将下面两段话进行学术翻译：图2a和b分别表示了在不同的径向位置处表观气速对FCC和玻璃珠颗粒的概率密度分布的影响结果。当循环通量为145 kgm2 · s时随着表观气速的升高FCC和玻璃珠的概率密度分布曲线的峰值均降低且峰宽逐渐减小曲线峰出现的位置逐渐向低浓度区域移动。这可能归因于当循环通量一定时风速越高气固之间曳力增加颗粒更容易被带离扩径段从而造成管内颗粒浓度降低。从图中还可以看出在相同工况下管

The impact of the superficial gas velocity on the probability density distribution (PDD) of the FCC and glass bead particles at different radial positions is shown in Figures 2a and b. As the superficial gas velocity increases, the peak of the PDD curves for both the FCC and glass bead particles decreases, and the peak width gradually narrows, shifting towards lower concentration regions. This can be attributed to the increase in drag force between the gas-solid phases with higher gas velocity. As a result, the particles are more likely to be carried away from the expansion section, leading to a decrease in particle concentration. Additionally, the PDD curves at the wall region exhibit the widest distribution, indicating the highest particle concentration level. The PDD curves in the transition region to the center region show similar distributions at low gas velocity, and exhibit a low concentration peak and narrow peak width at high gas velocity. These observations suggest that the particle flow near the wall region is relatively stable, while the difference in particle flow between the transition and center regions increases with increasing gas velocity. This may be attributed to the presence of wall effects, which limit the disturbance of the gas flow on the particles, resulting in more gas flowing through the center region of the bed and increasing the instability factor of the gas flow on the particle flow. Furthermore, the trend of the PDD distribution with respect to both the superficial gas velocity and the circulation flux is opposite, further demonstrating the relationship between the local particle concentration and the overall concentration in the bed.

Comparing Figures 2a and b shows the impact of particle density on the PDD distribution. At the wall region, the PDD curve for glass beads is wider than that of FCC, with a higher probability of high concentration distribution. The more discrete PDD distribution for glass beads indicates a more complex particle motion structure in the expansion section than for FCC. However, as the gas velocity increases, this difference gradually decreases. This is because the high density of glass beads increases the resistance to upward particle motion, causing a greater degree of backmixing at the wall region at low gas velocity, resulting in higher particle concentration. At high gas velocity, the difference in particle aggregation caused by particle density decreases, resulting in a more similar particle concentration distribution. In contrast, in the center region of the bed, the PDD curve for FCC particles is wider than that of glass beads, with a higher probability density peak corresponding to a higher particle concentration. Consistent with the trend shown in Figure 1, this can be attributed to the greater gravitational force acting on the higher density glass beads, resulting in an enhanced transverse motion trend during the upward motion of the gas-solid mixture in the center region, leading to a higher concentration of FCC particles than glass beads. Additionally, compared to FCC, the impact of superficial gas velocity on the PDD distribution of glass beads is greater in the wall and transition regions.