Turbulence Modeling via Data Assimilation and Machine Learning for Separated Flows over Airfoils

Reynolds-averaged Navier-Stokes (RANS) models, which are known for their efficiency and robustness, are widely used in engineering applications. However, RANS models do not provide satisfactory predictive accuracy in many engineering-relevant flows with separation. Aiming at the difficulties of turbulence modeling for separated flows at high Reynolds number, this paper constructs turbulence models using data assimilation technique and deep neural network (DNN). Due to the uncertainty of traditional turbulence models, the parameters of Spalart-Allmaras (SA) turbulence model are optimized with experimental data to provide high-fidelity flowfields. Then DNN model maps the mean flow variables to eddy viscosity and replaces the SA model to be embedded within a RANS solver by iterative mode. Different from many existing studies, this DNN model does not depend on traditional turbulence models during the simulation process. This approach is applied to turbulent attached and separated flows and can significantly improve the accuracy for new flow conditions and airfoil shapes. Results show that the mean relative error of lift coefficient above the stall decreases by over 57% for all the airfoils.