A numerical study of fully developed laminar flows in pipes with two planar curvatures

The spectral element method is applied on unstructured tetrahedral elements to solve the Navier–Stokes equations for fully developed laminar flow in pipes with two planar curvatures. Specific implementations of the spectral element method to double curved pipes and parallelization are described. Previous studies on flows in pipes focused on constant curvature or torsion geometries, as well as pipes with varying curvature. This study focuses on the periodic variation of both the curvature as well as torsion by analysing a pipe having two planar curvatures. The effects of the three parameters defining the pipe are studied to isolate the curvature and torsion effect on the magnitude and angle of the secondary flow. Furthermore, the geometric effects on the wall shear stress are studied, as it is an important fluid flow property, especially in blood flows. Copyright © 2006 John Wiley & Sons, Ltd.