It has been found that the static pressure distribution along the axial direction of liquid kerosene is lower than that of the gaseous kerosene under the same flow condition and overall equivalent ratio from previous studies. To further investigate this phenomenon, a compressible two-phase parallel simulation method is utilized to analyze the mixing and combustion characteristics of gaseous and liquid kerosene jets in a cavity-based supersonic combustor. The numerical results are consistent with the experiments and demonstrate that gaseous injection leads to a cavity shear layer that dives deeper into the cavity, forming two recirculation zones in the front and rear of the cavity. In contrast, the cavity shear layer is closer to the mainstream during liquid injection, and only a large recirculation zone is formed in the rear of the cavity. As a result of the cavity shear layer and the recirculating flow, the fuel vapor of gaseous injection accumulates in the front of the cavity, while for the liquid injection, the fuel vapor disperses in the cavity, cavity shear layer, and the region above, and the rear of the cavity has a higher fuel vapor concentration than the front. This unique fuel distribution causes the combustion area to be concentrated in the cavity during the gaseous injection but dispersed inside and downstream of the cavity during the liquid injection. As a result, forming a thermal throat under the same conditions is more challenging during liquid injection, and the generated static pressure distribution is lower than that during the gaseous injection.

Lack of consideration of certain important flow characteristics leads to obvious limitations in supersonic flow description by the standard SST turbulence model developed for incompressible flow. To improve the prediction accuracy of the SST model in complex supersonic flows involved in hypersonic propulsion systems, the shock wave and compressibility effects were introduced based on the flow characteristics. The shock/turbulent boundary layer discriminant function and compressible effect discriminant function were used to locate the region where the model parameters or modeling assumptions of the standard SST model failed, and the turbulence model was improved directionally. Examples of supersonic plate boundary layer flow, supersonic compression corner separation flow, supersonic complex shock train flow in an isolator and HIFiRE-2 supersonic internal flow were used for testing. The results show that the improved model has the same prediction ability as the standard SST model for turbulent boundary layers, but significantly improves the prediction ability of shock-wave involved flows and adverse-pressure-gradient induced separating flows.