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The Toms phenomenon: turbulent pipe flow of dilute polymer solutions

Published online by Cambridge University Press:  28 March 2006

P. S. Virk ,
E. W. Merrill ,
H. S. Mickley ,
K. A. Smith  and
E. L. Mollo-Christensen
P. S. Virk
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
E. W. Merrill
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
H. S. Mickley
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
K. A. Smith
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts
E. L. Mollo-Christensen
Affiliation:
Department of Meteorology, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

Drag reduction caused by dilute, distilled water solutions of five polyethylene oxides, molecular weights from 80,000 to 6,000,000, in turbulent pipe flow was studied experimentally in 0·292 and 3·21 cm ID pipes. It was found that the onset of drag reduction occurs at a well-defined wall shear stress related to the random-coiling effective diameter of the polymer. Laminar to turbulent transition is not, in general, delayed. The extent of drag reduction induced by a homologous series of polymers in a given pipe is a universal function of concentration, flow rate, and molecular weight. The maximum drag reduction possible is limited by an asymptote that is independent of polymer and pipe diameter. Flow structure measurements in a single polymer solution, 1000 ppm of molecular weight 690,000, showed that the mean flow follows an ‘effective slip’ model. In this, the mean velocity profile consists of a ‘Newtonian plug’ convected along at an additional, ‘effective slip’ velocity. The turbulent flow structure follows the ‘effective slip’ model towards the pipe wall, but is significantly different from Newtonian towards the pipe axis; in particular, the inertial subrange observed in isotropic Newtonian turbulence was absent in an energy spectrum taken on the pipe axis in the polymer solution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 30 , Issue 2 , 9 November 1967 , pp. 305 - 328
Copyright
© 1967 Cambridge University Press

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