# An Analysis of the Factors Influencing Dual Separation Zones on a Plate
## 4 Result and Discussion
### Effect of Expansion Waves
#### 4.2.1 Variation in Parameters  
The merging process of the dual separation zones in this study exhibits a relatively smooth transition. During the merging process, the flow field undergoes a gradual transformation from separated states to merged states, representing a transitional evolution rather than the abrupt state transition observed in other investigations on the dual-separation-zone merging process [18]. Since there are no visually discernible differences between the critical merging state and fully merged state of dual separation zones, wall surface flow field parameters are utilized to assist in the determination of the flow field state. Figure 8 shows the wall pressure curves corresponding to flow fields of the SG with different lengths under the same shock-generating point. The hollow rings on the curves along the flow direction denote the separation and reattachment points of the first and second separation zones, respectively. When the length of G increases from \(l_{1}\) to \(l_{2}\), the amplitude of the pressure rise in the first separation zone intensifies. To match the downstream pressure increase, the separation point S\({}_{1}\) of SZI shifts upstream, while the reattachment point R\({}_{1}\) moves slightly downstream, resulting in an elongation of the length of the first separation zone (L\({}_{51}\)). For the second separation zone, the length of the separation zone L\({}_{52}\) shows a slight increase with a growth rate significantly smaller than that of L\({}_{51}\)  
Figure 7: Mach number contour of different lengths of G under the same T. For the case: (a) \(l_{1}\); (b) \(l_{2}\); (c) \(l_{3}\). Its growth mainly depends on the forward movement of the separation point S\({}_{2}\), while the reattachment point remains almost unchanged compared to the flow field corresponding to \(l_{1}\). The rearward movement of the expansion waves leads to an increase in the size of the dual separation zones, thereby reducing the distance between them. When the length of the shock generator is further extended to \(l_{3}\), the dimensions of the dual separation zones expand significantly. In this model, the dual separation zones are completely merged, leaving only a pair of hollow rings on the pressure curve, which correspond to the separation and reattachment points of the merged separation region, respectively. To investigate the influence of the expansion wave position on the entire mergence and re-separation process, the variation in length of the first separation zone L\({}_{S1}\) and increment in the shock travel distance \(d_{S}\) are extracted under different shock generator lengths. The x-coordinate of the shock wave generation point corresponding to the actual critical fusion flow field decreases with the increase in shock generator length; that is, the farther the expansion wave is from the first separation zone, the more likely the dual separation zones are to merge. During the merging process, the length of the first separation zone continuously increases, and the amplitude of variation becomes increasingly steep with the elongation of the shock generator. The length of the separation zone before merging also increases accordingly. Due to the different absolute positions of the mergence point of the dual separation zones under different lengths of shock generators, for the convenience of comparation, the relative distance between the dual separation zones \(d_{s-r}\) is defined to reflect the moving steps required for the DSZ to complete the mergence:  
\[d_{s-r,n}=X_{T,n}-X_{T,c}\]  
In the above equation, \(X_{T,c}\) denotes the x-coordinate of the shock-generating point in the critical merging state of the dual separation zones, which is called the critical generating point, while \(X_{T,n}\) is the x-coordinate of the shock-generating point in the current flow field. Thus, the mergence points of the dual separation zones of different models uniformly correspond to \(d_{s-r}=0\) mm.