The gas–liquid mixing process of a liquid jet in supersonic crossflow with a gas–liquid momentum ratio of 7.67 in the near-wall region is investigated numerically. The two-phase flow large eddy simulation is based on the Eulerian–Lagrangian approach and considers the droplet–wall interaction. The results indicate the penetration depth and the lateral extension width, which are in good agreement with the experimental data. The [Formula: see text] shape, especially the spray foot structure of spray in the cross-sectional plane, is captured well. The transport process of spray toward the wall and the formation of spray foot are systematically studied. Under the influence of the upper CVP (counter-rotating vortex pair), partial droplets in the center region of the spray are transported to the near-wall region and move toward both sides when encountering the wall CVP. Under the current gas–liquid momentum ratio, droplets collide with the wall mainly in the central region at the bottom, which will produce splashed droplets. Affected by the horseshoe vortex, the instantaneous distribution of droplets on both sides near the wall shows stripes shape. The spray foot structure forms the shape that is narrow on the top and wide on the bottom and is mainly formed by splashed droplets. Some splashed droplets in the low-speed boundary layer constitute the lower half of the spray foot; meanwhile, some splashed droplets enter mainstream and constitute the upper half of the spray foot. Moreover, the spray is mainly distributed in the core region, and the spray concentration is very sparse in the spray foot region.

To explain the phenomenon observed in previous experiments of kerosene-ignition failure in scramjet combustors as the kerosene temperature increases, we numerically investigate the mixing characteristics of a kerosene jet injected into a cavity-based supersonic combustor at different injection temperatures by using a compressible two-phase flow large-eddy simulation based on the Eulerian–Lagrangian approach. The results indicate that, upon injecting kerosene at high temperatures, the flow field preceding the leading edge of the cavity is similar to a typical gas jet in supersonic crossflow. The wall counter-rotating vortex pair (CVP) develops more fully and eventually becomes the main vortex pair. This evolution of the wall CVP modifies the cavity shear layer and alters the local flow-field characteristics near the cavity. Upon injecting kerosene at high temperatures, its evaporation rate increases sharply and the cavity recirculation zone enlarges, which causes more kerosene vapor to be entrained into the cavity. Because the kerosene-vapor temperature is lower than that of the low-speed fluid in the cavity, a significant amount of kerosene vapor entering the cavity not only makes the mass fraction of kerosene in the cavity exceed the fuel stoichiometric mass fraction but also reduces the temperature in the cavity, which negatively impacts the ignition process. The ignition delay time is much longer when the injection temperature is high, which is consistent with the inability of the initial flame kernel to form in the experiment.

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In accordance with high-speed schlieren results, the flow instabilities in the subsonic–supersonic mixing layer with a convective Mach number of 0.19 are investigated in detail. In the incipient stage of the mixing layer, wave structures caused by the pressure gradient affect the evolution of the Kelvin–Helmholtz vortexes. The dynamic mode decomposition (DMD) analysis reveals that the pressure gradient from the subsonic side to the supersonic side promotes flow instability. At this time, the Kelvin–Helmholtz vortexes mode is found to be dominant. A high temporal resolution is proven to play an important role in the DMD analysis to capture high-frequency modes.