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Turbulent Taylor–Couette flow with stationary inner cylinder

Published online by Cambridge University Press:  21 June 2016

R. Ostilla-Mónico ,
R. Verzicco  and
D. Lohse
R. Ostilla-Mónico*
Affiliation:
Physics of Fluids Group, Mesa$+$ Institute and J.M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands School of Engineering and Applied Sciences and Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, MA 02138, USA
R. Verzicco
Affiliation:
Physics of Fluids Group, 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 Industriale, University of Rome ‘Tor Vergata’, Via del Politecnico 1, Roma 00133, Italy
D. Lohse
Affiliation:
Physics of Fluids Group, Mesa$+$ Institute and J.M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany
*
†Email address for correspondence: rostillamonico@g.harvard.edu
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Abstract

A series of direct numerical simulations were performed of Taylor–Couette (TC) flow, the flow between two coaxial cylinders, with the outer cylinder rotating and the inner one fixed. Three cases were considered, where the Reynolds number of the outer cylinder was $Re_{o}=5.5\times 10^{4}$, $Re_{o}=1.1\times 10^{5}$ and $Re_{o}=2.2\times 10^{5}$. The ratio of radii ${\it\eta}=r_{i}/r_{o}$ was fixed to ${\it\eta}=0.909$ to mitigate the effects of curvature. Axially periodic boundary conditions were used, with the aspect ratio of vertical periodicity ${\it\Gamma}$ fixed to ${\it\Gamma}=2.09$. Being linearly stable, TC flow with outer cylinder rotation is known to have very different behaviour than TC flow with pure inner cylinder rotation. Here, we find that the flow nonetheless becomes turbulent, but the torque required to drive the cylinders and level of velocity fluctuations was found to be smaller than those for pure inner cylinder rotation at comparable Reynolds numbers. The mean angular momentum profiles showed a large gradient in the bulk, instead of the constant angular momentum profiles of pure inner cylinder rotation. The near-wall mean and fluctuation velocity profiles were found to coincide only very close to the wall, showing large deviations from both pure inner cylinder rotation profiles and the classic von Karman law of the wall elsewhere. Finally, transport of angular velocity was found to occur mainly through intermittent bursts, and not through wall-attached large-scale structures as is the case for pure inner cylinder rotation.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent convection
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 799 , 25 July 2016 , R1
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Copyright
© 2016 Cambridge University Press 

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