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 $\unicode[STIX]{x1D6FC}=4^{\circ }$ , a Reynolds number $Re_{c}=3\times 10^{6}$ 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 ( $St=f\cdot c/U_{\infty }\simeq 0.06{-}0.07$ , where $St$ is the Strouhal number, $f$ the shock oscillation frequency, $c$ the chord length and $U_{\infty }$ 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 $U_{c}/U_{\infty }\simeq 0.4$ (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.