Control of linear instabilities in two-dimensional airfoil boundary layers

The present study deals with the control of linear, modal and non-modal growth of perturbations in a trapezoidal wing boundary layer. The asymmetric NACA 2515 airfoil is chosen for the analysis. The boundary layer velocity profiles, at different locations on the airfoil, are obtained using the Falkner-Skan equations. The non-modal linear stability theory is used to obtain the amplification of the initial perturbations, for which the state-space approach is adopted. The control is brought about using a Linear Quadratic Regulator (LQR) controller by the means of addition of fluid momentum in the wall-normal direction from the wing surface. Maximum transient energy growth is calculated across a range of wavenumber pairs, and control is applied to the pair with the highest energy growth. In this numerical analysis, we show that the transient growth is higher towards the trailing edge because of the adverse pressure gradient of the flow. Upon control actuation, the reduction in the transient energy growth of perturbations is achieved up to a maximum of 54.6%.