# Influence of Incident Shock on Fuel Mixing in Scramjet
## 4 Results and Discussion
### Cold Flow Structure  
The design of the aircraft's forebody and inlet was symmetrical along the spanwise axis, with the flight attitude maintaining a zero-sideslip angle. In the scramjet, the reflected shock waves exhibited quasi-two-dimensional characteristics in the core flow, unaffected \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **P/Pa** & **T/K** & **Ma** & **Attack** \\ \hline X-51-like vehicle & 2028.14 & 223.04 & 5.51 & 1 \\ Fuel jet & 1,600,000 & 923 & 1 & None \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Incoming conditions. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Length of Isolator** & **Number of Jets** \\ \hline Case 1 & 263.56 mm & 1 (center) \\ Case 2 & 388.15 mm & 1 (center) \\ Case 3 & 504 mm & 1 (center) \\ Case 4 & 263.56 mm & 3 \\ Case 5 & 388.15 mm & 3 \\ Case 6 & 504 mm & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Schemes of fuel injectors and inflow. Figure 11: Shock wave distribution of the vehicle integration of internal and external flows. by corner region interference. As shown in Figure 12, the results revealed that the intensity of the reflected shock waves and their interactions with the upper and lower wall surfaces were virtually identical between the central plane of the jet (z = 0) and the midplane between the two jets (z = 0.042). Given this consistency, the z = 0 plane was selected for subsequent analyses of the cold flow field, as it provided a representative view without introducing complexity from variations across different planes. To investigate the effects of isolator length variations on the mixing of a jet cavity under non-uniform inflow conditions, the leading edge of the cavities for three different conditions has been aligned in Figure 13, to compare the flow field changes in the injection segment and the cavity segment. Notably, case 3, when contrasted with case 1, exhibits a reduction in the isolator length by approximately one period of the incident shock wave. As can be seen from Figure 13, the shock wave distributions of both are almost identical. The primary distinction arose from the increased length of the isolator, which led to more frequent reflections of the incident shock wave. This increased reflection diminished the shock compression effect, thereby causing variations in the magnitude of density gradients. Consequently, the compression impact of the reflected shock wave positioned in front of the cavity was notably stronger in case 3 compared to case 1 [39]. However, the distinction in shock wave compression effects between case 1 and case 3 was relatively minor, exerting a negligible influence on the turbulent boundary layer, the channel's core flow, and the flow field within the cavity recirculation zone. This resulted in a highly comparable flow structure, as shown in Figure 14. In cases 1 and 3, the incident shock wave was reflected from the lower wall towards the upper wall, positioned between the injection hole and the leading edge of the cavity. Consequently, as the airflow encountered this shock wave, there was a marked pressure increase, which resulted in a higher pressure just ahead of the cavity compared to the pressure inside the cavity, as illustrated in Figure 15. This elevated pressure created a localized expansion zone, encouraging the airflow to expand into the cavity and inducing the shear layer's collapse into it. Furthermore, Figure 16 demonstrated a decrease in average pressure subsequent to the airflow's passage through the cavity. Figure 12: Shock wave comparison across different sections. Figure 13: Shock wave distribution for different cases. Due to the reduction in the length of the isolation section, the occurrence of shock wave reflections was reduced by approximately half a cycle compared to cases 1 and 3. As a result, the flow field structure in case 2 significantly differed from that observed in the previous cases. More specifically, as the airflow neared the cavity, it encountered a localized low-pressure zone.