Direct numerical simulation of high aspect ratio spanwise-aligned bars

TL;DR

This study uses direct numerical simulations to explore how high aspect ratio spanwise-aligned bars influence turbulent flow, revealing that roughness effects depend on bar width rather than height at high aspect ratios.

Contribution

The paper demonstrates that for high aspect ratio bars, the roughness function depends primarily on the bar spacing, challenging traditional classifications of roughness types.

Findings

Roughness function depends on bar spacing at high aspect ratios.

Deep roughness with large height-to-width ratio shows non-$k$-type behavior.

Flow 'sees' only the gap width between bars at high aspect ratios.

Abstract

We conduct minimal-channel direct numerical simulations of turbulent flow over two-dimensional rectangular bars aligned in the spanwise direction. This roughness has been often described as $d$-type, as the roughness function $\Delta U^+$ is thought to depend only on the outer-layer length scale (pipe diameter, channel half height or boundary layer thickness). This is in contrast to conventional engineering rough surfaces, named $k$-type, for which $\Delta U^+$ depends on the roughness height, $k$. The minimal-span rough-wall channel is used to circumvent the high cost of simulating high Reynolds number flows, enabling a range of bars with varying aspect ratios to be investigated. The present results show that increasing the trough-to-crest height ($k$) of the roughness while keeping the width between roughness bars, $\mathcal{W}$, fixed in viscous units, results in non-$k$-type behaviour although this does not necessarily indicate $d$-type behaviour. Instead, for deep surfaces with $k/\mathcal{W}\gtrsim 3$, the roughness function appears to depend only on $\mathcal{W}$ in viscous units. In these situations, the flow no longer has any information about how deep the roughness is and instead can only `see' the width of the fluid gap between the bars.