Improvement of the free-interaction theory for shock wave/turbulent boundary layer interactions

Free-interaction theory is widely used for the analysis and modeling of the flow structure for shock wave/turbulent boundary layer interactions (SWTBLIs). However, many studies have demonstrated that the value of the nondimensional pressure rise function at the plateau should not be treated as a universal constant, which is an assumption taken in the traditional free-interaction theory. Such an assumption brings huge uncertainty to the theoretical prediction of shock wave/boundary layer interaction flows. To improve the accuracy of free-interaction theory, numerical simulations on the incident shock wave/turbulent boundary layer interactions are carried out in this study over an extensive flow range (Ma = 2.0-5.0, Reδ = 7.4 × 10-7.29 × 10). Utilizing the simulated flow field structures and literature data, this paper analyzes the essential influencing factors for determining the plateau pressure. Two nondimensional parameters—the incompressible shape factor of the incoming boundary layer and the nondimensional separation-bubble height—are identified as the essential influencing factors for the nondimensional pressure rise function at the plateau. A new scaling rule is proposed by taking these two nondimensional parameters into consideration, and the experimental data of the SWTBLIs after scaling collapse well onto a single curve with an R value of 0.918. The experimental data used to validate the scaling rule include incident and ramp SWTBLIs and the leading SWTBLIs in shock trains. The proposed scaling rule can be used to establish more accurate theoretical predicting models for SWTBLIs.