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Geometric decomposition of the conformation tensor in viscoelastic turbulence

Published online by Cambridge University Press:  12 March 2018

Ismail Hameduddin Open the ORCID record for Ismail Hameduddin [Opens in a new window] ,
Charles Meneveau Open the ORCID record for Charles Meneveau [Opens in a new window] ,
Tamer A. Zaki Open the ORCID record for Tamer A. Zaki [Opens in a new window]  and
Dennice F. Gayme Open the ORCID record for Dennice F. Gayme [Opens in a new window]
Ismail Hameduddin*
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA
Charles Meneveau
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
Tamer A. Zaki
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
Dennice F. Gayme
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA
*
†Email address for correspondence: ismailh@jhu.edu
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Abstract

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

JFM classification

Waves/Free-surface Flows: Channel flow Non-Newtonian Flows: Non-Newtonian Flows Turbulent Flows: Turbulent Flows

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 842 , 10 May 2018 , pp. 395 - 427
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© 2018 Cambridge University Press 

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