Numerical prediction of threedimensional timedependent viscoelastic extrudate swell using differential and algebraic models
type de publication 
article dans une revue internationale avec comité de lecture 
date de publication 
2011 
auteur(s) 
Mompean Gilmar; Thais Laurent; Tomé M.F.; Castelo Antonio 
journal (abréviation) 
Computers & Fluids (Comput Fluid) 
volume (numéro) 
44 (1) 
 
pages 
68 – 78 
résumé 
This study investigates the numerical simulation of threedimensional timedependent viscoelastic free surface flows using the Upper Convected Maxwell (UCM) constitutive equation and an algebraic explicit model. This investigation was carried out to develop a simplified approach that can be applied to the extrudate swell problem. The relevant physics of this flow phenomenon is discussed in the paper and an algebraic model to predict the extrudate swell problem is presented. It is based on an explicit algebraic representation of the nonNewtonian extrastress through a kinematic tensor formed with the scaled dyadic product of the velocity field. The elasticity of the fluid is governed by a single transport equation for a scalar quantity which has dimension of strain rate. Mass and momentum conservations, and the constitutive equation (UCM and algebraic model) were solved by the threedimensional timedependent finite difference method. The free surface of the fluid was modeled using a markerandcell approach. The algebraic model was validated by comparing the numerical predictions with analytic solutions for pipe flow. In comparison with the classical UCM model, one advantage of this approach is that computational workload is substantially reduced: the UCM model employs six differential equations while the algebraic model uses only one. The results showed stable flows with very large extrudate growths beyond those usually obtained with standard differential viscoelastic models. 
mots clés 
Extrudate swell; Threedimensional free surface flows; Viscoelastic fluids; Algebraic viscoelastic model; Finite difference method 
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