||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 extra-stress tensor, Mompean et al., J.
Non-Newt. 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 Oldroyd-B constitutive
model allow to evaluate a posteriori the weight of extra-stress 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 near-viscometric kinematics, whereas some
departures are observed in the very near region of the corner entrance.