Role of Shocks in Transonic Bending-Torsion Flutter

The formation of part-chord shock waves at transonic speeds causes a rapid decrease in the dynamic pressure at which a wing flutters, commonly known as the “transonic dip”. Yet, owing to the complexity of the coupled aeroelastic system, no simple physical explanation has been given for why these shocks are destabilizing. This paper investigates the role of shocks in transonic bending-torsion flutter using three-dimensional unsteady Reynolds-averaged Navier-Stokes calculations of the AGARD 445.6 wing. By performing an energy analysis across different Mach numbers, it is shown that the transonic dip is almost entirely caused by changes in the phase difference between the flutter aeroelastic mode’s bending and torsion motions. A simplified model for the aeroelastic system is then presented, which demonstrates that these changes in bending-torsion phase with Mach number occur predominantly due to changes in a single generalized aerodynamic force (GAF). Through visualizing the unsteady pressures during forced oscillations, the changes in this crucial GAF are directly related to the formation of shocks and the changes in shock structure with Mach number, thereby explaining the role of shocks in producing the transonic dip. Finally, it is demonstrated how this physical understanding may be used to inform structural design changes that improve flutter.