Torque scaling in small-gap Taylor-Couette flow with smooth or grooved wall

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.