将下面两段话进行学术翻译：图4显示了扩径段不同高度上循环通量对颗粒浓度标准差的影响规律。由图4a可知由中心向边壁移动过程中当循环通量较低Gs = 8、23kgm2·s时 FCC颗粒浓度标准差在中心和过渡区域基本保持不变而在边壁区域逐渐增大并在管壁位置达到最大值说明边壁处的流动稳定性最低。当循环通量较高Gs = 325kgm2·s时标准差沿径向出现明显增加的变化趋势具体地标准差在中心区域最小随着向边

Figure 4 illustrates the influence of circulating flux on the standard deviation of particle concentration at different heights in the expansion section. As shown in Figure 4a, when the circulating flux is low (Gs = 8, 23 kg/m2·s), the standard deviation of FCC particle concentration remains unchanged in the central and transition regions while gradually increasing towards the wall region, reaching its maximum value at the pipe wall, indicating the lowest flow stability at the wall. When the circulating flux is high (Gs = 32.5 kg/m2·s), the standard deviation exhibits a significant radial increase trend, with the minimum value in the central region and an obvious increase towards the wall. With the increase of circulating flux, the standard deviation at each radial position increases, indicating that the overall gas-solid flow structure within the expansion section changes and the gas-solid fluctuation becomes stronger with the increase of feed rate. Compared to the central region, the standard deviation in the wall region shows a greater variation with wind speed, suggesting that the fluctuation of solid phase concentration in the wall region is larger than that in the central region, which may be related to the unstable particle back-mixing motion under turbulent disturbance. As the axial position in the expansion section increases, the influence of wind speed on the standard deviation of particle concentration gradually decreases due to the stabilization of particle flow with the increase of axial position. As shown in Figure 4b, the basic rules of glass bead particles in the axial and radial directions are similar to those of FCC particles with the change of wind speed. However, with the increase of circulating flux, the increase in the standard deviation of glass bead concentration at the wall is significantly higher than that of FCC, and this trend becomes more pronounced with the increase of bed height. This indicates that when particles with higher density flow in the expansion section, the particle flow at the wall becomes more unstable with the increase of circulating flux. With the increase of bed height, the carrying capacity of the gas phase further decreases, and the phase separation process intensifies, resulting in larger fluctuations in particle concentration. In addition, unlike FCC, at the same low flux condition, the distribution of the standard deviation of glass bead concentration along the radial direction remains consistent throughout the expansion section at Gs = 32.5 kg/m2·s, and there exists an obvious boundary of particle concentration fluctuation among the central, transition, and wall regions.