Wind tunnel wall interference correction for transonic airfoils with data-reduced ensemble Kalman filter

The uncertain factors in wind tunnel experiments, especially the interference effects, will cause the flow around the test model to differ from that under the free flow condition. The wind tunnel wall interference effects are challenging to be eliminated, especially in transonic flow regions where classical linear correction methods are ineffective. To address this issue, an efficient wind tunnel wall interference correction framework based on data assimilation is proposed for steady and shock buffet flows around the airfoils in the transonic region in this work. The ensemble Kalman filter (EnKF) is used to find the combination of inflow conditions, which minimizes the differences between the pressure coefficients measured in the wind tunnel experiment and those estimated by computational fluid dynamics (CFD). The polynomial chaos expansion method is used to propagate uncertainty in the forecast step of the EnKF in order to improve efficiency. Typical wind tunnel wall interference correction problems are studied, including two steady cases: the transonic flow around the Royal Aircraft Establishment 2822 (RAE2822) and the National Aerospace Laboratory 7301 (NLR7301) airfoils, and one unsteady case: the transonic shock buffet on the National Aeronautics and Space Administration supercritical (phase 2)-0714 (NASA SC(2)-0714) airfoil. It is demonstrated that with the corrected Mach number and angle of attack, the estimated CFD results are in better agreement with the measured experimental data than traditional linear methods and the computational efficiency is improved compared to the original EnKF.