**5.1.1 Mesh parameters and boundary conditions**


The boundary conditions for both cases are shown in Table 5 and Table 6.

In addition, tests were made with a 500.000 control volume mesh with same block distribution (the description of volume distribution in the meshes, are presented in Table 7). Obtaining similar results with the 100.000 control volume mesh. Both meshes are shown in Figure 4.


Table 5. Boundary conditions for the Case 1.

Fluid Dynamics of Gas – Solid Fluidized Beds 51

Numeric calculations performed (Vreman, Geurts, and Kuerten 1997; Chow and Moin 2003) showed that the required values to obtain an accurate numerical solution, it is necessary to use a ratio dx 0.25 for the second order spatial scheme, and a ratio dx < 0.5 for the sixth

The values of dx presented in Table 7 are within the range recommended in the literature (Chow and Moin 2003; Agrawal et al. 2001; van Wachem 2000; Ahmed and Elghobashi 2000;

Figure 5 presents the solid volume fraction time evolution for the mesh II with superficial velocity 1 m/s. At the beginning, the solids present in the riser are forced to flow in the

When the bed of solids starts to expand, it is observed high solid particle concentration at the center of the tube and near the walls (Figure 5). This reordering of solid particles is a counteraction in order to offer a lower resistance to the gas flow. This type of flow regime is known as pre-fluidized bed.It is important to mention that one of most relevant characteristics of the fluidization is the high contact area between the solid particles and the fluid. In this way, a cubic meter of particles of 100 micron contains a superficial area of around 30000 m2. The advantage of this high surface area is reflected in a high mass and

Fig. 5. Evolution of the volume fraction field in a fluidized bed at 0, 11, 35, 70, 90, 132, 165,

Figure 6 shows the similarity between results presented by Miller and Gidaspow (1992). Here it is represented the regions of high and low solid concentration. Near the walls

The annular-core behavior is something that detrimental in the units of Fluid Catalytic Cracking (FCC), since big fraction of the oil is converted in a region where the catalyst works less efficient. In addition to this, the particles that flow at center core are expose to bigger concentrations of oil compounds, which is something that produces faster deactivation of the catalyst. One the strategies to solve this issue is to inject pressurized gas in perpendicular direction to the flow in the reaction zone. Another solution is to include rings connected to

walls, with the purpose of redirecting the solids from the wall towards the center.

order scheme.

Vreman, Geurts, and Kuerten 1997).

upward direction, similar to a plug flow.

heat transfer rates between the solid and the fluid.

185, 198, 220, 242, 264, 275, 290, and 317 ms.

velocity is negative and near the center velocity is positive.


Table 6. Boundary conditions for the Case 2.


Table 7. Volume discretization of the meshes.

Fig. 4. Schematic diagram of the Table 7 meshes. Up: Mesh I. Down: Mesh II

50 Advanced Fluid Dynamics

Out *Opening* = atmospheric pressure

Mesh dxdp Volumes Number dx I 15 99900 0.05 II 10 467313 0.08

Particles = *No slip* Gas = No slip

Particle mass flow equal to the output

In Gas velocity = 1 m/s

Initial height Bed height = 0.05 m Particles 120 μm, 2400 kg.m-3

Fig. 4. Schematic diagram of the Table 7 meshes. Up: Mesh I. Down: Mesh II

Wall

Table 6. Boundary conditions for the Case 2.

Table 7. Volume discretization of the meshes.

Numeric calculations performed (Vreman, Geurts, and Kuerten 1997; Chow and Moin 2003) showed that the required values to obtain an accurate numerical solution, it is necessary to use a ratio dx 0.25 for the second order spatial scheme, and a ratio dx < 0.5 for the sixth order scheme.

The values of dx presented in Table 7 are within the range recommended in the literature (Chow and Moin 2003; Agrawal et al. 2001; van Wachem 2000; Ahmed and Elghobashi 2000; Vreman, Geurts, and Kuerten 1997).

Figure 5 presents the solid volume fraction time evolution for the mesh II with superficial velocity 1 m/s. At the beginning, the solids present in the riser are forced to flow in the upward direction, similar to a plug flow.

When the bed of solids starts to expand, it is observed high solid particle concentration at the center of the tube and near the walls (Figure 5). This reordering of solid particles is a counteraction in order to offer a lower resistance to the gas flow. This type of flow regime is known as pre-fluidized bed.It is important to mention that one of most relevant characteristics of the fluidization is the high contact area between the solid particles and the fluid. In this way, a cubic meter of particles of 100 micron contains a superficial area of around 30000 m2. The advantage of this high surface area is reflected in a high mass and heat transfer rates between the solid and the fluid.

Fig. 5. Evolution of the volume fraction field in a fluidized bed at 0, 11, 35, 70, 90, 132, 165, 185, 198, 220, 242, 264, 275, 290, and 317 ms.

Figure 6 shows the similarity between results presented by Miller and Gidaspow (1992). Here it is represented the regions of high and low solid concentration. Near the walls velocity is negative and near the center velocity is positive.

The annular-core behavior is something that detrimental in the units of Fluid Catalytic Cracking (FCC), since big fraction of the oil is converted in a region where the catalyst works less efficient. In addition to this, the particles that flow at center core are expose to bigger concentrations of oil compounds, which is something that produces faster deactivation of the catalyst. One the strategies to solve this issue is to inject pressurized gas in perpendicular direction to the flow in the reaction zone. Another solution is to include rings connected to walls, with the purpose of redirecting the solids from the wall towards the center.

Fluid Dynamics of Gas – Solid Fluidized Beds 53

Pilot plant scale riser reactor (Bader, R., Findlay, J. and Knowlton, TM 1988). Riser height: 13 m, riser diameter 0.3 m. Entrance with angle 60°, gas superficial velocity 3.7 m and solids

Fig. 8. Solids volumetric fraction in the center of the riser. Simulation time 15 sec. Left to right: LES Smagorinsky, LES WALE, LES Dynamic model, Detached Eddy Simulation (DES).

In the Figure 8 can be observed that the solid particles enter to the reactor uniformly distributed, after a short distance these particles start falling due to the gravity and they start flowing over the wall of the inclined pipe. After this, the solids fall into a turbulent zone where they get mixed. Some of the particles will continue falling over the vertical wall opposite to the

entrance. The core-annular zone is formed at some height in the middle of the column.

**5.2 Case 3** 

flux 98 kg/(s.m^2) as shown in Figure 8.

Fig. 6. Comparison of solid phase velocity profile presented by Miller and Gidaspow (1992) with the CFD simulations (-▲-) and experimental data performed by Samuelsberg and B. H. Hjertager (1996) (●).

To get an impression regarding the flow behavior inside the column, the time averaged solid volume fraction is plotted at different column heights, 0.16 m, 0.32 m and 0.48 m (Figure 7). Here it can be observed the strong tendency of the solid particles to be near the wall.

Fig. 7. Axial profile of the solid phase volume fraction fields in the center (left) and radial profiles at 0.48 m, 0.32 m, 0.16 m (right up to down). Superficial velocity 0.36 m s-1
