Flow singularity and slip velocity in plane extrudate swell computations
type: Item
instance of: scholarly article
title: Flow singularity and slip velocity in plane extrudate swell computations
zbMATH Open document ID: 0653.76007
DOI: 10.1016/0377-0257(88)80022-3
author: R. D. Wesson
author: Tasos C. Papanastasiou
published in: Journal of Non-Newtonian Fluid Mechanics
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/2027.42/27521
review text: It is common knowledge that flows of viscoelastic liquids with stress singularities, like the extrudate swell flow, pose formidable obstacles to numerical computations at relatively low Weissenberg number. This paper describes an effort toward alleviating the stress singularity by means of a slip boundary condition at the die wall. The Oldroyd-B and the upper-convected Maxwell differential constitutive equations were used for simplicity and computational efficiency. With a no-slip boundary condition it was found that for Newtonian, upper-convected Maxwell and Oldroyd-B liquids the global solution was always mesh-dependent until the Newtonian iteration diverged at very fine tessellations in the vicinity of the static contact line. With a natural slip boundary condition the global solution became mesh-independent a the same tessellations. Moreover, the macroscopic predictions became independent of the amount of slip in a relatively broad region of slip coefficient. The Newton iteration converged up to Weissenberg number 0.6 with a no-slip boundary condition and up to 1.7 with a slip boundary condition for the upper- convected Maxwell liquid. For the Oldroyd-B liquid the maximum Weissenberg number was 0.85 without slip and 1.866 with slip. Although slip velocity, surface tension and Newtonian viscosity (or retardation time) enhanced some numerical stability in general, it appears unlikely that they could advance viscoelastic computations significantly. In the limiting case of no swelling, at infinity large surface tension, the analytical solution for Newtonian and, a second order fluid showed: (a) elasticity increases the strength of the singularity that exists for Newtonian liquid at the contact line, and thus Newton iteration is expected to diverge at coarser and coarser tessellations as the elasticity increases in agreement with the finite element findings. (b) Finite element predictions for the same flow agreed with the analytical solution in the vicinity of the si…
Mathematics Subject Classification ID: 76A10
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4066497
zbMATH Keywords: viscoelastic liquids
zbMATH Keywords: extrudate swell flow
zbMATH Keywords: slip boundary condition
zbMATH Keywords: upper-convected Maxwell differential constitutive equations
zbMATH Keywords: global solution
zbMATH Keywords: Newtonian iteration
MaRDI profile type: Publication
OpenAlex ID: W2044456604
description: scientific article; zbMATH DE number 4066497