Progress in local-variable-based transition-turbulence models for subsonic and transonic boundary layers

The accurate prediction of boundary layer transition represents a persistent and extensively studied challenge in fluid mechanics and aircraft aerodynamic design. It is well recognized that, due to the limitations in computational efficiency and shape complexity, high-resolution numerical simulation techniques and classical stability theory are hard to be applied in the numerical simulation and optimization of complex aircraft designs. The classical correlation-based Langtry and Menter model and laminar kinetic energy model, incorporating stability analysis results, offer efficient solution strategies under the Reynolds-averaged Navier-Stokes framework. Nonetheless, these models rely heavily on the range of available experimental data, which significantly restricts their applicability. Therefore, the Amplification Factor Transport (AFT) transition model anchored in linear stability theory foundations was derived from the findings of Coder and Maughmer and has since been adopted for transition prediction across a variety of complex geometries. This model not only incorporates the analytical foundation of linear stability theory, but also predicts the maximum envelope N value through a transport equation. It enables all non-local variables to be solved locally, ensuring compatibility with massively parallel computational fluid dynamics solvers. This paper systematically introduces the modeling concepts and key variable solution strategies of the currently prevalent transition-turbulence models based on local variables. It emphasizes the evolution of AFT transition frameworks, highlighting their progression from applications in the transition from 2D to 3D compressible boundary layer Tollmien-Schlichting waves, together with the formation of stationary crossflow vortices. In conclusion, this paper addresses the remaining challenges of the amplification factor transport transition model and explores potential directions for its future development.