Abstract: A transition model, γ-Re_{θ t}-f_Re, considering flow compressibility is developed from the original γ-Re_{θ t}transition model framework. The compressibility correction is introduced for the existing transition criteria, and the original transition correlation function based on incompressible flow is modified using the Reynolds number compressibility analogy relation obtained by the reference temperature method. To achieve model localization, an additional Reynolds number compressibility analogy relation f_Re transport equation is constructed. The developed γ-Re_{θ t}-f_Re transition model is used to examine the transition cases under different flow conditions and compared with the basic γ-Re_{θ t} transition model. The numerical simulation results show that the γ-Re_{θ t}-f_Re transition model achieves seamless unified simulation capability from low speed to high speed. It is automatically restored to the basic γ-Re_{θ t} transition model under low speed flow conditions, while significantly improves the prediction of the flow transition trigger position and transition zone development under supersonic and hypersonic flow conditions.

Key words: flow transition, hypersonic, γ-Re_{θ t} transition model, reference temperature method, compressibility correction