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机会与挑战-EDEM在工业中的应用

Industrial application of DEM: Opportunities and Challenges

John Favier

DEM Solutions Ltd, 20 York Place, Edinburgh, EH1 3EP, UK

 

DEM is now being applied to a wide range of industrial particulate solids handling and processing problems. The growing uptake by the process industries is rapidly expanding its application beyond the more traditional areas of mining and geo-mechanics. Continuing improvements in the price/performance of high performance computing makes DEM a realistic tool for use in a broad range of industrial product and process design and optimization. The breadth of application of DEM presents a number of challenges including benchmarking, model parameter estimation and coupling with other CAE methods. Establishment of independent benchmarks and reference cases are required to help in promoting the value of DEM to industry. DEM model parameter estimation is an area of growing interest with the objective of providing robust methods combining single particle and bulk measurements. Use of DEM in providing engineering solutions often requires coupling with other, usually continuum-based, CAE tools such as CFD, FEA and RBD. There is also increasing interest in coupling heat and mass transfer models, chemical kinetics and population balance models with DEM. This paper examines some of the opportunities and challenges facing DEM and we comment with reference to a number of specific industrial applications.

 

Keywords: DEM, Industrial application, EDEM, multi-physics simulation, CAE coupling, product design, process design, heat transfer, mass transfer, chemical kinetics, population balance, discrete element modelling, model validation, benchmarking

 

I. Introduction

 

In the last two decades the use of the Discrete Element Method (DEM) has progressed from small-scale twodimensional simulations to modelling of much larger and more complex 3D applications in industry. The advent of high-performance desktop computers now enables solution of systems containing large numbers of particles in timescales acceptable within an industrial design and R&D environment. The uptake of DEM by industry is also dependant upon the ease-of-use of any software, its compatibility with other design and simulation tools and the tools provided for data analysis and visualisation. In this paper we briefly review an example of a typical industrial application modelled using EDEMTM, a multi-purpose DEM software tool (www.dem-solutions.com) to show how a basic problem is approached. We then look at some examples of how the industrial application of DEM is being extended by development of coupled solutions combining DEM with continuum analysis methods to model particle-fluid, particle-structure and particle-electromagnetic interactions.

 

Fig 1 shows a snapshot taken from simulation of a screw auger emptying a hopper. This model was created by importing the CAD model of the screw auger, housing and hopper into EDEM. The screw auger was selected

Figure 1 Distribution of particle velocity (left) and particle compressive force of particles in a screw auger emptying from a hopper (right).

 

as a rotating part and a rotational velocity specified. Particle shapes were created and the mechanical properties required by the contact force model were specified. Particles were initialised by placing a “Particle FactoryTM ” in the region above the hopper and generating particles at the rate desired within the hopper. The particles can be generated within any virtual or solid geometry with a range of size and shape distribution. The simulation contains 200,000 particles of pellet shape each made of two overlapped spheres and was run on a desktop PC. Post-processing of results allows the full range of particle properties to be visualised. In the example shown the velocity distribution and the distribution of compressive force within the particle bulk has been visualised.

 

Typically industry is interested in exploring multiple design options and optimising operating conditions. Visualisation provides useful immediate information and can reveal the location of critical areas and bottlenecks. Further analysis of the simulation data is usually required to extract metrics which are relevant to the particular industrial application. These may be metrics which relate directly to what is or could be measured on the physical system or may be new metrics which can only be estimated from a DEM simulation. The latter highlights the benefit of using DEM for simulation of particular processes within a design context; it provides a means of looking inside a process and produces information which cannot be obtained experimentally. There is also growing use of techniques based on local-averaging to homogenise discrete data within a control volume. This also provides a direct link to continuum analysis methods which can benefit from use of particle-scale information.

 

Tools such as EDEM provide a CAE modelling environment for engineers to carry out DEM analysis on their real-world applications. The usefulness of the tool of course depends on the quality of the information it provides to the user. Choice of contact model, representation of particle properties and size distribution, accounting for non-contact forces will govern the degree to which the predicted behaviour matches the behaviour of the physical system. A considerable body of literature has been published over the last two decades addressing many aspects the application of DEM. A comprehensive summary of the most commonly employed methods is provided in a review by Zhu et al [1].

 

In industrial application of DEM the emphasis is often on the relative performance of different design and process options. Although the particulate system is being represented at the particle-scale the degree of approximation to actual physical conditions varies according to need. For example, most DEM simulations idealise the particle shape. The models used for both contact and non-contact forces are also idealisations of the physical behaviour which is usually much more complex. Nonetheless, despite these idealisations, DEM has been proven to provide a good approximation of the bulk mechanics of many particulate systems.

