### DEM with DNS

A numerical study of 3D cylindrical fluidized bed by means of combined computational fluid dynamics (CFD) and discrete element method (DEM) was carried out. For particles motion Newton's second law and for the flow field 3D compressible Navier-Stokes equations in generalized curvilinear coordinates in conservative form were used. The Navier-Stokes equations were solved with high order compact finite difference scheme by fully implicit flux decomposition method. Furthermore Non-Reflecting Boundary Conditions (NRBC) was used for outflow boundary.

In the numerical study of this work, a cylindrical fluidized bed with 7.5 cm diameter and 50 cm height, filled with 10000 particles. The diameter and density of particles were 2mm and 1100 kg/m3, respectively. A jet of gas was introduced into the bed via a central hole with jet velocity of 8 m/s (u = 5umf).   As could be seen in this figure, particles that are at the center of the bed accelerate very fast and move vertically in the bed. The initial acceleration of the particles is so high that they almost travel 50 cm in the bed. This high acceleration is due to the high vertical drag force exerted on particles due to high gas velocity in the central area of the bed. But, particles in the annulus of this area do not move very noticeably in the vertical direction. This is mainly due to the low gas velocity in this region. The gas velocity in this region is low for two reasons. First, the gas does not introduce the bed from near the walls. Second, wall effects induce a velocity boundary layer in which the gas velocity is low near the wall of the bed. If the simulation has been permitted to continue for a longer time, the transient state of the bed would have been vanished and a better solid flow pattern would be obtained. Since the time required for the calculation is very high (around 1 month), this results has not been obtained yet.   For low Mach number flows, changes in density are low, but as it can be seen in these figures, with upcoming the particles the density of fluid before them increases. Moreover, the velocity vectors in center of the cylinder are high. This flow pattern is in accordance with a gas flow pattern in a cylinder with boundary layer. According to the continuity relation, while the gas velocity increases, the density of gas decreases. This result shows that the presented model and the implemented method can predict compressibility behavior of the gas very well.