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Optimal Taylor–Couette flow: direct numerical simulations

Published online by Cambridge University Press:  19 February 2013

Rodolfo Ostilla ,
Richard J. A. M. Stevens ,
Siegfried Grossmann ,
Roberto Verzicco  and
Detlef Lohse
Rodolfo Ostilla*
Affiliation:
Department of Science and Technology, Mesa+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Richard J. A. M. Stevens
Affiliation:
Department of Science and Technology, Mesa+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Department of Mechanical Engineering, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA
Siegfried Grossmann
Affiliation:
Department of Physics, University of Marburg, Renthof 6, D-35032 Marburg, Germany
Roberto Verzicco
Affiliation:
Department of Science and Technology, Mesa+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Dipartimento di Ingegneria Meccanica, University of Rome ‘Tor Vergata’, Via del Politecnico 1, Roma 00133, Italy
Detlef Lohse
Affiliation:
Department of Science and Technology, Mesa+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
*
†Email address for correspondence: R.Ostillamonico@utwente.nl
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Abstract

We numerically simulate turbulent Taylor–Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh–Bénard flow. Reynolds numbers of $R{e}_{i} = 8\times 1{0}^{3} $ and $R{e}_{o} = \pm 4\times 1{0}^{3} $ of the inner and outer cylinders, respectively, are reached, corresponding to Taylor numbers $Ta$ up to $1{0}^{8} $ . Effective scaling laws for the torque and other system responses are found. Recent experiments with the Twente Turbulent Taylor–Couette ( ${T}^{3} C$ ) setup and with a similar facility in Maryland at very high Reynolds numbers have revealed an optimum transport at a certain non-zero rotation rate ratio $a= - {\omega }_{o} / {\omega }_{i} $ of about ${a}_{\mathit{opt}} = 0. 33$ . For large enough $Ta$ in the numerically accessible range we also find such an optimum transport at non-zero counter-rotation. The position of this maximum is found to shift with the driving, reaching a maximum of ${a}_{\mathit{opt}} = 0. 15$ for $Ta= 2. 5\times 1{0}^{7} $ . An explanation for this shift is elucidated, consistent with the experimental result that ${a}_{\mathit{opt}} $ becomes approximately independent of the driving strength for large enough Reynolds numbers. We furthermore numerically calculate the angular velocity profiles and visualize the different flow structures for the various regimes. By writing the equations in a frame co-rotating with the outer cylinder a link is found between the local angular velocity profiles and the global transport quantities.

JFM classification

Convection: Convection

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Papers
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Journal of Fluid Mechanics , Volume 719 , 25 March 2013 , pp. 14 - 46
Copyright
©2013 Cambridge University Press

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