Direct numerical simulation of a supersonic turbulent boundary layer subjected to a concave surface

Direct numerical simulation is performed to investigate the flow physics of a supersonic turbulent boundary layer subjected to a longitudinal concave surface. Two physically consistent approaches are exploited to determine the boundary layer edge, and it is found that this turbulent boundary layer becomes noticeably thinned on the concave surface, which reflects the pronounced role of rise in density during this flow compression. In general the boundary layer is highly distorted, as manifested by wall pressure properties. Examinations of velocity statistics reveal that the scaling well established in canonical turbulence is violated in this distorted case. Mean streamwise velocity neither conforms to the universal log law nor obeys the velocity-defect law. Considerable increase is observed for Reynolds stresses throughout the concave surface, pointing to the effect of turbulence amplification. Nevertheless, the stress-bearing turbulent motions have barely changed in character, as evidenced by the quadrant analysis and structure parameter. The turbulence amplification is then understood by inspecting the production term of turbulent kinetic energy. We demonstrate that the outer boundary layer holds an increasingly important contribution to the total turbulence production throughout the concave surface. Accordingly, the amplification of turbulent kinetic energy is prominent in the outer layer. More insights are provided by inspecting the energy spectra. We find the outer-layer large structures are highly energized, even with an energy peak appearing in the lower-wake region, and they superimpose substantial large-scale energies on the near-wall region. Structural analyses demonstrate the organized turbulent motions, which are well scaled in canonical turbulence, have generally changed in their characteristic lengthscales under the influence of concave surface. Importantly, the flow visualization reveals stronger footprints overlaid onto the near-wall region, which suggests enhanced inner-outer interactions. This perspective, aided by the spanwise two-point correlations, is moreover supported by the quantification of amplitude modulation through a mathematical diagnostic tool. Results demonstrate that turbulence modulation is still governed by log-region superstructures, whereas the modulation strength has noticeably increased throughout the concave surface.