Real-time estimation and control of flow over a NACA0012 airfoil using resolvent-based tools*

This study aims to estimate and attenuate unsteady fluctuations in the near wake of a NACA 0012 airfoil at Ma = 0.3, Re=5,000, and α = 6^○ using the resolvent-based estimation and control tools recently developed by Martini et al. (J. Fluid Mech. 937:A19, 2022). The mean flow for the linearized compressible Navier-Stokes operator is obtained using direct numerical simulation, and resolvent analysis is performed as a preliminary step to validate our implementation and to gain insight into the flow physics and appropriate sensor and actuator placement. The resolvent-based estimation and control kernels are computed using a matrix-free approach, resulting in low computational cost without the need for a priori model reduction. A Wiener-Hopf formalism is used to optimally enforce causality for the estimation and control kernels. We show that our method can reduce the unsteady fluctuations in the near wake, and we investigate how this affects the aerodynamic performance of the airfoil.