Sensitivity Analysis of the Leading Global Modes of the Flow Around a NACA 4412 Airfoil

Two-and three-dimensional modes developing on a steady spanwise-homogeneous laminar separated flow over a NACA 4412 airfoil have been numerically investigated using global linear stability theory. Considering variations of both the Reynolds number and the angle of attack, the two-dimensional von Kármán mode results to be always the leading mode since for all conditions examined it is more unstable than the three-dimensional von Kármán modes and the three-dimensional stationary modes, associated with the formation on the airfoil surface of large-scale separation patterns akin to stall cells. Sensitivity of the global modes is investigated numerically through adjoint-based methods in order to predict regions of the flow which are most sensitive to a modification of the base flow and the application of a steady force. Interestingly, the instability’s growth rate sensitivity function displays an extended region upstream of the separation bubble wherein a streamwise oriented force has a net stabilizing effect. Aerodynamic performances can thus be possibly improved by leveraging the boat-tailing effect induced by tangential jet actuators localized in this particular region of the flow.