Application of riblets to separating turbulent boundary layers

Abstract

We conduct direct numerical simulations of separating turbulent boundary layers (TBLs) over triangular riblets with tip angles $90^o$ (T9) and $60^o$ (T6). Our setup follows the separating TBL study of Wu et al.\ ({\it J. Fluid Mech.}, vol.\ 883, 2020, p.\ A45). An equilibrium zero pressure-gradient (ZPG) TBL is generated at a reference location, followed by imposition of a Gaussian suction profile to create a separation bubble. The ZPG TBLs over the riblets and the benchmark smooth case have matched momentum thickness Reynolds number $Re_{\theta_0} = 583$ (friction Reynolds number 224). We employ a well-validated spectral-element solver, and leverage its unstructured-grid nature to generate an optimal grid, based on the size of turbulent scales across the TBL. At the reference location, the T9 and T6 riblets respectively increase and reduce drag, with viscous-scaled spacings $52$ and $13$. We discover that for both riblet cases, the mean separation location occurs at a distance of $140\theta_0$ downstream of the reference location, $18\%$ shorter than the mean separation distance for the smooth case ($170\theta_0$). This outcome is related to the progressive enhancement of the Kelvin-Helmholtz (KH) rollers over the riblets, owing to the continuous rise in the adverse pressure-gradient. The KH rollers penetrate into the turbulent separation bubble, with significantly larger size and coherence compared to their counterparts upstream of the mean separation location.