Turbulence closure for high Reynolds number airfoil flows by deep neural networks

The combination of turbulence big data with artificial intelligence is an active research topic for turbulence study. This work constructs black-box algebraic models to substitute the traditional turbulence model by the artificial neural networks (ANN), rather than correcting the existing turbulence models in most of current studies. We mainly focused on flows past airfoils at high Reynolds (Re) numbers. Our previous work has developed a turbulence model for flows at different Mach (Ma) number and angles of attack (AOA) with fixed Re number and achieved satisfying results. Nevertheless, for turbulence with variable Re numbers, the generalization ability of the model can not be enhanced effectively by simply increasing the train data. To model the nonlinearity of various turbulent effects at high Re number, prior knowledge about scaling analysis is integrated into the model design and deep neural networks (DNN) is adopted as the framework. Considering the different scaling characteristics, the flow field is divided into different regions and two individual ANN models are built separately. Besides, the combination of regularization, limiters, and stability training is adopted to enhance the robustness of the proposed model. The results of Spallart-Allmaras (SA) model are used as the datasets and reference to the modeling evaluation. The proposed model is trained by six flows around NACA0012 airfoil and applicative to different free stream conditions and airfoils. It is found that the results calculated by the proposed model, such as eddy viscosity, velocity profile, drag coefficient and so on, agree well with reference data, which validate the generalization ability of the model. This work shows the prospect of turbulence modeling by machine learning methods.