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Keplerian turbulence in Taylor–Couette flow of dilute polymeric solutions

Published online by Cambridge University Press:  27 November 2024

Fenghui Lin Open the ORCID record for Fenghui Lin [Opens in a new window] ,
Jiaxing Song Open the ORCID record for Jiaxing Song [Opens in a new window] ,
Nansheng Liu Open the ORCID record for Nansheng Liu [Opens in a new window] ,
Luoqin Liu Open the ORCID record for Luoqin Liu [Opens in a new window] ,
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]  and
Bamin Khomami Open the ORCID record for Bamin Khomami [Opens in a new window]
Fenghui Lin
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Jiaxing Song
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Nansheng Liu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Luoqin Liu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Bamin Khomami
Affiliation:
Department of Chemical and Biomolecular Engineering, University of Tennessee, Knoxville, TN 37996, USA
*
†Email address for correspondence: [email protected]
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Abstract

Turbulent flow induced by elastorotational instability in viscoelastic Taylor–Couette flow (TCF) with Keplerian rotation is analogous to a turbulent accretion disk destabilized by magnetorotational instability. We examine this novel viscoelastic Keplerian turbulence via direct numerical simulations (DNS) for the shear Reynolds number ($Re$) ranging from $10^2$ to $10^4$. The observed characteristic flow structure consists of penetrating streamwise vortices with axial length scales much smaller than the gap width, distinct from the classic centrifugally induced Taylor vortices, which have axial lengths of the gap width. These intriguing vortices persist for the wide $Re$ range considered and give rise to intriguing scaling behaviour in key flow quantities. Specifically, the characteristic axial length of the penetrating vortices is shown to scale as $Re^{-0.22}$; the angular momentum transport scales as $Re^{0.42}$; the kinetic and elastic boundary-layer thicknesses based on angular velocity and hoop stress near the inner cylinder wall scale as $Re^{-0.48}$ and $Re^{-0.49}$, respectively. This implies that the viscoelastic Keplerian turbulence belongs to the classical turbulent regime of TCF with the Prandtl–Blasius-type boundary layer. Furthermore, we present an analytical relation between the viscous and elastic dissipation rates of kinetic energy and the angular momentum transport and in turn demonstrate its validity using our DNS data. This study has paved the way for future research to explore astrophysics-related Keplerian turbulence and angular momentum transport via the scaling relations of the analogous TCF of dilute polymeric solutions.

JFM classification

Non-Newtonian Flows: Viscoelasticity Turbulent Flows: Rotating turbulence
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 1000 , 10 December 2024 , R3
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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Footnotes

‡

Present address: Max Planck Institute for Dynamics and Self-Organization, Göttingen 37077, Germany

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