Blood flow in bends: models, methods and simulations
The pulsatile flow in a curved elastic pipe of circular cross
section is investigated. The unsteady flow of a viscous fluid and
the wall motion equations are written in a toroidal coordinate
system, superimposed and linearized over a steady state solution.
Being the main application relative to the vascular system, the
radius of the pipe is assumed small compared with the radius of
curvature. This allows an asymptotic analysis over the curvature
parameter. The model results in an extension of the Womersley's
model for the straight elastic tube. A numerical solution is found
for the first order approximation and computational results are
finally presented, demonstrating the role of curvature in the wave
propagation and in the development of a secondary flow.
