Pressure field in flow through uniform straight pipes with varying wall cross curvature.

Pressure fields in rigid smooth straight tubes with an axially uniform cross section, in which an incompressible Newtonian fluid flows steadily, have been determined. Five cross section shapes are used. The reference cross section S0 is slightly elliptic (ellipticity of 1.005). Four cross section shapes, which mimic collapsed vessels in an uniformly frozen state, are defined according to the curvature of their opposite faces (the mid-face is located on the minor axis) Sq (parallel faces), St (face folding), Sc (point contact between faces) and Sl (line contact). These four selected cross shapes are characterized by large changes in both the cross sectional shape and area with respect to S0. The cross shapes are obtained from the computation of the deformation under uniform transmural pressures, without extension, of a thin-walled conduit of infinite length and of homogeneous purely elastic walls of constant thickness. The Navier-Stokes equations are solved using the finite element method for the five tubes summation operator0, summation operatorq, summation operatort, summation operatorc and summation operatorl, which are associated with S0,Sq,St,Sc and Sl, respectively. The numerical tests are performed with the same value of the volume flow rate whatever the tube configuration for three Reynolds numbers ( [See text] ). The present work is aimed at studying the pressure field for the design of the flow chamber in which endothelial cells are cultured. This field is used not only to define a new relative pressure index to determine the entry length but also to estimate the wall shear stress when the flow is fully developed.