Weakly nonlinear behaviour of transonic buffet on airfoils

In transonic flow conditions, buffeting associated with finite-amplitude lift fluctuations can limit the operational envelope of an aircraft. For both airfoils and wings, these oscillations have been linked to global flow instabilities that arise from a Hopf bifurcation. We employ a combination of numerical simulations and global stability analysis to investigate the near-critical behaviour of the oscillatory buffet-onset instability on airfoils. The flow is governed by the unsteady Reynolds-averaged Navier–Stokes equations, with a basic state provided by a steady-state solution. In the weakly nonlinear formulation, the disturbance amplitude is described by the Landau equation. The linear growth rate can be determined from either the simulations or the stability analysis, and the Landau constant is derived from simulations resulting in finite-amplitude equilibrium states. The results show that the Landau constant is nearly independent of Mach number and angle of attack for a given airfoil. Using the Landau constant derived from a small number of simulations, the stability analysis can be employed to efficiently capture the essential finite-amplitude behaviour needed to estimate the buffet-onset boundary. The stability analysis is shown to capture the envelope of lift oscillations during a continuous pitch of an airfoil, from pre-buffet through post-buffet lift levels.