Wavelet Decomposition Energy Shares of FCC Particles and Glass Beads in an Expansion Section: Influence of Particle Density and Wind Speed

Figure 10 shows the distribution of wavelet decomposition energy shares of FCC particles and glass beads concentration fluctuations at different apparent wind speeds in the expansion section. As shown in Figure 10a, the energy share is mainly concentrated at the mesoscale level, followed by the macroscale level, and the microscale level has the lowest energy share at different radial positions. This indicates that the movement of particle aggregates dominates the particle phase flow in the expansion section. At the mesoscale level, the energy share decreases with increasing wind speed. This is because when the wind speed is low, the drag force on particles decreases, making it easier for them to gather and enhance the mesoscale movement of aggregates. At the same time, as the radial position moves towards the center of the pipe, the difference in the mesoscale energy share with wind speed decreases, indicating that the effect of wind speed on the mesoscale structural movement at the wall of the pipe is greater than at the center. At the microscale level, the energy share decreases with increasing wind speed, indicating that the intensity of particle collision and other movements at the particle level decreases at high wind speeds due to the decrease in particle concentration inside the expansion pipe. Conversely, at the macroscale level, the energy share increases with increasing wind speed, and the increase is greatest at the edge of the wall, indicating that the overall flow intensity inside the expansion pipe increases with increasing wind speed, and the effect of the wall is amplified. In addition, the micro energy share gradually increases towards the center of the pipe, indicating that the movement of particles at the center of the pipe is more intense than at the wall. The larger macro energy share at the wall than at the center indicates that under the comprehensive influence of wind speed and pipe structure, the macro gas-solid flow at the wall is more complex.

According to Figure 10b, the distribution of energy shares of glass beads at different scales is consistent with that of FCC particles, with the maximum energy share distributed at the mesoscale level, followed by the macroscale and microscale levels, indicating that the flow structure of the two materials is similar. Similarly, with increasing wind speed, the energy share of glass beads decreases at the micro and mesoscale levels and increases at the macroscale level. However, compared with FCC particles, under the current operating conditions, the energy share of glass beads decreases at the microscale level and increases at the macroscale level, indicating that the increase in particle density weakens the movement intensity at the particle level, which is related to the decrease in interaction between particles with large density. Correspondingly, particle aggregation causes an increase in movement intensity at larger scales. At different radial positions, with increasing apparent wind speed, the change in energy share of glass beads at different scales is greater in the wall and transition regions than in the center region compared to FCC particles. This indicates that particles with high density are more sensitive to wind speed in the expansion section as a whole. Taking the macro energy share as an example, the mixed flow of glass beads and gas is more affected by the combined influence of the pipe structure and operating conditions than FCC particles.