Modal Analysis of a Laminar-Flow Airfoil under Buffet Conditions at Re = 500,000

Abstract

An airfoil undergoing transonic buffet exhibits a complex combination of unsteady shock-wave and boundary-layer phenomena, for which prediction models are deficient. Recent approaches applying computational fluid mechanics methods using turbulence models seem promising, but are still unable to answer some fundamental questions on the detailed buffet mechanism. The present contribution is based on direct numerical simulations of a laminar flow airfoil undergoing transonic buffet at Mach number M = 0.7 and a moderate Reynolds number Re = 500, 000. At an angle of attack α = 4∘, a significant change of the boundary layer stability depending on the aerodynamic load of the airfoil is observed. Besides Kelvin Helmholtz instabilities, a global mode, showing the coupled acoustic and flow-separation dynamics, can be identified, in agreement with literature. These modes are also present in a dynamic mode decomposition (DMD) of the unsteady direct numerical solution. Furthermore, DMD picks up the buffet mode at a Strouhal number of St = 0.12 that agrees with experiments. The reconstruction of the flow fluctuations was found to be more complete and robust with the DMD analysis, compared to the global stability analysis of the mean flow. Raising the angle of attack from α = 3∘ to α = 4∘ leads to an increase in strength of DMD modes corresponding to type C shock motion. An important observation is that, in the present example, transonic buffet is not directly coupled with the shock motion.