Analysis of a transonic laminar shock buffet system using a large-eddy simulation*

A wall-resolved large-eddy simulation (LES) of transonic shock buffet on the OALT25 supercritical laminar airfoil is configured at a 4-degree angle-of-attack in a Mach 0.735 freestream. The chord-length-based Reynolds number is 1 million. The simulation was conducted using sixth-order compact finite difference methods with an explicit subgrid-scale model and hybrid central-Riemann fluxes for shock-capturing. The data from the LES used for analysis is collected over a range of 260 convective time units at the statistically stationary state. The extended laminar boundary layer, flow separation, transition-to-turbulence, turbulent vortex shedding, and propagation of acoustic waves are well resolved. Signal processing shows that the oscillation of the lift and drag coefficients are dominated by the shock buffet and turbulent vortex shedding at Strouhal numbers of approximately 0.1 and 0.55 respectively. The spectral proper orthogonal decomposition (SPOD) analysis indicates that the flow system exhibits low-rank behavior at the two frequencies. The principal unsteady flow and wave features can be identified from the first SPOD mode at the peak frequencies, and several feedback paths are observed.