Transonic buffet and incompressible low-frequency oscillations at high Reynolds numbers

Abstract: Coherent, self-sustained oscillations of the flow over aircraft wings can lead to unsteady loads that detrimentally affect aircraft safety and stability, thus limiting the flight envelope. Two such types of oscillations are the low-frequency oscillations (LFO) observed in flow over airfoils close to stall in the incompressible regime and transonic buffet, which occurs at high speeds and involves oscillating shock waves. The possibility that these two are linked has been explored only recently at low Reynolds numbers (Re ~ O(1e4)) and natural transition conditions (Moise et al., J. Fluid Mech., vol. 981, 2024, p. A23). However, the shock wave structure in the transonic regime under these conditions differs substantially when compared to high Reynolds number flows, and it is unknown whether a connection can be established at high Reynolds numbers. This study investigates this possibility by performing incompressible and compressible URANS simulations at Re = 1e7. We show that transonic buffet exists for a narrow range of freestream Mach numbers across a wide range of angles of attack, and that buffet-like oscillations are observed at higher angles even in the absence of shock waves. Using a spectral proper orthogonal decomposition (SPOD), we show that the dominant modes associated with these oscillations are strongly correlated for all cases, even in the absence of shock waves. Furthermore, using a fully incompressible URANS framework, we capture LFO at the same Reynolds number and confirm the connection between these two phenomena using SPOD. These results imply that neither shock waves nor compressibility is necessary to sustain such low-frequency oscillations, suggesting that the fundamental mechanism governing them is related to flow separation. This can potentially help in improved control strategies to extend the flight envelope by mitigating buffet or LFO.