Converged solutions of the Newtonian extrudate-swell problem

Both the axisymmetric and the planar Newtonian extrudate‐swell problems are solved using the standard and the singular finite element methods. In the latter method, special elements that incorporate the radial form of the stress singularity are used around the exit of the die. The convergence of eac...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 1999-02, Vol.29 (3), p.363-371
Main Authors: Georgiou, Georgios C., Boudouvis, Andreas G.
Format: Article
Language:English
Subjects:
Applied fluid mechanics
Capillary flow
Computational methods in fluid dynamics
convergence
Convergence of numerical methods
Exact sciences and technology
extrudate-swell
Finite element method
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hydrodynamics, hydraulics, hydrostatics
Physics
Problem solving
Reynolds number
singular finite elements
Stress concentration
Surface tension
Swelling
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Summary:Both the axisymmetric and the planar Newtonian extrudate‐swell problems are solved using the standard and the singular finite element methods. In the latter method, special elements that incorporate the radial form of the stress singularity are used around the exit of the die. The convergence of each of the two methods with mesh refinement is studied for various values of the Reynolds and the capillary numbers. The numerical results show that the singular finite elements perform well if coarse or moderately refined meshes are used, and appear to be superior to the standard finite elements only when the Reynolds number is low and the surface tension is not large. The standard finite elements perform better as the surface tension or the Reynolds number are increased. This implies that the effect of the stress singularity on the accuracy of the numerical solution in the neighborhood of the die exit becomes less significant when the Reynolds number is high or the surface tension is large. Copyright © 1999 John Wiley & Sons, Ltd.
ISSN:0271-2091
1097-0363
DOI:10.1002/(SICI)1097-0363(19990215)29:3<363::AID-FLD792>3.0.CO;2-D