Study of spatially developing supersonic turbulent boundary layers subjected to convex and concave curvatures

Wall-resolved large eddy simulations are employed to investigate spatially developing supersonic turbulent boundary layers over concave and convex surfaces with different radii of curvature. The geometries studied consist of a finite flat plate followed by a convex surface attached to its upper side and a concave surface attached to its lower side. Four configurations are investigated, including two convex and two concave surfaces. Mild and moderate radii of curvature are considered. For the mild curvature, the flow over the convex surface does not exhibit separation, while the flow over the concave surface features compression waves that do not coalesce into a shock wave. In contrast, the moderate-curvature cases exhibit separation on the convex side and shock formation on the concave side. These flow setups enable a direct comparison between high-speed turbulent boundary layers developing over convex and concave surfaces, which is relevant for the design of supersonic turbomachinery and control surfaces of supersonic aircraft. In all cases, the freestream Mach number is set to 2.0, and the Reynolds number is 500,000, based on the inlet velocity and axial chord. The aim of this study is to analyze the influence of surface curvature and their subsequent effects of favorable and adverse pressure gradients, as well as bulk dilatation and compression, on the mean flow quantities, turbulence statistics and turbulent structures.