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Asymptotic drag reduction states in turbulent Taylor vortex flow of dilute polymeric solutions: interplay between large-scale structures and polymer chains dynamics

Published online by Cambridge University Press:  15 April 2025

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] ,
Zi-Mo Liao Open the ORCID record for Zi-Mo Liao [Opens in a new window] ,
Nansheng Liu Open the ORCID record for Nansheng 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
Zi-Mo Liao
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
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
*
Corresponding authors: Nansheng Liu, [email protected]; Bamin Khomami, [email protected]
Corresponding authors: Nansheng Liu, [email protected]; Bamin Khomami, [email protected]
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Abstract

Direct numerical simulations in a low-curvature viscoelastic turbulent Taylor vortex flow, with Reynolds numbers ranging from 1500 to 8000 and maximum chain extensibility ($L$) from 50 to 200, reveal a maximum drag reduction (MDR) asymptote. Compared with the classical MDR observed in planar wall-bounded shear flows, that is, drag reduction (DR) is $\sim -80\, \%$, this MDR state achieves only moderate levels of DR ($\sim -60\,\%$). This is due to the existence of large-scale structures (LSSs). A careful examination of the flow structures reveals that the polymer–turbulence interaction suppresses small-scale vortices and stabilizes the LSSs. These structural changes in turn lead to a reduction of Reynolds stress, and consequently to a DR flow state. Although Reynolds stress does not vanish as observed in classical MDR states, the small-scale vortices that heavily populate the near-wall region are also almost completely eliminated in this flow state. Concurrently, significant polymer stresses develop as a consequence of the interaction between polymer chains and LSSs that partially offset the magnitude of DR, leading to MDR asymptotes with moderate levels of DR. Moreover, we demonstrate that polymer deformation, i.e. deviation from the equilibrium state, is directly correlated with the LSSs dynamics, while the polymer deformation fluctuation displays a universal property in the MDR state. Hence, it is not surprising that the extent of DR exhibits a non-monotonic dependence on the maximum chain extensibility. Specifically, the variation in $L$ alters the incoherent and coherent angular momentum transport by small- and large-scale flow structures, respectively. To that end, the most DR flow state occurs at a moderate value $L=100$. Overall, this study further supports the universal property of polymer-induced asymptotic states in wall-bounded turbulence and paves the way for mechanistic understanding of drag modification that arises from the interaction of polymers with small- and large-scale flow structures.

JFM classification

Flow Control: Drag reduction Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1009 , 25 April 2025 , A24
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© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

†

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

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