Ensemble-Based State Estimator for Aerodynamic Flows

Abstract

Regardless of the plant model, robust flow estimation based on limited measurements remains a major challenge in successful flow control applications. Aiming to combine the robustness of a high-dimensional representation of the dynamics with the cost efficiency of a low-order approximation of the state covariance matrix, a flow state estimator based on the ensemble Kalman filter is applied to two-dimensional flow past a cylinder and an airfoil at high angle of attack and low Reynolds number. For development purposes, the numerical algorithm is used as both the estimator and as a surrogate for the measurements. Estimation is successful using a reduced number of either pressure sensors on the surface of the body or sparsely placed velocity probes in the wake. Because the most relevant features of these flows are restricted to a low-dimensional manifold of the state space, asymptotic behavior of the estimator is shown to be achieved with a small ensemble size. The relative importance of each sensor location is evaluated by analyzing how they influence the estimated flowfield, and optimal locations for pressure sensors are determined. Covariance inflation is used to enhance the estimator performance in the presence of unmodeled freestream perturbations. A combination of parametric modeling and augmented state methodology is used to successfully estimate the forces on immersed bodies subjected to deterministic and random gusts.