## 4 Full-Flow Field Simulation
### Flow Structures  
To analyze the stream in the test section, schlieren photography was used, except for in the simulation. The light of the schlieren device passed through the sidewalls of the test section to provide side views of the flow field. The exposure time of the camera was about 2.5 us and the photographs obtained with a framing rate of 7000 fps. The schlieren photographs and the numerical contours of Mach numbers of the three cases are presented in Figure 9. The optical view of the schlieren ranged from 32 mm to 110 mm downstream of the nozzle exit, which is labeled with the blue dotted lines. The structures in the flow field, i.e., shock waves, mixing layers, boundary layers, were observed, and patterns and locations of these structures showed good agreement in the numerical contours and the schlieren graphs.  
Before the flow entered the test section, a pair of expansion waves were generated due to expansion of the flow path. A little recirculation zone appeared at the tip of the splitter plate after the primary and secondary flow met in the test section, and a pair of shock waves appeared. The expansion waves and shock waves reflected at the walls and were transmitted downstream, forming a series of diamond regions in the test section.  
As is labeled in Figure 9a, the mixing layer experienced a laminar mode, a transitional mode, and finally developed into a complete turbulent mode. The schlieren view was mainly in the transitional region. After a short distance of the laminar mode, it began to wriggle and generated a series of regular small-scale vortex structures due to K-H instability. As the mixing layer developed, the vortex structures wiggled, entraining fluid, and became twisted and stretched, finally evolving into large-scale structures. The larger convective Mach number made the K-H vortex structures larger, which resulted in stronger K-H instability.  
Interactions between the shock waves and the mixing layer are shown in Figure 9. The vortexes of the mixing layer became irregular after they intersected with the shock waves. However, it seems that the shock waves only disturbed the mixing layer locally because the fluctuation of the vortexes disappeared quickly after the intersection of the shock waves and the mixing layer, which is consistent with the research of [PERSON] [21]. The influences of the interactions to the shock waves and the mixing layer differed in the three cases. In case 1, the shock waves caused the mixing layer to deflect downwards, which can be seen in Figure 9a,b, although the deflection location of the numerical simulation seemed a little behind the schlieren, and the shock waves bent when crossing the mixing layer, which was not observed in the other two cases shown in Figure 9c-f.  
Interactions between shock waves and the boundary layer can also be seen in Figure 9. Recirculation zones formed at the reflection point of the shock waves on the wall due to the inverse pressure gradient before and after the oblique shock waves, which is consistent with the results of NPLS [22] and IC-PLS [19]. The pattern of the recirculation zone also affected the reflection of the shock waves. Two parallel shock waves close to each other can be observed at the back of the first recirculation in both the numerical contour and the schlieren photograph in Figure 9a,b of case 1 because the recirculation zones were smaller compared to that of case 2 and 3 in Figure 9c-f, in which there was a larger distance between the shock waves at the first recirculation zone in the boundary layer.