Application of riblets to separating turbulent boundary layers

TL;DR

This study uses direct numerical simulations to investigate how two triangular riblet geometries (T9 and T6) affect a zero-pressure-gradient turbulent boundary layer that separates under a strong adverse pressure gradient. Building on Wu et al. 2020, the authors impose a Gaussian suction to trigger separation and compare riblet cases against a smooth-wall reference, solving the incompressible Navier–Stokes equations with a spectral-element method. They find that both riblets shorten the mean separation distance by about 18% (to ~140 θ0) and, under increasing APG, produce substantial drag reductions linked to enhanced, larger Kelvin–Helmholtz rollers that penetrate into the separation bubble. The work highlights the pivotal role of KH roller dynamics in riblet-assisted drag modification during separation, with implications for diffuser and trailing-edge design in aerospace applications.

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 $Re_{θ_0} = 583$ (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 $140θ_0$ downstream of the reference location, $18\%$ shorter than the mean separation distance for the smooth case ($170θ_0$). 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.

Figures (7)

• Figure 1: Channel flow setup at $Re_\tau = 400$ over (a,c) T950, and (b,d) T615 riblets (from Table \ref{['tab:channel']}). (a,b) visualize the instantaneous streamwise velocity $u$ near the riblet crest and on the side boundaries. (c,d) visualize the instantaneous $\hat{C}_f$ over the streamwise ($x$) and azimuthal ($\xi$) coordinates. Contours of $\hat{C}_f = 0$ are highlighted in green.
• Figure 2: Mean velocity profiles for the cases from Table \ref{['tab:channel']} compared with the reference data of Endrikat et al. (2021). The shaded region ($y^+ > 100$) is discarded, as the reference profiles are from a reduced-domain channel flow simulation.
• Figure 3: (a) Flow setup and visualization for the T9 case. The $xz$-plane visualization is near the riblets crest with the patches of flow reversal $(u < 0)$ enveloped with green isoline. (b) Mean velocity profiles at $x=0$ for the smooth case and the T9 case compared with the reference profiles of Schlatter & Örlü (2010) (Ref. ZPG) and Wu et al. (2020) (Ref. SBL).
• Figure 4: Quadratic elements on a $yz$-plane for the T9 case.
• Figure 5: Comparison of separating TBL over smooth wall between our cases (Table \ref{['tab:sbl']}) and the reference study of Wu et al. (2020). (b) Streamwise variation of $C_f$, and (c) mean velocity profiles at $x/\theta_0 = 100, 300, 500, 700$ as indicated in (a) with vertical dashed lines.