## 3 Results and Discussion
### Extraction and Analysis of Burst Events  
The early studies on burst events were conducted by [PERSON] and colleagues at Stanford University in the United States [21], who used flow visualization techniques to study the streak structures in the near-wall region of turbulence. They found that low-speed streak structures underwent a process of rising, oscillating, breaking, and ejecting in some of the early investigations into burst events. With the rapid development of computational capabilities, detection methods for near-wall burst events have also been continuously improved. [PERSON] and [PERSON] et al. [54; 55; 56] divided the motion of fluid particles into four quadrants to better extract these structures: Q1 events: u\({}^{\prime}>0\), v\({}^{\prime}>0\); Q2 events: u\({}^{\prime}<0\), v\({}^{\prime}>0\); Q3 events: u\({}^{\prime}<0\), v\({}^{\prime}<0\); Q4 events: u\({}^{\prime}>0\), v\({}^{\prime}<0\), where Q2 events correspond to ejection and Q4 events correspond to sweep. The introduction of this method effectively addressed the issues of burst event detection methods at the time, and subsequent methods have been based on this concept. This paper employs the new quadrant division method proposed by [PERSON] et al. [57] to extract ejection and sweep structures. The detection function is:  
Figure 10: Autocorrelation coefficient of streamwise fluctuation velocity in the z-direction: (**a**) clean water flow field; (**b**) two-phase flow field. Figure 12 presents normal fluctuating velocity cloud maps of burst events in the self-sustaining mechanism. The burst events in this region dominate the transformation between streamwise vortices and streak structures; therefore, changes in the burst events in this region can not only reflect the level of Reynolds shear stress but also explain the reasons for the changes in the streak structures mentioned earlier. Compared to the normal height of \(y^{+}=90\), the intensity of burst events at the normal height of \(y^{+}=30.5\) is lower, and the scale is smaller. At this normal height, the pattern of changes in burst events caused by the riblet walls is consistent with that at the height of \(y^{+}=90\). However, in both flow fields, the inhibitory effect of particles on burst events is only manifested in the reduction in their scale, but the intensity of normal fluctuations velocity in the core areas of ejection and sweep slightly increases. This indicates that particles have suppressed the scale of burst events in this range, compressing more normal fluctuation into their core regions. Figure 11: Normal fluctuating velocity cloud image of ejection–sweep events under different wall surfaces at \(y^{+}=90\): (**a**) clear water field ejection event; (**b**) liquid–solid two-phase flow field ejection event; (**c**) clear water field sweep event; (**d**) liquid–solid two-phase flow field sweep event. Previous studies have shown that, in the buffer zone, ejection events contribute to 70% of the Reynolds shear stress, and even in the logarithmic region, under a zero pressure gradient, the contribution of ejection events to Reynolds shear stress is higher than that of sweep events [8]. After the addition of particles, the number of sweep events does not change significantly; on the contrary, the number of ejection events varies greatly. Therefore, it can be inferred that in the buffer layer and logarithmic law region where the self-sustaining process occurs, changes in ejection events are an important factor affecting frictional resistance. Figure 13 shows the distribution pattern of ejection events at two normal heights for each wall. Unlike the distribution pattern of streamwise vortex quantities, the number of ejection events does not show a clear decrease with the increase in normal height, but is distributed with small fluctuations around the average value.