# An Analysis of the Factors Influencing Dual Separation Zones on a Plate
## 4 Result and Discussion
### Effect of Incident Shock Intensity  
In addition to the trailing expansion waves, the intensity of the incident shock wave \(\alpha\) is also a critical factor influencing the merging and re-separating process of dual separation zones. Given the non-negligible discrepancies in shock angles induced by models from different angles, the shock-generating position is no longer suitable as a measurement standard for the distance between dual separation zones. Furthermore, as the sizes of separation zones induced by shock waves of varying intensities also differ significantly, the relative distance between the dual separation zones \(d_{s-r}\) is retained to mitigate the  
Figure 10: Velocity of in case with different \(l\). For the case (**a**) \(l=l_{1}\); (**b**) \(l=l_{2}\); (**c**) \(l=l_{3}\). influence caused by the scale change in the first separation zone and evaluate the relative distance between dual separation zones. When \(d_{s-r}=-7\) mm, the wall pressure curves under different shock intensities depict distinct stage characteristics. As the angle of the shock generator increases, the dual separation zones tend to approach the merged state. By shifting the shock generator 5 mm downstream, it was observed that the flow field states of the 13\({}^{\circ}\) and 15\({}^{\circ}\) cases remained unchanged from those shown in Figure 11a, with both residing in the segment from M\({}_{\text{t}}\) to M\({}_{\text{e}}\). In contrast, the 11\({}^{\circ}\) case transitioned from the initially merging state (M\({}_{\text{s}}\)-M\({}_{\text{t}}\)) to the nearly merged one (M\({}_{\text{t}}\)-M\({}_{\text{e}}\)). Additionally, for identical increments of \(d_{S}\), weaker incident shock intensities demonstrate larger pressure ratio growth during the mergence. The reattachment point of the first separation zone is marked in Figure 11 with circles, and the coordinate of the corresponding point is cited aside the circle. As illustrated in Figure 8, the pressure increases for the 11-15\({}^{\circ}\) models are 25.16%, 12.27%, and 7.16%, respectively. Overall, for the same relative distance, a larger shock angle results in a smaller separation interval distance and a shorter pressure drop segment after the pressure plateau of the SZI. This indicates that under the 11\({}^{\circ}\) configuration, the flow field parameters exhibit the fastest variation rate for the same growth in shock travel distance, with merging occurring more rapidly. Additionally, stronger shock wave intensity leads to an earlier onset of mergence, while requiring a longer merging distance. Furthermore, the peak of the wall pressure decreases with the expansion of the separation zones. The overall pressure curves in the figure rises with enhanced incident shock intensity. However, regarding the peak wall pressure specifically, stronger incident shocks result in lower peak values. The reason why this phenomenon occurs is that when the length of the shock generator and the incoming flow Mach number remain constant, a stronger incident shock corresponds to more intense trailing-edge expansion waves. These expansion waves exert a greater influence on the second separation zone, consequently leading to reduced wall pressure peaks. Figure 9 shows the variation curves of the pressure integral under different shock wave intensities and shock travel distances. Compared with the average integral value P\({}_{\text{avg}}\), the variation in the wall pressure integral values under different \(d_{S}\) is less than 1%, which can be considered constant. The wall pressure integral value can be regarded as the normal resultant force acting on the flat plate. For the merging and re-separating process of dual separation zones induced by fixed-intensity incident shock waves, the normal resultant force on the flat plate remains unchanged regardless of flow field state variations; hence, P\({}_{\text{i}}\) remains constant.