Numerical investigation of the turbulent boundary layer over a bump

Abstract

Large-eddy simulation (LES) has been used to calculate the flow of a statistically two-dimensional turbulent boundary layer over a bump. Subgrid-scale stresses in the filtered Navier–Stokes equations were closed using the dynamic eddy viscosity model. LES predictions for a range of grid resolutions were compared to the experimental measurements of Webster et al. (1996). Predictions of the mean flow and turbulence intensities are in good agreement with measurements. The resolved turbulent shear stress is in reasonable agreement with data, though the peak is over-predicted near the trailing edge of the bump. Analysis of the flow confirms the existence of internal layers over the bump surface upstream of the summit and along the downstream trailing at plate, and demonstrates that the quasi-step increases in skin friction due to perturbations in pressure gradient and surface curvature selectively enhance near-wall shear production of turbulent stresses and are responsible for the formation of the internal layers. Though the flow experiences a strong adverse pressure gradient along the rear surface, the boundary layer is unique in that intermittent detachment occurring near the wall is not followed by mean-flow separation. Certain turbulence characteristics in this region are similar to those previously reported in instantaneously separating boundary layers. The present investigation also explains the driving mechanism for the surprisingly rapid return to equilibrium over the trailing flat plate found in the measurements of Webster et al. (1996), i.e. the simultaneous uninterrupted development of an inner energy-equilibrium region and the monotonic decay of elevated turbulence shear production away from the wall. LES results were also used to examine response of the dynamic eddy viscosity model. While subgrid-scale dissipation decreases/increases as the turbulence is attenuated/enhanced, the ratio of the (averaged) forward to reverse energy transfers predicted by the model is roughly constant over a significant part of the layer. Model predictions of backscatter, calculated as the percentage of points where the model coefficient is negative, show a rapid recovery downstream similar to the mean-flow and turbulence quantities.