将下面进行学术翻译：图14是典型操作条件下玻璃珠与FCC颗粒浓度波动信号在扩径段和等径段内的小波能量分布对比图。可以看到等径段内两种颗粒在各尺度上的能量份额分布和扩径段相同但对相同径向位置上的同一流动尺度不同密度颗粒在扩径段和等径段的能量份额变化既有相同之处也存在差异。以边壁区域为例玻璃珠在宏观尺度的能量份额随着高度增加增大而FCC颗粒的能量则减少而两种颗粒在扩径段内的介观尺度能量份额均大于等径段

Figure 14 shows a comparison of the wavelet energy distribution of glass beads and FCC particles concentration fluctuations under typical operation conditions in the expanding and equidiameter sections. It can be observed that the energy share distribution of the two types of particles at various scales in the equidiameter section is the same as that in the expanding section. However, for the same flow scale at the same radial position, the energy share changes of the particles with different densities in the expanding and equidiameter sections are both similar and different. Taking the wall region as an example, the energy share of glass beads at the macroscopic scale increases with the height, whereas that of FCC particles decreases. However, at the mesoscopic scale in the expanding section, the energy share of both types of particles is greater than that in the equidiameter section, indicating an increased complexity of the effect of particle properties on the gas-solid flow in the variable-diameter riser.

Consistent with the previous section, the energy share at the mesoscopic and macroscopic scales of glass beads is higher than that of FCC particles in each radial position in the expanding section, while the energy share at the microscopic scale is lower than that of FCC particles. However, in the equidiameter section, the energy share at the mesoscopic and microscopic scales of FCC particles is higher than that of glass beads, while the macroscopic scale share is still lower than that of glass beads. This may be due to the fact that the dense glass bead particles tend to accumulate and retain more in the expanding section than FCC particles, resulting in a decrease in the glass bead concentration in the upper equidiameter section. The above phenomena also indicate that the effect of particle density properties on the macroscopic flow is consistent in the expanding and equidiameter sections, but has opposite effects on the micro-mesoscopic flow structure and motion intensity in the expanding and equidiameter sections. Moreover, the change in energy share at the macroscopic scale due to particle density in the equidiameter section is greater than that in the expanding section, indicating that the macroscopic gas-solid flow structure in the expanding section is less affected by particle properties, i.e., the flow state is more stable. The effect of particle density on the energy share distribution at the micro-mesoscopic scales in the equidiameter and expanding sections does not show a consistent rule at each radial position, implying the complexity of particle migration, collision, and agglomerate motion. In addition, at the same radial position, as the particle density increases, the change in energy share at the microscopic scale for particle flow in the expanding and equidiameter sections decreases, while the difference in energy share at the mesoscopic and macroscopic scales increases.