 

Two issues are critical to the application of DEM to industrial problems: i) determination of the DEM “material model”, i.e. the combination of the contact & non-contact force models and values of the model parameters, and ii) limitations of problem size relative to particle number and scaling. The DEM material model is chosen to provide the best approximation of bulk behaviour. The challenge is to determine the best model for the material relative to the conditions in which it is handled or processed – in simple terms, whether it is a quasi-static or a dynamic process. Research is needed to develop methodologies for optimising a DEM material model for a chosen bulk particulate material against measured data from laboratory scale tests. The available tests and options for the material models are quite well known but much of the research focus to date has been on direct measurement of single particle properties. While any knowledge of the inertial and mechanical properties of single particles is desirable, single particle measurements are not practical for many types of particle and for application by industry.

 

The limitations imposed by computing power relative to numbers of particles in a simulation ultimately constrain the application of DEM at any scale. Parallel processing is now becoming standard in DEM simulation and this is helping to increase the scale of problem which can be solved. While the domain size continues to grow as compute power/$ increases, depending on the type of information required, and the scale of problem in the region of interest, various techniques such as particle size scaling, cut-off of the smaller size fraction, and particle shape approximation can be employed. It is always necessary to exercise care when employing such techniques but they have been shown to be effective for many applications.

 

Another approach to the problem of scale is to take a multi-scale approach as is commonly employed in industries such as pharmaceutical manufacture which deal with powders and fine particulates. The relative effect of operating conditions on particle behaviour at the particle-scale is explored by simulating directly at that scale and using this information as a guide to assessing the effect of changes to design and process conditions at the process scale. The multi-scale approach combining DEM with other, usually continuum, models has great potential and is a growing area of research.

 

As the applications of DEM increase and it is deployed by industry to help solve real world problems there is an increasing demand for solutions which require use of other numerical techniques alongside DEM. Commercially this means coupling between DEM software and other tools and solvers. The principles of coupled DEM-CFD are now established (see Zhu et al, 2007 for references) and the technique has been applied to a range of particlefluid systems including fluidisation, pneumatic transport, cyclone separation and blast furnaces. The integration of this capability with heat and mass transfer and population balance models will further increase the application of this type of simulation. Coupling DEM with structural analysis and dynamics also has great potential for simulation of particle-structure interactions. The other area of growing application is particle-electromagnetic interactions. In addition to electrostatic forces between particles many processes include interaction between particles, electric and magnetic fields such as printing processes using charged powder and magnetised carrier particles. As the particle size scale gets smaller the influence of electromagnetic interactions increases and is an area where DEM is starting to provide solutions.

 

II. Particle-Structure Interaction (PSI)

 

The use of DEM to estimate the loads exerted by granular material on structures such as conveyors, hoppers and excavation buckets is now well established. The advent of CAD-enabled DEM codes such as EDEM which can easily handle complex equipment geometry now enables many other types of particle-structure interaction (PSI) to be modeled and allows the development of more advanced models which couple DEM with multi-body dynamics (MBD) and finite element analysis (FEA) codes. Other forms of PSI models include wear analysis, e.g analysis of the wear of lifter bars in tumbling ball mills [2] shot impact energy analysis during shot peening [3] and shear box simulation [4].

 

There are a number of challenges in coupling DEM with continuum-based solvers for solution of PSI problems depending on the machine dynamics, the relative size of the particulates and structural components and the timescale to be simulated.

 

The simplest form of PSI model is one-way coupling where the DEM solver provides load-sets for use in the structural analysis. This is effective for coupled DEM-FEA analysis of bodies which do not deform significantly or for wear and impact energy analysis. This type of coupling, and more advanced bi-directional coupling, requires the use of the FEA (or other solver) surface mesh representation of the boundary surfaces by the DEM solver. For a DEM solver which can handle an irregular tessellated surface mesh this is simply a matter of book-keeping, parsing the mesh file for nodes, edges and faces. The advantage of using the same mesh is that the loads on the boundary surface element by the DEM are in a 1:1 relationship with the FEA mesh. This type of PSI model is adequate for simulation quasi-static processes, or at least treatment of transient problems, such as loading of an excavation bucket, as a sequence of quasi-static problems.

