Flow resistance over heterogeneous roughness made of spanwise-alternating sandpaper strips

The Reynolds number dependent flow resistance of heterogeneous rough surfaces is largely unknown at present. The present work provides novel reference data for spanwise-alternating sandpaper strips as one idealized case of a heterogeneous rough surface. Experimental data are presented and analysed in direct comparison with drag measurements of homogeneous sandpaper surfaces and numerical simulations. Based on the homogeneous roughness data the related challenges and sensitivities for the evaluation of roughness functions from experiments and simulations are discussed. A hydraulic channel height is suggested as an alternative measure for the drag impact of rough surfaces in internal flows.
For the investigated heterogeneous roughness it is found that turbulent flow does not exhibit a fully-rough flow behaviour, indicating that the assignment of an equivalent sand grain height as commonly applied for homogeneous roughness is not possible. A prediction of the drag behaviour of rough strips based on an average between rough and smooth drag curves appears promising, but requires further refinement in order to capture the impact of turbulent secondary flows and spatial transients linking smooth and rough surface parts.
While turbulent secondary flow induced by the roughness strips yield significant spanwise variation of the mean velocity profile for the investigated rough strips we show that the spanwise averaged velocity profiles collapse reasonably well with a smooth or homogeneous rough wall flow. This allows to extract a global roughness function from the spanwise averaged flow field in good agreement with the one deduced from global pressure drop measurements.

目前，依赖雷诺数（Reynolds number）的非均匀粗糙表面（heterogeneous rough surfaces）流动阻力仍未被充分认知。本研究针对作为非均匀粗糙表面理想化模型之一的展向交替砂纸条（spanwise-alternating sandpaper strips），提供了全新的基准参考数据。文中给出了实验数据，并与均匀砂纸表面（homogeneous sandpaper surfaces）的阻力测量结果及数值模拟（numerical simulations）结果开展直接对比分析。基于均匀粗糙表面的实验数据，本文讨论了从实验与数值模拟中评估粗糙度函数（roughness functions）所面临的相关挑战与敏感性。此外，本文提出将水力通道高度（hydraulic channel height）作为内流（internal flows）中粗糙表面阻力影响的替代表征参数。
针对所研究的非均匀粗糙表面，研究发现湍流流动并未呈现完全粗糙流动特性，这表明无法像常规应用于均匀粗糙表面那样，为其指定等效砂粒高度（equivalent sand grain height）。基于粗糙与光滑壁面阻力曲线的平均值来预测粗糙条的阻力行为颇具前景，但仍需进一步优化，以捕捉连接光滑与粗糙表面区域的湍流二次流（turbulent secondary flows）与空间瞬变（spatial transients）的影响。
尽管由粗糙条诱发的湍流二次流会导致所研究的粗糙条的平均速度剖面（mean velocity profile）出现显著的展向变化，但本文证明，展向平均（spanwise averaged）后的速度剖面可与光滑壁面或均匀粗糙壁面流动较好地重合。这使得我们能够从展向平均流场中提取全局粗糙度函数（global roughness function），其结果与通过全局压降测量（global pressure drop measurements）推导得到的全局粗糙度函数吻合良好。