Investigation of various approaches to the modeling of laminar-turbulent transition in compressible separated flows

The interaction of a laminar boundary layer with a shock wave at a Mach number $\mathrm{M}=1.43$ is studied by numerical simulation. The results obtained by direct numerical simulation are compared with the results of calculations using the Reynolds-averaged Navier–Stokes (RANS) equations supplemented with different turbulence models describing laminar-turbulent transition. The possibility of determining the position of the flow turbulence zone based on linear stability theory and the $\mathrm{e}^N$-method is estimated. Comparison of the numerical simulation with experimental data shows that the engineering RANS methods can be used to study supersonic flows in which transition to turbulence occurs in regions of interaction of the shock wave with the boundary layer.