 

Fig 2 illustrates how the DEM analysis can provide a load-set for structural analysis. It shows the distribution of particle contact forces on the screw auger from the simulation shown in Fig 1.

 

 

The force gradient has been interpolated from the individual contact forces. Similarly the forces can be interpolated and distributed between nodes of a surface mesh in an FE analysis.

 

When the structure is moved by some motive force or is moved by particles then the kinematics of the structure must be provided to the DEM model. If the force exerted by the particles on the structure can change the dynamics of the structure then a full coupling between the solvers is required. In EDEM the built-in default is strain-based definition of the kinematics of the structural geometry components. A means is provided to couple EDEM with another solver which solves the dynamic response of the structure to the loading relative to any other applied forces. EDEM provides the loadsets and the other solver passes back the new position of the geometry.

 

Here we look at two different PSI models solved using EDEM. The first example is a shot peening simulation in which EDEM is used to estimate the distribution of shot impact energy on the surface of a workpiece. The second example illustrates the coupling of EDEM with MSC.Easy5 and MSC.ADAMS to simulate the operation of a drag-line bucket.

 

Shot Peening

 

Shot peening is a process used to produce compressive residual stresses in the surface layers of a wide range of metal components from gears, aerofoil blades, engine blocks to medical instruments. It entails impacting a surface with metallic or ceramic particles (shot) with force sufficient to create plastic deformation. Current methods of measuring the efficiency of peening using Almen strips (metallic strips which deform relative to the impacting force) are limited by the aggressive nature of the process and provide only indirect estimation of the peening effect. DEM simulation enables calculation of surface impact energy with a much high resolution than physical measurement methods and offers a means of optimizing the peening process with respect to control of peening parameters and location and orientation of the work-piece.

 

Shot peening is usually carried out using either wheel peening or nozzle peening equipment. The latter is used for more complex geometries requiring arbitrary movement of the stream of shot relative to the work-piece geometry. Here we are simulating the nozzle peening of aerofoil blades. The objective in nozzle peening is to optimize the nozzle position, shot mass flow rate and velocity relative the surface geometry to ensure the residual stresses develop uniformly across the surface, particularly in areas of the component subject to high loading during operation. The challenge for the simulation is to capture shot velocity distributions and to provide good predictions of the impact energy on the material surface.

 

Figure 3 Particle velocity distribution on the aerofoil blades. The blades are rotating with a linear velocity of 1 m/s. The velocity of the shot exiting the nozzle is 75 m/s.

 

Figure 3 shows the velocity distribution obtained from simulation of shot peening of the blades of a turbine compressor using EDEM. The snapshot illustrates one of the difficulties in shot peening complex geometries where rebounding shot can interfere with the incoming stream of shot so reducing the degree of coverage and the impact energy.

 

By tracking each individual particle the amount of energy transferred to the geometry and the energy lost to other shot particles during each collision can be calculated. By combining the amount of energy imparted to each geometry element in the model, a map of energy transfer to the peened surface can be produced. Figure 4 shows the predicted energy distribution resulting from a first pass of the nozzle over the blades.

 

Figure 4 Distribution of shot impact energy on the aerofoil blades predicted by the DEM simulation. Red indicates the highest and blue the lowest concentration of impact energy

 

The DEM simulation predicts that this particular operating condition produces a highest concentration of impact energy near the top of each fan blade. The generation of compressive residual stresses is directly correlated with the concentration of impact energy delivered to the surface. By simulating a matrix of conditions the peening process can be optimized to produce the desired coverage. The DEM simulation also allows a check on the efficiency of an existing peening process and provides a means of avoiding poor quality peening or even damage to component parts.

 

Multi-body Dynamics Coupling

 

Integration of DEM with multi-body dynamics simulation and control provides a unique method of coupling particle and machine dynamics. This is a relatively new area of CAE but has a lot of potential. One important area of application is simulation of the operation of dragline buckets, mining and excavation equipment and agricultural implements.

 

EDEM can be coupled with any software which has an interface capable of exchanging data with an integrating module. A coupling has been developed for MSC.Easy5 which is used to control the operation of equipment as it interacts with granular material. MSC.Easy5 is used to simulate hydraulic, mechanical and electrical control systems responding to forces applied through linkages, actuators and contact loads. It can be coupled to MSC.ADAMS, a multi-body dynamics simulation tool. A coupled EDEM-Easy5-ADAMS solution has been developed which integrates particle and machine dynamics and hydraulic control simulation.

