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On predicting abrupt contraction flows with differential and algebraic viscoelastic models

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2002
auteur(s) Mompean Gilmar
journal Computers & fluids
volume (numéro) 31 (8)
  
pages 935 – 956
résumé The numerical simulation of flows through a planar contraction at low Reynolds number is considered for Newtonian and for viscoelastic fluids. The recently proposed algebraic extra-stress model (AESM) derived from the differential constitutive equation for an Oldroyd-B fluid is extended to a Phan-Thien–Tanner fluid. The approach is based on the exact polynomial representation using a three-term tensor basis. It is also shown that the algebraic formulation reproduces exactly the extra-stress tensor components for pure shear and for pure elongation flow. A parameter based on the strain rate and the rotation rate tensors is presented to identify the regions of the flow where the AESM model produces exact results. A second-order numerical scheme accurate in time and space, based on the finite volume method using a staggered grid has been applied to solve the conservation and constitutive equations for the Newtonian and viscoelastic flows. The numerical simulations for the viscoelastic fluids have been done using the classical constitutive equations in a differential form and the algebraic extra-stress model. Excellent agreement between the extra-stress values is obtained with the two different approaches, showing the viability of AESM.
mots clés Viscoelastic flows; algebraic viscoelastic models; oldroyd-B fluid; Planar contraction; Finite volume method
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