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Investigation of the secondary flow by convergent-divergent riblets in a supersonic turbulent boundary layer over a compression ramp

In this paper, the effect of the secondary flow induced by convergent-divergent riblets in supersonic turbulent boundary layers over a 24o compression ramp at Mach number 2.9 is studied via direct numerical simulation. Two riblet cases with the wavelength Λ being 1.1 δ and 1.65 δ are conducted to examine their impact on the secondary rolling motion, momentum transfer, flow separation and unsteady shock motion. As the flow develops over the riblet section, both the size and intensity of the secondary rolling motion tend to increase. For the riblet case with Λ/ δ=1.1, a single rolling mode is observed within a half wavelength, while a pair of co-rotating vortical structures is obtained for Λ/ δ=1.65. The results reveal that the secondary flow contributes to the increase of both the mean momentum flux and turbulent fluctuations. By using the spanwise averaging, the mean momentum flux contributed from the dispersive stress and compressible effect caused by the secondary flow is identified. Both components appear to enhance the near-wall momentum mixing, and a larger enhancement is observed for Λ/ δ=1.1 where the intensity of the secondary flow is stronger. Compared to the baseline case, the area of the separation zone at Λ/δ=1.1 and Λ/ δ=1.65 is decreased by 56% and 38%, respectively. For all the cases, the low-frequency motion near the foot of the shock is observed. In comparison, the frequency of the low-frequency motion for the riblet case is two times higher than that in the baseline case, owing to the reduction of the separation area and length.