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On the maximum drag reduction due to added polymers in Poiseuille flow

Published online by Cambridge University Press:  27 July 2010

JAMES D. WOODCOCK ,
JOHN E. SADER  and
IVAN MARUSIC
JAMES D. WOODCOCK*
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3010, Australia
JOHN E. SADER
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia
IVAN MARUSIC
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3010, Australia
*
†Email address for correspondence: j.woodcock@pgrad.unimelb.edu.au
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Abstract

The addition of elastic polymers to turbulent liquids is known to produce significant drag reduction. In this study, we prove that the drag in pipe and channel flows of an unforced laminar fluid constitutes a lower bound for the drag of a fluid containing dilute elastic polymers. Further, the addition of elastic polymers to laminar fluids invariably increases drag. This proof does not rely on the adoption of a particular constitutive equation for the polymer force, and would also be applicable to other similar methods of drag reduction, which are also achieved by the addition of certain particles to a flow. Examples of such methods include the addition of surfactants to a flowing liquid and the presence of sand particles in sandstorms and water droplets in cyclones.

JFM classification

Flow Control: Drag reduction
Type
Papers
Information
Journal of Fluid Mechanics , Volume 659 , 25 September 2010 , pp. 473 - 483
Copyright
Copyright © Cambridge University Press 2010

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References

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