# Influence of Incident Shock on Fuel Mixing in Scramjet
## 4 Results and Discussion
### Mixing Efficiency  
Mixing efficiency is an important indicator for assessing combustion based on fuel mixing. In order to further explore the influence of uniform and non-uniform incoming conditions on mixing, this section will quantitatively compare the mixing efficiency under different inflow conditions. To measure the mixing degree of fuel and oxygen in the flow, the mixing efficiency is calculated using Equations (30) and (31). Figure 27: Fuel iso-surface distribution for different cases. Figure 26: Penetration depth for all cases. As shown in Figure 28, where A denoted the leading edge of the cavity and B denoted the trailing edge, (b) provided a detailed magnification of the region in (a), the mixing efficiency of fuel started to mix with air from the injection hole on the lower wall surface, and as the air continues to flow downstream, the mixture of fuel and air becomes more complete gradually, and the mixing efficiency increases accordingly. The horseshoe vortex, formed due to the impingement of the jet, plays a pivotal role in the vicinity of the downstream wall. In comparison with case 1, the jet in case 3 induces a more extensive separation zone. This enlarged separation zone leads to a broader influence of the horseshoe vortex and intensifies the \"stirring\" effect. As illustrated in Figure 29, the counter-rotating vortex pair facilitates the transport of fuel to more distant areas, leading to an enhanced uniformity in the fuel distribution across the engine's span. Furthermore, as the boundary layer becomes thicker, the collision between the side jets and the central jet becomes more intense as they follow the vortices toward the spanwise direction. This increased interaction leads to the formation of new vortices, which in turn enhance fuel transport. Therefore, when the penetration depths are similar, the mixing efficiency of case 3 is higher than that of case 1. Despite having the smallest separation zone and thus the narrowest fuel propagation area in the spanwise direction, case 2 exhibits the deepest penetration depth. This indicates that, upon reaching the leading edge of the cavity, a deeper penetration depth can locally facilitate a higher mixing efficiency, surpassing the effect of fuel dispersing along the spanwise direction due to vortices, so as in case 5, where the mixing efficiency at the cavity leading edge is higher than that in cases 4 and 6. In case 5, an interesting phenomenon was observed: The interaction between the side jets and the cavity sidewalls, as well as with the central jet, was relatively weak. This diminished interaction resulted in the jet morphology on both sides remaining highly similar to that of the jets located on the central plane, and this similarity persisted, causing nearly identical mixing efficiencies between case 2 and case 5 for an extended period before reaching the leading edge of the cavity. During the downstream propagation of the fuel, it was observed that a greater amount of fuel from the sides was entrained into the corner regions, resulting in a lower mixing efficiency for case 5 compared to case 2 starting from x = 2.21. In case 4 and case 6, the jets generated larger separation zones, prompting an earlier interaction between the side jets and the sidewalls. Consequently, more fuel from the sides was channeled into the corner areas. Despite maintaining identical flow direction, injection location, and injection conditions, the mixing efficiency before the leading edge of the cavity was reduced compared to case 1 and case 3. In case 3, the larger separation zone enhanced the fuel transport capacity along the spanwise direction, thereby achieving higher mixing efficiency compared to case 1. However, the same factor in case 6 led to more side fuel being entrained into the corner areas, increasing the fuel concentration in these zones and reducing the mixing efficiency compared to case 4. Figure 28: Mixing efficiency for all cases.