School of Mechanical Science and Engineering, Huazhong University of Science and Technology, No.1037, Luoyu Road, Wuhan, China, 430074.
Phys Rev E. 2018 Mar;97(3-1):033110. doi: 10.1103/PhysRevE.97.033110.
The torque in the Taylor-Couette flow for radius ratios η≥0.97, with smooth or grooved wall static outer cylinders, is studied experimentally, with the Reynolds number of the inner cylinder reaching up to Re_{i}=2×10^{5}, corresponding to the Taylor number up to Ta=5×10^{10}. The grooves are perpendicular to the mean flow, and similar to the structure of a submersible motor stator. It is found that the dimensionless torque G, at a given Re_{i} and η, is significantly greater for grooved cases than smooth cases. We compare our experimental torques for the smooth cases to the fit proposed by Wendt [F. Wendt, Ing.-Arch. 4, 577 (1993)10.1007/BF02084936] and the fit proposed by Bilgen and Boulos [E. Bilgen and R. Boulos, J Fluids Eng. 95, 122 (1973)10.1115/1.3446944], which shows both fits are outside their range for small gaps. Furthermore, an additional dimensionless torque (angular velocity flux) Nu_{ω} in the smooth cases exhibits an effective scaling of Nu_{ω}∼Ta^{0.39} in the ultimate regime, which occurs at a lower Taylor number, Ta≈3.5×10^{7}, than the well-explored η=0.714 case (at Ta≈3×10^{8}). The same effective scaling exponent, 0.39, is also evident in the grooved cases, but for η=0.97 and 0.985, there is a peak before this exponent appears.
在外径比 η≥0.97 的泰勒-库埃特流中，对光滑或带有凹槽壁的静止外筒进行了实验研究，内筒的雷诺数达到 Re_{i}=2×10^{5}，对应的泰勒数达到 Ta=5×10^{10}。这些凹槽垂直于平均流动方向，类似于潜水电机定子的结构。研究发现，在给定的 Re_{i}和 η下，带有凹槽的情况的无量纲扭矩 G 明显大于光滑情况。我们将实验得到的光滑情况的扭矩与 Wendt [F. Wendt, Ing.-Arch. 4, 577 (1993)10.1007/BF02084936]提出的拟合和 Bilgen 和 Boulos [E. Bilgen and R. Boulos, J Fluids Eng. 95, 122 (1973)10.1115/1.3446944]提出的拟合进行了比较，结果表明这两种拟合都超出了小间隙的范围。此外，在光滑情况下，另一个无量纲扭矩（角速度通量）Nu_{ω}在最终状态下表现出有效的标度规律 Nu_{ω}∼Ta^{0.39}，这发生在较低的泰勒数 Ta≈3.5×10^{7}，比研究充分的 η=0.714 情况（在 Ta≈3×10^{8}）要低。在带有凹槽的情况下也存在相同的有效标度指数 0.39，但在 η=0.97 和 0.985 时，在出现这个指数之前会出现一个峰值。