 

Here we show the application of the coupled solution to simulation of the operation of a dragline bucket. Dragline bucket designers and operators wish to maximize the rate of fill while minimizing the power consumption and the rate of wear of the bucket. Coupling the particle and machine dynamics solvers provides the dynamic loading cycle to the MBD model which is great improvement on methods available previously which require use of static or arbitrary load-sets as input to the MBD model. This enables the dynamic system response to local conditions (particulate material properties, terrain) to be modeled. The solution is being used to improve the control system, better integrate automatic with operator control, and improve bucket and mechanical system design.

 

A schematic of operation of coupling is shown in Fig 5. The bucket dynamics are calculated in ADAMS and the position and velocity passed to Easy5 which models system hydraulics and can incorporate other control loops mimicking operator control. The kinematic data for the bucket is transferred to EDEM which calculates the resultant particle forces and moments on the bucket. The reaction forces are transferred via Easy5 to ADAMS which computes the loads on joints, components and hydraulics and new bucket dynamics.

 

Figure 5 Schematic of the coupling of EDEM-Easy5-ADAMS simulating the operation of a dragline bucket

 

This fully coupled DEM-machine dynamics and control simulation solution provides a means of transient analysis of the excavation process. It is a powerful tool for design and optimization of dragline bucket structural design and improvement of the control system and is being used to improve the design of dragline systems to prolong bucket life, and increase operational efficiency. Coupling DEM with rigid body dynamic simulation enables modeling of any particle-machine system in which force feedback is necessary to properly model the machine kinematics. It can be used to simulate other excavation and soil-machine interactions such as soil-tire, soil-track, agricultural implements and mining equipment.

 

III. Particle-Fluid Interaction (PFI)

 

Simulation of particle-fluid interaction (PFI) is an important component of many industrial applications of DEM. When the particle solid fraction of a particle-fluid system is low enough (less than 10%) and the particle Reynolds numbers are not too high then it is often possible to model the system using DEM alone by applying a fluid drag force calculated from an imposed fluid flow field. When the momentum exchange between the fluid and particles is large enough to significantly influence the fluid flow then a fully coupled DEM-CFD solution is required.

 

Simulation of particle-fluid systems using coupled DEM-CFD is now well established in application to fluidized and bubbling beds and pneumatic transport in particular. Simulation of PFI at the particle-scale overcomes many of the limitations inherent in continuum models used in CFD simulation of particle-fluid systems. The introduction of coupling between commercial DEM and CFD codes such as the coupling between EDEM and FLUENT expands the application of the technique to more complex geometries and process conditions which required the use of unstructured meshes. Increasing computational power is also increasing the range of industrial applications which can be addressed.

 

Another form of PFI is the interaction between a high pressure fluid and a porous or bonded media. Examples include oil & gas drilling operations where high pressure drilling mud strongly influences drilling efficiency, fraccing (the generation of cracks in the rock surrounding a well bore), high pressure concrete storage vessels, erosion of pipes and valves. Simulation of many of these systems is highly challenging and requires a combination of DEM with other techniques.

 

Here we examine two applications involving two different types of PFI modeling, pneumatic transport and deep well rock drilling.

 

Pneumatic Conveying

 

Pneumatic conveying has become the preferred method of transport of particulates in many handling and processing operations. Much of the design of these systems is based on empirical or semi-empirical methods which tend to be very system and material specific as well as requiring a lot of calibration. One of the weaknesses is that there is no universal governing equations which can handle the transition from dilute to dense phase. Particularly difficult to model is intermittent flow when particles start to stagnate in the pipe and then move again – either by entrainment from the surface layers or as a plug.

 

In this example co-simulation of EDEM with FLUENT is used to model the pneumatic transport of polystyrene beads in a pipe. The challenge is capture the transition from dilute to dense flow. The examples shown here are taken from a study which explored a range of particle mass flow rate relative to air flow rate. Fig 6 shows the three regimes. Changes in characteristic behavior have been observed in experimental studies of such a system. The accuracy of the pressure drop predictions were found to be dependent on the initial particle conditions, the particle rolling friction, the pipe wall roughness and the choice of turbulence model employed [5].

 

Figure 6 Simulation of pneumatic transport of polystyrene beads in a horizontal pipe at different air flow rates and particle loading giving a) dilute flow with particles in suspension, b) intermittent flow with particles depositing in the pipe, and c) dense flow with particles moving as a plug.

