## 3 Results
### Determination of the Minimum Velocity of Bubbling Regime  
Further, a series of calculations was carried out to determine the minimum gas velocity at which the regime becomes bubbling. These calculations are necessary because the grid forms relatively narrow channels, and the layer may tend to be in the slugging regime at velocities slightly higher than the minimum required fluidization velocity. It was determined that when the gas velocity reaches 1.4 m/s and higher, then the periodic undamped pressure fluctuations are observed (Figure 7b). Figure 7: Dependence of the area-weighted average pressure at the inlet of the simulated cell on the process time at a gas velocity of (**a**) 1.3 m/s; (**b**) 1.4 m/s. According to the visualization of the solution presented in Figure 8, it can be seen that the formed gas bubbles occupy the entire cross-section of the simulated cell, i.e., the fluidized bed with slugging fluidization is observed. This is due to the narrow space (in our case, the narrowness of the distribution grid cells) and the relatively large particle size (see Section 1). That is, macrostructures, such as gas bubbles, occupy the entire horizontal cross-section of the distribution device cell. Such a regime has a negative effect on the processes in the bed, since it excludes the mixing of particles, and, at the same time, it has significant uniformity (strictly periodic pressure fluctuation). To switch over from this fluidization to a bubbling or turbulent regime, it is necessary to increase the gas velocity. However, the simulation was carried out only for one cell of one particle layer, and the loss of gas velocity due to hydraulic resistance should be taken into account in order to ensure the bubbling of the upper layers of particles. To do this, it is necessary to increase the gas velocity at the inlet up to such values that the velocity would be greater than 1.4 m/s at the inlet of the last layer of particles. It was found that when passing through the particle layer, the gas velocity drops by \(\sim\)17%, from 1.4 m/s to 1.1-1.2 m/s, as shown in Figure 9.  
However, it should be noted that with a significant increase in gas velocity at the inlet to the first layer, the particles will be carried away and they will beat against the support grid of the second layer, which can cause their destruction or rapid erosion. This is a restriction of the number of granular material layers. Based on the simulation results shown further in Figures 10-13, it is noticeable that some particles are close to hitting at the support grid of the next layer. The upper group of seven particles in Figure 13 (highlighted in red) at \(t=0.57\) s is located at a distance of under 1.5 cm from the support grid. Hence, an increase in gas velocity above 3 m/s is impractical. Since it is necessary to ensure the bubbling regime of the upper particle layers, taking into account the layer hydraulic resistance losses, therefore, the optimal number of layers equal to four was adopted. Having assumed that the gas will lose \(\sim\)17% of the velocity in each layer of particles, 3 m/s was chosen as the optimal value. The simulation results obtained, namely inlet pressure and visualization of particle positions and velocities, are shown in Figures 10-13 at 0, 0.15, 0.39, 0.45, 0.54, and 0.57 s, respectively. The time intervals are a random choice. From the data presented, it can be seen that an increase in gas velocity by more than two times significantly affected both the fluidization regime and its uniformity (pressure fluctuations became chaotic, Figure 10). The regime approached the turbulent fluidization; however, as the gas velocity decreased due to the hydraulic resistance of the layers, the fluidization uniformity increased. Figure 8: Visualization of the obtained solution (color means particle velocity). Figure 10: Dependence of the area-weighted average gas pressure at the inlet of the simulated cell of the distribution device on the process time at a gas velocity of 3 m/s.