Connecting transonic buffet with incompressible low-frequency oscillations on aerofoils

Abstract

Self-sustained, low-frequency, coherent flow unsteadiness over rigid, stationary aerofoils in the transonic regime is referred to as transonic buffet. This study examines the role of shock waves in sustaining this transonic phenomenon and its relation to low-frequency oscillations (LFO) that occur in flow over aerofoils in the incompressible regime (Zaman et al., J. Fluid Mech., vol. 202, 1989, pp. 403–442). This is investigated by performing large-eddy simulations of the flow over a NACA0012 profile for a wide range of flow conditions under free-transition conditions. At low Reynolds numbers, zero incidence angle and sufficiently high free-stream Mach numbers, $M$ , transonic buffet occurs with shock waves present in the flow. However, when $M$ alone is lowered, self-sustained, periodic oscillations at a low frequency are observed even though shock waves are absent and the entire flow field remains subsonic at all times. At higher incidence angles, the oscillations are sustained at progressively lower $M$ and are present even at $M=0.3$ , where compressibility effects are low. A spectral proper orthogonal decomposition (SPOD) shows that the spatial structure of these oscillations is consistent for all cases. The SPOD modes are topologically similar, suggesting a connection between transonic buffet and LFO in the incompressible regime. Comparisons with other studies examining transonic buffet on various aerofoils, under forced-transition and fully turbulent conditions support this hypothesis. Future studies using tools of global linear stability analysis, especially at high free-stream Reynolds numbers are required to examine whether the underlying mechanisms of transonic buffet and incompressible LFO are the same.