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Nonlinear dynamics of viscoelastic flow in axisymmetric abrupt contractions

Published online by Cambridge University Press:  26 April 2006

Gareth H. McKinley ,
William P. Raiford ,
Robert A. Brown  and
Robert C. Armstrong
Gareth H. McKinley
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
William P. Raiford
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Robert A. Brown
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Robert C. Armstrong
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

The steady-state and time-dependent flow transitions observed in a well-characterized viscoelastic fluid flowing through an abrupt axisymmetric contraction are characterized in terms of the Deborah number and contraction ratio by laser-Doppler velocimetry and flow visualization measurements. A sequence of flow transitions are identified that lead to time-periodic, quasi-periodic and aperiodic dynamics near the lip of the contraction and to the formation of an elastic vortex at the lip entrance. This lip vortex increases in intensity and expands outwards into the upstream tube as the Deborah number is increased, until a further flow instability leads to unsteady oscillations of the large elastic vortex. The values of the critical Deborah number for the onset of each of these transitions depends on the contraction ratio β, defined as the ratio of the radii of the large and small tubes. Time-dependent, three-dimensional flow near the contraction lip is observed only for contraction ratios 2 [les ] β [les ] 5, and the flow remains steady for higher contraction ratios. Rounding the corner of the 4:1 abrupt contraction leads to increased values of Deborah number for the onset of these flow transitions, but does not change the general structure of the transitions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 411 - 456
Copyright
© 1991 Cambridge University Press

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