Optimal Taylor-Couette flow: Radius ratio dependence

Abstract

Taylor-Couette flow with independently rotating inner (i) and outer (o) cylinders is explored numerically and experimentally to determine the effects of the radius ratio η on the system response. Numerical simulations reach Reynolds numbers of up to Re_i=9.5 x 10^3 and Re_o=5x10^3, corresponding to Taylor numbers of up to Ta=10^8 for four different radius ratios η=r_i/r_o between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor-Couette (T^3C) setup, reach Reynolds numbers of up to Re_i=2x10^6$ and Re_o=1.5x10^6, corresponding to Ta=5x10^{12} for η=0.714-0.909. Effective scaling laws for the torque J^ω(Ta) are found, which for sufficiently large driving Ta are independent of the radius ratio η. As previously reported for η=0.714, optimum transport at a non-zero Rossby number Ro=r_i|ω_i-ω_o|/[2(r_o-r_i)ω_o] is found in both experiments and numerics. Ro_opt is found to depend on the radius ratio and the driving of the system. At a driving in the range between {Ta\sim3\cdot10^8} and {Ta\sim10^{10}}, Ro_opt saturates to an asymptotic η-dependent value. Theoretical predictions for the asymptotic value of Ro_{opt} are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.

Submitted to JFM, 28 pages, 17 figures