Reynolds-number dependence of the near-wall flow over irregular rough surfaces

Abstract

The Reynolds-number dependence of turbulent channel flow over two irregular rough surfaces, based on scans of a graphite and a grit-blasted surface, is studied by direct numerical simulation. The aim is to characterise the changes in the flow in the immediate vicinity of and within the rough surfaces, an area of the flow where it is difficult to obtain experimental measurements. The average roughness heights and spatial correlation of the roughness features of the two surfaces are similar, but the two surfaces have a significant difference in the skewness of their height distributions, with the graphite sample being positively skewed (peak-dominated) and the grit-blasted surface being negatively skewed (valley-dominated). For both cases, numerical simulations were conducted at seven different Reynolds numbers, ranging from $Re_{\unicode[STIX]{x1D70F}}=90$ to $Re_{\unicode[STIX]{x1D70F}}=720$. The positively skewed surface gives rise to higher friction factors than the negatively skewed surface in all cases. For the highest Reynolds numbers, the flow has values of the roughness function $\unicode[STIX]{x0394}U^{+}$ well in excess of $7$ for both surfaces and the bulk flow profile has attained a constant shape across the full height of the channel except for the immediate vicinity of the roughness, which would indicate fully rough flow. However, the mean flow profile within and directly above the rough surface still shows considerable Reynolds-number dependence and the ratio of form to viscous drag continues to increase, which indicates that at least for some types of rough surfaces the flow retains aspects of the transitionally rough regime to values of $\unicode[STIX]{x0394}U^{+}$ or $k^{+}$ well in excess of the values conventionally assumed for the transitionally to fully rough threshold. This is also reflected in the changes that the near-wall flow undergoes as the Reynolds number increases: the viscous sublayer, within which the surface roughness is initially buried, breaks down and regions of reverse flow intensify. At the highest Reynolds numbers, a layer of near-wall flow is observed to follow the contours of the local surface. The distribution of thickness of this ‘blanketing’ layer has a mixed scaling, showing that viscous effects are still significant in the near-wall flow.