On the structure and dynamics of secondary flows over multi-column roughness in channel flow

TL;DR

This work investigates how spanwise-heterogeneous, clustered roughness arranged in multi-column patterns shapes secondary flows in turbulent channel flow using large-eddy simulations. By systematically varying intra-column gaps and comparing staggered versus aligned layouts, the authors identify the dimensionless inter-column gap $s_a/H$ as the critical parameter controlling mean flow polarity, and they interpret the mean structures with energy-transport tubes that reveal entrainment pathways of mean kinetic energy. The study uncovers three regimes in $s_a/H$ and demonstrates that instantaneous secondary flows are unsteady and chaotic, with delta-scale patterns emerging as time-averaged artifacts; conditional averaging shows frequent polarity reversals in the intermediate regime. The findings provide a comprehensive picture of how roughness clustering governs both the mean structure and temporal dynamics of secondary flows, with direct implications for surface drag, convective heat transfer, and scalar transport in engineering surfaces with complex roughness.

Abstract

Secondary flows induced by spanwise heterogeneous surface roughness play a crucial role in determining engineering-relevant metrics such as surface drag, convective heat transfer, and the transport of airborne scalars. While much of the existing literature has focused on idealized configurations with regularly spaced roughness elements, real-world surfaces often feature irregularities, clustering, and topographic complexity for which the secondary flow response remains poorly understood. Motivated by this gap, we investigate multi-column roughness configurations that serve as a regularized analog of roughness clustering. Using large-eddy simulations, we systematically examine secondary flows across a controlled set of configurations in which cluster density and local arrangement are varied in an idealized manner, and observe that these variations give rise to distinct secondary flow polarities. Through a focused parameter study, we identify the spanwise gap between the edge-most roughness elements of adjacent columns, normalized by the channel half-height, as a key geometric factor governing this polarity. In addition to analyzing the time-averaged structure, we investigate how variations in polarity affect the instantaneous dynamics of secondary flows. Here, we find that the regions of high- and low-momentum fluid created by the secondary flows alternate in a chaotic, non-periodic manner over time. Further analysis of the vertical velocity signal shows that variability in vertical momentum transport is a persistent and intrinsic feature of secondary flow dynamics. Taken together, these findings provide a comprehensive picture of how the geometric arrangement of roughness elements governs both the mean structure and temporal behavior of secondary flows.

Figures (17)

• Figure 1: a) Schematic of roughness element arrangement (not to scale; flow direction: bottom to top) and b) mean streamwise velocity at mid-element height (flow direction: left to right) for S2-5-2 case.
• Figure 2: Schematic of length scales considered in the roughness element arrangement. $s_l$: spanwise gap between adjacent elements of the same wider column, $s_w$: width of the wider column, $s_a$: spanwise gap between adjacent elements of different wider columns, $s_y$: spanwise gap between centers of different wider columns.
• Figure 3: a) Spatially averaged mean streamwise velocity, b) velocity defect and c) root mean squared velocity profiles for the cases considered in table \ref{['tab:staggered reversal']}. The black dashed line in (a) denotes the log-law slope. $\hat{z} = (z-d)/(H-d)$.
• Figure 4: Pseudocolor plot of vertical velocity for different cases mentioned in table \ref{['tab:staggered reversal']}, taken at a streamwise location coinciding with the elements. a) S2-5-2, b) S2.75-5-2, c) S3.5-5-2, d) S4-5-2. Black arrows indicate the vectors of spanwise and vertical velocity. Green line indicates contour of 95% of horizontally-averaged maximum mean streamwise velocity.
• Figure 5: Pseudocolor plot of turbulent kinetic energy (tke) for different cases mentioned in table \ref{['tab:staggered reversal']}, taken at a streamwise location coinciding with the elements. a) S2-5-2, b) S2.75-5-2, c) S3.5-5-2, d) S4-5-2. Green line indicates contour of 20% of maximum tke on the visualized plane.