# An Analysis of the Factors Influencing Dual Separation Zones on a Plate
## 4 Result and Discussion
### Effect of Expansion Waves
#### 4.2.2 Variation in Evolution  
Further analysis was conducted on the variations in flow field parameters during the merging and re-separating process of dual separation zones. Taking the horizontal coordinate of the separation point in the first separation zone, \(X_{\mathrm{S1}}\), as an example, its velocity curve manifests a smooth-fluctuating-smooth variation trend. The rapid change phase corresponds to the merging (re-separating) process, and the variations in parameters return to stability after the transition of the flow field state is completed. The variation in \(X_{\mathrm{S1}}\) between adjacent moving steps is defined as the nth-step position increment \(\Delta X_{\mathrm{S1,n}}\). This parameter is influenced by both changes in boundary conditions and the merging process. To focus on the impact of mergence, the inherent influence of boundary conditions must be eliminated from the single-step position increment \(\Delta X_{\mathrm{S1}}\). Since the first separation zone before mergence moves smoothly downstream as \(\mathrm{d_{S}}\) increases, with its velocity consistent with the moving speed of the shock generator, the shock travel distance within one single step is considered as the inherent influence of \(\mathrm{d_{S}}\) growth on \(X_{\mathrm{S1}}\). This relationship is defined by the following formula:  
\[\mathrm{V_{S1,n}}=(X_{\mathrm{S1,n+1}}-X_{\mathrm{S1,n}}-\Delta\mathrm{d})/ \Delta\mathrm{d}=\Delta X_{\mathrm{S1,n}}/\Delta\mathrm{d}-1\]  
where \(1\leq\mathrm{n}\leq\mathrm{N}-1\), and \(\Delta\mathrm{d}\) is a fixed value of 0.1 mm. N stands for the total calculated moving steps. \(\mathrm{V_{S1}}\) is referred to as the change velocity of the first separation point, and \(\mathrm{V_{S1,n}}\) denotes the ratio of the first separation point position change induced by the mergence (re-separation) to the position change caused by variations in the boundary condition during the nth moving step. \(\mathrm{V_{S1,n}}\) reflects the variation rate of the flow field throughout the entire process of mergence and re-separation. As shown in Figure 10, the abscissa symbolizes the shock travel distance during the merging and re-separating process of each model rather than the actual position of the shock generator. In other words, the x-coordinates in different subplots with the same value corresponds to different SG positions in the actual flow field. The black polyline in the figure along the positive direction of the horizontal axis corresponds to the entire process of the flow field transitioning from the fully separated state to the fully merged state. As the shock generator translates downstream, the flow field crosses the merging initiation point \(\mathrm{M_{s}}\) to enter the merging stage. With the further movement of the SG, the polyline passes the merging termination point \(\mathrm{M_{e}}\), marking the end of the merging stage, and dual separation zones become fully merged. The red polyline corresponds to the entire process of re-separation. To facilitate a comparison with the variation during the mergence, the re-separation curve displayed in the figure represents the negative value of the actual change rate during the re-separation process. For re-separation, the movement direction of the shock generator is opposite to the merging process. The incident shock wave gradually moves away from the wedge. The flow field transitions from the fully merged state through the re-separating initiation point \(\mathrm{R_{s}}\) into the re-separating stage, and concludes the re-separating stage at the re-separating termination point \(\mathrm{R_{e}}\), returning the flow field to the fully separated state. Here, a full cycle of the dual separation zone merging and re-separating process is completed. For shock generators with different lengths, the shock travel distance experienced during the flow field state transition remains approximately 4.1 mm, which is defined as the merged characteristic length \(L_{m}\).