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Optimal Taylor–Couette flow: radius ratio dependence

  • Rodolfo Ostilla-Mónico (a1), Sander G. Huisman (a1), Tim J. G. Jannink (a1), Dennis P. M. Van Gils (a1), Roberto Verzicco (a1) (a2), Siegfried Grossmann (a3), Chao Sun (a1) and Detlef Lohse (a1)...
Abstract
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 $\eta $ on the system response. Numerical simulations reach Reynolds numbers of up to $\mathit{Re}_i=9.5\times 10^3$ and $\mathit{Re}_o=5\times 10^3$ , corresponding to Taylor numbers of up to $\mathit{Ta}=10^8$ for four different radius ratios $\eta =r_i/r_o$ between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor–Couette ( $\mathrm{T^3C}$ ) set-up, reach Reynolds numbers of up to $\mathit{Re}_i=2\times 10^6$ and $\mathit{Re}_o=1.5\times 10^6$ , corresponding to $\mathit{Ta}=5\times 10^{12}$ for $\eta =0.714\mbox{--}0.909$ . Effective scaling laws for the torque $J^{\omega }(\mathit{Ta})$ are found, which for sufficiently large driving $\mathit{Ta}$ are independent of the radius ratio $\eta $ . As previously reported for $\eta =0.714$ , optimum transport at a non-zero Rossby number $\mathit{Ro}=r_i |\omega _i-\omega _o |/[2(r_o-r_i)\omega _o]$ is found in both experiments and numerics. Here $\mathit{Ro}_{opt}$ is found to depend on the radius ratio and the driving of the system. At a driving in the range between $\mathit{Ta}\sim 3\times 10^{8}$ and $\mathit{Ta}\sim 10^{10}$ , $\mathit{Ro}_{opt}$ saturates to an asymptotic $\eta $ -dependent value. Theoretical predictions for the asymptotic value of $\mathit{Ro}_{opt}$ 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.

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Corresponding author
Email address for correspondence: R.Ostillamonico@utwente.nl
References
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