Supersonic turbulent flows over sinusoidal rough walls

Direct numerical simulations were performed to characterize fully developed supersonic turbulent channel flows over isothermal rough walls. The effect of roughness was incorporated using a level-set/volume-of-fluid immersed boundary method. Turbulence statistics of five channel flows are compared, including one reference case with both walls smooth and four cases with smooth top walls and bottom walls with two-dimensional (2-D) and three-dimensional (3-D) sinusoidal roughnesses. Results reveal a strong dependence of the turbulence on the roughness topography and the associated shock patterns. Specifically, the 2-D geometries generate strong oblique shock waves that propagate across the channel and are reflected back to the rough-wall side. These strong shocks are absent in the smooth-wall channel and are significantly weaker in cases with 3-D roughness geometries, replaced by weak shocklets. At the impingement locations of the shocks on the top wall in the 2-D roughness cases, localized augmentations of turbulence shear production are observed. Such regions of augmented production also exist for the 3-D cases, at a much weaker level. The oblique shock waves are thought to be responsible for a more significant entropy generation for cases with 2-D surfaces than those with 3-D ones, leading to a higher irreversible heat generation and consequently higher temperature values in 2-D roughness cases. In the present supersonic channels, the effects of roughness extend beyond the near-wall layer due to the shocks. This suggests that outer layer similarity may not fully apply to a rough-wall supersonic turbulent flow.