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a1.gif (929 bytes)llied Environmental Technologies, Inc. has developed a variety of unique two-dimensional (2D) and three-dimensional (3D) proprietary computer programs involving the DEM. technique. Using these programs, we can simulate almost any possible solid particle shape, and predict their behavior. The Discrete Element Method (DEM.) has been developed in the scientific-engineering community starting from the early eighties, although the idea of this technique is very old. Predominantly, this technique allows the solving of the problem of granular medium dynamics, i.e., the dynamics of a medium consisting of a large number of solid particles and their interaction with each other.

t1.gif (918 bytes)here are three basic areas of the solid material handling, which could benefit from DEM applications, where: (1) -solid particulate is a waste or a by-product to be disposed of, for example, bottom or fly ash in a power utility industry; (2) -solid particulate is an ingredient in a process, for example, cement or rock products industries, and (3) -solid particulate material is a new product that, in case of wastage, has a substantial cost involved, for example pharmaceutical industries and as such.

t1.gif (918 bytes)he DEM.'s principal idea is very simple. Unlike a Computational Fluid Dynamics approach (CFD), in DEM one does not need to know the equation of state of a medium. Instead, one computes motion of each particle separately, using simple laws of Newtonian mechanics. The forces of the interaction between the particles in the system and particles and solid obstacles in the system, which are required for the numerical solution of the equation of particles motion, are usually determined based on the overlap of the particles. The particles in this technique are normally not allowed to deform and allowed to overlap slightly; this overlap generates elastic forces. However, recent developments resulted in programs that allow particles to be deformed as well). The most popular law of particles interaction is linear-elastic-viscous in normal direction and linear-elastic-frictional in tangential direction, but any interaction law can be used (for example Hertzian one).

e1.gif (933 bytes)ngineers need better ways of optimizing designs of process and material handling related equipment and storage vessels that come into contact with solids/fluid media. These may include, but not be limited to applications such as:

Solid particles crushing or sizing;

Particles discharging from unlimited variety of hopper shapes into storage or process vessels;

Solids drying in rotary dryers and kilns;

Screw type conveying systems;

Pneumatic conveying systems;

Fluidized bed combustion, solid fuel feed, ash classification, etc.

Selective physical separation of mixed solids and dense media;

Particles interaction in moving bed (s) environment for applications such as filtration, transport, absorption, adsorption, etc.

t1.gif (918 bytes)his technique offers several principal advantages compare to the standard CFD and experimental approaches for the solution of the problems involving the dynamics of granular medium. First, since granular medium can behave both as a solid and as a fluid under the different loading conditions, choosing the right equation of state for the CFD calculations was traditionally very difficult. Even for the simplest problem, such as flow from the hopper, this uncertainty of the equation of state exists. This problem is naturally eliminated in the DEM technique, which can accurately model the transition from the fluid-like to solid-like behavior and vice versa.

a1.gif (929 bytes)nother advantage of the DEM approach is that virtually any information could be obtained from this technique: Stresses in a granular medium, velocities, bulk densities, flow rates and so on, since virtually everything is known to a computer "experimenter or a programmer. This is a big advantage with respect to the experimental approach, since in experiments only very limited information is usually available.

t1.gif (918 bytes)he limitation of the DEM approach is usually the amount of computer memory that it requires, in fact, this was the principal obstacle in this technique development until the early eighties. Today, a computer with 64 MB of memory allows to carry out the calculations for about 60,000 particles, which is usually enough to predict behavior and to simulate complex and large systems. The rapid development of the computer technology has made until recently unfeasible DEM problems easy to compute.

p1.gif (924 bytes)resently, the DEM state of the art software is reasonably well developed for the solution of the problems that do not involve the fluid-solid interaction, thus, it is used mostly in the cases where the interaction with fluid can be neglected. For example, simulating solid particles flow from hoppers, and so on. However the work has already begun for the fluid-solid interaction DEM model, and so far looks very promising. Upon completion of the DEM solid-fluid interaction models, one can expect the numerical solutions for problems such as moving and fluidized bed(s) and so on, which are very important. The other direction of DEM development that is very significant for the industry, is the incorporation of attrition and comminution processes (breakage of solid particles) in the model. Work in this area has already been started as well.

f1.gif (929 bytes)inally, unlike the CFD approach, there are virtually no limitations placed on the boundary conditions, such as flow rates, etc. Given the proper time step, a DEM technique is a very reliable and stable one.

t1.gif (918 bytes)his technique will help engineers solve design problems cost-effectively by simulating solids-fluid flow and other physical phenomena in place of the expensive bench-scale and field experimentation. It could allow testing of various physical and material shapes and patterns, examining new design ideas, and optimizing designs for a variety of applications.

everal examples of the 2D and 3D motion of solid particles through a hopper are illustrated in the following figures; one for the round particles of the same size and the other for elliptic (grain shaped) particles of different sizes. These particles are dyed to show the motion only. Properties of the particles of different color are the same in this example.


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