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Wall shear stress in a laminar flow through a collapsed tubewith wall contact

Published online by Cambridge University Press:  14 September 2005

S. Naili ,
M. Thiriet  and
C. Ribreau
S. Naili*
Affiliation:
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
M. Thiriet
Affiliation:
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
C. Ribreau
Affiliation:
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
*
naili@univ-paris12.fr marc.thiriet@inria.fr ribreau@univ-paris12.fr
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Abstract

The present work aims at studying mainly the wall shear stress ofa laminar steady flow of an incompressible Newtonian fluid whichis conveyed through a collapsed tube with a straight centreline.This tube is composed of a tapered segment, a contact segmentwhere the opposite walls touch and a reopening segment. The tubegeometry and steady flow characteristics are obtained frommeasurements in a collapsed tube. The Navier-Stokesequations associated with the classical boundary conditions aresolved using the finite element method. The tridimensional flowresults from the tube configuration. In particular, the flowconsists of two side-jets due to two tear-drop shaped outerpassages in the downstream contact segment associated withreversed flow. In order to compute both the stream-wise andcross-wise components of the shear stress on the wall, a localbasis is defined in each wall node. Downstream of the contactsegment, flow is separated in two jets which are studied thoughthe help of the velocity field and the wall shear stress.

Keywords

Type
Research Article
Information
The European Physical Journal - Applied Physics , Volume 31 , Issue 3 , September 2005 , pp. 195 - 209
Copyright
© EDP Sciences, 2005

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References

Abdul Nour, A., Cannon, R., Jaffrin, M.Y., Innov. Tech. Biol. Med. 10, 133 (1989)
Dion, B., Naili, S., Renaudeaux, J.P., Ribreau, C., Med. Biol. Eng. Comput. 33, 196 (1995) CrossRef
Dion, B., Naili, S., Renaudeaux, J.P., Ribreau, C., Med. Biol. Eng. Comput. 33, 838 (1995)
Vischer, D., Peter, P., La Houille Blanche 2, 123 (1985) CrossRef
Knowlton, F.P., Starling, E.H., J. Physiol. 44, 206 (1912) CrossRef
Oates, G.C., Med. Biol. Eng. 13, 773 (1975) CrossRef
Comolet, R., Acad, C. R.. Sci. Paris, Série B 283, 41 (1976)
Shapiro, A.H., J. Biomech. Eng.-T. ASME 99, 126 (1977) CrossRef
M. Thiriet, S. Naili, A. Langlet, C. Ribreau, Modelling of thin walled tubes with a flowing fluid and their applications in the study of the collapse of anatomic vessels, edited by C. Leondes, Biomechanical Systems: Techniques and Applications, volume IV of Biofluid Methods in Vascular and Pulmonary Systems (CRC Press, 2001), Chap. 10, pp. 1–43
Pedley, T.J., J. Biomech. Eng.-T. ASME 114, 60 (1992) CrossRef
M. Heil, O.E. Jensen, Flows in deformable tubes and channels – theoretical models and biological applications, edited by T.J. Pedley, P.W. Carpenter, Flow in Collapsible Tubes and Past Other Highly Compliant Boundaries, (Kluwer, Dordrecht, Netherlands, 2003), Chap. 2, pp. 15–50.
Heil, M., Pedley, T.J., J. Fluid. Struct. 9, 237 (1995) CrossRef
Hazel, A.L., Heil, M., J. Fluid Mech. 486, 79 (2003) CrossRef
M. Benmbarek, Écoulement laminaire permanent dans un modèle de veine, Ph.D. thesis, Université Paris XII, 1997
Thiriet, M., Ribreau, C., Mec. Ind. 1, 349 (2000)
Haond, C., Ribreau, C., Boutherin-Falson, O., Finet, M., Eur. Phys. J. Appl. Phys. 8, 87 (1999) CrossRef
Naili, S., Thiriet, M., Ribreau, C., Eur. Phys. J. Appl. Phys. 17, 139 (2002) CrossRef
M. Thiriet, S. Naili, C. Ribreau, Comput. Modeling Eng. Sci. 3, 4, 473 (2003)
Bassez, S., Flaud, P., Chauveau, M., J. Biomech. Eng.-T. ASME 123, 58 (2001) CrossRef
Bertram, C.D., Ribreau, C., Med. Biol. Eng. Comput. 27, 357 (1989) CrossRef
C. Ribreau, S. Naili, M. Bonis, A. Langlet. J. Biomech. Eng.-T. ASME 115, 4(A), 432 (1993)
O. Pironneau, The finite element methods for fluids (John Wiley & Sons, 1989)
M.D. Gunzburger, Navier-stokes equations for incompressible flows: finite element methods. edited by R. Peyret, Handbook of computational fluid mechanics (Academic Press, 1996), Chap. 3, pp. 99–157
Project GAMMA. Automatic mesh generation and adaptation methods, inria (france), 2003. Web page http://www.inria.fr/recherche/equipes/gamma.en.html
TetMesh-GHS3D, Simulog (France), 1993
R. Glowinski, Numerical methods for nonlinear variational problems (Springer-Verlag, New York, 1984)
K. Boukir, Y. Maday, B. Metivet, A high order characteristics method for incompressible navier-stokes equations. in Proceedings of International Conference on Spectral and High Order Method, Montpellier (France), June, 1992
Pironneau, O., Numer. Math. 38, 309 (1982) CrossRef
M. Thiriet, Étude des écoulements dans les voies respiratoires intrathoraciques proximales et les artères de gros calibre de la circulation systémique, Ph.D. thesis, Habilitation à Diriger des Recherches, Université Denis Diderot, 1994
Bertram, C.D., Godbole, S.A., J. Biomech. Eng.-T. ASME 119, 357 (1997) CrossRef
Ribreau, C., Naili, S., Langlet, A., J. Fluid. Struct. 8, 183 (1994) CrossRef