variavel0=<b>Gilmar Mompean</b> - gilmar.mompean@eudil.fr Université des Sciences et Tecnologies de Lille, E
<b>Roney Leon Thompson</b> - roney@mec.puc-rio.br Pontifícia Universidade Católica
<b>Paulo Roberto de Souza Mendes</b> - pmendes@mec.puc-rio.br Pontifícia Universidade Católica
<b>Abstract.</b> 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-Metzener, Phan-Thien-Tanner, etc). The formulation is developed for three-dimensional time-dependent flows. In a previous work, Mompean et al., 1998 obtained a non-objective algebraic model. This inconsistency is now removed introducing the relative-rate-of-rotation 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 analisys 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.
<b>Keywords.</b> viscoelasticity fluid, constitutive model, relative-rate-of-rotation tensor, general objective time derivative.