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On the consequences of material frame-indifference in algebraic stress models

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2005
auteur(s) Thais Laurent; Mompean Gilmar; Helin Lionel
journal (abréviation) Theoretical and Computational Fluid Dynamics (Theor Comput Fluid Dynam)
volume (numéro) 19 (1)
  
pages 1 – 22
résumé The principle of material frame-indifference (MFI) is a fundamental and controversial principle of continuum mechanics which has been invoked recently to derive nonlinear algebraic models for stresses of viscoelastic liquids. The purpose of the present study is to identify regions of a flow field where MFI should be considered. Such regions are identified by computing the angular velocity of the principal directions of the rate-of-deformation tensor in order to obtain an Euclidean objective vorticity tensor. An analysis is carried out for uniform shear and extensional flows, and for a Couette flow. The method is then applied to the planar flow through an abrupt 4:1 contraction and to the two-dimensional stream past a circular cylinder. The main results are: (i) MFI should be taken into account in regions characterized by the transition between two different kinematics \\textbf{and} a significant velocity magnitude (ii) MFI can be safely ignored in regions of pure viscometric behavior as well as in recirculation regions. The consequences of MFI being taken into account are then examined upon using the Euclidean objective vorticity tensor in a simple algebraic constitutive law for viscoelastic fluids.
mots clés Material frame-indifference -- Euclidean objectivity -- Algebraic stress models
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