Direct numerical simulation of the two-dimensional speed bump flow at increasing Reynolds numbers

Abstract

The Speed Bump flow model was designed by Boeing to provide a mildly three-dimensional flow with separation from a very smooth surface, strongly controlled by the turbulence. Experiments are conducted by several teams, as are simulations, over a range of Reynolds numbers. Direct Numerical Simulations (DNS) are not possible for the full 3D geometry of width L, leading several groups to conduct DNS over a two-dimensional geometry, in other words the cross-section of the full geometry, with periodic lateral conditions and a typical domain width of 0.04L. This does not allow precise comparisons with experiment, but code-to-code comparison is instructive. A shallow separation bubble is present, as intended. The domain width becomes marginal after reattachment, where the boundary layer is much thicker. The Reynolds number based on L has been 106, so far in the literature, which causes partial relaminarization and tends to defeat the purpose of testing turbulence models. Flow visualisation is clear on this. Here, we present results at the Reynolds number 106 and 1.4 × 106, and the higher value essentially eliminates relaminarization. Detailed results are shown, including studies of domain width, grid resolution, and numerical dissipation. The turbulence models give inaccurate results for skin friction, already in the intense favourable pressure gradient, which causes the formation of an internal boundary layer; the separation prediction on the other hand is reasonable. The wall curvature seems to play a role. The present results also provide trustworthy data to test Large-Eddy Simulation (LES), especially if using a Wall Model (WMLES). The comparisons will have a preliminary character until the results of the ongoing detailed experiments and of DNS at even higher Reynolds number and with a wider domain are available and carefully compared.