Tridimensional flow in uniformly collapsed tubes: wall shear stress

¹ Université Paris XII – Val-de-Marne, Faculté des Sciences et Technologie, Laboratoire de Mécanique Physique (CNRS UMR 7052 B2OA) , 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France
² INRIA, Projet M3N, BP 105, 78153 Le Chenay Cedex, France
³ Université Pierre et Marie Curie, Laboratoire d'Analyse Numérique (UMR 7598), 75252 Paris Cedex 05, France
⁴ IUT de Cachan, 9 avenue de la division Leclerc, BP 140, 94234 Cachan Cedex, France

Corresponding authors: naili@univ-paris12.fr marc.thiriet@inria.fr christian.ribreau@iut-cachan.u-psud.fr

Received: 26 June 2001
Revised: 8 November 2001
Accepted: 15 November 2001
Published online: 15 February 2002

Abstract

The present work is aimed at studying both the entry length and the wall shear stress in a laminar steady flow of an incompressible Newtonian fluid. The fluid is conveyed through rigid straight tubes with axially uniform cross sections which correspond to the characteristic collapsed states. The cross section shapes have been defined from the collapse of an infinitely long elastic tube subjected to an uniform transmural pressure on its lateral surface. For each tube configuration, the Navier-Stokes equations are solved by using the finite element method for three Reynolds numbers. The numerical tests are performed with the same value of the volume flow-rate whatever the tube configuration. The maximum axial fluid velocity is used to define an index which aims to estimate the entry length. The results are described and analyzed in order to exhibit the link between the cross section shape, the velocity field and the wall shear stress in vessel configurations which mimic collapsed veins, especially when the opposite walls are in contact.