Eur. Phys. J. Appl. Phys. 31, 195-209 (2005)
https://doi.org/10.1051/epjap:2005059

Wall shear stress in a laminar flow through a collapsed tube with wall contact

¹ Laboratoire de Mécanique Physique, CNRS UMR 7052 B2OA, Faculté des Sciences et Technologie, Université Paris XII–Val-de-Marne, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France
² Laboratoire Jacques-Louis Lions, CNRS UMR 7598, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France, and Inria, action REO, BP 105, 78153 Le Chesnay Cedex, France

Corresponding authors: naili@univ-paris12.fr marc.thiriet@inria.fr ribreau@univ-paris12.fr

Received: 13 May 2004
Revised: 25 March 2005
Accepted: 17 May 2005
Published online: 14 September 2005

Abstract

The present work aims at studying mainly the wall shear stress of a laminar steady flow of an incompressible Newtonian fluid which is conveyed through a collapsed tube with a straight centreline. This tube is composed of a tapered segment, a contact segment where the opposite walls touch and a reopening segment. The tube geometry and steady flow characteristics are obtained from measurements in a collapsed tube. The Navier-Stokes equations associated with the classical boundary conditions are solved using the finite element method. The tridimensional flow results from the tube configuration. In particular, the flow consists of two side-jets due to two tear-drop shaped outer passages in the downstream contact segment associated with reversed flow. In order to compute both the stream-wise and cross-wise components of the shear stress on the wall, a local basis is defined in each wall node. Downstream of the contact segment, flow is separated in two jets which are studied though the help of the velocity field and the wall shear stress.