# Experimental Study of the Formation and Evolution of Gas Jets in Supersonic Combustion Chambers
## 3 Results
### Statistical Properties of the Flow Field  
Figure 12 shows the average flow field images obtained after image processing (as described in Section 2.2.2) for each test. Bow shock, generated by jet blocking, and barrel-shaped shock waves, generated by jet expansion, could be seen in all cases. The angle of bow of the shock wave increased gradually with the jet angle or jet momentum flux ratio. However, when the jet angle was greater than 90\({}^{\circ}\), the change on the bow shock angle was no longer obvious. The initial position of the bow shock gradually rose, indicating that a further increase of the jet angle will mainly affect the range of the pre-jet separation area. On the other hand, for the barrel shock wave, the Mach disk was not obvious when the jet angle was obtuse. The analysis shows that the shear vortex generated by the windward position of the barrel shock wave caused shielding and fluctuation of the Mach disk. Figure 11: The mainstream velocity (U) along the longitudinal direction behind the bow shock. Figure 12: Diagram of the average flow field for all the tests, see the legends. To quantitatively describe the changes of the flow field structural parameters under various working conditions, the position and angle (\(\beta\)) of the bow shock, as well as the mainstream velocity (U) and deflection angle (\(\theta\)) behind the bow shock, were calculated from Figure 12. The results are shown in Figures 13 and 14. This process uses the complete gas hypothesis. Figure 13 shows that, within the studied field of view (\(-\)3 d to 8 d), the bow shock in all tests had the maximum angle (70\({}^{\circ}\) to 80\({}^{\circ}\)) at the starting position, and monotonically decreased to about 30\({}^{\circ}\) along the flow direction. In Figure 14, the mainstream velocity behind the bow wave also shows a monotonous increase, from about 600 to 1700 m/s. However, the mainstream deflection angle after the bow shock showed different characteristics. Except for a jet angle of 30\({}^{\circ}\), the mainstream deflection angle during all tests first increased and then decreased. This phenomenon indicates that, when the jet angle is between 30\({}^{\circ}\) and 60\({}^{\circ}\), the bow shock destruction occurs due to the blocking effect of the jet on the main stream. This results in a rapid decrease in the main stream velocity and deflection angle. In Figure 14, the orange dots and lines represent the velocity when Ma = 1. In addition, the green boxes represent the regions with y/d between 1 and 2 for the same jet angle and jet momentum ratio of 0.88. This region is considered as the region where the shear layer is located for each of the working conditions given in Figure 8. It can be seen that the shear layer was located in the supersonic mainstream when an acute jet angle was adopted. In this case, the development and evolution of the shear vortex also occurred in the supersonic region. The case of a 90\({}^{\circ}\) jet angle lies between the two. Since the vortex structure dissipates faster in the subsonic flow, it can be assumed that the shear vortex has a shorter flow direction range when an obtuse angle is adopted, which is also consistent with the abovementioned conclusion. Figure 13: Position and angle of the bow shock. It is worth mentioning that the four parameters studied above changed considerably in the upstream region of the jet nozzle, while in the downstream region these changes were relatively slow. This phenomenon indicates that the parameters of the flow field upstream of the jet nozzle change more significantly. To optimize the jet flow field, more attention should be paid to the area in front of the jet nozzle. The standard deviation, a statistic commonly used to reflect data fluctuation in statistics, was used to analyze the instability of the flow field. To compare and analyze each condition, all the standard deviation images were normalized, as shown in Figure 15. In addition, regions with standard deviations greater than 0.6 were defined as strong fluctuation regions.