Sinusoidally Pitching Foils in Transonic Flow: Insights into Flutter from Time Accurate Simulations

Abstract

The impact of shock formation and vortex dynamics on airfoil flutter in the transonic regime is investigated through a series of two-dimensional time-accurate simulations of a sinusoidally pitching airfoil at a Reynolds number of 10,000. To gain insight into transonic flutter in the fully nonlinear regime, an energy-based approach that employs prescribed kinematics is utilized. Flutter stability boundaries are identified as a function of the Mach number and the reduced velocity, the latter of which is a surrogate for structural stiffness or flight speed. The results show a subcritical instability near Mach numbers of M∞ = 0.7 for a range of oscillation frequencies. Additionally, three shock-induced mechanisms are identified that influence the transfer of energy from the flow to the airfoil. The primary mechanism is flow separation triggered by the generation of a lambda shock. The influence of the lambda-shock dynamics on airfoil flow separation is determined for different Mach numbers, providing insight into the well-known “transonic dip” observed in flutter boundaries.