Wall-Resolved Large-Eddy Simulations of Transonic Shock-Induced Flow Separation

Wall-resolved implicit large-eddy simulations based on spatial filtering are performed for shock-induced flow separation over an axisymmetric bump at a Mach number of 0.875 and a chord-based Reynolds number of 2.763 million. The incoming boundary layer has a momentum thickness Reynolds number of 6600 at 1.5 chords upstream of the bump. The calculations, which employ up to 24 billion grid points, simulate the experimental model of Bachalo and Johnson ( Transonic, Turbulent Boundary-Layer Separation Generated on an Axisymmetric Flow Model, AIAA Journal, Vol. 24, No. 3, 1986, pp. 437-443), except that the tunnel walls are ignored and free air is assumed. The effects of domain span and grid resolution are examined along with main flowfield features. The predicted shock position as well as separation and reattachment locations agree well with experiment. Grid convergence is observed in the attached region well upstream of separation. Two-point azimuthal correlations suggest that a span of at least 20 deg is needed in the attached region, whereas a 120 deg span appears insufficient for correlations to completely decay to zero by midspan in the separation/ reattachment region. Computed rms surface pressure fluctuations display a sharp primary peak at the shock foot and a broader secondary peak near the reattachment location. Simulations reveal evidence of low-frequency shock unsteadiness; however, a longer statistical sample is needed to investigate this phenomenon.