  This paper proposes a new data assimilation method for recovering high
fidelity turbulent 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 the flows including shock
wave discontinuities or separated flows at high angle of attack, the proposed
method can reconstruct high-fidelity turbulent flow field combining with
experimental distributed force coefficients. We firstly perform the POD
analysis to the turbulent eddy viscosity fields computed by SA model and obtain
the base POD modes. Then optimized the POD coefficients by global optimization
algorithm coupling with the Navier-Stokes equations solver. The high-fidelity
turbulent flied are recovered by several main modes, which can dramatically
reduce the dimensions of the system. The effectiveness of the method is
verified by the cases of transonic flow around the RAE2822 airfoil at high
Reynolds numbers and the separated flow at high angles of attack. The results
demonstrate that the proposed assimilation method can recover the turbulent
flow field which optimally match the experimental data, and significantly
reduce the error of pressure coefficients. The proposed data assimilation
method can offer high-fidelity field data for turbulent model based on machine
learning.
