Abstract

The low-frequency pressure fluctuations generated by a range of roughness configurations are explored for flows of roughness Reynolds numbers over 200 and blockage ratios above 73. Two-point analysis of the pressure fluctuations reveals that surfaces with high frontal solidity, \(\lambda\), and/or complex shear layer interactions near the elements, have structures which persist longer than structures on the smooth wall. A low-frequency pressure spectrum scaling based on the broadband convection velocity defect, \(U_{\text{e}}-{\overline{U}}_{\text{c}_{\text{b}}}\), is proven effective for all rough surfaces and the smooth wall. Here \(U_{\text{e}}\) is the boundary layer edge velocity, and \({\overline{U}}_{\text{c}_{\text{b}}}\) is the mean broadband convection velocity. A second scaling, which is more appropriate for a priori predictions, is also proposed. It uses the mean velocity defect, \(U_{\text{e}}-{\overline{U}}\) (where \({\overline{U}}\) is the mean boundary layer velocity), first proposed for velocity profiles by Zagarola and Smits (J Fluid Mech 373:33–79, 1998). Both scalings are effective because they are based on velocity defects proportional to the outer-layer shear stress which generates the pressure fluctuations. A re-examination of the outer-layer wall-similarity in the context of these new findings suggests that this concept is limited to a narrow range of turbulent boundary layer flows.

Graphical abstract

中文翻译：

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近平衡湍流边界层的低频压力波动

摘要

对于200以上的粗糙度雷诺数和73以上的阻塞率，研究了由一系列粗糙度配置产生的低频压力波动。对压力波动的两点分析表明，表面具有较高的正面强度，\（\ lambda \ ），和/或复杂的剪切层中的元素附近的相互作用，具有持续长于在光滑壁结构的结构。基于宽带对流速度缺陷\（U _ {\ text {e}}-{\ overline {U}} _ {\ text {c} _ {\ text {b}}} \的低频压力谱缩放），被证明对所有粗糙表面和光滑墙面都是有效的。这里\（U _ {\ text {e}} \）是边界层边缘速度，而\（{\ overline {U}} _ {\ text {c} _ {\ text {b}}} \}是宽带平均对流速度。还提出了第二缩放，其更适合于先验预测。它使用平均速度缺陷\（U _ {\ text {e}}-{\ overline {U}} \）（其中\（{\ overline {U}} \）是边界层平均速度）提出， Zagarola和Smits（J流体力学373：33–79，1998）提出的速度分布图。两种缩放都是有效的，因为它们基于速度缺陷，该速度缺陷与产生压力波动的外层剪切应力成比例。在这些新发现的背景下，对外层壁相似性的重新检验表明，这一概念仅限于湍流边界层流的狭窄范围。

图形概要