High-speed flows are characterized by strong compressibility and presence of narrow region of high gradients of parameters. The compressibility leads to a new phenomenon in comparison with the incompressible case: dilatation dissipation, work of pressure force and mass flux. Discontinuities in supersonic flow lead to considerable growth of turbulence production due to mean velocity gradients. It results in noticeable deviation from equilibrium in the vicinity of shocks. Therefore, different compressible and non- equilibrium modifications of two and three equations of turbulence models are considered in the paper. These modifications and some of their combinations are analyzed using numerical simulation of flow in and underexpanded supersonic jet with a complex shock-wave structure and a flow in a supersonic nozzle with separation. A new version of k?? turbulence model is presented which takes into account both compressibility and non-equilibrium effect and which allows calculate both the considered variants with good accuracyю
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