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Numerical modelling of two-dimensional melt fracture instability in viscoelastic flow

Published online by Cambridge University Press:  19 September 2018

Youngdon Kwon Open the ORCID record for Youngdon Kwon [Opens in a new window]
Youngdon Kwon*
Affiliation:
School of Chemical Engineering, Sungkyunkwan University, Seobu-ro 2066, Suwon, Gyeonggi-do 16419, Korea
*
†Email address for correspondence: [email protected]
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Abstract

Computationally modelling the two-dimensional (2-D) Poiseuille flow along and outside a straight channel with a differential viscoelastic constitutive equation, we demonstrate unstable dynamics involving bifurcations from steady flow to periodic melt fracture (sharkskin instability) and its further transition regime to a chaotic state. The numerical simulation first exposes transition from steady flow to a weak instability of periodic fluctuation, and in the middle of this periodic limit cycle (in the course of increasing flow intensity) a unique bifurcation into the second steady state is manifested. Then, a subcritical (Hopf) transition restoring this stable flow to stronger periodic instability follows, which results from the high stress along the streamlines of finite curvature with small vortices near the die lip. Its succeeding chaotic transition at higher levels of flow elasticity that induces gross melt fracture, seems to take a period doubling as well as quasiperiodic route. By simple geometrical modification of the die exit, we, as well, illustrate reduction or complete removal of sharkskin and melt fractures. The result as a matter of fact suggests convincing evidence of the possible cause of the sharkskin instability and it is thought that this fluid dynamic transition has to be taken into account for the complete description of melt fracture. The competition between nonlinear dynamic transition and other possible origins such as wall slip will ultimately determine the onset of the sharkskin and melt fractures. Therefore, the current study conceivably provides a robust methodology to portray every possible type of melt fracture if combined with an appropriate mechanism that also results in flow instability.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Non-Newtonian Flows: Rheology Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 595 - 615
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Copyright
© 2018 Cambridge University Press 

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Kwon Supplementary Material

Streamlines and extrudate surfaces on the contour of pressure at time instants 5 < t < 10 and De = 15.88: periodic sharkskin instability.

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Video 8.1 MB

Kwon Supplementary Material

Streamlines and extrudate surfaces on the contour of pressure at time instants 25 < t < 30 and De = 16.7: quasiperiodic sharkskin instability.

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Video 8.2 MB

Kwon Supplementary Material

Streamlines and extrudate surfaces on the contour of pressure at time instants 15 < t < 20 and De = 22: gross melt fracture instability.

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Video 8.8 MB

Kwon Supplementary Material

Streamlines and extrudate surfaces on the contour of pressure for the original die (with asymmetric mesh) at De = 16: sharkskin.

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Video 6.4 MB

Kwon Supplementary Material

Streamlines and extrudate surfaces on the contour of pressure for the modified die (with asymmetric mesh) of end slope 0.34 at De = 16: removal of sharkskin.

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Video 939.7 KB

Kwon Supplementary Material

Streamlines and extrudate surfaces on the contour of pressure for the original die (with asymmetric mesh) at De = 22: gross melt fracture.

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Video 8.2 MB

Kwon Supplementary Material

Streamlines and extrudate surfaces on the contour of pressure for the modified die (with asymmetric mesh) of end slope 0.6 at De = 22: removal of melt fracture.

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Video 776.3 KB