 

Figure 7 shows an example of particle build up during transition from the dilute phase to the dense phase predicted by the DEM-CFD model. The particles are moving at a higher velocity in (a) but are starting to slow down. By (b) they have slowed down sufficiently that the bed is building up at the inlet end. Later, in (c) the particles are continuing to slow down, and the bed has increased in depth but particles are starting to be lifted off from the top surface back in to the flow. As a result the bed moves down the pipe in successive stages of deposition and entrainment.

 

Figure 7 Particle build up – dilute to dense phase. 35,000 particles, inlet velocity 13 m/s. Particles input at 10% of the fluid velocity. Blue particles have the lowest velocity.

 

This DEM-CFD co-simulation model has enabled key flow regime parameters to be identified as part of the validation process. The objective is to use this technique to help improve the design of pneumatic transport systems. Accurate prediction of the pressure drop at a range of fluid velocities allows the dilute phase to be run at the lowest possible fluid flow rate and therefore decreases running costs and damage to the particles. Predicting the pressure drop for the dense phase pneumatic conveying scheme aids in the design of new systems that have low energy requirements. This study shows that coupled DEM-CFD can provide a means of investigating, troubleshooting and improving pneumatic transport equipment.

 

Deep well rock drilling

 

DEM is increasingly being used to model fracture of rock and cementitious materials. Particles are bonded together using brittle bonds. The strength of the bonds, as well as other factors such as particle mechanical properties and size distribution, controls the fracture properties of the rock simulant. Typically bonded models are calibrated using triaxial test data.

 

Most drilling operations use drilling fluid to lubricate the drill cutter and remove the cuttings. In a deep well the drilling fluid/mud is at very high pressure. Both the interaction between the cutter and rock, and the rock strength is altered by the high fluid pressure. In order to simulate such a system it is necessary to have a means of representing the solid-fluid boundary and applying fluid pressure to the boundary surface.

 

A 3D fluid pressure boundary has been developed for operation with a bonded particle model in EDEM. Figure 8 shows the boundary evolution predicted by EDEM as a result of the cutter moving through the bonded-particle bed. In this algorithm the boundary skin is represented as a mesh of triangular elements with vertices at sphere centres. Particle representation is shown on the left of this figure and fluid boundary element representation is shown on the right.

 

This type of simulation enables drill designers to better understand the interaction between the drilling fluid and the rock. It also provides load-sets for the cutters and drill bit which can be used in structural analysis of the drill bit.

 

Figure 8 Simplified model of a drill bit cutter removing a cutting by breaking bonded particles from a bed of bonded particles. The bed of particles is a rock simulant. The bond strength between the particles is calibrated to match the rock failure strength. The mesh shown in the image above is a 3D fluid boundary between the rock and drilling fluid.

 

IV. Particle-Electromagnetic Interaction (PEMI)

 

Interaction of charged or magnetized particles with each other and with electromagnetic fields is a key feature of processes such as magnetic separation, printing, electrophotography, dust and pollutant mitigation, and handling of metal and pharmaceutical powders. Simulation of these processes involves modelling both short and long range particle-particle, particle-surface and particle-field interactions. In EDEM the short range interactions are handled using external force models which can be programmed to incorporate the required exchange of charge and response to electric or magnetic field. Long range interactions introduce an additional computational overhead requiring solution of an N-body problem.

 

Electrostatic Coupling

 

Electrostatic forces dominate where particles are small and atmospheric humidity is low. Such is the case on the surface of the moon. Lack of an atmosphere means that particles comprising the lunar regolith are electrostatically charged with the result that they stick to the surface of equipment, space suits and sensors. NASA is developing techniques and devices to deal with charged particles encountered in the lunar environment. EDEM is being employed to investigate design options and determine the relative efficiency of process alternatives. One example is electrostatic screens for dust mitigation.

 

An electrostatic force model was implemented using EDEM’s API which enables application of body forces in addition to gravity. The challenge in this application was to account for tribocharging between particles and surfaces and to include a long-range electrostatic force model. The tribocharging model accounts for charge exchange between particles and equipment surfaces and the effects of neighbouring charged particles. A screened Coulomb force was incorporated which employed a screening term using a Debye length based on the local charge concentration. Details of the electrostatic algorithms are presented in Hogue et al [7].

 

Figure 9 shows the DEM model of an experiment designed to test the algorithms. Spherical particles were released from a cylindrical holder and travelled down an inclined plane. All materials were initially un-charged. Electrostatic charges developed in the particles relative to their time and position of contact with the surface. After leaving the plane the particles were collected in a Faraday cup which measured the total charge. Figure 9 shows snapshots of the particles on the plane for three different conditions; a model with no electrostatic force, unscreened electrostatic force model and a screened electrostatic force model.

