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Linear and nonlinear evolution of a localized disturbance in polymeric channel flow

Published online by Cambridge University Press:  05 November 2014

Akshat Agarwal ,
Luca Brandt  and
Tamer A. Zaki
Akshat Agarwal
Affiliation:
Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK
Luca Brandt
Affiliation:
Linné Flow Centre, SeRC, KTH Mechanics, Stockholm, SE-100 44, Sweden
Tamer A. Zaki*
Affiliation:
Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Present address: Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA. Email address for correspondence: t.zaki@jhu.edu
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Abstract

The evolution of an initially localized disturbance in polymeric channel flow is investigated, with the FENE-P model used to characterize the viscoelastic behaviour of the flow. In the linear growth regime, the flow response is stabilized by viscoelasticity, and the maximum attainable disturbance-energy amplification is reduced with increasing polymer concentration. The reduction in the energy growth rate is attributed to the polymer work, which plays a dual role. First, a spanwise polymer-work term develops, and is explained by the tilting action of the wall-normal vorticity on the mean streamwise conformation tensor. This resistive term weakens the spanwise velocity perturbation thus reducing the energy of the localized disturbance. The second action of the polymer is analogous, with a wall-normal polymer work term that weakens the vertical velocity perturbation. Its indirect effect on energy growth is substantial since it reduces the production of Reynolds shear stress and in turn of the streamwise velocity perturbation, or streaks. During the early stages of nonlinear growth, the dominant effect of the polymer is to suppress the large-scale streaky structures which are strongly amplified in Newtonian flows. As a result, the process of transition to turbulence is prolonged and, after transition, a drag-reduced turbulent state is attained.

JFM classification

Non-Newtonian Flows: Non-Newtonian Flows Instability: Transition to turbulence Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 760 , 10 December 2014 , pp. 278 - 303
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© 2014 Cambridge University Press 

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