Time-Series Velocity Field Reconstruction Based on Unsteady Pressure Sensors for Feedback Control of Separated Flow around an Airfoil

A low-dimensional flow field is estimated from unsteady pressure sensors data that can be attached to the airfoil surface, for feedback control of the flow field around an airfoil. The method estimates a low-dimensional flow field represented by proper orthogonal decomposition (POD) modes with a Kalman filter. In this study, we aim to improve the estimation accuracy of the method based on the Kalman filter and to investigate the effects of the Kalman filter hyperparameters, the number of POD modes to be estimated, and the time delay of the observations on the accuracy of the flow field estimation, based on wind tunnel test data. We also propose a nonlinear state-space model as a state-space representation, which is an improvement of the conventional linear state-space model, and perform estimation using an extended Kalman filter, and investigate the estimation accuracy in the same way. The analysis showed that the coefficients of the observation error covariance matrix, which is a hyperparameter of the Kalman filter, and the number of POD modes to be estimated contribute to the accuracy of the estimation. The consideration of the time delay of the observations did not improve the accuracy of the estimation.