Prediction of the high-Reynolds-number flow over a two-dimensional bump

Large eddy simulation (LES) has been applied to prediction of the high-Reynolds-number boundary layer flowing over a bump. Approximate boundary conditions were used in the LES to model the wall layer in which the instantaneous wall stress is correlated with the velocity at the first layer of grid points. Two formulations of the approximate boundary conditions were employed. In the first formulation, a constrained relation was used in which the mean wall shear stress is specified a priori either from experimental measurements or from a separate solution of the Reynolds-averaged Navier-Stokes (RANS) equations. In the second formulation, an unconstrained relation, which is based on an instantaneous power-law velocity profile, was used. Calculations were also performed in which the wall stress was computed directly, i.e., as if the near-wall flow were resolved. In the region resolved by the LES, the strong distortions of the mean flow, streamwise fluctuations, and turbulent shear stress are reasonably well predicted, and the relatively rapid recovery downstream of the trailing edge is also captured. However, neither LES nor RANS reproduces the plateau in skin friction measured upstream of the bump summit (attributed to early relaminarization in the experiments). LES predictions of the mean flow and turbulence intensities using the dynamic eddy viscosity model are relatively insensitive to the particular formulation of approximate boundary conditions. However, in calculations without a subgrid model, LES predictions exhibit large errors compared to experiments, and the quantitative levels of such errors are also sensitive to the choice of wall-layer model.