Effect of Circulating Mass Flux on Particle Concentration Distribution in an Expansion Section: FCC vs Glass Beads

Comparison of the probability density distribution of FCC particle concentration at different radial positions in the expansion section under operating conditions of circulating mass flux ranging from 14.5 to 32.5 kg/m2ﾷs and superficial gas velocity of 5 m/s is shown in Figure a. It can be observed that with the increase of circulating mass flux, the peak of probability density distribution increases and shifts towards the high concentration region, and the curve presents a wide distribution with a long tail. This indicates that with the increase of feed rate, the probability of localized high particle concentration in the tube increases, and the distribution range of particle concentration also increases. The change of probability density distribution is relatively small at low circulating mass flux, but a significant shift occurs when the circulating mass flux increases to 32.5 kg/m2ﾷs. Overall, compared with the wall and transition regions, the effect of circulating mass flux on particle concentration distribution in the central region of the expansion section is relatively small, indicating that the gas-solid flow in the central region of the expansion section is more stable. As the curve moves from the wall to the center, the peak tends to move towards the low concentration region, and the width gradually decreases, but the peak value increases. These changes are more obvious at high circulating mass flux. This indicates that the particle concentration is highest at the wall, and as it moves towards the center of the tube, the particle concentration gradually decreases. Within the current operating conditions, the probability density curve presents a single peak distribution, implying that the gas-solid flow in the expansion section is mainly dilute-phase flow. In addition, at low solid flux, particle concentration is mainly concentrated in the range of 0.01, indicating uniform and continuous local particle flow; at high solid flux, particle concentration distribution is more scattered, indicating that the fluctuation of particle flow in the expansion section increases with the increase of concentration, and there is a tendency for the development from a single dilute-phase structure to a coexistence of dilute and dense-phase structure.

Figure b shows the influence of circulating mass flux on the probability density distribution of glass bead concentration at different radial positions. It can be seen from the figure that the probability density distribution of glass beads and its variation trend with solid flux are generally consistent with that of FCC, indicating that materials with different densities have similar basic flow structures in the expansion section. At the same circulating mass flux, the PDD curve distribution of glass beads at the wall is wider than that of FCC, and the probability of high concentration particle distribution is increased. This is because the glass beads with high density at the wall undergo severe mixing, resulting in a large amount of particle aggregation, which leads to an increase in particle concentration at the wall, consistent with experimental observations. Moreover, the influence of circulating mass flux on the probability density distribution of glass bead at the wall is greater than that of FCC. By comparing the probability density distribution of FCC and glass beads in the transition and central regions, it can be found that there is little difference between the two under high mass flux conditions, but under low mass flux conditions, the probability density distribution of glass beads moves towards the low concentration region compared with FCC, indicating that the particle concentration of glass beads in this region is lower. This may be related to the fact that the particles with higher density in the expansion section tend to aggregate at the bottom due to the decrease of drag force, which weakens axial movement and enhances radial movement.