Direct numerical simulation of high aspect ratio spanwise-aligned bars

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 dtype, as the roughness function ΔU+ 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 ΔU+ 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, W, fixed in wall units, results in non-k-type behaviour. The roughness function appears to scale with W, suggesting that this is the only relevant parameter for very deep rough surfaces with k/W≥ 3. 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.