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In recent years, machine learning methods represented by deep neural networks(DNN) have been a new paradigm of turbulence modeling. However, in the scenarioof high Reynolds numbers, there are still some bottlenecks, including the lackof high-fidelity data and the convergence and stability problem in the couplingprocess of turbulence models and the RANS solvers. In this paper, we propose animproved ensemble kalman inversion method as a unified approach of dataassimilation and turbulence modeling for separated flows at high Reynoldsnumbers. The trainable parameters of the DNN are optimized according to thegiven experimental surface pressure coefficients in the framework of mutualcoupling between the RANS equations and DNN eddy-viscosity models. In this way,data assimilation and model training are combined into one step to get thehigh-fidelity turbulence models agree well with experiments efficiently. Theeffectiveness of the method is verified by cases of separated flows aroundairfoils(S809) at high Reynolds numbers. The results show that through jointassimilation of vary few experimental states, we can get turbulence modelsgeneralizing well to both attached and separated flows at different angles ofattack. The errors of lift coefficients at high angles of attack aresignificantly reduced by more than three times compared with the traditional SAmodel. The models obtained also perform well in stability and robustness.

A unified method of data assimilation and turbulence modeling for separated flows at high Reynolds numbers