commercial software ANSYS FLUENT 13 is used for computational studies. Unsteady behavior of gas–solid fluidized bed is simulated by using the Eulerian–Eulerian model coupled with the kinetic theory of granular flow. The two-equation standard k?? model is used to describe the turbulent quantities. The simulation predictions are compared with experimentally observed data on volume fraction, bed pressure drop and bed expansion ratio. The results of simulations are found to be in close agreement with the experimental observations, implying that computational fluid dynamics (CFD) can be used for the design of an efficient bench-scale catalytic fluidized bed reactor.     

A comparison of staggered solution schemes for coupled particle–continuum systems modeled with the Arlequin method

This contribution aims at a systematic investigation of staggered solution schemes for the computation of coupled domains having different resolutions in space, a problem frequently arising in multi-scale modeling of materials. To couple a standard finite element domain with a high resolution atomistic or coarse-grained, i.e. particle-based domain, a so-called bridging domain is considered. In this handshake region a total energy, which is the sum of the weighted energies of both domains, needs to be formulated. Interactions in the particle domain are modeled by potential functions, e.g. a harmonic potential in the simplest case or the Lennard-Jones potential to consider also anharmonic interactions between the particles. The main goal is to separate the computation of finite element and particle domains as much as possible, amongst others to calculate the different domains on several CPUs. In the present work, the governing equations of the coupling method are presented. The energy functions of continuum, particle domain and bridging domain are recapitulated and the coupling constraint is set up. For the sake of simplicity, these relations are reformulated for the case of a one dimensional system. On the one hand, this system is computed monolithically without any separation of domains. On the other hand, various staggered solution schemes are derived systematically. The relevant equations of each scheme are given in detail together with the sequent iteration steps. All staggered schemes are investigated qualitatively, e.g. by their convergence behavior, as well as quantitatively by comparing the staggered solutions with the monolithic solution.     

A comparison of microstructures and mechanical properties in a Cu–Zr alloy processed using different SPD techniques

Experiments were conducted to evaluate the microstructures and mechanical properties of a Cu–0.1 % Zr alloy processed using two different techniques of severe plastic deformation: equal-channel angular pressing (ECAP) and high-pressure torsion (HPT). The samples were processed at room temperature through ECAP for eight passes or through HPT for 10 turns. The results show HPT is more effective both in refining the grains and in producing a large fraction of grain boundaries having high angles of misorientation. Both procedures produce reasonably homogeneous hardness distributions but the average hardness values were higher after HPT. In tensile testing at 673 K, the highest strength and ductility was achieved after processing by HPT. This is attributed to the grain stability and high fraction of high-angle grain boundaries produced in HPT.     

Integration of manufacturing and distribution networks in a global car company – network models and numerical simulation

Global supply chain practices and their effects have received considerable attention over the last two decades. In the recent past, the need for integration across supply chains has been identified as a key for effective and efficient operations of supply chains. This is observed with the increasing trend of collaborative partnerships among supply chain partners. This paper presents an integrated approach for manufacturing and distribution networks within the supply chain system of a global car company. The paper shows that the integration of manufacturing and distribution networks creates the environment for effective planning of many components and execution/follow-up of those plans. These components include materials, resources, operations/activities, suppliers and customers. The main features of the integration include component integration at individual networks via use of a central warehouse. This integration reduces various interfacing steps between partners and enables representations of relationships (component precedence, parent-component and component-component). The proposed integrated model is numerically tested using past data from one of Japan's auto-makers, based in the emerging economy of Thailand. The paper concludes that the integrated supply network eliminates the need for interfacing of individual networks and enables simultaneous planning of many components as well as forward planning of supply components in global supply chain operations. It also shows that the integrated approach is capable of providing visibility, flexibility, and maintainability for further improvement in the supply network environment.     

Analytical investigation and numerical simulation of the stress–strain state in mechanically heterogeneous welded joints with a single-V butt weld

This paper aims to investigate the stress–strain state in mechanically heterogeneous welded joints with a single-V butt weld by an analytical model along with a numerical simulation. Analytical expressions for the stress–strain state in both the weld and the main material are proposed. In order to verify the proposed expressions, a numerical simulation of the stress–strain state in a mild welded joint with a single-V butt weld was carried out on the basis of the finite element method and the results were compared with the analytical solution obtained applying the proposed analytical model. EP-787 and JONI 13/45А steels were used for the weld while 15X2MFА steel was used for the main material in the analysed welded joints. A comparison of the analytical solution with the finite element analysis results showed a good agreement. The proposed equations could be used in design practice for calculations of the stress–strain state in welded joints.     

Effect of particle size distribution on the mechanical and electrical properties of reverse-offset printed Sn–Ag–Cu solder bumps

A reduction of the particle size used in solder pastes was shown to affect the electrical and mechanical properties of finely printed solder bumps. Sn–3.0Ag–0.5Cu solder nanoparticles were synthesized using a radio frequency thermal plasma system, and solder pastes were formulated for reverse-offset printing of solder bump arrays with a size of 30 µm. As the nanoparticle ratio in the paste increased, the degree of supercooling, ΔT, increased with a separation of the exothermic peaks for the solidification of β-Sn and the precipitation of intermetallic compounds (IMCs). The networks of finely precipitated IMCs formed at the boundaries of large β-Sn increased the shear strength to 73 MPa. However, insufficient flux deteriorated the electrical and mechanical properties because it delayed the solidification of primary β-Sn as well as the melting of the solder. As a result, the Sn–3.0Ag–0.5Cu solder paste containing a nanoparticle ratio of 25% exhibited an optimum printability for reverse-offset printing of solder bumps, and the resulting bumps had an electrical conductance of 0.4 mΩ and a shear strength of 73 MPa.     

Experimental and numerical investigation of effects of particle shape and size distribution on particles’ dispersion in a coaxial jet flow

In this study, an experimental and a numerical investigations are performed to investigate the effect of particle’s shape and size distribution on its dispersion behavior. Firstly, particle dispersion of pulverized coal and spherical polymer particles is observed by Particle Image Velocimetry (PIV) technique in the experiment. Secondly, a simulation is performed to analyze the particle dispersion in detail. Spherical and spheroidal motion models are applied to particle’s movement to investigate the shape effect. Furthermore, monodisperse and polydisperse for particles are applied to investigate the size distribution effect on the dispersion. Experimental results show that in the jet turbulence flow, pulverized coal particles, which have complex shapes and various sizes, have quite different dispersion behavior compared to spherical particles. In terms of the results of the simulation, this difference is mainly caused by the size distribution effect. Although particle’s shape affects the dispersity, it is weakened by the size distribution effect.     

Finite element modelling of rubber-like materials — a comparison between simulation and experiment

In this work finite element simulations are used based on the micro structure of polymers in order to transfer the information of the micro level to the macro level. The microscopic structure of polymers is characterized by a three-dimensional network consisting of randomly oriented chain-like macromolecules linked together at certain points. Different techniques are used to simulate the rubber-like material behaviour of such networks. These techniques range from molecular dynamics to the finite element method.The proposed approach is based on a so-called unit cell. This unit cell consists of one tetrahedral element and six truss elements. To each edge of the tetrahedron one truss element is attached which models the force-stretch behaviour of a bundle of polymer chains. The proposed method provides the possibility to observe how changes at the microscopic level influence the macroscopic material behaviour. Such observations were carried out in [1]. The main focus of this work is the validation of the proposed approach. Therefore the model is compared to different experimental data and other statistically-based network models describing rubber-like material behaviour.