The effects of non-linearities on wave propagation and time-averaged flow in elastic axi-symmetric vessels
Journal
IFMBE Proceedings
Journal Volume
31 IFMBE
Pages
1181-1184
Date Issued
2010
Author(s)
Abstract
In this paper, a power series and a Fourier series approach is used to solve the governing equations of motion in an elastic axi-symmetric vessel, assuming that blood is an incompressible Newtonian fluid. For vessels with wall stiffness in the arterial range, the viscosity reduces the wave speed by approximately 10 % and the non-linear terms increases it by approximately 5 % from that predicted by linear wave theory for inviscid fluids. When considering time-averaged flow, spatial perturbations in the flow field were observed, the amplitude being strongly dependent on the amplitude of the temporal perturbations, but only weakly dependent upon the nondimensional groups governing the equations of motion. This variation was strongly non-linear, increasing rapidly at large amplitudes of perturbation. A 10 % change in radius about its steady state value resulted in spatial perturbations of approximately 4 %. ? 2010 International Federation for Medical and Biological Engineering.
Subjects
Axisymmetric
Governing equations of motion
Incompressible Newtonian fluid
Inviscid fluids
Large amplitude
Linear wave theory
Navier Stokes
Non-linear
Nondimensional
Nonlinearities
Power series
Spatial perturbations
Steady-state values
Temporal perturbations
Timeaveraged flow
Wall stiffness
Wave speed
Biomechanics
Biomedical engineering
Biophysics
Fourier analysis
Fourier series
Harmonic analysis
Navier Stokes equations
Technical presentations
Wave propagation
Open channel flow
Type
conference paper