Entry Length and Wall Shear Stress in Uniformly Collapsed-Pipe Flow
M. Thiriet; S. Naili; and C. Ribreau

doi:10.3970/cmes.2003.004.473
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 4, No. 4, pp. 473-488, 2003
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Keywords collapsed tube flow, contact, entry length, finite element method, flow chamber design, wall shear stress.
Abstract The laminar steady flow of incompressible Newtonian fluid is studied in rigid pipes with cross configuration of a collapsed tube to determine both the entry length and the wall shear stress (WSS). The cross section shapes have been defined from the collapse of an infinitely long elastic tube subjected to an uniform transmural pressure. Five characteristic collapsed configurations, from the unstressed down to the point-contact states, with a finite and infinite curvature radius at the contact point, are investigated, although the wall contact is not necessary observed in veins. Such collapsed shapes induce cross gradient in WSS in straight pipes. The Navier-Stokes equations, associated with the classical boundary conditions, are solved using a finite element method. The numerical tests are performed with the same value of the volume flow rate whatever the tube configuration. Entry length, axial and cross variations in WSS are computed to design flow chambers in order to explore the mechanotransduction function of the endothelial cells.
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