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During the process of aerodynamic shape design of supersonic and hypersonic space planes, laminar flow design and boundary layer transition prediction play important roles in aero-thermal numerical simulations and aero-thermal protection design. Therefore, in this study, a computational fluid dynamics compatible transition closure model for high speed laminar-to-turbulent transitional flows is formulated with consideration of the analysis results from stability theory. The proposed model contains two transport equations to describe the transition mechanism using local variables. Specifically, the eddy viscosity of laminar fluctuations and intermittency factor are chosen to be the characteristic parameters and modeled by transport equations. Accounting for the dominant instability modes at supersonic/hypersonic conditions, the first- and second- modes are modeled using local variables through the analysis of laminar self-similar boundary layers. Then, the present transition model is applied with compressibility correctedk   $k$   -ω   $\omega$    shear stress transport turbulence model. Thus, as the main significance of the current work, the present model is enabled to capture the overshoot phenomena as well as predict the transition onset position. Finally, comparisons between the predictions using the present model and the wind tunnel experimental results of several well-documented flow cases are provided to validate the proposed transition turbulence model.

Modeling of Supersonic/Hypersonic Boundary Layer Transition Using a Single-Point Approach