Tridimensional flow in uniformly collapsed tubes: wall shear stress

摘要

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.