AN OBJECTIVE EXPLICIT FORMULATION BASED ON THE OLDROYD-B CONSTITUTIVE EQUATION

Abstract

In the present paper is shown how to obtain an objective explicit algebraic
extra-stress model (AESM) based on differential constitutive equations for
viscoelastic flows (Oldroyd B, White-Metzner, Phan-Thien-Tanner, etc).
The formulation is developed for three-dimensional time-dependent flows.
In a previous work, Mompean, 1998 obtained a non-objective algebraic
model. This inconsistency is now removed introducing the relative-rate-ofrotation
tensor making the model frame-invariant. A new generalized
objective time derivative is also introduced, giving flexibility to the model.
Calculations are performed with an Oldroyd B based AESM for a 4:1
contraction flow, showing good agreement with the original constitutive
differential model. Several results with particular derivatives are obtained
and an analysis guided by a flow type classifier is given. This formulation
is able to include a prediction, not present in the Oldroyd B model, the
viscometric second normal stress difference, N2.