Secondary Flows and Near-Wall Turbulence in Channel Flow with Longitudinal Ribs

Abstract: This study employs the Large Eddy Simulation (LES) to investigate secondary flows and near-wall turbulence induced by two types of surface-mounted longitudinal ribs, namely rectangular and triangular, in a channel flow. The friction Reynolds number, based on friction velocity and channel height H, is set at 220. The rib aspect ratio W/h, where W and h represent the width and height of the rib, is 2, and the rib spacing, S is 0.6H. The results indicate formation of two counter-rotating vortices between the adjacent ribs for both the cases considered. The roughness function is higher with the rectangular rib as compared to that of the triangular rib. At the location of the mid-plane on the rectangular ribs, the wall shear stress is relatively lower as compared to that of the location of mid-plane between the ribs. Conversely, for the case of triangular rib, the opposite pattern is observed. Normal Reynolds stress exhibits strong anisotropic behaviour near the wall for both the cases, overlapping above 0.4H. Between 0.4H and 0.8H, the variation in normal Reynolds stresses is linear. Near the wall, higher production of turbulent kinetic energy (TKE) and normal Reynolds stresses are observed with the triangular rib as compared to those of the rectangular rib. The ratio of production to dissipation is unity in the log-law region.

• The paper reveals that rib geometry, particularly triangular versus rectangular cross-sections, dramatically alters secondary flow strength and near-wall turbulence.
• It employs high-fidelity LES with a dynamic Smagorinsky model to resolve turbulent structures and capture nuanced wall shear stress variations.
• Results indicate that triangular ribs enhance cross-stream transport and TKE production, offering practical insights for optimizing flow control strategies.

Secondary Flows and Near-Wall Turbulence Due to Longitudinal Ribs in Channel Flow

Introduction

The paper "Secondary Flows and Near-Wall Turbulence in Channel Flow with Longitudinal Ribs" (2607.10699) presents a comprehensive LES study on the influence of spanwise-heterogeneous surface roughness—implemented as longitudinal ribs with rectangular and triangular cross-sections—on wall-bounded turbulent channel flows. By fixing the Reynolds number ($Re_{\tau} = 220$), the rib aspect ratio ($W/h = 2$), and the rib spacing ($S = 0.6H$), the work isolates the effect of rib geometry on secondary flows, wall shear stress, Reynolds stresses, and TKE production, contributing new insights into comparative roughness phenomenology across rib shapes.

Methodology

Employing a dynamic Smagorinsky subgrid-scale closure within the LES paradigm, the study resolves the dynamics of the large-scale energy-carrying structures while adequately modeling unresolved small-scale motions. Grid resolutions ($\Delta x^+ = 22.35$, $\Delta z^+ = 2.23$, and first-$y^+$ grid point at 1.12) are selected to ensure accurate capture of near-wall turbulence. Boundary conditions enforce periodicity in axial and spanwise directions, with no-slip at the bottom wall and free-slip at the upper wall.

Velocity initialization uses stochastic perturbations, and force balance is established by equating viscous and pressure forces for different rib geometries, facilitating accurate calculation of the friction velocity across cases. Validation against DNS benchmarks confirms the accuracy of mean flow representation.

Results and Discussion

Mean Flow and Secondary Motions

Both rib types induce paired counter-rotating secondary vortices, with the vertical core location marginally higher for rectangular ribs. Notably, the secondary velocity magnitude and cross-stream transport are stronger for trianglular ribs. The absence of a dead zone near the triangular rib base—contrasted by its presence for rectangular ribs—is significant for local flow reattachment and energy redistribution.

The deviation from the classical log-law in mean streamwise velocity profiles is quantified via the roughness function ($\Delta U^+$), which is higher for rectangular ribs ($\Delta U^+ = 2.8$) than for triangular ribs ($\Delta U^+ = 2.1$). This indicates enhanced momentum loss for the former geometry.

Wall Shear Stress and Anisotropy

Distinct patterns in wall shear stress are found between geometries: rectangular ribs show reduced shear at the mid-rib and maxima at rib edges, while triangular ribs display the opposite trend. This nontrivial geometric dependence implies that mean shear distribution and, by implication, drag characteristics are sensitive to rib cross-section shape.

Near-wall normal Reynolds stress components reveal marked anisotropy below $y/H = 0.4$; above that height, profiles collapse and trend linearly toward the outer boundary layer. The spanwise component systematically exceeds the cross-stream component, emphasizing the role of ribs in amplifying three-dimensionality in fluctuation statistics.

Turbulent Kinetic Energy Dynamics

Triangular ribs are associated with higher near-wall TKE production and normal Reynolds stresses when compared to rectangular ribs, consistent with enhanced secondary flow and reduced dead-zone formation. Both geometries manifest a two-peak structure in TKE production, corresponding to wall and rib-induced features. The vertical displacement of the second production peak (slightly higher for rectangular ribs) aligns with above-mentioned differences in secondary vortex core locations.

A noteworthy claim is that the ratio of TKE production to dissipation regains unity (i.e., local equilibrium) within the log-law region in both cases, underscoring the validity of turbulence closure assumptions there.

Implications and Future Directions

The fidelity with which rib geometry modulates secondary flows, wall-bounded turbulence statistics, and mean drag provides actionable insight for engineering flow control strategies. In practical applications (e.g., heat exchangers, drag-reducing surfaces), the geometric sensitivity demonstrated here suggests that optimal riblet/ridge design must transcend simple roughness amplitude considerations, directly accounting for cross-sectional shape and arrangement to control secondary circulations and near-wall turbulence energetics.

Future directions may pursue higher Reynolds numbers, complex rib arrangements (e.g., chevrons, staggered arrays), and active flow manipulation superposed on passive roughness modifications. Coupling with heat transfer metrics and extending analyses to non-canonical geometries would strengthen the relevance of these findings to industrial and environmental flows.

Conclusion

This work systematically interrogates the mechanistic role of rib shape on secondary flow generation, wall stress distribution, and turbulent statistics in channel flow using LES. Triangular ribs exhibit enhanced secondary cross-stream motion, higher TKE production, and a lower roughness function than rectangular counterparts. The results provide a robust foundation for tuning surface roughness morphology for targeted manipulation of turbulent wall-bounded flows, advancing both theoretical and applied turbulence research.