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Linear stability analysis of channel flow of viscoelastic Oldroyd-B and FENE-P fluids

Published online by Cambridge University Press:  25 November 2013

Mengqi Zhang ,
Iman Lashgari ,
Tamer A. Zaki  and
Luca Brandt
Mengqi Zhang
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, S-100 44 Stockholm, Sweden
Iman Lashgari
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, S-100 44 Stockholm, Sweden
Tamer A. Zaki
Affiliation:
Mechanical Engineering, Imperial College, London SW7 2AZ, UK
Luca Brandt*
Affiliation:
Linné Flow Centre and SeRC (Swedish e-Science Research Centre), KTH Mechanics, S-100 44 Stockholm, Sweden
*
†Email address for correspondence: luca@mech.kth.se
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Abstract

We study the modal and non-modal linear instability of inertia-dominated channel flow of viscoelastic fluids modelled by the Oldroyd-B and FENE-P closures. The effects of polymer viscosity and relaxation time are considered for both fluids, with the additional parameter of the maximum possible extension for the FENE-P. We find that the parameter explaining the effect of the polymer on the instability is the ratio between the polymer relaxation time and the characteristic instability time scale (the frequency of a modal wave and the time over which the disturbance grows in the non-modal case). Destabilization of both modal and non-modal instability is observed when the polymer relaxation time is shorter than the instability time scale, whereas the flow is more stable in the opposite case. Analysis of the kinetic energy budget reveals that in both regimes the production of perturbation kinetic energy due to the work of the Reynolds stress against the mean shear is responsible for the observed effects where polymers act to alter the correlation between the streamwise and wall-normal velocity fluctuations. In the subcritical regime, the non-modal amplification of streamwise elongated structures is still the most dangerous disturbance-growth mechanism in the flow and this is slightly enhanced by the presence of polymers. However, viscoelastic effects are found to have a stabilizing effect on the amplification of oblique modes.

JFM classification

Instability: Instability Non-Newtonian Flows: Non-Newtonian Flows

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Type
Papers
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Journal of Fluid Mechanics , Volume 737 , 25 December 2013 , pp. 249 - 279
Copyright
©2013 Cambridge University Press 

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Footnotes

‡

Current address: Département Fluides, Thermique, Combustion, Institut PPrime, CNRS–Université de Poitiers–ENSMA, Poitiers, France.

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