In order to reduce friction and wave drag on the wings of more efficient next generation aircraft, it is important to understand laminar-turbulent boundary-layer transition and shockwave interactions. In this contribution, fully-resolved direct numerical simulations of Dassault Aviation's V2C profile at transonic conditions and a Reynolds number of half a million are presented. Kelvin-Helmholtz instabilities appear in the shear layers on the pressure-and suction-sides, followed by a self-sustained laminar-turbulent transition process promoted by the stretching of rib vortices between larger co-rotating structures. Multiple acoustic structures interacting with the boundary layer are also observed, together with upstream-propagating shock waves. Regions of flow separation on the suction side exhibit unsteadiness with Strouhal numbers in the range of St ≈ 0.5 − 0.6. This is distinct from a standing wave oscillation in lift at St = 0.12, which agrees well with transonic buffet frequencies, reported for experiments on the same airfoil at higher Reynolds numbers. The insensitivity of the principal results to the chosen grid resolution and spanwise domain size is carefully established.

Transonic buffet is an unsteady flow phenomenon that limits the safe flight envelope of modern aircraft. Scale-resolving simulations with span-periodic boundary conditions can provide detailed insight into the flow physics associated with buffet and can help to calibrate simplified models that are needed, for example, to develop more efficient wings based on laminar-flow supercritical sections. However, such simulations are often feasible only for severely restricted spanwise domains. In the current contribution, we analyse an unswept laminar-flow wing section (of Dassault Aviation's V2C profile) at a moderate Reynolds number of Re = 500,000 and a Mach number of M = 0.7 with spanwise domains equal to 5% and 100% of the airfoil chord. An implicit large-eddy simulation methodology, using a spectral error estimator to control the action of a high-order filter, is first validated against direct numerical simulations and then used for the domain width study. Quantitative differences, due to domain size, include an increase in amplitude and regularity of the buffet oscillations in the wider domain. Nevertheless, space-time analysis shows that key physical phenomena such as upstream-propagating shock waves are properly represented in the narrow domain and there is limited sensitivity to domain size of the aerodynamic coefficients. Even in the very wide domain, which is an order of magnitude wider than the largest turbulent structures measured at the trailing edge, certain features remain two-dimensional, including the shock and expansion waves that interact with the boundary layer upstream of transition. The transition mechanism is found to have subtle variations during a typical buffet cycle, with Kelvin-Helmholtz structures prominent during low-lift phases and oblique modes developing behind shock/boundarylayer interactions during high-lift phases. The availability of the wide-domain data is used for further study of the buffet mechanism, considering phase-averaged data and instantaneous flow fields to show the global structure of the buffet oscillation.

Transonic buffet refers to the self-sustained periodic motion of shock waves observed in transonic flows over wings and can limit the flight envelope of aircraft. Based on the boundary layer characteristics at the shock foot, buffet has been classified as laminar or turbulent and the mechanisms underlying the two have been proposed to be different (Dandois et al., J. Fluid Mech., vol. 18, 2018, pp. 156–178). The effect of various flow parameters (freestream Mach and Reynolds numbers and sweep and incidence angles) on laminar transonic buffet on an infinite wing (Dassault Aviation's supercritical V2C aerofoil) is reported here by performing large-eddy simulations (LES) for a wide range of parameters. A spectral proper orthogonal decomposition identified the presence of a low-frequency mode associated with buffet and high-frequency wake modes related to vortex shedding. A flow reconstruction based only on the former shows periodic boundary-layer separation and reattachment accompanying shock wave motion. A modal reconstruction based only on the wake mode suggests that the separation bubble breathing phenomenon reported by Dandois et al. is due to this mode. Together, these results indicate that the physical mechanisms governing laminar and turbulent buffet are the same. Buffet was also simulated at zero incidence. Shock waves appear on both aerofoil surfaces and oscillate out of phase with each other indicating the occurrence of a Type I buffet (Giannelis et al., Aerosp. Sci. Technol., vol. 18, 2018, pp. 89–101) on a supercritical aerofoil. These results suggest that the mechanisms underlying different buffet types are the same.

An airfoil undergoing transonic buffet exhibits a complex combination of unsteady shockwave 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.