Assessment of a general equilibrium assumption
for development of algebraic viscoelastic models
type de publication 
article dans une revue internationale avec comité de lecture 
date de publication 
2007 
auteur(s) 
Mompean Gilmar; Thais Laurent 
journal (abréviation) 
Journal of NonNewtonian Fluid Mechanics (J. NonNewtonian Fluid Mech) 
volume (numéro) 
145 (1) 
 
pages 
41 – 51 
résumé 
Abstract: The recent development of algebraic explicit stress models (AESM) for
viscoelastic fluids rests upon a general equilibrium assumption, by invoking a
slow variation condition on the evolution of the viscoelastic anisotropy tensor
(the normalized deviatoric part of the extrastress tensor, Mompean et al., J.
NonNewt. Fluid Mech., 111, 2003). This equilibrium assumption can take various
forms depending on the general ob jective derivative which is used in the slow
variation assumption. The purpose of the present paper is to assess the validity
of the equilibrium hypothesis in different flow configurations.
Viscometric flows (pure shear and pure elongation) are first considered to show
that the Harnoy derivative (Harnoy, J. Fluid Mech., 3, 1976) is a suitable
choice as an objective derivative that allows the algebraic models to retain the
viscometric properties of the differential model from which they are derived. A
creeping flow through a 4:1 planar contraction then serves as a benchmark for
testing the equilibrium assumption in a flow exhibiting complex kinematics.
Results of numerical simulations with the differential OldroydB constitutive
model allow to evaluate a posteriori the weight of extrastress terms in
different regions of the flow. Computations show that the equilibrium assumption
making use of the Harnoy derivative is globally well verified. The assumption is
exactly verified in flow regions of nearviscometric kinematics, whereas some
departures are observed in the very near region of the corner entrance. 
mots clés 
viscoelastic flows simulation; Algebraic explicit stress models;equilibrium assumption; 4:1 planar contraction; Finite volume method. 
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