Large-eddy simulation of laminar transonic buffet

A large-eddy simulation of laminar transonic buffet on an airfoil at a Mach number M = 0.735, an angle of attack alpha = 4 degrees, a Reynolds number Re-c 3 x 10(6) has been carried out. The boundary layer is laminar up to the shock foot and laminar/turbulent transition occurs in the separation bubble at the shock foot. Contrary to the turbulent case for which wall pressure spectra are characterised by well-marked peaks at low frequencies (St=f.c/U-infinity similar or equal to 0.06-0.07, where St is the Strouhal number, f the shock oscillation frequency, c the chord length and U-infinity the free-stream velocity), in the laminar case, there are also well-marked peaks but at a much higher frequency (St =1.2). The shock oscillation amplitude is also lower: 6% of chord and limited to the shock foot area in the laminar case instead of 20% with a whole shock oscillation and intermittent boundary layer separation and reattachment in the turbulent case. The analysis of the phase-averaged fields allowed linking of the frequency of the laminar transonic buffet to a separation bubble breathing phenomenon associated with a vortex shedding mechanism. These vortices are convected at U-c/U-infinity similar or equal to 0.4 (where U-c is the convection velocity). The main finding of the present paper is that the higher frequency of the shock oscillation in the laminar regime is due to a different mechanism than in the turbulent one: laminar transonic buffet is due to a separation bubble breathing phenomenon occurring at the shock foot.