Numerical Investigation of Double Transonic Dip Behaviors in Supercritical Airfoil Flutter

Abstract

This numerical study examines the behavior of the double transonic dip with a supercritical airfoil. A two-dimensional model of a wing section with two degrees of freedom was used for the investigation. The flowfield was modeled by solving the unsteady Reynolds-averaged compressible Navier–Stokes equations using the Spalart–Allmaras turbulence model, and the equations of motion were solved to determine the structural dynamics. The present model successfully captured the behavior of the double transonic dip on the flutter boundary of the supercritical airfoil, which contrasts with the well-known behavior of the single transonic dip exhibited by conventional symmetric airfoils. Although the mechanism of the first dip at a lower Mach number corresponded to that of the well-known conventional transonic dip, the second dip at a higher Mach number was uniquely observed for the supercritical airfoil. The analysis established that, for the supercritical airfoil, the motion of the shock wave over the upper surface was significantly affected by the behavior of the boundary layer around the highly cambered aft region of the lower surface during flutter. The behavior of the boundary layer involving the separation and reattachment over the lower surface caused the unusual shock wave motion over the upper surface under the Mach number condition at the bottom of the second dip. This motion exerted negative damping forces on the motion of the airfoil, thereby becoming the primary contributor to generating the second dip experienced by the supercritical airfoil.