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Large-eddy simulation and modelling of Taylor–Couette flow

Published online by Cambridge University Press:  12 March 2020

W. Cheng Open the ORCID record for W. Cheng [Opens in a new window] ,
D. I. Pullin  and
R. Samtaney
W. Cheng*
Affiliation:
Mechanical Engineering, Physical Science and Engineering Division,King Abdullah University of Science and Technology, Thuwal23955-6900, Saudi Arabia Graduate Aerospace Laboratories, California Institute of Technology, CA91125, USA
D. I. Pullin
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, CA91125, USA
R. Samtaney
Affiliation:
Mechanical Engineering, Physical Science and Engineering Division,King Abdullah University of Science and Technology, Thuwal23955-6900, Saudi Arabia
*
†Email address for correspondence: [email protected]
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Abstract

Wall-resolved large-eddy simulations (LES) of the incompressible Navier–Stokes equations together with empirical modelling for turbulent Taylor–Couette (TC) flow are presented. LES were performed with the inner cylinder rotating at angular velocity $\unicode[STIX]{x1D6FA}_{i}$ and the outer cylinder stationary. With $R_{i},R_{o}$ the inner and outer radii respectively, the radius ratio is $\unicode[STIX]{x1D702}=0.909$. The subgrid-scale stresses are represented using the stretched-vortex subgrid-scale model while the flow is resolved close to the wall. LES is implemented in the range $Re_{i}=10^{5}{-}10^{6}$ where $Re_{i}=\unicode[STIX]{x1D6FA}_{i}R_{i}d/\unicode[STIX]{x1D708}$ and $d=R_{o}-R_{i}$ is the cylinder gap. It is shown that the LES can capture the salient features of the flow, including the quantitative behaviour of spanwise Taylor rolls, the log variation in the inner-cylinder mean-velocity profile and the angular momentum redistribution due to the presence of Taylor rolls. A simple empirical model is developed for the turbulent, TC flow for both a stationary outer cylinder and also for co-rotating cylinders. This consists of near-wall, log-like turbulent wall layers separated by an annulus of constant angular momentum. Model results include the Nusselt number $Nu$ (torque required to maintain the flow) and measures of the wall-layer thickness as functions of both the Taylor number $Ta$ and $\unicode[STIX]{x1D702}$. These are compared with results from measurement, direct numerical simulation and the LES. A model extension to rough-wall turbulent flow is described. This shows an asymptotic, fully rough-wall state where the torque is independent of $Re_{i}/Ta$, and where $Nu\sim Ta^{1/2}$.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 890 , 10 May 2020 , A17
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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