# Influence of Incident Shock on Fuel Mixing in Scramjet
## 1 Introduction  
The scramjet is an important solution for future high-speed flight [1; 2; 3]; it is usually composed of an inlet, an isolator, a combustion chamber, and a nozzle. As an important component of the scramjet, the performance of the combustion chamber has a significant impact on the entire propulsion system and even the hypersonic aircraft. The air enters the combustion chamber at supersonic speed, and the residence time of fuel in the combustion chamber is very short. How to efficiently mix the fuel is a major challenge in solving the scramjet problem [4]. The transverse jet is a simple and effective method to enhance mixing. [PERSON] et al. [5], [PERSON] et al. [6], and [PERSON] et al. [7] studied supersonic transverse jets using numerical simulations, analyzed the generation and transfer process of vortex structures in the flow field through high-precision numerical simulation methods, and described the fuel mixing mechanism based on the structural characteristics of the flow field. [PERSON] et al. [8; 9; 10] studied supersonic transverse jets and found that multiple air jets can improve the penetration depth of fuel and increase the efficiency of fuel mixing through various arrangements of air and fuel jets. [PERSON] et al. [11; 12] studied the fuel mixing characteristics of air-hydrogen coaxial jets and reached similar conclusions. [PERSON] et al. [13] studied a spanwise inclined jet in supersonic crossflow and found that the asymmetric flow caused by the spanwise inclined jet leads to the interaction between the main counter-rotating vortex and the separated flow, resulting in a clockwise vortex. [PERSON] et al. [14] studied the laws of fuel penetration depth and mixing efficiency by varying the incoming flow angle and found that the incoming flow angle significantly altered the flow field structure. A positive incoming flow angle increased the mixing efficiency, while a negative angle restricted fuel mixing. However, it is difficult to maintain stable combustion of fuel in the combustion chamber with only a transverse jet, and a cavity is a solution to this problem [15]. The low-velocity recirculation zone in the cavity allows the fuel to stay in the combustion chamber for more time, which also provides a low-velocity region for ignition in the combustion chamber, with low total pressure loss [16]. However, the coupling of the jet and the cavity can produce complex flow field structures; so researchers have conducted many studies combining the cavity with transverse jets. [PERSON] et al. [17] used numerical simulation to investigate the influence of the shape of the cavity (square and trapezoidal) on the mixing of ethylene fuel with a transverse jet and found that a trapezoidal cavity enhances fuel mixing and flame stability. [PERSON] et al. [18] researched the transverse jet flow in a cavity and found that due to the interaction between the shear layer and the jet wakes, new streamwise vortices were formed, which enhanced mass exchange inside and outside the cavity. [PERSON] et al. [19] found that by adjusting the position of the transverse jet and the depth of the cavity, the shear layer structure changes when the jet is injected near the cavity leading edge, which enhances the interaction between the shear layer and the fuel, increases the mass of fuel inside the cavity, and enhances fuel mixing and combustion performance. [PERSON] et al. [20] studied the influence of injection position and cavity trailing edge height on fuel mixing. In order to achieve higher mixing efficiency, jetting on the leading wall of the cavity is suitable for lower cavity trailing edge conditions; while injection of the opposing multi-jets on the trailing edge of the cavity requires a higher cavity trailing edge to achieve higher mixing efficiency. One of the factors affecting mixing is the structure of the recirculation zone in the cavity. [PERSON] et al. [21] studied the influence of the cavity structure on the jet flow.