Defeating the High Weissenberg Number Problem

2002 ◽  
pp. 173-199
Keyword(s):  
Weissenberg Number ◽  
Number Problem

Re-entrant corner flows of upper convected Maxwell fluids: the small and high Weissenberg number limits

2006 ◽  
Vol 462 (2076) ◽  
pp. 3749-3774 ◽  
Author(s):  
J.D Evans
Keyword(s):  
Maxwell Fluid ◽  
Weissenberg Number ◽  
Singular Limit ◽  
Core Region ◽  
Small Reduction ◽  
Asymptotic Structure ◽  
Singular Limits ◽  
Maxwell Fluids ◽  
Number Problem ◽  
Corner Flows

We discuss here the steady planar flow of the upper convected Maxwell fluid at re-entrant corners in the singular limits of small and large Weissenberg number. The Weissenberg number is a parameter representing the dimensionless relaxation time and hence the elasticity of the fluid. Its value determines the strength of the fluid memory and thus the influence of elastic effects over viscosity. The small Weissenberg limit is that in which the elastic effects are small and the fluid's memory is weak. It is an extremely singular limit in which the behaviour of a Newtonian fluid is obtained in a main core region away from the corner and walls. Elastic effects are confined to boundary layers at the walls and core regions nearer to the corner. The actual asymptotic structure comprises a complicated four-region structure. The other limit of interest is the large Weissenberg limit (or high Weissenberg number problem) in which the elastic effects now dominate in the main regions of the flow. We explain how the transition in solution from Weissenberg order 1 flows to high Weissenberg flows is achieved, with the singularity in the stress field at the corner remaining the same but its effects now extending over larger length-scales. Implicit in this analysis is the absence of a lip vortex. We also show (for the main core region) that there is a small reduction in the velocity field at the corner and walls where it becomes smoother. This high Weissenberg number limit has a six-region local asymptotic structure and comment is made on its relevance to the case in which a lip vortex is present.

scholarly journals High Weissenberg Number Problem and Numerical Simulation of an Annular Extrudate Swell of Viscoelastic Fluids.

Seikei-Kakou ◽  
1997 ◽  
Vol 9 (10) ◽  
pp. 817-824 ◽  
Author(s):  
Shuichi TANOUE ◽  
Jiro KOGA ◽  
Toshihisa KAJIWARA ◽  
Yoshiyuki IEMOTO ◽  
Kazumori FUNATSU
Keyword(s):  
Numerical Simulation ◽  
Viscoelastic Fluids ◽  
Weissenberg Number ◽  
Extrudate Swell ◽  
Number Problem

scholarly journals Toward a solution to the high Weissenberg number problem

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2100073-2100074
Author(s):  
David Trebotich
Keyword(s):  
Weissenberg Number ◽  
Number Problem

scholarly journals Log-Conformation Representation of Hiperbolic Conservation Laws with Source Term

2014 ◽  
Vol 15 (3) ◽  
pp. 293
Author(s):  
Luciene Aparecida Bielça Silva ◽  
Messias Meneguette
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Source Term ◽  
Weissenberg Number ◽  
Advection Equation ◽  
Numerical Instability ◽  
Hyperbolic Conservation ◽  
Number Problem

<pre>The objective of this work is to study, through a simpler equation, the statement that the numerical instability associated to the high number of Weissenberg in equations with source term can be resolved by the use of the so called logarithmic representation conformation. We will focus on hyperbolic conservation laws, but more specifically on the advection equation with source term. The source term imposes a necessity of an elastic balance, as well as the CFL convective balance for stability. We will see that the representation of such equation by log-conformation removes the restriction of stability inherent to the elastic balance pointed out by [3] as the cause of high Weissenberg number problem (HWNP).</pre>

Log-Conformation and Square Root-Conformation Transformations in High Weissenberg Number Flows

2019 ◽  
Author(s):  
Beatriz Liara Carreira ◽  
Analice Costacurta Brandi ◽  
Laison Junio da Silva Furlan ◽  
Matheus Tozo de Araujo ◽  
Leandro Franco de Souza
Keyword(s):  
Weissenberg Number ◽  
Square Root
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