We experimentally investigate the influence of alternating rough and smooth walls on bubbly drag reduction (DR). We apply rough sandpaper bands of width $s$ between $48.4\,mm$ and $148.5\,mm$, and roughness height $k = 695\,{\mu}m$, around the smooth inner cylinder (IC) of the Twente Turbulent Taylor-Couette facility. Between sandpaper bands, the IC is left uncovered over similar width $s$, resulting in alternating rough and smooth bands, a constant pattern in axial direction. We measure the DR in water that originates from introducing air bubbles to the fluid at (shear) Reynolds numbers $\textit{Re}_s$ ranging from $0.5 \times 10^6$ to $1.8 \times 10^6$. Results are compared to bubbly DR measurements with a completely smooth IC and an IC that is completely covered with sandpaper of the same roughness $k$. The outer cylinder is left smooth for all variations. Results are also compared to bubbly DR measurements where a smooth outer cylinder is rotating in opposite direction to the smooth IC. This counter rotation induces secondary flow structures that are very similar to those observed when the IC is composed of alternating rough and smooth bands. For the measurements with roughness, the bubbly DR is found to initially increase more strongly with $\textit{Re}_s$, before levelling off to reach a value that no longer depends on $\textit{Re}_s$. This is attributed to a more even axial distribution of the air bubbles, resulting from the increased turbulence intensity of the flow compared to flow over a completely smooth wall at the same $\textit{Re}_s$. The air bubbles are seen to accumulate at the rough wall sections in the flow. Here, locally, the drag is largest and so the drag reducing effect of the bubbles is felt strongest. Therefore, a larger maximum value of bubbly DR is found for the alternating rough and smooth walls compared to the completely rough wall.

中文翻译：

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轴向变化的砂纸粗糙度对 Taylor-Couette 湍流中气泡减阻的影响

我们通过实验研究了交替的粗糙壁和光滑壁对气泡减阻 (DR) 的影响。我们在 Twente 的光滑内圆柱 (IC) 周围应用宽度在 $48.4\,mm$ 和 $148.5\,mm$ 之间的粗糙砂纸带，粗糙度高度 $k = 695\,{\mu}m$湍流 Taylor-Couette 设施。在砂纸带之间，IC 在相似的宽度 $s$ 上未被覆盖，导致交替的粗糙和光滑的带，轴向上的恒定图案。我们测量了由于在（剪切）雷诺数 $\textit{Re}_s$ 范围内从 $0.5 \times 10^6$ 到 $1.8 \times 10^6$ 向流体中引入气泡而产生的水中 DR。结果与使用完全光滑的 IC 和完全覆盖有相同粗糙度 $k$ 砂纸的 IC 的气泡 DR 测量值进行比较。对于所有变化，外圆柱体都保持光滑。结果还与气泡 DR 测量进行了比较，其中光滑的外圆柱体与光滑的 IC 以相反的方向旋转。这种反向旋转会引起二次流动结构，这些结构与 IC 由交替的粗糙和光滑带组成时观察到的结构非常相似。对于粗糙度测量，发现气泡 DR 最初随着 $\textit{Re}_s$ 增加得更强烈，然后趋于平稳，达到不再依赖于 $\textit{Re}_s$ 的值。这归因于气泡的更均匀的轴向分布，这是由于在相同的 $\textit{Re}_s$ 下与完全光滑的壁上的流动相比，流动的湍流强度增加了。可以看到气泡在流动的粗糙壁部分积聚。在这里，在当地，阻力最大，因此感觉气泡的减阻效果最强。因此，与完全粗糙的壁相比，交替的粗糙壁和光滑壁的气泡 DR 的最大值更大。