Direct numerical simulation of supersonic turbulent flows on compression–expansion surfaces subjected to arc wall confinements

This study employed direct numerical simulations to investigate supersonic turbulent flows over compression–expansion surfaces using three configurations with a shared geometric centerline, including an S-shaped ramp, an S-shaped half-open pipe, and an S-shaped pipe. Through comparative analysis, the influences of arc wall confinements on boundary layers are systematically uncoupled in both streamwise and spanwise directions. The streamwise concave curvature induces compression, lifting low-momentum fluids outward from the walls, reducing the scale of velocity streaks, and amplifying vorticity production. In contrast, the streamwise convex curvature promotes expansion, resulting in opposite modifications in these turbulence characteristics. Compared to the S-shaped ramp, both the S-shaped half-open pipe and S-shaped pipe significantly enhance secondary flows, which are manifested as a pair of large-scale counter-rotating vortices, and yield higher pressure peak values, while attenuating velocity fluctuations and turbulent kinetic energy on the bottom wall. However, the presence of spanwise arc wall confinements substantially alters the spatial development of turbulence within the boundary layer, leading to non-uniform distributions of Reynolds normal and shear stresses at different azimuthal positions. From the bottom wall to the free-stream plane of the S-shaped half-open pipe, the peak value of wall pressure decreases and the longitudinal velocity fluctuations intensify, accompanied by a downstream shift in the variation curves of wall pressure, turbulent kinetic energy, and skin friction coefficient. This investigation contributes to elucidating the underlying mechanisms of supersonic flow under coupled streamwise and spanwise curvature, which is scientifically valuable for the engineering application of supersonic intakes.