Abstract：[Objective] Transition is one of the most significant progressions in fluid mechanics. Accurate boundary layer transition prediction is also essential for a complete understanding of the production of turbulent boundary layers and the optimization of airfoil shapes for industrial applications. Turning turbulence models can accurately forecast transition by including an empirical turning criterion, a low Reynolds number viscous flow field characteristic, or an intermittency component for flow in the transition zone. As for the conventional turbulence models using Reynolds averaging method, such as the k-ε and the k-ω models, accurately forecasting this phenomenon is tough since the transition process is poorly characterized or described. [Methods] A functional correction relation for the G-Y model is suggested and put to the test in the calculations to increase its precision and usefulness for forecasting boundary layer development and transitional features across flat plates. The coefficient of substance Cs had the problem of discontinuous distribution and intermittent values in the original model. This work provided a correlation formula between Cs and the drift vector Reynolds number ReT to solve this problem. The drift vector Reynolds number ReT is built using the G-Y model's drift velocity and vector to describe the strength of local turbulent pulsations. With the aid of physical understanding, the Cs-ReT relationship is produced, resulting in a continuous distribution of the real degree coefficient with ReT variation, close to 0 at the location of mild turbulent pulsation and close to 2/3 at the location of strong turbulent pulsation. The turbulent viscosity is bound by the size of the real degree coefficient at the point of weak turbulent pulsation by solving the discrete distribution's initial problem in this manner. [Results] A solver for the modified G-Y turbulence model was made using the open-source program OpenFOAM. The CFD numerical simulations and validation were then performed for the tests involving the T3A and T3B transitions as well as the conventional flat plate boundary layer. The G-Y model's computational findings showed that: (1) The formula of Cs and ReT considerably increased the G-Y model's accuracy for boundary layer instances and gave the model the ability to forecast transitions. The G-Y model accurately predicted the transitional positions of the two boundary layer experiments, T3A and T3B. (2) Results of the modified G-Y model were in good agreement with the experimental and theoretical values for the distribution of surface friction coefficients before and after the turn. The relative error of the friction coefficients in the segment just entering turbulence was only 3%. (3) The G-Y model accurately replicated the transition from laminar to turbulent flow, which caused the velocity profile of the boundary layer to change from fullness to loss. [Conclusions] The findings show that the improved G-Y model has clear advantages over the established k-ω model in terms of its ability to accurately simulate the boundary layer transition process of a flat plate. This model can be used to investigate the properties of boundary layer transitions in greater depth.
孙逸凡, 朱炜, 吴玉新, 祁海鹰. Gao-Yong湍流模型对边界层转捩的适用性研究[J]. 清华大学学报（自然科学版）, 2023, 63(4): 642-648.
SUN Yifan, ZHU Wei, WU Yuxin, QI Haiying. The applicability study of Gao-Yong turbulence model to boundary layer transitions. Journal of Tsinghua University(Science and Technology), 2023, 63(4): 642-648.
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2023, Vol. 63 
