Abstract Direct numerical simulations (DNSs) of spatially developing turbulent boundary layers (TBLs) over two-dimensional (2D) rod-roughened walls and three-dimensional (3D) cuboid-roughened walls are conducted to investigate the effects of the roughness height on the flow characteristics in the outer layer. The rod elements are periodically aligned along the downstream direction with a pitch of px/θin = 12, and the cuboid elements are periodically staggered with a pitch of px/θin = 12 and pz/θin = 3, where px and pz are correspondingly the streamwise and spanwise pitches of the roughness and θin is the momentum thickness at the inlet. The first surface roughness is placed 80θin downstream from the inlet, leading to a step change from a smooth to rough surface. The rod and cuboid roughness height (k) is varied in the range of 0.1 ≤ k/θin ≤ 1.8 (13 ≤ δ/k ≤ 285), respectively (δ is the boundary layer thickness), and the Reynolds number based on the momentum thickness (θ) is varied in the range of Reθ = 300 ~ 1400. For each case, the self-preservation form of the velocity-defect and the turbulent Reynolds stresses is achieved along the downstream direction. As the roughness height increases, the roughness function (ΔU+) extracted from the mean velocity profiles increases, although the velocity-defect profiles for the rough-wall cases show good agreement with the profile from the smooth-wall case. The magnitude of the Reynolds stresses in the outer layer increases with an increase of k/δ. The outer layer similarity between the flows over the rough and smooth-walls is found when δ/k ≥ 250 and 100 for the 2D rod and 3D cuboid, respectively. The continuous increase of the Reynolds stresses in the outer layer with an increase of k/δ is explained by a large population of very long structures over the rough-wall flows. Because the characteristic width of the structures increases continuously with an increase of k/δ for the rod and cuboid roughness, a wide width of the structures leads to frequent spanwise merging between adjacent structures. The active spanwise merging events with an increase of k/δ increase the streamwise coherence of the structures with the appearance of significant meandering.

中文翻译：

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湍流边界层中粗糙度高度对棒状和长方体粗糙壁的影响

摘要 对二维 (2D) 棒状粗糙壁和三维 (3D) 长方体粗糙壁上空间发展的湍流边界层 (TBL) 进行直接数值模拟 (DNS)，以研究粗糙度高度对表面粗糙度的影响。外层的流动特性。杆单元沿下游方向周期性排列，间距 px/θin = 12，长方体单元周期性交错，间距 px/θin = 12 和 pz/θin = 3，其中 px 和 pz 分别为粗糙度的流向和展向节距，θin 是入口处的动量厚度。第一个表面粗糙度位于入口下游 80θin，导致从光滑表面到粗糙表面的阶跃变化。棒状和长方体粗糙度高度 (k) 在 0.1 ≤ k/θin ≤ 1 的范围内变化。8 (13 ≤ δ/k ≤ 285)，(δ 是边界层厚度)，基于动量厚度 (θ) 的雷诺数在 Reθ = 300 ~ 1400 的范围内变化。对于每种情况，沿下游方向实现速度缺陷和湍流雷诺应力的自保形式。随着粗糙度高度的增加，从平均速度剖面中提取的粗糙度函数 (ΔU+) 增加，尽管粗糙壁情况下的速度缺陷剖面与光滑壁情况下的剖面显示出良好的一致性。外层雷诺应力的大小随着 k/δ 的增加而增加。当 δ/k ≥ 250 和 100 分别为 2D 棒和 3D 长方体时，发现粗糙壁和光滑壁上的流动之间的外层相似性。外层雷诺应力随着 k/δ 的增加而持续增加，这是由粗壁流上大量非常长的结构所解释的。由于结构的特征宽度随着棒状和长方体粗糙度 k/δ 的增加而不断增加，因此结构的宽度过宽导致相邻结构之间频繁的展向合并。随着 k/δ 的增加，活跃的展向合并事件增加了结构的流向相干性，并出现了明显的蜿蜒曲折。宽阔的结构导致相邻结构之间频繁的展向合并。随着 k/δ 的增加，活跃的展向合并事件增加了结构的流向相干性，并出现了明显的蜿蜒曲折。宽阔的结构导致相邻结构之间频繁的展向合并。随着 k/δ 的增加，活跃的展向合并事件增加了结构的流向相干性，并出现了明显的蜿蜒曲折。