Numerical Study of Transonic Buffet on a Supercritical Airfoil

The flow of the Bauer–Garabedian–Korn (BGK) No. 1 supercritical airfoil is investigated by the solution of the unsteady Reynolds-averaged Navier–Stokes equations with a two-equation lagged k–ω turbulent model. Two steady cases (M = 0.71, α= 1.396 deg and M = 0.71, α= 9.0 deg) and one unsteady case (M = 0.71, α= 6.97 deg), all with a far-stream Reynolds number of 20 × 106, are computed. The results are compared with available experimental data. The computed shock motion and the evolution of the concomitant flow separation are examined. Space-time correlations of the unsteady pressure field are used to calculate the time for pressure waves to travel downstream within the separated region from the shock wave to the airfoil trailing edge and then back from the trailing edge to the shock outside the separated region. The reduced frequency so calculated agrees well with the computed buffet frequency, supporting the signal propagation mechanism for buffet proposed by Lee (Lee, B. H. K., “Oscillation Shock Motion Caused by Transonic Shock Boundary-Layer Interaction,” AIAA Journal, Vol. 28, No. 5, 1990, pp. 942–944).