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Polymer mixing in shear-driven turbulence

Published online by Cambridge University Press:  07 August 2007

T. VAITHIANATHAN ,
ASHISH ROBERT ,
JAMES G. BRASSEUR  and
LANCE R. COLLINS
T. VAITHIANATHAN
Affiliation:
Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY 14853–7501, USA
ASHISH ROBERT
Affiliation:
Department of Mechanical & Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802, USA
JAMES G. BRASSEUR
Affiliation:
Department of Mechanical & Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802, USA
LANCE R. COLLINS*
Affiliation:
Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY 14853–7501, USA
*
‡Author to whom correspondence should be addressed. [email protected]
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Abstract

We investigate numerically the influence of polymer mixing on shear-driven turbulence. Of particular interest is the suppression of mixing that accompanies drag reduction with dilute polymer solutions. The simulations use the finite extensible nonlinear elastic model with the Peterlin closure (FENE-P) to describe the polymer stresses in the momentum equation, with polymer concentration allowed to vary in space and time. A thin slab of concentrated polymer was placed in an initially Newtonian homogeneous turbulent shear flow on a plane perpendicular to the mean velocity gradient, and allowed to mix in the gradient direction while actively altering the turbulence. The initially higher concentration of polymer near the centreplane suppressed production of turbulent kinetic energy and Reynolds stress in that region, while turbulence outside the polymer-rich region remained shear-dominated Newtonian turbulence. The rate of mixing in the shear direction was severely damped by the action of the polymer compared to a passive scalar in the corresponding Newtonian turbulent shear flow. This, in part, was a result of the same damping of vertical velocity fluctuations by the polymer that leads to the suppression of momentum flux. However, the cross-correlation between the polymer concentration and vertical velocity fluctuations was also suppressed, indicating that the explanation for the reduction in polymer mixing involves both the suppression of vertical velocity fluctuations and an alteration of turbulence structure by the polymer–turbulence interactions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 585 , 25 August 2007 , pp. 487 - 497
Copyright
Copyright © Cambridge University Press 2007

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Footnotes

†

Present address: Clear Science Corp., 663 Owego Hill Rd., Harford, NY 13784-0233, USA

References

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