Investigation on the vortical structures by the Liutex method in turbulent channels at Reτ = 180 with scalloped and triangular riblet control

Riblets are a series of small protrusions formed along the flow direction, which have been extensively studied as a passive turbulent drag reduction technique. Experiments and numerical simulations have shown that well-designed riblets can significantly reduce drag in turbulent flows, making them highly promising and valuable for various applications. In this study, we focus on a scalloped riblet, which is designed by smoothly connecting two third-order polynomials, and thus the sharpness of the tip and the curvature of the valley can be well defined. We conduct direct numerical simulations of turbulent channel with smooth plate, scalloped riblet-mounted and triangular riblet-mounted walls. Width in wall units of W⁺ = 20 and height-width ratio of γ = 0.5 are selected for both riblet cases. Compared with the smooth plate case, the scalloped riblet case achieves an 8.68% drag reduction, while the triangular riblet case achieves a 4.79% drag reduction. The obtained drag reduction rate of the triangular riblet is consistent with previous experiments and simulations, and the results indicate that the scalloped riblet is more effective in reducing drag and deserves further investigation. We compare turbulent statistics of the scalloped riblet case with those of the triangular riblet case. The mean velocity profiles of riblets are similar, but both the Reynolds shear stress and second-order statistics of velocity fluctuations and Liutex are significantly reduced in the scalloped riblets controlled turbulent channel, indicating that the scalloped riblet can more effectively suppress the spanwise and wall-normal turbulent intensity near the wall. We also compare the pre-multiplied spectra of streamwise velocity and streamwise Liutex component for the three cases to investigate the energy distribution and characteristics of Liutex distribution. The Liutex vortex identification method is also utilized to analyze the instantaneous flow field, which provides insights into the flow field and could be beneficial for the further optimization of riblet.