 

  

Fig 9 Snapshots from DEM simulations illustrating of the effect of electrostatic charging of particles using a model with and without use of screening

 

Fig 10 Average separation of particles as they travel down the plane calculated as the mean distance of the particles from a line

 

Electrostatic charging of the particles results in spreading out of the particles as they travel down the slope due to charge repulsion. An analysis of the relative separation of the particles on the slope is shown in Figure 10. Screening by other particles reduces the repulsive force on an individual particle. Experimental observation of glass beads shows similar behavior to that predicted by the EDEM model using a screening term.

 

One advantage of using DEM simulation of processes under lunar conditions is that gravitational effects can be accounted for much more easily than in experiments on earth. The electrostatic force model described here can also be applied under terrestrial conditions in processes such as handling of toner and carrier powder in printers, tribocharging of pharmaceutical powders during mixing and filling and dust extraction systems. One of the challenges in this type of modeling is accounting for the long-range electrical forces. This requires attention to efficient calculation of N-body interactions. The model described above employs a screening distance which limits the number of particles whose charge interaction must be calculated. Nonetheless, the computational

overhead can be significant and care needs to be taken when implementing N-body algorithms to control the time spent in the algorithm.

 

V. Conclusions

 

A number of examples of the application of DEM to industrial problems have been presented. Much DEM work to date has focussed on particle-particle interactions. Standard applications of DEM in industry implement algorithms developed to approximate the particle-particle interaction. These are usually extended to particlesurface interactions using similar approximations. It is now possible using DEM software tools such as EDEM to combine complex equipment geometry and kinematics with particle dynamics simulation in the same model.

 

In the last decade techniques have been developed to model particle-fluid interaction and this is now being applied to industrial problems. There is need for development of multi-scale methods which integrate discretecontinuum models with continuum models at the process scale. DEM has a key role to play in improving current continuum techniques which fail to account properly for local variation in the concentration and properties the solid phase in particle-fluid systems.

 

Particle-structure interaction modelled using coupled DEM-FEA and DEM-MBD and other analyses is also of growing interest to industry. DEM can provide the dynamic load conditions on structures so providing a critical parameter required for transient analysis of stress and dynamics of structures interacting with particulate media.

 

Particle-electromagnetic interaction is an inherent part of modelling particle-particle interaction but its importance depends on the scale. As particles get smaller the influence of the PEMI increases. Simulation of particles in an electric or magnetic field is of benefit to several industrial applications.

 

The use of DEM simulation by industry to help solve difficult problems is growing rapidly. Effective application requires good software tools and robust methods for deriving DEM material model parameters for bulk particulates. The opportunities for application of DEM are likely to increase as the range of problems which can be addressed increases and are shown to give results. There is a need for development of robust, generic techniques for calibrating DEM models for particular real bulk materials. Standard benchmarks based on well defined experiments also need to be established to provide a reference point for industrial as well as academic users of DEM technology.

 

VI. References

[1] Discrete particle simulation of particulate systems: Theoretical developments. HP Zhu, ZY Zhou, RY Yang, AB Yu, Chemical Engineering Science, 62, 3378-3396 (2007)

[2] McBride, A.T. and Powell, M.S. (2006) A structured approach to modelling SAG mill liner wear - Numerical modelling of liner evolution. Proceedings International autogenous and semiautogenous grinding technology 2006, Sep.24-27, Ed. Mular et al, Published CIM. Vol. III, pp.120-132.

[3] A numerical simulation to relate the shot peening process parameters to the induced residual stresses, T. Hong, JY Ooi , J Favier, B. Shaw, 9th International Conference on Shot Peening, Paris, 2005.

[4] Simulation of a Direct Shear Box Experiment using EDEM, Andres D. Orlando, Shunying Ji, Hayley H. Shen and John Favier, DEM07 (2007).

[5] Pneumatic Conveying of Solids, R. Marcus, L. Leung, G. Klinzing and F. Rizk, Chapman and Hall (1990).

[6] Numerical simulation of particle motion in dense phase pneumatic systems. J. Xiang and D McGlinchey. Granular Matter Vol 6, (2004).

[7] Calculating the Trajectories of Triboelectrically charged particles using Discrete Element Modelling (DEM), M Hogue, C Calle, D Curry, P Weitzman, ESA 2007 Annual Conference.

 




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