Sensitivity Analysis For Active Control of Transonic Airfoil Buffet*

We perform a numerical study of a transonic flow over a NACA 0012 airfoil at freestream Mach number M_∞=0.7, angle of attack α=7^o  and Reynolds number Re=3×10⁶. We employ unsteady Reynolds-averaged Navier-Stokes equations with Spalart-Allmaras (SA) turbulence model, which reveals a distinct presence of a large scale shock oscillation (termed as "buffet") and an associated sizeable separation region. 

Active control mechanisms in the form of blowing and synthetic jets are evaluated to determine their effect on the buffet phenomenon. As a starting point, three blowing jets are employed on the suction side in the post-shock region with a jet amplitude of 0.1×U_∞ (where U_∞ is the freestream velocity) and a blowing angle of 20^o to the local surface. A significant drop in the flow separation is observed along with a clear buffet suppression and an increase in the lift. 

We further employ an accurate discrete adjoint approach to compute the sensitivity of the lift-to-drag ratio to each of the actuation parameters with the aim of improving the flow characteristics. The adjoint approach is implemented using algorithmic differentiation (AD) technique and the sensitivities match those obtained through perturbation analysis.