A new data assimilation method of recovering turbulent mean flow field at high Reynolds numbers

This paper proposes a new data assimilation method for recovering the high-fidelity turbulent mean flow field around airfoil at high Reynolds numbers based on experimental data, which is called Proper Orthogonal Decomposition Inversion (POD-Inversion) data assimilation method. Aiming at flows including shock wave discontinuities or separation at high angles of attack, the proposed method can reconstruct the high-fidelity mean flow field combined with experimental force coefficients. We firstly perform the POD analysis to turbulent eddy viscosity fields computed by the SA model and obtain base POD modes. Then the POD coefficients are optimized by global optimization algorithm coupling with computational fluid dynamics (CFD) solver. The high-fidelity turbulent mean flow fields are recovered by several main modes, which can dramatically reduce dimensions of the system. The effectiveness of the method is verified by cases of transonic flow around the RAE2822 airfoil at high Reynolds numbers and the separated flow around S809 airfoil at high angles of attack. The results demonstrate that the proposed data assimilation method can recover turbulent flow fields which optimally match the experimental data, and can significantly reduce the error of aerodynamic coefficients. Furthermore, the proposed method can provide high-fidelity mean field data to establish turbulence models based on machine learning.